Calibration of radar and tracking of space object

Abstract

To calibrate radars and track space objects.SOLUTION: Some of such technologies enable a technique for calibrating a radar based on using an elemental antenna (A) which can be embedded on a housing for housing a set of antenna elements or an antenna (B) mounted to a reflector (108). Some of such technologies enable a radar site containing a first 1 D phased array (112) and a second 1 D phased array (112). The first 1 D phased array sends a set of signals and receives a set of reflections based on the set of signals, and the second 1 D phased array receives the set of reflections.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This patent application claims the benefit of U.S. Provisional Patent Application No. 62 / 914,304, filed October 11, 2019, which is hereby incorporated by reference in its entirety for all purposes.

[0002] The present disclosure relates to radar calibration and tracking of space objects. [Background technology]

[0003] There are various techniques for tracking various space objects (e.g., low-orbit objects, satellites, and debris). For example, some space objects can be tracked via 2D phased array radar. However, these systems have technical disadvantages due to their large size, technical complexity, and high economic cost. Some of these technical disadvantages can be overcome by steerable dish radar. However, these systems also have technical disadvantages due to their low tracking rate, mechanical steering, and limited beam capabilities. Summary of the Invention

[0004] In general, the present disclosure enables various techniques for calibrating radar and tracking space objects. For example, some such techniques enable techniques for calibrating radar based on the use of (a) element antennas that can be embedded in a housing that houses a set of antenna elements, or (b) antennas attached to a reflector. For example, some such techniques enable a radar site including a first 1D phased array and a second 1D phased array, where the first 1D phased array transmits a set of signals and receives a set of reflections based on the set of signals, and the second 1D phased array receives the set of reflections.

[0005] According to an exemplary embodiment involving radar calibration, calibration can be accomplished by transmitting a signal from each of a plurality of phased array antennas and measuring the transmit phase of each transmitted signal as it is received at each of the one or more calibration antennas, where one transmit phase is measured for each phased array antenna-calibration antenna combination. The embodiment further includes receiving a signal at each of the plurality of phased array antennas from each of the one or more calibration antennas and measuring a receive phase for each received signal at each of the plurality of phased array antennas, where again one receive phase is measured for each phased array antenna-calibration antenna combination. Each measured transmit phase and each measured receive phase is then adjusted by a phase offset associated with a corresponding one of the one or more calibration antennas, where the phase offset for each one of the one or more calibration antennas is greater than or equal to zero. A single transmit phase correction may then be calculated for each of the multiple phased array antennas, where the single transmit phase correction for a given one of the phased array antennas is based on a weighted average of the offset-adjusted and measured transmit phases associated with the given one of the phased array antennas and one or more calibration antennas. Similarly, a single receive phase correction may be calculated for each of the multiple phased array antennas, where the single receive phase correction for a given one of the phased array antennas is based on a weighted average of the offset-adjusted and measured receive phases associated with the given one of the phased array antennas and one or more calibration antennas. The single transmit phase correction for each of the multiple phased array antennas and the single receive phase correction for each of the multiple phased array antennas are then stored for use in adjusting the phases of the multiple phased array antennas during radar operation.

[0006] According to another exemplary embodiment involving radar calibration, calibration can be achieved for each of a plurality of radar assemblies, each including an antenna and a plurality of phased array antennas, by transmitting a signal from a first antenna to each of the plurality of phased array antennas and measuring the receive phase of the signal as received at each of the plurality of phased array antennas, and also receiving the transmitted signal from each of the plurality of phased array antennas at the first antenna and measuring the transmit phase for each signal transmitted by the plurality of phased array antennas as received at the first antenna. A transmit channel phase correction can then be calculated for each of the plurality of phased array antennas based on the corresponding transmit phase measurement of each of the plurality of phased array antennas adjusted by a loopback phase value corresponding to the radar assembly in which each individual phased array antenna is located. A receive channel phase correction can also be calculated for each of the plurality of phased array antennas based on the corresponding receive phase measurement of each of the plurality of phased array antennas adjusted by a loopback phase value corresponding to the radar assembly in which each individual phased array antenna is located. The plurality of phased array antennas can then be calibrated during radar operation based on the transmit and receive channel phase corrections.

[0007] In yet another embodiment, the multiple phased array antennas can be further calibrated during radar operation based on the transmit and receive channel phase corrections, as well as the inter-radar assembly transmit phase offset and the inter-radar assembly receive phase offset. This can be achieved by calculating an inter-radar assembly transmit phase offset for each of the multiple radar assemblies and an inter-radar assembly receive phase offset for each of the multiple radar assemblies. An internal transmit phase offset can then be calculated for each of the multiple phased array antennas by adjusting the transmit channel phase corrections of each of the multiple phased array antennas by the inter-radar assembly transmit phase offset calculated for the corresponding radar assembly in which each of the multiple phased array antennas is located. Similarly, an internal receive phase offset can be calculated for each of the multiple phased array antennas by adjusting the receive channel phase corrections of each of the multiple phased array antennas by the inter-radar assembly receive phase offset calculated for the corresponding radar assembly in which each of the multiple phased array antennas is located. The internal transmit phase offset for each of the plurality of phased array antennas and the internal receive phase offset for each of the plurality of phased array antennas can then be stored, and the phased array antennas can be calibrated during radar operation based on the corresponding internal transmit phase offsets and the total internal receive phase offset. [Brief explanation of the drawings]

[0008] [Figure 1] 1 illustrates an embodiment of a radar site according to the present disclosure. [Figure 2] 1 shows a diagram of a radar site according to the present disclosure. [Figure 3] 1 illustrates multiple views of a radar site according to the present disclosure. [Figure 4] 1 shows a diagram of a radar site according to the present disclosure. [Figure 5] 1 shows a diagram of a radar site according to the present disclosure. [Figure 6] 1 shows a diagram of a radar site according to the present disclosure. [Figure 7] 1 shows a diagram of a radar site according to the present disclosure. [Figure 8] 1 illustrates several embodiments of transmitting or receiving assemblies according to the present disclosure. [Figure 9] 1 illustrates an embodiment of multiple transmitting or receiving assemblies supported via a catwalk according to the present disclosure. [Figure 10] 1 illustrates an embodiment of a diagram of a radar site according to the present disclosure. [Figure 11] 1 illustrates an embodiment of a diagram of a dispatching control center and a 1D phased array according to the present disclosure. [Figure 12] 1 illustrates an embodiment of a frame supporting a 1D phased array on a trough reflector according to the present disclosure. [Figure 13] 1 illustrates an embodiment of a process for determining an initial orbit determination in the context of a pair of diagrams illustrating satellite orbits intersecting a first field of view and a second field of view according to the present disclosure. [Figure 14] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 15] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 16] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 17] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 18] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 19] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 20] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 21] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 22] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 23] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 24] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 25] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 26] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 27] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 28] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 29] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 30] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 31] 1 illustrates an embodiment of a process and software architecture for determining an initial orbit determination according to the present disclosure. [Figure 32] 1 illustrates an embodiment of an interferometric technique according to the present disclosure. [Figure 33] 1 illustrates an embodiment of an interferometric technique according to the present disclosure. [Figure 34]1 is a flowchart of external radar calibration according to an exemplary embodiment of the present disclosure. [Figure 35] FIG. 1 illustrates an example of a radar assembly and a phased array antenna for calculating relative phase offsets. [Figure 36] FIG. 1 illustrates an exemplary configuration of two adjacent radar assemblies and signals used in inter-radar assembly phase calibration, according to an exemplary embodiment of the present disclosure. [Figure 37] 10 is a flowchart of inter-channel phase calibration according to an exemplary embodiment of the present disclosure. [Figure 38-1] 10 is a flowchart for calculating a transmit and receive radar-to-radar assembly phase offset according to an exemplary embodiment of the present disclosure. [Figure 38-2] 10 is a flowchart for calculating a transmit and receive radar-to-radar assembly phase offset according to an exemplary embodiment of the present disclosure. [Figure 39(a)] FIG. 2 illustrates signals used to calculate transmit and receive cross-phase measurements, according to an exemplary embodiment of the present disclosure. [Figure 39(b)] FIG. 2 illustrates signals used to calculate transmit and receive cross-phase measurements, according to an exemplary embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0009] In general, the present disclosure enables various techniques for calibrating radar and tracking space objects. For example, some such techniques enable radar calibration techniques based on the use of (a) element antennas that can be embedded in a housing containing a set of antenna elements, or (b) antennas attached to a reflector. For example, some such techniques enable a radar site including a first 1D phased array and a second 1D phased array, where the first 1D phased array transmits a set of signals and receives a set of reflections based on the set of signals, and the second 1D phased array receives the set of reflections. The present disclosure will now be more fully described with reference to Figures 1-39, in which various embodiments of the present disclosure are shown. The present disclosure may be embodied in many different forms and should not be construed as necessarily limited to the embodiments disclosed herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the various concepts of the present disclosure to those skilled in the art.

[0010] Various terms used herein can refer to direct or indirect, complete or partial, temporary or permanent, action or inaction. For example, when an element is referred to as being "on," "connected to," or "coupled to" another element, the element can be directly on the other element, connected to or coupled to the other element, or intervening elements can be present, including indirect or direct variations. In contrast, when an element is referred to as being "directly connected to" or "directly coupled to" another element, there are no intervening elements present.

[0011] The various terms used herein are for the purpose of describing embodiments and are not necessarily intended to limit the disclosure. As used herein, the various singular forms "a," "an," and "the" are intended to include the plural forms unless the context clearly dictates otherwise. The various terms "comprises," "includes," and / or "comprising," "including," when used herein, specify the presence of stated features, integers, steps, operations, elements, or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or groups thereof.

[0012] As used herein, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or." That is, unless otherwise specified or clear from the context, "X utilizes A or B" is intended to mean any of the set of natural inclusive permutations. That is, if X utilizes A, X utilizes B, or X utilizes both A and B, then "X utilizes A or B" is satisfied under any of the above cases.

[0013] Unless otherwise specified, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by those skilled in the art to which this disclosure belongs. Various terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning consistent with the meaning in the context of the relevant art, and should not be interpreted in an idealized and / or overly formal sense unless explicitly defined in this specification.

[0014] Furthermore, relative terms such as "lower," "belower," "upper," and "upper" may be used herein to describe the relationship of one element to another element as shown in the accompanying set of illustrative drawings. Such relative terms are intended to encompass different orientations of the illustrated technology in addition to the orientation depicted in the accompanying set of drawings. For example, if a device in the accompanying set of drawings is turned over, elements described as being "below" other elements would be oriented "upper" other elements. Similarly, if a device in one of the illustrative drawings is turned over, various elements described as being "below" or "below" other elements would be oriented "upper" other elements. Thus, various illustrative terms such as "lower" and "lower" can encompass both an orientation of upper and lower.

[0015] As used herein, the terms "about" or "substantially" refer to a + / - 10% variation from the nominal value / term. Such a variation is always included in any given value / term provided herein, whether or not such a variation is specifically referred to.

[0016] Terms such as "first," "second," and the like may be used herein to describe various elements, components, regions, layers, and / or sections, but these elements, components, regions, layers, and / or sections should not necessarily be limited by such terms. These terms are used to distinguish one element, component, region, layer, or section from another element, component, region, layer, or section. Thus, a first element, component, region, layer, or section discussed below could be referred to as a second element, component, region, layer, or section without departing from the various teachings of the present disclosure.

[0017] Features described with respect to particular embodiments may be combined and subcombined in and / or with various other embodiments. Also, different aspects and / or elements of the embodiments as disclosed herein may be combined and subcombined in a similar manner. Furthermore, some embodiments, whether individually and / or collectively, may be components of larger systems, and other procedures may take precedence and / or their application may be modified in other ways. Furthermore, some steps may be required before, after, and / or concurrently with the embodiments as disclosed herein. It should be noted that, at least as disclosed herein, any and / or all methods and / or processes may be performed, at least in part, by at least one entity in any manner.

[0018] Embodiments of the present disclosure are described herein with reference to illustrations of idealized embodiments (and intermediate structures) of the present disclosure. As such, variations from the illustrated shapes as a result, for example, of manufacturing techniques and / or tolerances, are to be expected. Thus, the various embodiments of the present disclosure should not be construed as necessarily limited to the various shapes of regions shown herein but should include, for example, deviations in shapes that result from manufacturing.

[0019] As disclosed herein, any and / or all elements can be formed from the same structurally continuous piece, e.g., unitary, and / or can be separately manufactured and / or connected, e.g., assembly and / or module. As disclosed herein, any and / or all elements can be manufactured via any manufacturing process, whether additive manufacturing, subtractive manufacturing, and / or any other type of manufacturing. For example, some manufacturing processes include three-dimensional (3D) printing, laser cutting, computer numerical control routing, milling, pressing, stamping, vacuum forming, hydroforming, injection molding, lithography, etc.

[0020] FIG. 1 illustrates an embodiment of a radar site according to the present disclosure. FIGS. 2-7 illustrate multiple views of a radar site according to the present disclosure. FIG. 8 illustrates multiple embodiments of multiple transmit or receive assemblies according to the present disclosure. FIG. 9 illustrates an embodiment of multiple transmit or receive assemblies supported via a catwalk according to the present disclosure. FIG. 10 illustrates an embodiment of a radar site view according to the present disclosure. FIG. 11 illustrates an embodiment of a dispatching control center and a view of a 1D phased array according to the present disclosure. FIG. 12 illustrates an embodiment of a frame supporting a 1D phased array on a trough reflector according to the present disclosure. FIG. 13 illustrates an embodiment of a process for determining an initial orbit determination in light of a pair of views showing the orbit of a satellite intersecting a first field of view and a second field of view according to the present disclosure. FIGS. 14-31 illustrate an embodiment of a process for determining an initial orbit determination, a software architecture therefor, and a comparison of results for determining the orbit of a space object using a TLE technique and results for determining the orbit of a space object using an initial orbit determination technique according to the present disclosure. FIGS. 32-33 illustrate an embodiment of an interferometric technique according to the present disclosure.

[0021] A defined area 100 (e.g., a radar site, enclosed area, fenced area) has a volume of earth 102 and a pad 104 (e.g., concrete, rubber), where the volume of earth 102 supports the pad 104. As shown in FIG. 2, the defined area 100 has a fence line 114 surrounded by a property line 116. The volume of earth 102 rests on the ground, although this can be omitted. The pad 104 houses a first radar pair 120a and a second radar pair 120b.

[0022] As shown in Figure 5, the pad 104 has a first island supporting a first radar, a second island supporting a second radar, and a bridge spanning the first and second islands. As shown in Figure 7, the pad 104 is arranged so that the first and second islands are offset relative to one another (for tracking purposes). However, it should be noted that these configurations can be varied. For example, the bridge can be omitted, the first and second islands can be unoffset, or the pad 104 can be omitted.

[0023] The first radar pair 120a includes a first radar having a first frame 106, a first trough reflector 108 (also referred to as a parabolic cylinder antenna, a parabolic cylindrical antenna, or a parabolic trough antenna), a first catwalk 110, and a first 1D phased array 110. The first frame 106 (e.g., U-shaped or C-shaped with a set of support legs) is positioned within the defined area 100. The first trough reflector 108 is positioned within the defined area 100, fixed (e.g., fastened) to the first frame 106, and has a first shape (e.g., U-shaped, C-shaped), a first vertical trough (e.g., extending in the Z dimension in FIGS. 1, 4, and 5), and a first scale (e.g., size). For example, the first trough reflector 108 can be formed by a group of panels (e.g., metal, alloy, steel, mesh, grid) placed directly adjacent to one another to form a top surface configured to reflect various signals (e.g., radio, optical, etc.). For example, if at least some of the panels are mesh panels with holes therein (e.g., contributing to low cost), the holes can be sized to be smaller than the operating wavelength of the first 1D phased array 110. For example, a small-aperture mesh provides high reflectivity and low leakage. Signal leakage through the mesh increases the antenna backlobe and system temperature. Antenna backlobe refers to energy radiated from the antenna in a direction opposite to the primary radiation direction. An increased backlobe reduces antenna energy radiated in the primary direction. Large-aperture mesh is low-cost, lightweight, and has reduced wind loads. These factors are taken into consideration when designing the mesh openings. Additionally, painting the mesh can protect the material from weathering. White paint reflects sunlight from the trough surface, thereby minimizing thermal deformation of the structure. The materials and methods used to construct the trough reflector can help lower the cost of the first radar. Note that, as shown in Figure 12, the first trough reflector 108 can include a group of calibration antennas 146. How these antennas 146 are used is described further below.

[0024] As shown in FIG. 9 , the first 1D phased array 112 is formed (or arranged) in a first line. The first 1D phased array 112 is disposed within the defined region 100 in the first line. The first 1D phased array 112 is supported (e.g., elevated) by the first frame 106 above the first trough reflector 108 so that the first 1D phased array 112 transmits a set of signals (e.g., radio) through the first trough reflector 108 and receives a set of reflections based on the set of signals through the first trough reflector 108. For example, as shown in FIG. 6 , there may be a reflection pattern 200 in which the first 1D phased array 112 can transmit a set of signals toward the trough reflector 108, which then reflects the set of signals in various directions (e.g., from vertical). For example, the set of signals and the set of reflections can be transmitted and received in a V-shape (e.g., 11 o'clock, 2 o'clock). When the set of signals is reflected by a space object (e.g., a low-orbit object, a satellite, debris), the set of reflections is received through the first trough reflector 108 and then reflected towards the first 1D phased array 112.

[0025] The first radar pair 120a includes a second radar having a second frame 106, a second trough reflector 108 (also referred to as a parabolic cylinder antenna, a parabolic cylindrical antenna, or a parabolic trough antenna), a second catwalk 110, and a second 1D phased array 110. The second frame 106 is disposed within the defined area 100. The second trough reflector 108 is disposed within the defined area 100 and is fixed (e.g., fastened) to the second frame 106 and has a second shape (e.g., U-shaped, C-shaped), a second longitudinal trough (e.g., extending in the Z dimension in FIGS. 1, 4, and 5), and a second scale (e.g., size). For example, the second trough reflector 108 can be formed by a group of panels (e.g., metal, alloy, steel, mesh, grid) placed directly adjacent to one another to form a top surface configured to reflect various signals (e.g., radio, optical). For example, if at least some of the panels are mesh panels with holes therein (e.g., contributing to low cost), the holes can be sized to be smaller than the operating wavelength of the second 1D phased array 110. For example, a small-aperture mesh provides high reflectivity and low leakage. Signal leakage through the mesh increases the antenna backlobe and system temperature. Antenna backlobe refers to energy radiated from the antenna in a direction opposite to the primary radiation direction. An increased backlobe reduces antenna energy radiated in the primary direction. Large-aperture mesh is low-cost, lightweight, and has reduced wind loads. These factors are taken into consideration when designing the mesh openings. Additionally, painting the mesh can protect the material from weathering. White paint reflects sunlight from the trough surface, thereby minimizing thermal deformation of the structure. The materials and methods used in the construction of the trough reflector can help lower the cost of the first radar. Note that, as shown in Figure 12, the second trough reflector 108 can include a group of calibration antennas 146. How these antennas 146 are used is described further below.

[0026] The second shape of the second trough reflector 108 is identical to the first shape of the first trough reflector 108. The second longitudinal valley of the second trough reflector 108 is parallel to the first longitudinal valley of the first trough reflector 108. However, the second scale of the second trough reflector 108 is smaller than (but may be equal to or larger than) the first scale of the first trough reflector 108. For example, the first trough reflector 108 and the second trough reflector 108 have the same shape and orientation (and spacing from one another), but the second trough reflector 108 is a smaller version of the first trough reflector 106. Such a configuration is technically advantageous for various reasons. For example, such a configuration may enable efficient (a) determination of the initial trajectory of a space object, (b) determination of range data to the space object, (c) determination of Doppler data for the space object, (d) angle data for the space object, (e) performance of radar interferometry for the space object, etc. For example, an array of 1D parabolic arrays 108 may be configured to operate together to perform measurements on a satellite by one or more transmit-receive arrays 108 and one or more receive-receive arrays 108 measuring polarization or performing interferometry to obtain a 3D location of the target.

[0027] As shown in FIG. 9 , the second 1D phased array 110 forms a second line (or is arranged in a second line) parallel to the first line. The second 1D phased array 110 is disposed within the defined region 100 in the second line. The second 1D phased array 112 is supported (e.g., elevated) by the second frame 106 above the second trough reflector 108 so that the second 1D phased array 110 does not transmit signals through the second trough reflector 108. However, the second 1D phased array 110 receives a set of reflections based on the set of signals through the second trough reflector 108. For example, as shown in FIG. 6 , when a set of signals from the first 1D phased array is reflected off a space object (e.g., a low-orbit object, satellite, debris), a reflection pattern 200 may exist, and the set of reflections is then received through the second trough reflector 108 and then reflected back toward the second 1D phased array 112. For example, a set of reflections can be received in a V-shape (e.g., at 11 o'clock, 2 o'clock). Such a configuration is technically advantageous for a variety of reasons. For example, such a configuration allows for efficient (a) determination of the initial trajectory of a space object, (b) determination of range data to the space object, (c) determination of Doppler data for the space object, (d) angle data for the space object, and (e) performance of radar interferometry for the space object. For example, an array of 1D parabolic arrays 108 can be configured to work together to perform measurements on a satellite by measuring polarization or performing interferometry to obtain the 3D location of the target, such as one or more transmit-receive arrays 108 and one or more receive-receive arrays 108.

[0028] Note that for each first radar (a many-to-one correspondence), there may be two or more (e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, tens, hundreds, or thousands) of second radars. These second radars may be located inside or outside the defined area 100, regardless of whether the first longitudinal valley of the first trough reflector 108 is parallel to at least two of the longitudinal valleys of the second trough reflector 108 of the second radar. How far these second radars (e.g., trough reflectors) are from the first radar or from each other depends on the signal frequency (e.g., approximately 15 meters from the focal point). For example, the second radars may be randomly distributed within the defined area 100, but accuracy may improve as the distance between the first radar and at least two of the second radars or between at least two of the second radars increases.

[0029] Each of the first and second radars includes a respective catwalk 110 having a first leg 110L, a second leg 110L, and a platform 110P. The first leg 110L is fixed (e.g., assembled, fastened, monolithic) to each frame 106 within the defined area 100. The first leg 110L extends over a respective trough reflector 108. The second leg 110L is fixed (e.g., assembled, fastened, monolithic) to each frame 106 within the defined area 100. The second leg 110L extends over a respective trough reflector 108. The platform 110P is fixed (e.g., assembled, fastened, monolithic) to the first leg 110L and the second leg 1110L within the defined area 100. The platforms 110P extend along (or over) the respective longitudinal valleys of the trough reflectors 108 and house (e.g., support) the respective 1D phased arrays 112. The first radar platform 110P can extend parallel to the second radar platform 110P. Note that there are respective ladders spanning between the pad 104 and the platforms 110P for physical access to each catwalk 110.

[0030] As shown in Figures 1, 3, 4, 5, and 9, the catwalk 110 can be an upright A-shape so that the platform 110P extends over each trough reflector 108. However, as shown in Figure 12, the catwalk 110 can be a tilted V-shape or a tilted A-shape. Regardless of how the catwalk 110 is shaped, the catwalk 110 supporting the first 1D phased array 112 can be structurally identical to the catwalk 110 supporting the second 1D phased array 112, but at a larger scale (scaling up from the second to the first). Similarly, the first radar has a proportionally larger focus than the second radar. For example, as shown in Figure 3, the focus of the first radar is 4 meters, while the focus of the second radar is 2 meters (50% scale down). Similarly, as shown in Figure 3, the first trough reflector 108 and the second trough reflector 108 are centrally aligned.

[0031] As shown in FIG. 8 , the first 1D phased array 112 or the second 1D phased array 112 may include a set of housings 300. In such a configuration, the housings 300 may be positioned on the respective platforms 110P directly adjacent (e.g., side-by-side) to one another on the respective trough reflectors 108 (as shown in FIGS. 1 , 5 , and 9 ). Each housing 300 may include a set of antenna elements 302 (e.g., patch antennas) arranged in a row on its respective housing 300 and facing the respective trough reflector 108. For example, each housing 300 or each antenna element 302 may be electronically steered to simultaneously beam in different directions, whether independent of or dependent on one another.

[0032] As shown in FIGS. 2, 10, and 11, the defined area 100 includes a container 118 having an interior area sized for a user (e.g., a technician) to enter, navigate, and exit. For example, the container can include a shipping container, an intermodal container, a building, a tent, a cabin, a booth, a truck, a van, a bus, or other fixed or mobile structure (e.g., on land, in the air, or at sea). For example, the container 118 can be towable, placeable on a truck bed, liftable by a crane, or assembled on-site. The container 118 can be weather-resistant (e.g., in rain, snow, wind, or desert environments) and can have various climate control mechanisms (e.g., air conditioning, vents, humidifiers, dehumidifiers). The container 118 can receive power from a power line, a renewable energy source, a generator, or be battery-powered, any of which can be local or remote to the container 118, whether inside or outside the defined area 100. The container 118 may include plastic, metal, cloth, rubber, wood, alloy, or other suitable material that avoids signal interference with the radar pairs 120a and 120b. The container 118 rests on the pad 104 but may be spaced apart from the pad 104. The container 118 is spaced apart (e.g., avoids physical contact) from the first frame 106, the first trough reflector 108, the first 1D phased array 112, the second frame 106, the second trough reflector 108, and the second 1D phased array 112.

[0033] As shown in FIGS. 10-11 , to operate the first and second radars, the container 118 acts as a dispatching control center and includes logic (e.g., circuitry, a processor, memory, a transmitter, a receiver, a signal splitter) disposed within an interior area. The logic communicates with the first and second 1D phased arrays such that the logic controls the first and second 1D phased arrays. The logic includes a processor 134 (e.g., a server, a GPU, an accelerator card) disposed within the container 118, a transmitter 138 disposed within the container 118, a set of radio frequency (RF) receivers 136 disposed within the container 118, and a network interface 140 (e.g., an RF fiber interface) disposed within the container 118. The transmitter 138 and the set of RF receivers 138 are communicatively disposed (e.g., interposed) within the container 118 between the processor 134 and the network interface 140.

[0034] 11 , the first 1D phased array 112 transmits a set of signals to the first trough reflector 108, and the processor 134 controls how these signals are generated and transmitted. Thus, external to (or within) the container 118 is a signal splitter 142 that receives data from the network interface 140 as originally transmitted by the processor 134 and splits this data for distribution among the housings 300 for transmission by the antenna 302. Thus, the signal splitter 142 is coupled (e.g., electrically, communicatively) to the logic (e.g., the processor 134, the transmitter 138, the network interface 140) and the first 1D phased array 112 (e.g., the housing 300), such that a set of signals is generated based on the signal splitter receiving a set of data from the logic and splitting the set of data for distribution to the housings 300 of the first 1D phased array. However, because each of the first 1D phased array 112 and the second 1D phased array 112 receives reflections from space objects based on a set of signals, there is a group of signal combiners 144 outside (or inside) the container 118. The group of signal combiners 144 combines the sets of reflections from space objects and transmits them to the processor 134 via the network interface 140 and the RF receiver 136. Note that the processor 134 transmits data to the transmitter 138 and receives data from each RF receiver 136. Note that the transmitter 138 similarly transmits data to the network interface 140. Note that each RF receiver 136 similarly receives data from the network interface 140. Further, note that the network interface 140 transmits data to the signal splitter 142 and receives data from the combiner 144. Further, note that the splitter 142 transmits data to the housing 300 and the combiner 144 receives data from the housing 300.

[0035] The first 1D phased array 112 transmits a set of signals through the first trough reflector 108 based on a first circular polarization and receives a set of reflections through the first trough reflector 108 based on a second circular polarization. The first circular polarization is not the same as the second circular polarization (e.g., quadrant offset). The first circular polarization can be opposite to the second circular polarization. However, the second 1D phased array 112 receives a set of reflections through the second trough reflector 108 based on the first circular polarization and the second circular polarization.

[0036] As shown in FIG. 8 , each of the housings 300 is weatherproof (e.g., in rain, snow, wind, or desert environments) and avoids signal interference between the first radar and the second radar, as disclosed herein. Furthermore, each of the housings 300 has a group of cables / cords 310 extending outward therefrom (e.g., from the top or side). The cables / cords 310 are communicatively coupled to the logic of the container 118 (e.g., the processor 134) and provide power to enable various transmit / receive signal operations, as disclosed herein. Furthermore, each of the housings 300 has a first plate 304 and a second plate 306 arranged relative to one another to form an L-shape or a T-shape. The first plate 304 houses a linearly arranged antenna 302 (e.g., a patch antenna) thereon. As disclosed herein, the first plate 304 faces the respective trough reflector 108 during transmit / transmit. A second plate 306 extends into each housing 300 and houses various circuits that drive / power the antennas 302. Thus, when the antennas 302 are transmitting toward their respective trough reflectors 108, the plate 306 is not visible from the outside due to its extension into the respective housing 300. Each housing 300 also includes an antenna 308 extending outward therefrom (an elementary antenna). The antenna 308 is not disposed on the plate 304 but is spaced therefrom (e.g., within about 2 inches). The antenna 308 is configured to calibrate each of the first radar or second radar as disclosed herein.

[0037] As shown in FIGS. 1, 2, 5, 7, 10, and 13, the defined area 100 includes a first pair 120a and a second pair 120b of radars. The second pair 120b is similar or identical to the radar pair 120a (e.g., in shape, material, or operation). For example, the second pair 120b includes a third radar and a fourth radar. The third radar includes a third frame 106, a third trough reflector 108 (also referred to as a parabolic cylindrical antenna, a parabolic cylindrical antenna, or a parabolic trough antenna), and a third 1D phased array 112. The third frame 106 is disposed within the defined area 100. The third trough reflector 108 is disposed within the defined area 100, is fixed to the third frame 106, and has a third shape, a third longitudinal valley, and a third scale. Similar to the first radar pair 120a, a third 1D phased array 112 is positioned within the defined region 100 and supported by a third frame 106 on a third trough reflector 108, such that the third 1D phased array 112 transmits a set of signals through the third trough reflector 108 and receives a set of reflections from space objects based on the set of signals through the third trough reflector 108. Similarly, the fourth radar includes a fourth frame 106, a fourth trough reflector 108 (also referred to as a parabolic cylinder antenna, a parabolic cylindrical antenna, or a parabolic trough antenna), and a fourth 1D phased array 112. The fourth frame 106 is positioned within the defined region 100. The fourth trough reflector 108 is positioned within the defined region 100 and fixed to the fourth frame 106, and has a fourth shape, a fourth longitudinal trough, and a fourth scale. Similar to the first radar pair 120a, the fourth shape is the third shape, the fourth longitudinal valley extends parallel to the third longitudinal valley, and the fourth scale is smaller than the third scale. A fourth 1D phased array 112 is positioned within the defined region 100. Similar to the first radar pair 120a, the fourth 1D phased array 112 is supported by the fourth frame 106 on the fourth trough reflector 108, such that the fourth 1D phased array 112 does not transmit signals through the fourth trough reflector 108 but receives a set of reflections from space objects based on the set of signals through the fourth trough reflector 108.

[0038] Note, however, that as shown in Figures 1, 2, 5, 10, and 13, the first radar pair 120a and the second radar pair 120b are directed toward different (e.g., opposite) sides of the sky (e.g., different fields of view). This configuration can be achieved in various ways. For example, this configuration can be achieved when the second trough reflector 108 of the first radar pair 120a is positioned between the first trough reflector 108 of the first radar pair 120a and the fourth trough reflector 108 of the second radar pair 120b. Similarly, this configuration can be achieved when the fourth trough reflector 108 of the second radar pair 120b is positioned between the second trough reflector 108 of the first radar pair 120a and the third trough reflector 108 of the second radar pair 120b. Similarly, this configuration can be achieved when the second radar of the first radar pair 120a and the fourth radar of the second radar pair 120b are positioned between the first radar of the first radar pair 120a and the third radar of the second radar pair 120b. Furthermore, this configuration can be achieved when the Rx / Rx radar is positioned between the Tx / Rx radar. As a result, a set of reflections from space objects received by the first 1D phased array and the second 1D phased array form a first field of view, and a set of reflections received by the third 1D phased array and the fourth 1D phased array form a second field of view, where the first field of view does not overlap with the second field of view (coverage of different sky regions). This configuration is technically advantageous for various reasons. For example, when the processor 134 is in communication with the first 1D phased array 112, the second 1D phased array 112, the third 1D phased array 112, and the fourth 1D phased array 112, the processor 134 can be programmed to track an orbiting space object within a first field of view (first radar pair 120a) and a second field of view (second radar pair 120b) such that the orbiting space object can be detected at least twice in a single pass over the defined area 100 from within the defined area 100. For example, there may be a 1D phased array Operations Control Center (OCC) interface. In particular, the radar site 100 includes a pair of 1D phased array 112 radars illuminating a parabolic trough reflector 108.The trough reflector 108 is composed of eight octopods 300, each of which can have eight transmit-receive antenna elements. The TxRx troughs 108 (large) transmit and receive, while the RxRx troughs 108 (small) receive only. The TxRx troughs 108 transmit and receive in a single (but opposite) polarization, while the RxRx troughs 108 receive in both polarizations. The troughs 108 are managed by the OCC 118, which generates the transmit signal on the server using a digital transceiver. The transmit signal is sent over fiber (e.g., RF over fiber) to a 64-way (or fewer or more) splitter that feeds all octopods 300. On receive, the octopods 30 are grouped into batches of eight (or fewer or more) and combined using passive optical techniques. The received signal is converted to RF in the OCC and sent to the server array 134 for processing. Similarly, for the RxRx trough 108, the receiver signal is routed to the OCC 118.

[0039] For the first radar pair 120a and the second radar pair 120b, the second longitudinal valley can extend parallel to the fourth longitudinal valley, or the first longitudinal valley can extend parallel to the third longitudinal valley. Note, however, that this configuration may be different if the second longitudinal valley does not extend parallel to the fourth longitudinal valley, or if the first longitudinal valley does not extend parallel to the third longitudinal valley.

[0040] As shown in FIGS. 11-31, another technical advantage of the defined region 100 having the first radar pair 120a and the second radar pair 120b arises in determining the initial trajectory of a space object. In particular, the processor 130 can be in communication with the first 1D phased array 112, the second 1D phased array 112, the third 1D phased array 112, and the fourth 1D phased array 112. Thus, as shown in FIGS. 15-20, the processor 134 can be programmed to cause the first 1D phased array 112 and the second 1D phased array 112 to detect a space object within a first field of view based on a set of reflections from the space object as received by the first trough reflector 108 and the second trough reflector 108. As shown in FIG. 13, this is done based on the trajectory of the space object (e.g., a satellite) that intersects with the first field of view (1D) of the first radar pair 120a. 15-20, the processor 134 can then determine an initial trajectory (e.g., orbital data) for the space object based on this set of reflections. For example, this can be done based on obtaining a first tracklet from the first trough reflector 108 and a second tracklet from the second trough reflector 108, selecting a best candidate (e.g., a dynamic measurement fitter) from each of the first and second tracklets, and then inferring the initial trajectory based on the best tracklet.

[0041] An initial orbit can be determined for various reasons. For example, an initial orbit can be determined when a space object is not listed in a record of a set of records (e.g., new space object) in a database (e.g., relational, in-memory, No-SQL, graphical, cloud) off-chip from a processor (e.g., an Amazon cloud computing instance), where the set of records corresponds to a set of space objects other than the space object. For example, an initial orbit can be determined when a space object recorded in a record of a database (e.g., relational, in-memory, No-SQL, graphical, cloud) off-chip from a processor (e.g., an Amazon cloud computing instance) has not had orbital parameters (e.g., velocity, height, current position, expected position) corresponding to the space object for a predetermined period of time (e.g., space object data is stale, no measurements have been made for a predetermined period of time, or minimal measurements have been made, and the orbit of a known space object needs to be reinitialized).

[0042] Regardless of why the initial orbit is determined, the processor 134 can create a schedule for the third 1D phased array 112 and the fourth 1D phased array 112 to detect the space object after the initial orbit of the space object is determined. For example, the schedule can include an expected date, time, and location of the space object for the second radar pair 120b. The processor 134 can then cause the third 1D phased array 112 and the fourth 1D phased array 112 to detect the space object within the second field of view based on a set of reflections from the space object as received by the third trough reflector 108 and the fourth trough reflector 108 according to the schedule. This is done based on the orbit of the space object (e.g., a satellite) that intersects with the second field of view (1D) of the second radar pair 120b. The processor 134 can then take an action related to the initial orbit in response to the space object being detected within the second field of view based on the second set of reflections according to the schedule. Some of such actions may include modifying the initial trajectory so that a new trajectory (e.g., trajectory data) is formed, maintaining the initial trajectory as is, creating a new trajectory (e.g., trajectory data) based on the initial trajectory, etc. Note that because an orbiting space object may be detected at least twice in a single pass over the defined region 100 from within the defined region 100, the processor 134 should be located within the defined region 100 to minimize latency and facilitate real-time processing, because there may be a short period of time (e.g., seconds, tens of seconds) between when the space object is detected by the first radar pair 120a and when the space object is scheduled to be detected by the second radar pair 120b.

[0043] For example, an initial orbit determination based on multiple troughs 108 can be made. In particular, a user (e.g., an engineer, a satellite operator, an insurance company) may desire to be able to detect and form an initial orbit determination for various uncataloged (e.g., not included in a database of cataloged space objects) space objects (e.g., satellites) at a single radar site 110, allowing the user to maintain a knowledge store for those space objects and add their data to a catalog (e.g., database). Thus, a target (e.g., a satellite) can be detected at a first trough 108 or a first pair of troughs 108 as disclosed herein, where at least some measurements include a series of range, Doppler, and angle measurements. These measurements are then used to form an initial orbit (which should be performed relatively quickly or in real time). A prediction is then made as to when and where the target will cross the second trough 108 or the second pair of troughs 108. The second trough 108 or the second pair of troughs 108 is then scheduled to detect the target. This should occur relatively quickly or in real time, as the passage of the second trough 108 or second pair of troughs 108 may be tens of seconds after detection at the first trough 108 or first pair of troughs 108. Detections are then made at the second trough 108 or second pair of troughs 108 based on a schedule. The data is then combined to form an initial orbit determination, which can then be used for follow-up at other radar sites, whether similar or dissimilar to radar site 100.

[0044] As shown in Figures 22-31, with regard to the software architecture that enables the determination of the initial trajectory, there may be a group of scripts (e.g., Python, JavaScript), where one of these scripts performs various environment functions (e.g., file paths, basic settings, input / output library declarations, function calls), and another of these scripts performs various operations in the backend (e.g., time format conversion, trajectory formula conversion, cost function minimization, residual calculation).

[0045] As shown in FIG. 23, a group of scripts is contained within a module that receives data from a configuration file and data from tracklets for each of the first and second radar pairs 120a and 120b. The data from the tracklets is provided by preprocessors provided by each of the first and second radar pairs 120a and 120b. Within the module, the scripts communicate with each other bidirectionally. For example, some measurements and fitted measurement pairs can be sent from one of the scripts (environment functions). Similarly, some fitted parameters, data from the Lambert solver, and fitted initial trajectory data can be sent from one of the scripts (backend). How these operations are performed is shown in FIGS. 24-31.

[0046] 32-33, another technical advantage of having radar pair 120a or radar pair 120b arises when performing radar interferometry. In particular, processor 134 can communicate with first 1D phased array 112 (or third 1D phased array 112) and second 1D phased array 112 (or fourth 1D phased array 112). The processor can then be programmed to perform radar interferometry on the detected space object based on the first 1D phased array 112 transmitting a set of signals toward the space object via the first trough reflector 108 (or the third trough reflector 108) and receiving a set of reflections from the space object by the first 1D phased array 112 (or the third 1D phased array 112) via the first trough reflector 108 (or the third trough reflector 108) and by the second 1D phased array 112 (or the fourth 1D phased array 112) via the second trough reflector 108 (or the fourth trough reflector 108). Radar interferometry can include converting a set of time series formed from the set of independent data channels into optimal range, radial velocity, radial acceleration, and x / y offset geometry.

[0047] As disclosed herein, the use of the first radar pair 120a or the second radar pair 120b enables capture of at least some of the various interferometric metrics to accurately determine the location of a target (e.g., a space object, a satellite) within the beam from the respective 1D phased arrays reflected by the respective trough reflectors 108. Figure 32 shows a sample configuration of receive channels. Here, the TxRx trough reflector 108 (large) is sub-digitized into groups of four (black dots). Note that the RxRx trough reflector 108 (small) has a single channel (blue dot). The RxRx trough reflector 108 is separated from the TxRx trough reflector 108 in the perpendicular direction, and such an arrangement provides a unique interference baseline that provides sensitivity to target placement in the y direction. Subsampling the aperture of the TxRx trough reflector 108 provides sensitivity to target placement in the x direction.

[0048] The separation of the trough reflectors 108 is selected to create a clear image of the target location. If the trough reflectors 108 are spaced too far apart, resolution will increase, but grating lobes will provide ambiguity to the target location. By adding more RxRx trough reflectors 108, it is possible to achieve both greater accuracy and clearer location information.

[0049] As shown in Figure 33, the data from the sub-channels are combined to form an interferometric estimate of the target placement within the beam. Generally, the main goal is to convert a single set of time series from several independent data channels into optimal range, radial velocity, radial acceleration, and x / y offset placement (relative to the nominal beam center). Per-channel phase residuals and per-channel optimal signal levels are also generated. The per-channel values ​​are useful for evaluating and updating the phase calibration.

[0050] As shown in Figures 32-33, a key input to the process is the initial detection of the target. Target data is identified by a standard (non-coherent) detection approach. Target data can also be provided by a high-fidelity state vector. The input includes estimates of range and radial velocity, so extensive searching in these dimensions is not necessary. Sources for some of these values ​​include previously performed coherent or incoherent processing, or the high-fidelity state vector. For example, the error in the input range / Doppler values ​​should be less than 1 km and 100 m / s, respectively, although this can vary as needed.

[0051] As shown in FIG. 33, the processor 134 (e.g., an interferometer processor) can be programmed to mix the time series with the nominal radial velocity and acceleration. The processor 134 can then demodulate the ranges of interest. Note that the number of ranges of interest is assumed to be less than approximately 1 km, although this can be changed as needed. The processor 134 can then filter / downsample the data. Note that this is the only downsampling stage in this module due to the small number of ranges and radial velocities of interest. The processor can then perform interpolation within the ranges. The processor 134 can then calculate the complex Fourier spectrum of each channel. The processor 134 can then fit and interpolate the ranges / velocities / accelerations to form an optimal complex visibility. The processor can then resample the visibility to a 2D UV grid and convert it to a composite image. The processor 134 can then identify peak signals in the composite image to find the optimal target placement. The processor 134 can then find the individual channel phase errors through self-calibration using the target placement and assumption of a point source.

[0052] For example, as disclosed herein, the present disclosure discloses a radar design for tracking space objects. The radar can include multiple reflectors 108, each illuminated by a 1D phased array feed 112 capable of nominally operating in the S-band frequency range. The reflectors 108 can come in pairs, one capable of transmitting and receiving (first radar) and the other capable of receiving only (second radar). This combination can measure the range, range velocity (e.g., Doppler), and two-dimensional angle of a space object passing through the field of view (FOV). The latter can use radar interferometry methods. For example, an instantiation can include at least two pairs of reflectors 108 on a given site (e.g., within a defined, zoned, or enclosed area 100). One pair 120a is oriented or directed at a set angle in one direction (e.g., 20 degrees off vertical), while the other pair 120b is oriented or directed at a set angle in another direction (e.g., 20 degrees off vertical), which may be the opposite direction. This combination allows measurements of a space object to be taken at multiple points in a single pass over the site as the space object traverses the FOV and used to construct an initial orbit determination (IOD) of the space object. While Figures 1-39 show several dimensions, orientations, and parameters, it should be noted that these dimensions, orientations, and parameters are exemplary and may be varied, either larger or smaller, as desired.

[0053] As shown in Figures 1-39, a site-level design 100 for a radar tracking system can include a pair of radar troughs 108. The radar troughs 108 can include an array of electronic boxes 300 (or housings or containers) called octapods. Each trough 108 enables accurate measurements of the range, range-rate (e.g., Doppler), and angle of a space object. Furthermore, the radar tracking system can enable a method for estimating an angle to a target (e.g., a space object) by digitizing a group of octapods 300 within a single trough, and a method for estimating a second angle to the target by using an Rx / Rx trough and combining them to accurately estimate the target's placement within the radar beam. The radar tracking system also enables a calibration measurement system.

[0054] As shown in Figures 1-39, a site design can include two (or more or fewer) large reflectors 108 (Tx / Rx reflectors), two (or more or fewer) small reflectors 108 (Rx / Rx reflectors), a traffic control center 118 (e.g., in a shipping container or another enclosure), and cables / power plants / grounding / internet / fencing, etc. The reflectors 108 can come in pairs, i.e., one large Tx / Rx reflector 108 and a smaller Rx / Rx reflector 108. The Tx / Rx reflector 108 can transmit one circularly polarized light and receive the other. The Rx / Rx reflector 108 can receive both polarizations. The Tx / Rx system can be divided into four (or more or fewer) segments to perform interference angle measurements (top / bottom in Figure 3). The Rx / Rx system allows for angle measurements in other dimensions (left / right in Figure 3).

[0055] As shown in Figures 1-39, the reflector 108 may include a steel beam frame 106 (or another material or another metal or alloy), a plurality of aluminum (or another material or another metal or another alloy) mesh panels attached (e.g., fastened, glued, interlocked, interlocked, or bonded) to the reflector, a catwalk 110 providing access to the focus zone, and transmit and receive electronics 300 (eight arms) at the focus zone that illuminate the mesh panels.

[0056] The reflector 108 may be a parabolic trough, i.e., a cylindrical paraboloid, and may be designed to point at a particular angle (e.g., 20 degrees) from vertical, while the focusing array is oriented to point straight down toward the ground, pad, vehicle (e.g., land, sea, air), or platform in which the reflector 108 is housed. Note that the particular angle is not limited to about 20 degrees, but can be greater or less, whether vertical or non-vertical (e.g., between about 0 degrees and about 90 degrees).

[0057] For a phased array radar to operate effectively, it may be necessary to accurately calibrate the electronic and cable phase delays of some, each, many, most, or all paths. This signal calibration can be accomplished in several ways. One approach to signal calibration has some, many, most, or all of the eight arms 300 have a calibration antenna 308 on them. Various switches in the eight arms 300 allow signals to be transmitted from that antenna 308 and received at an element 302, transmitted at an element 302 and received at that antenna 308, and transmitted from one eight arm 300 to another eight arm 300. Additionally, signals can be looped through various parts of the RF chain to measure and calibrate phase. Another approach to signal calibration has several antennas 146 embedded in the surface of the reflector 108. Signals can be transmitted from the calibration antenna 146 and received at the eight arm elements 300, or transmitted from the eight arms 300 and received at the calibration antenna 146 to measure phase and amplitude. This configuration / technique, combined with a theoretical model of the phased array, can be used to calibrate the phased array. Yet another approach to signal calibration is to have a calibration antenna in the far field of up to eight elements of the array, although more or less is possible. Thus, the calibration antenna can be used to measure the beam pattern of the eight-arm 300 or overlapping elements of the eight-arm 300. An adaptive beamforming approach can be implemented that adjusts the beam pattern to best fit a theoretical model of the gain pattern. This approach only allows for the signal strength to be utilized, not the phase of the resulting pattern.

[0058] At a given site, there may be many (more than two) pairs of reflectors 108, such as 2, 3, 4, 5, 6, 7, 8, 9, 10, tens, hundreds, thousands, or even more, including all intermediate values ​​therein. Additionally, there may be multiple Rx / Rx troughs 108 for a given Tx / Rx trough (e.g., a many-to-one correspondence). For example, there may be at least 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, tens, hundreds, thousands, or even more, including all intermediate values ​​therein. These Rx / Rx 108 may be positioned adjacent to or around a given Tx / Rx 108, whether feet, yards, or miles apart, depending on the desired angle. These Rx / Rx 108 can also be arranged in a line (e.g., train style) in sequence or consecutively, or in a closed (e.g., O, D, P) or open (e.g., U, C, J, S, L) configuration relative to the Tx / Rx.

[0059] As shown in FIGS. 1-39, a system may include a frame 106, a reflector 108 supported via the frame 106, a catwalk 110 extending above the reflector 108, and a phased array 112 supported via the catwalk 110 and oriented toward the reflector 108 so as to track a space object. The frame 106 may be supported via an earth volume 102 or the ground. The frame 106 may be supported via a vehicle (e.g., land, sea, or airborne). The frame 106 may be supported via an ocean platform, including any body of water platform. The phased array 112 is a 1D phased array. The phased array 112 may operate in the S-band frequency range. The phased array 112 may be oriented toward the ground. The phased array 112 may transmit multiple first signals via the reflector 108 and receive multiple second signals (e.g., reflections) via the reflector 108. The phased array 112 can avoid transmitting signals through the reflector 108 and still receive signals (e.g., reflections) through the reflector 108. The reflector 108 can be a parabolic trough. The reflector 108 can be a cylindrical paraboloid. The phased array 112 and reflector 108 can be positioned such that the phased array 112 directs signals to the reflector 108, which reflects the signals at a non-perpendicular angle. The non-perpendicular angle can be between about 0 and 90 degrees, and within that range can be less than about 80 degrees, less than about 70 degrees, less than about 60 degrees, less than about 50 degrees, less than about 40 degrees, less than about 30 degrees, less than about 25 degrees, greater than about 5 degrees, greater than about 10 degrees, greater than about 15 degrees, between about 15 degrees and about 25 degrees, about 20 degrees, or the like. The phased array 112 and the reflector 108 can be positioned such that the phased array 112 directs a plurality of signals to the reflector 108, which reflects the signals at a perpendicular angle. The pad 104 can support the frame 106. The pad 106 can be positioned such that the reflector 108 extends between the pad 106 and the catwalk 110. The pad 106 can be positioned such that the reflector 108 extends between the pad 104 and the phased array 112.The shipping container 118 includes a set of logic (e.g., circuits, cables, switches, amplifiers, encoders) in control communication with the phased array 112. The pad 104 can support the shipping container 118. The phased array 112 can transmit circularly polarized light. The phased array 112 can enable measurement of an interference angle along a vertical axis, where the interference angle is associated with a space object. The phased array 112 can enable measurement of an angle along a horizontal axis, where the angle is associated with a space object. The frame 106 or the catwalk 110 can include a metal or alloy. The reflector 108 can include multiple mesh panels. At least one of the mesh panels can include a metal or alloy. The catwalk 110 or the reflector 108 can be assembled (e.g., fastened, mated, interlocked, glued) to the frame. The phased array 112 can include multiple housings 300 that are separate and distinct from one another. The housings 300 can be arranged vertically and linearly along the catwalk 110. At least one of the housings 300 can house multiple antennas 302 linearly spaced apart from one another. At least one of the antennas 302 can be a patch antenna. The housings 300 can be arranged along a catwalk so that the antennas are linearly aligned together. At least one of the housings 300 can house a calibration antenna 308. At least one of the housings 300 can house multiple patch antennas 302 and multiple switches, where the switches are coupled to the calibration antenna 308 and the patch antennas 302 such that (1) the calibration antenna 308 transmits a first signal and at least one of the patch antennas 302 receives a second signal, and (2) at least one of the patch antennas 302 transmits a third signal and the calibration antenna 308 receives a fourth signal. At least two of the housings 300 can transmit at least two signals to each other. At least one of the housings 300 loops a signal through various portions of a radio frequency (RF) chain to measure or calibrate signal phase.The reflector 108 may include a trough with a surface, and the antenna 146 may be embedded in the surface. The antenna 146 may transmit a signal to the phased array 112 so that at least one of the signal's phase or signal amplitude is measured. The phased array 112 may transmit a signal to the antenna 146 so that at least one of the signal's phase or signal amplitude is measured. The catwalk 110 may be supported via A-shaped posts. For example, the catwalk 110 may span multiple A-shaped posts. The catwalk 110 may be supported via non-A-shaped posts (e.g., J-shaped, T-shaped, L-shaped, J-shaped, V-shaped, M-shaped, C-shaped, U-shaped, D-shaped). For example, the catwalk 110 may span multiple posts. Regardless of the shape, the posts may include metal, alloy, plastic, wood, rubber, or other materials. The catwalk 110 may be suspended above the reflector via multiple lines (eg, ropes, cables, chains).

[0060] 1-39 , there may be a system including a radiation reflector 108 and a phased array 112 including a first housing 300 and a second housing 300. The first housing 300 may house a plurality of first patch antennas 302 facing the parabolic reflector 108, where the first patch antennas 302 are linearly spaced apart from one another. The second housing 300 may house a plurality of second patch antennas 302 facing the parabolic reflector 108, where the second patch antennas 302 are linearly spaced apart from one another. The first housing 300 may be positioned adjacent to the second housing 300 such that the first patch antennas 302 and the second patch antennas 302 are linearly aligned together to receive a plurality of signals via the parabolic reflector 108. The signals are a plurality of first signals, and the first housing 300 is positioned adjacent to the second housing 300 such that the first patch antenna 302 and the second patch antenna 302 are linearly aligned together to transmit a plurality of second signals through the parabolic reflector 108. The phased array 112 may be a 1D phased array.

[0061] 1-39, a system may include a first assembly including a first frame 106, a first reflector 108 supported via the first frame 106, a first catwalk 110 extending over the first reflector 108, and a first phased array 112 supported via the first catwalk 110 and directed toward the first reflector 108. The first phased array 112 may transmit a plurality of first signals via the first reflector 108, and the first phased array 112 may receive a plurality of second signals (e.g., reflections from a space object based on the first signals) via the first reflector 108. The system may include a second assembly including a second frame 106, a second reflector 108 supported via the second frame 106, a second catwalk 110 extending over the second reflector 108, and a second phased array 112 supported via the second catwalk 110 and directed toward the second reflector 108. The second phased array 112 does not transmit signals via the second reflector 108, and receives a plurality of third signals (e.g., reflections from space objects based on the first signals) via the second reflector 108. The first signals are transmitted in a general direction offset perpendicularly, and the second and third signals are received in a general direction offset perpendicularly.

[0062] 1-39, a system may include a first radar pair 120a including a first assembly and a second assembly. The first assembly includes a first frame 106, a first reflector 108 supported via the first frame 106, a first catwalk 110 extending over the first reflector 108, and a first phased array 112 supported via the first catwalk 110 and oriented toward the first reflector 108. The first phased array 112 transmits a plurality of first signals via the first reflector 108, and receives a plurality of second signals (e.g., reflections from space objects based on the first signals) via the first reflector 108. The second assembly includes a second frame 106, a second reflector 108 supported via the second frame 106, a second catwalk 110 extending over the second reflector 108, and a second phased array 112 supported via the second catwalk 110 and directed toward the second reflector 108. The second phased array 112 does not transmit signals via the second reflector 108, and the second phased array 112 receives a plurality of third signals (e.g., reflections from space objects based on the first signals) via the second reflector 108. The system may include a second radar pair 120b including a third assembly and a fourth assembly. The third assembly includes a third frame 106, a third reflector 108 supported via the third frame 106, a third catwalk 110 extending over the third reflector 108, and a third phased array 112 supported via the third catwalk 110 and directed toward the third reflector 108. The third phased array 112 transmits a plurality of fourth signals via the third reflector 108, and the third phased array 112 receives a plurality of fifth signals (e.g., reflections from a space object based on the fourth signals) via the third reflector 108. The fourth assembly includes a fourth frame 106, a fourth reflector 108 supported via the fourth frame 106, a fourth catwalk 110 extending over the fourth reflector 108, and a fourth phased array 112 supported via the fourth catwalk 110 and directed towards the fourth reflector 108.The fourth phased array 112 does not transmit a signal through the fourth reflector 108, and the fourth phased array 112 receives a plurality of sixth signals (e.g., reflections from space objects based on the fourth signal) through the fourth reflector 108. The system may include a defined area 110 (e.g., a fenced area, an enclosed area, an elevated area, a visually distinct area) including a first radar pair 120a and a second radar pair 120b. The first radar pair 120a is oriented off-vertically in a first direction, and the second radar pair 120b is oriented off-vertically in a second direction (e.g., different, non-overlapping, or opposite directions) to enable tracking of space objects at multiple points (e.g., in a V-like fashion).

[0063] Radar Calibration As noted above, this disclosure not only describes various embodiments of radar systems for tracking space objects, but also describes radar calibration embodiments. While the radar calibration embodiments described herein below relate to the radar system embodiments described above, the radar calibration embodiments are not necessarily limited to the specific radar system embodiments described above.

[0064] The performance of any radar system, such as the radar system described herein for initializing the trajectory of a space object and then tracking the space object, is highly dependent on the accuracy of the radar. As those skilled in the art will readily appreciate, radars must be periodically calibrated to ensure accuracy. This is particularly true for phased array radar systems, as each element of a radar array can exhibit inherent differences in amplitude and phase due to, for example, manufacturing tolerances associated with hardware components and RF cables, temperature, equipment age, drift over time, etc. Therefore, to ensure the accuracy of a radar system, it is imperative to quantify the differences associated with the radar, or each radar element, and adjust the radar as a function of the quantified differences to remove the effects of the differences and equalize the radar elements.

[0065] Two radar calibration techniques are described below. Both techniques involve calibrating the phase of the radar, more specifically, the phase of each phased array element of the radar. The first technique is referred to herein as external phase calibration, while the second technique is referred to as internal phase calibration. As described below, internal phase calibration includes two calibration processes: inter-radar assembly phase calibration and channel phase calibration. Both external and internal phase calibration techniques are described according to some exemplary embodiments.

[0066] External phase calibration The external phase calibration technique is "external" because it involves transmitting radar signals from multiple phased array antennas (radar elements) located within one or more radar assemblies to one or more calibration antennas embedded in the surface of a far-field radar reflector (herein "reflector" or "trough"). It also involves receiving signals at each of the multiple phased array antennas transmitted from each of the one or more calibration antennas.

[0067] In the exemplary embodiment of the radar system described above, the radar assemblies housing the phased array antennas are referred to as eight-armed units because, in a preferred embodiment, each radar assembly comprises eight phased array antennas. See, e.g., FIG. 8 (reference numeral 302). It will be understood that the radar assemblies may include fewer or more than eight phased array antennas without departing from the spirit of the present invention. Furthermore, in a preferred embodiment, the multiple phased array antennas are linearly arranged, as described above. See, e.g., FIG. 3. However, it will be understood that the arrangement of the phased array antennas may be other than linear. For ease of discussion, the external phase calibration will be described with reference to a radar system according to the exemplary embodiment described above comprising 32 linearly arranged eight-armed units (or radar assemblies). Fewer or more than 32 eight-armed units are certainly within the scope of the present invention. See, e.g., FIG. 11 (showing 64 eight-armed units). As noted, each eight-armed unit houses eight phased array antennas, also linearly arranged. Thus, in this example, the overall antenna array comprises 256 linearly arranged phased array antennas. See, for example, FIG.

[0068] The antenna array is disposed above the aforementioned reflector. See, for example, FIGS. 1-5 (reference numeral 108). As previously described, one or more calibration antennas are embedded in the surface of the reflector. While the present invention contemplates two or more calibration antennas embedded in the reflector, the exact number of calibration antennas may vary according to exemplary embodiments of the present invention, including only one calibration antenna. It is understood that the use of two or more calibration antennas provides independent measurements and allows for a more faithful calibration. For ease of explanation, external phased calibration will be described with reference to five embedded calibration antennas. In a preferred embodiment, the calibration antennas are arranged in a single linear array, distributed as far apart as possible from each other, but are generally evenly distributed relative to the phased array antenna located above the reflector. In other embodiments, the calibration antennas may be arranged along first, second, or more linear paths. In still other embodiments, the calibration antennas may be distributed in a nonlinear array. Those skilled in the art will appreciate that distributing the calibration antennas as evenly as possible about the phased array antenna will improve the accuracy of the calibration process, and that arranging the calibration antennas linearly will simplify some of the calculations required for calibration, particularly the calculation of the free space constants described below.

[0069] External phase calibration 3400 will now be described with reference to Figure 34. According to step 3401, each of a plurality of phased array antennas N transmits (tx) a signal, where N is equal to 256. As explained above, the reference to 256 phased array antennas is for ease of discussion, and more or less than 256 are within the scope of the present invention. The 256 phased array antennas are housed in 32 radar assemblies or arms. The phase (φ) of each transmitted signal is tx ) is measured at each of the M calibration antennas. For simplicity, M is equal to 5. Therefore, the result is the transmission phase ( n,m φ tx) results in an MxN (M=5, N=256) array of measurements, where the superscripts n, m indicate that the transmitted signal is from one of the phased array antennas n, relative to one of the calibration antennas m.

[0070] According to step 3403, a similar process as above is performed in the opposite direction, i.e., each of the multiple phased array antennas N receives (rx) a signal transmitted from each of the M calibration antennas. The phase (φ rx ) is also measured. The result is m,n φ rx ) an MxN array of phase measurements, where the superscripts m,n indicate that the transmitted signal is from one of the calibration antennas m relative to one of the phased array antennas n.

[0071] According to a preferred embodiment, each phased array antenna-calibration antenna pair ( n,m φ tx ) are performed separately, as indicated by decision block 3402 of FIG. 34. Similarly, as indicated by decision block 3404 of FIG. 34, the transmit phase measurements for each calibration antenna-phased array antenna pair ( m,n φ rx ) are performed separately. However, in other embodiments, the transmit phase measurements may be performed wholly or partially simultaneously, and the receive measurements may be performed wholly or partially simultaneously.

[0072] The next step in external phase calibration is to calculate the free-space phase between each phased array antenna and the calibration antenna pair (n, m). k φ const The free space phase of a given phased array antenna and calibration antenna pair (n,m) is n,m k φ const is correlated to the distance D between the phased array antenna and its counterpart calibration antenna pair. Those skilled in the art can calculate the free space phase of each phased array antenna-calibration antenna pair (n, m) by n,m k φ constIt will be appreciated that the radii of the antennas can be measured in advance and, as noted above, a linear array of calibration antennas simplifies these measurements.

[0073] According to step 34 of FIG. 34, the free space phase of each phased array antenna and calibration antenna pair (n, m) is calculated. n,m k φ const is the measured transmission phase ( n,m φ tx ) and the result is an MxN array of phase values ​​( n,m φ tx - n,m k φ const ) Similarly, the free space phase of each phased array antenna and the calibration antenna pair is n,m k φ const is the measured receive phase ( m,n φ rx ) and the result is an MxN array of phase values ​​( m,n φ rx - m,n k φ const )

[0074] Step 3407, in a preferred embodiment, includes pre-calculating weighting factors for each phased array antenna-calibration antenna pair (n, m): Weighting factor for a given one of the phased array antenna-calibration antenna pairs (n, m) n、m W is correlated to the distance D between the phased array antenna and its paired calibration antenna. In a preferred embodiment, the weighting factors for the phased array antenna n and the calibration antenna m are n、m W is 1 / D 2 where D is, as stated, the physical distance between phased array antenna n and calibration antenna m. Those skilled in the art will appreciate that when there is only one calibration antenna, the phase offset due to the placement of the phased array antenna relative to the single calibration antenna can be considered negligible.

[0075] In step 3407, an average phase offset is established for each calibration antenna, where the first calibration antenna in the set is used as a reference and assigned an average phase offset of zero. See FIG. 35. The average phase offsets for all other calibration antennas are referenced to the first calibration antenna. For example, if there are five calibration antennas, step 3407 includes calculating four average phase offsets, with the first calibration antenna preferably located at an end relative to the other calibration antennas and having a zero average phase offset, as described above. The second calibration antenna has an average phase offset referenced to the average phase offset of the first calibration antenna. The third calibration antenna has an average phase offset referenced to the second calibration antenna, and so on. The calculation of the average phase offset for the first and second calibration antennas will now be described in more detail, with the understanding that the calculation of the average phase offset for the second and third calibration antennas, the calculation of the average phase offset for the third and fourth calibration antennas, and the calculation of the average phase offset for the fourth and fifth calibration antennas all proceed in the same manner.

[0076] For each pair of adjacent calibration antennas, it is necessary to identify the number of phased array antennas with the smallest difference in weighting coefficients for the first calibration antenna and the second calibration antenna of the two adjacent calibration antennas. This means that the difference between the weighting coefficients of a given phased array antenna and the first calibration antenna (subtracted) and the weighting coefficients of the same phased array antenna and the second calibration antenna is small compared to the other phased array antennas. In a preferred embodiment, eight phased array antennas with the smallest difference in weighting coefficients for the first calibration antenna and the second calibration antenna are identified. See FIG. 35 (reference numbers n1 to n8). Typically, this results in the phased array antenna that is closest to both the first and second calibration antennas of the pair. For each of the eight phased array antennas n1 to n8, the transmission phase is measured at both the first calibration antenna and the second calibration antenna. Therefore, for each of the eight phased array antennas, the transmission phase measured for the first calibration antenna is calculated as follows:n,c1 φ tx and the transmission phase measured for the second calibration antenna n,c2 φ tx For each of the phased array antennas, the measured transmission phase of the first calibration antenna and the measured transmission phase of the second antenna are subtracted from each other to obtain eight offset phase values. The offset phase of each of the eight phased array antennas with respect to the first calibration antenna and the second calibration antenna is given by n1,c2 φ オフセット , n2,c2 φ オフセット , n3,c2 φ オフセット , n4,c2 φ オフセット , n5,c2 φ オフセット , n6,c2 φ オフセット , n7,c2 φ オフセット , n8,c2 φ オフセット From these, the average phase offset of the second calibration antenna relative to the first calibration antenna can be expressed as c2 φ オフセット can be calculated.

[0077] Further, the same procedure is followed to calculate the average phase offset for other calibration antenna pairs according to step 3407. Thus, for five calibration antennas, four average phase offsets are calculated. c2 φ オフセット (phase offset between the second and first calibration antennas), c3 φ オフセット (phase offset between the third and second antennas), c4 φ オフセット (phase offset between the fourth and third calibration antennas), c5 φ オフセット , (phase offset between the fifth and fourth calibration antennas).

[0078] In step 3409 of FIG. 34, for each phased array antenna along a corresponding row M of the MxN transmit array and the MxN receive array, one or more average phase offsets 0, c2 φオフセット , c3 φ オフセット , c4 φ オフセット , c5 φ オフセット is applied (added) to the measured phase (adjusted to the free space phase). So, for example, in row 1 (M=1) MxN The N(256) measured phase values ​​of the transmission array ( n,m φ tx-n,m k φ const ), an offset of zero (0) is added to each measured phase value because there is no offset associated with the first (end) calibration antenna, as explained above. The N (256) measured phase values ​​( n,m φ tx - n,m k φ const ) for each of c2 φ オフセット An offset of is added to each measured phase value. The N (256) measured phase values ​​( n,m φ tx - n,m k φ const ) for each of c2 φ オフセット + c3 φ オフセット An offset of is added to each measured phase value. The N (256) measured phase values ​​( n,m φ tx - n,m k φ const ) for each of c2 φ オフセット + c3 φ オフセット + c4 φ オフセット is added to each measured phase value. Also, the N (256) measured phase values ​​( n,m φ tx - n,m k φ const ) for each ofc2 φ オフセット + c3 φ オフセット + c4 φ オフセット + c5 φ オフセット An offset of is added to each measured phase value.

[0079] Therefore, the phase value obtained for each row of the MxN transmit array can be expressed as: ( n,m φ tx - n,m k φ const +0)-where m=1, n=1~256 ( n,m φ tx - n,m k φ const +0+ c2 φ オフセット )-where m=2, n= 1~256 ( n,m φ tx - n,m k φ const +0+ c2 φ オフセット + c3 φ オフセット )-where m=3, n= 1~256 ( n,m φ tx - n,m k φ const +0+ c2 φ オフセット + c3 φ オフセット + c4 φ オフセット )-where m=4, n= 1~256 ( n,m φ tx - n,m k φ const +0+ c2 φ オフセット + c3 φ オフセット + c4 φ オフセット + c5 φオフセット )-where m=5, n= 1~256

[0080] Furthermore, according to step 3409, the average phase offset c2 φ オフセット , c3 φ オフセット , c4 φ オフセット , c5 φ オフセット is applied in the same way to the measured phase (adjusted for free space phase) of each phased array antenna along the corresponding row M of the MxN receive array. Thus, the phase value obtained for each row of the MxN receive array can be expressed as: ( n,m φ rx - n,m k φ const +0)-where m=1, n=1~256 ( n,m φ rx - n,m k φ const +0+ c2 φ オフセット )-where m=2, n= 1~256 ( n,m φ rx - n,m k φ const +0+ c2 φ オフセット + c3 φ オフセット )-where m=3, n= 1~256 ( n,m φ rx - n,m k φ const +0+ c2 φ オフセット + c3 φ オフセット + c4 φ オフセット )-where m=4, n= 1~256 ( n,m φ rx - n,m k φ const +0+c2 φ オフセット + c3 φ オフセット + c4 φ オフセット + c5 φ オフセット )-where m=5, n= 1~256

[0081] In the final step of Figure 34, step 3411, a weighted average of the MxN transmit array is calculated on the M axis. This results in a vector of phase length N. These are the resulting transmit phase corrections. A weighted average of the MxN receive array is calculated on the M axis. This results in a vector of phase length N. These are the resulting receive phase corrections. The transmit and receive phase corrections can then be saved and applied to the transmit and receive operations of a radar system such as the radar system described above.

[0082] Internal phase calibration The internal phase calibration technique is "internal" because it involves transmitting radar signals between multiple phased array antennas (often referred to as radar elements) and a field probe located within a radar assembly or octagon, or between one or more phased array antennas and a field probe located in another (e.g., adjacent) radar assembly or octagon. Unlike the external phase calibration embodiments described above, there is no calibration antenna embedded in the far-field reflector. In a preferred embodiment, internal phase calibration involves two calibration processes, as described above: inter-radar assembly phase calibration and channel phase calibration. Both of these internal phase calibration processes are described in more detail below.

[0083] To aid in understanding the internal phase calibration process, including inter-radar assembly phase calibration and channel phase calibration, reference is made to FIG. 36. Two exemplary radar assemblies are shown in FIG. 36. Hereinafter, the radar assemblies are referred to as eight-arm units, as in the preferred embodiment, and each radar assembly includes eight phased array antennas, represented as circles in FIG. 36, in each of two eight-arm units m and n. Each eight-arm unit also includes a field probe, represented as a square in each of eight-arm units m and n. In at least one exemplary embodiment, the phased array antenna is a patch antenna, as shown in FIG. 8. However, as those skilled in the art will readily appreciate, the phased array antenna can be a different type of antenna. With respect to the field probe, those skilled in the art will understand that it can be a prick antenna, a patch antenna, a dipole antenna, or the like. Therefore, the present invention is not limited to a particular type of antenna.

[0084] Furthermore, for ease of discussion, and to be consistent with the external phase calibration described above, the internal phase calibration will be described for 32 eight-arm, and therefore 256 total, linearly arranged phased array antennas.

[0085] Inter-Channel Phase Calibration Figure 37 is a flow diagram illustrating inter-channel phase calibration 3700, according to a preferred embodiment. As shown, in step 3701, the field probe of a first octet, e.g., octet n in Figure 36, transmits a signal to, and is received by, each of the phased array antennas of octet n. The phase of the signal received at each of the phased array antennas is measured. By way of example, the phase measured at the first (leftmost) phased array antenna of octet n is: n 1φ rx,calwhere "n" denotes octet n, "1" denotes the first (leftmost) phased array antenna of octet n, "rx" denotes that the phase is associated with the received signal at the phased array antenna, and "cal" denotes that the phase is associated with the channel phase calibration. Further, according to step 3701, this same process is repeated for all of the phased array antennas, which in the example preferred embodiment includes 256. Thus, the result is m k φ rx,cal where "m" in this case generally represents the number of eight arms and "k" generally represents an eight-arm m phased array antenna.

[0086] In step 3703, the reverse process is performed. That is, each phased array antenna of each of the eight arms transmits a signal to a field probe. For example, in FIG. 36, the eighth (rightmost) phased array antenna of arm m transmits a signal to, and is received by, the field probe of arm m. The phase of the signal received at the field probe is measured. As an example, the phase measured at the field probe of a signal transmitted by the eighth (rightmost) phased array antenna of arm m is: m 8φ tx,cal where "m" denotes octoleg m, "8" denotes the eighth (rightmost) phased array antenna of octoleg m, "tx" denotes that the phase is associated with the signal transmitted by the phased array antenna, and "cal" denotes that the phase is associated with the channel phase calibration. Further, according to step 3703, this same process is repeated for all of the phased array antennas, which is 256 in the example preferred embodiment. Thus, the result is m k φ tx,cal This results in 256 transmission phase measurements, expressed as

[0087] At this point, transmit and receive phase measurements ( m k φ tx,caland m k φ rx,cal Note that ) reflects the phase contribution of the entire system. Thus, for example, a phase measurement associated with a given one of the octadpoles reflects the phase contribution from that octadpoles' electronics and the cables connecting that octadpoles to the corresponding transmitter and receiver hardware. The phase measurement also reflects the free-space phase due to the physical space between the corresponding phased array antenna and calibration antenna pair.

[0088] In step 3705 of FIG. 37, an internal loopback phase measurement is performed for each arm. m φ ループ As those skilled in the art will appreciate, loopback phase measurements reflect the phase contribution due to the transmitted signal traveling from the transmitter through the cable to the octave and then back through the return cable to the receiver, but bypassing the octave antenna. Because loopback phase measurements can change significantly over time, especially with temperature changes, it is necessary to measure the loopback phase of each octave during channel phase calibration.

[0089] Next, a transmit phase offset for each phased array antenna is calculated and a receive phase offset for each phased array antenna is calculated in step 3707. These transmit and receive phase offsets can be expressed as: m k φ tx =-[( m k φ tx,cal - m φ ループ )+( m φ K-k φ const )] m k φ rx =-[( m k φ rx,cal - m φ ループ )+( m φ K-k φ const )]

[0090] In the above channel phase offset representation, m k φ tx and m k φ rx represents the channel phase correction to be used for each phased array antenna k of eight arms m during radar transmit and receive operations, respectively. m k φ tx,cal and m k φ rx,cal represents the measured phase values, which are the result of step V103 above. m φ ループ is the internal loopback phase of arm m measured in step V105 above. k φ const is the free space phase calculated for eight-arm m phased array antenna k. As explained in the external calibration, the free space phase is a function of the physical distance between antenna k and the eight-arm m calibration antenna. Finally, m φ K represents other phases that are constant with respect to the octagon m, which are pre-measured in a laboratory environment, as will be understood by those skilled in the art. These constants may include, for example, the internal phase between the transmit cable connecting the transmitter to the octagon and the receive cable connecting the octagon to the receiver. These constants may also include, for example, the internal phase contributions due to the transmit signal from the input of the octagon to the field probe and the receive signal from the field to the output of the octagon. Again, those skilled in the art will understand that the transmit and receive phase offsets are all pre-measured in a laboratory and are described above. m k φ tx and m k φ rx The reader will understand and appreciate the values ​​of these constants that are taken into account when calculating

[0091] Internal phase calibration between eight arms As mentioned above, the transmit and receive channel phase offsets m k φ tx andm k φ rx and applying it to the radar transmit and receive operations, in a preferred embodiment, the inter-arm transmission phase offset m θ tx and the inter-arm receive phase offset m θ rx is also calculated for each arm m, and the transmit and receive channel phase offsets associated with arm m m k φ tx and m k φ rx Transmit and receive channel phase offsets m k φ tx and m k φ rx , and the transmit and receive phase offset between the eight legs. m θ tx and m θ rx Adding these together gives the total internal transmit phase offset for each channel (i.e., each phased array antenna channel): m k Θ tx and the total internal receive phase offset for each channel m k Θ rx Therefore, the total internal transmit and receive phase offsets are m k Θ tx and m k Θ rx reflects both the channel phase offset and the inter-arm offset and is generally expressed as: m k Θ tx = m θ tx + m k φ tx m k Θ rx = m θ rx + m k φ rx

[0092] 38 is a flow chart illustrating a method 3800 for calculating the transmit and receive phase offset between eight arms. m φ ループ is measured for each octet. Loopback phase is described above and is well known in the art. As mentioned above, for simplicity of explanation, there are 32 octets. Therefore, in step 3801, 32 loopback phase measurements are taken. 1 φ ループ ~ 32 φ ループ is obtained.

[0093] In step 3803, for each arm m, a transmission calibration phase m k φ tx,cal are measured at the field probe for the signal transmitted by the first phased array antenna (k=1) and the signal transmitted by the eighth phased array antenna (k=8) of the eight-arm. The transmit calibration phases are m 1φ tx,cal and m 8φ tx,cal Furthermore, the receive calibration phase m k φ rx,cal are measured at each of the first and eighth phased array antennas of the eight-arm for signals transmitted by the eight-arm field probes. The receive calibration phases are, respectively, m 1φ tx,cal and m 8φ tx,cal These calibration phase measurements are shown in Figure 39(a).

[0094] In step 3805 of Figure 38, several cross phases are measured for each adjacent octet pair, e.g., octet pair mn, as shown in Figure 39(b). The cross phases are m,n 8φ tx,calwhere m, n, and 8 indicate that the signal is transmitted from the phased array antenna 8 in arm m to the field probe in arm n. The cross phase is m,n 1φ rx,cal where n, m, and 1 indicate that the signal is transmitted from the field probe in arm m to the phased array antenna 1 of arm n. The cross phase is n,m 1φ tx,cal where n, m, and 1 indicate that the signal is transmitted from phased array antenna 1 in arm n to the field probe in arm m. Finally, n,m 8φ rx,cal where n, m, and 8 indicate that the signal is transmitted from the field probe in arm n to the phased array antenna 8 of arm m. Thus, for each pair of adjacent arms, e.g., arm pair mn, there are two cross-phase measurements measured at arm n and two cross-phase measurements measured at arm m.

[0095] In step 3807, m,n Δφ tx,X , the inter-octet transmission phase for each octet pair mn and nm is calculated as a function of the loopback phase measurements (step 3801), the transmission calibration phase measurements (step 3803), the cross-phase measurements (step 3805), and several other phases that are constant for each octet, as explained above in the discussion of channel phase calibration. Similarly, in step 3807, m,n Δφ rx,X The inter-arm receive phase for each octet pair mn and nm is calculated in a similar manner, as represented by: In a preferred embodiment, the inter-arm transmit and receive phases for each octet pair mn and nm are calculated in a similar manner, as represented by: m,n Δφ tx,X and m,n Δφ rx,Xcan be expressed as follows: m,n Δφ tx,X =( m,n k φ tx,X - m k φ tx,cal )+( m φ ループ - N / 2 φ ループ )+( m φ K - k φ const ) m,n Δφ rx,X =( m,n k φ rx,X - m k φ rx,cal )+( m φ ループ - N / 2 φ ループ )+( m φ K - k φ const )

[0096] In the above equation, the contribution of the loopback phase to the inter-arm transmission and reception phase is m φ ループ - N / 2 φ ループ It is important to note that the equation is given by, where: N / 2 φ ループ represents the reference loopback phase measurement at reference octagon r, which in the preferred embodiment is the octagon physically located in the middle of the linearly aligned octagons. Since there are N octagons, the reference octagon r physically located in the middle of the N octagons is octagon N / 2, or r=N / 2. In alternative embodiments, a different one of the N octagons may be used.

[0097] It is also important to note that in the preferred embodiment, the phased array antennas at both ends of all octets, i.e., Phased Array Antenna 1 (k=1) and Phased Array Antenna 8 (k=8), are used to transmit and receive the signals necessary to measure the calibration phase as described in step 3803, and to transmit and receive the signals necessary to measure the cross-phase as described in step 3805. However, according to alternative embodiments, it is certainly possible to use antennas other than Phased Array Antenna 1 and Phased Array Antenna 8 within the scope of the present invention. In still other embodiments, the field probes in each octet can be used to transmit and receive signals from field probes in adjacent octets to measure the cross-phase, thus eliminating the use of phased array antennas.

[0098] In step 3809 of Figure 38, the inter-arm transmit phase values ​​and inter-arm receive phase values ​​are used to calculate the angular average for each pair of adjacent arms mn and nm. In a preferred embodiment for calculating the angular average, the following equation is used: m,n Δφ X =∠[exp(i· m,n Δφ Xrx,X )+exp(i· m,n Δφ Xtx,X )]

[0099] The result of calculating the angle average for each pair of adjacent octarm pairs is a one-dimensional matrix y containing 2(N-1) angle averages, one for each pair of N-1 adjacent octarms mn and one for each pair of N-1 adjacent octarms nm. Again, N is the number of octarms. Also, for ease of discussion, in our exemplary embodiment, N=32. In this example, the y matrix has 62 angle averages and can be expressed as follows:

number

[0100] In step 3811 of FIG. 38, the transmission phase between the eight arms is m φ tx and the inter-arm receiving phase m φ rx Again, if the number of eight arms, N, is 32, the range of m is 1 to 32. Therefore, the transmission phase between the eight arms is m φ tx and the inter-arm receiving phase m φ rx In calculating , the final result is 2N inter-arm phase values, i.e., 32 transmit phase values ​​and 32 receive phase values ​​for each of the N arms. The 32 transmit phase values ​​and 32 receive phase values ​​can be represented by a matrix x as shown below:

number

[0101] In the above matrix x, the elements are the inter-arm transmission phase offsets for each arm N. m θ tx or reception phase offset between eight arms m θ rx where m=1 to N, and m θ tx = m φ tx,com - r φ tx,com where: m θ rx = m φ rx,com - r φ rx,com Furthermore, as shown, the transmission phase offset between the eight arms is m θ tx and the inter-arm receive phase offset m θ rxis calculated relative to a reference octagon r. As noted above, the reference octagon r is, in a preferred embodiment, the octagon physically located in the middle of the N octagons. Thus, the reference octagon r is octagon N / 2. Those skilled in the art will appreciate that calculating the inter-octagon phase relative to a single octagon, specifically the reference octagon r(N / 2), simplifies the calculation. However, as noted, octagons other than octagon N / 2 are within the scope of the present invention.

[0102] Considering the above explanation, the matrix can be written as follows: x= 1 θ tx , 2 θ tx … N θ tx , 1 θ rx , 2 θ rx … N θ rx ), where: m θ tx = m φ tx,com - r φ tx,com where: m θ rx = m φ rx,com - r φ rx,com is.

[0103] The relationship between the matrix y calculated above in step 3809 and the matrix x is given as follows: y=Ax

[0104] where A is a solver matrix with dimensions (2(N-1)) x (2(N-1)). Using well-known linear algebra techniques, one skilled in the art can solve the above matrix x, resulting in the N inter-arm transmission phases, 1 θ tx , 2 θ tx … N θ tx , and N eight-arm inter-reception, 1 θ rx , 2 θ rx… N θ rx These phase values ​​are then used to calculate the total internal transmit phase offset referenced above, as repeated below: m k Θ tx and total internal receive offset m k Θ rx can be calculated. m k Θ tx = m θ tx + m k φ tx m k Θ rx = m θ rx + m k φ rx

[0105] If there are 32 eight-arm sections, each containing eight phased array antennas, as in this example, then the above calculations yield a total of 256 internal transmit phase offsets. m k Θ tx where k=1 to 256, resulting in a total of 256 internal receive phase offsets. m k Θ rx There is, and here too, k = 1~256 These internal phase offsets can then be applied to the transmit and receive radar operations to improve the accuracy of the radar system.

[0106] In the preferred embodiment described above, inter-arm phase calibration is based on the phased array antenna of each arm and the arms themselves being aligned in a linear configuration. Inter-arm phase calibration is also based on measuring the cross-phase of adjacent arms. This allows well-known linear methods to be used to solve the matrix x above, as described above. Nevertheless, it is within the scope of the present invention to configure the arms in a non-linear arrangement. It is also within the scope of the present invention to measure the cross-phase of non-adjacent arms. However, the inter-arm transmission phase of the matrix xm θ tx and the inter-arm receiving phase m θ rx To solve this, we need to use nonlinear methods, which are more complicated but well known.

[0107] As mentioned earlier, one specific phase contribution can change significantly over time, primarily due to temperature changes. The specific phase contribution is the loopback phase m φ ループ In accordance with a preferred embodiment of the present invention, the internal calibration is updated using loopback phase measurements that are updated more frequently. Thus, the previously calculated inter-arm transmit and receive phase values ​​are m θ tx,old and m θ rx,old If represented by m θ tx,new and m θ rx,new The periodically updated inter-arm transmit and receive phase values, denoted as m φ loop,new In a preferred embodiment, periodically updated inter-arm transmit and receive phase values m θ tx,new and m θ rx,new can be calculated as follows, although other calculations are within the scope of the present invention: m θ tx,new = m θ tx,old -1 / 2( m φ loop,new - m φ loop,old )+1 / 2( r φ loop,new- r φ loop,old ) m θ rx,new = m θ rx,old -1 / 2( m φ loop,new - m φ loop,old )+1 / 2( r φ loop,new-r φ loop,old )

[0108] In the above equation, the periodically updated inter-arm transmission and reception phase values m θ tx,new and m θ rx,new is based on the updated loopback phase values ​​at each arm N relative to the reference arm r. Again, the updated inter-arm transmit and receive phase values m θ tx,new and m θ rx,new will be applied to transmit and receive radar operation in the same manner as above, at least until a completely new internal calibration is performed that includes both channel phase calibration and inter-arm phase calibration. m θ tx,new and m θ rx,new The periodic update of is shown in step 3813 of FIG.

[0109] The various corresponding structures, materials, acts, and equivalents of all means or step-plus-function elements in the various claims below are intended to include any structure, material, or act for performing the function in combination with the elements of other claims as specifically claimed. The various embodiments were chosen and described in order to best explain the various principles of the disclosure and its various practical applications, and to enable others skilled in the art to understand the disclosure in various embodiments with various modifications suited to the particular uses contemplated.

[0110] This detailed description has been presented for various purposes of illustration and explanation, but is not intended to be completely exhaustive and / or to limit this disclosure to the various forms disclosed. Numerous modifications and variations in technique and structure will be apparent to those skilled in the art without departing from the scope and spirit of the present disclosure, as set forth in the various claims that follow. Accordingly, such modifications and variations are intended to be part of this disclosure. The scope of the present disclosure is defined by the various claims, including known and unforeseeable equivalents at the time of filing of this disclosure.

[0111] The following items are further provided with respect to this disclosure:

[0112] (1) A radar calibration method comprising: transmitting a signal from each of a plurality of phased array antennas and measuring a transmission phase of each transmitted signal as it is received at one or more calibration antennas, one transmission phase being measured for each phased array antenna-calibration antenna combination; receiving a signal at each of the plurality of phased array antennas from each of the one or more calibration array antennas and measuring a receive phase for each received signal at each of the plurality of phased array antennas, one receive phase being measured for each phased array antenna-calibration antenna combination; adjusting each measured transmit phase and each measured receive phase by a phase offset associated with a corresponding one of the one or more calibration antennas, wherein the phase offset associated with each one of the one or more calibration antennas is greater than or equal to zero; calculating a single transmit phase correction for each of the plurality of phased array antennas, the single transmit phase correction for a given one of the phased array antennas being based on a weighted average of the offset-adjusted, measured transmit phases associated with the given one of the phased array antennas and the one or more calibration antennas; calculating a single receive phase correction for each of the plurality of phased array antennas, the single receive phase correction for a given one of the phased array antennas being based on a weighted average of the offset-adjusted, measured receive phases associated with the given one of the phased array antennas and the one or more calibration antennas; storing the single transmit phase correction for each of the plurality of phased array antennas and the single receive phase correction for each of the plurality of phased array antennas to adjust the phases of the plurality of phased array antennas during radar operation.

[0113] (2) measuring the free-space phase offset for each phased array antenna-calibration antenna pair; 10. The method of claim 1, further comprising: adjusting the measured transmit phase for each phased array antenna-calibration antenna pair; and adjusting the measured receive phase for each phased array antenna-calibration antenna pair by the measured free-space offset for the corresponding phased array antenna-calibration antenna pair.

[0114] (3) The method of (1), wherein the plurality of phased array antennas are linearly aligned with respect to each other.

[0115] (4) The method of (3), wherein the one or more calibration antennas are embedded in a surface of a radar reflector.

[0116] (5) The method of (4), wherein the number of calibration antennas is greater than one and the calibration antennas are spaced apart from the plurality of phased array antennas.

[0117] (6) The method of (5), wherein the calibration antenna is linearly aligned with and uniformly distributed across the plurality of phased array antennas.

[0118] (7) The method of (6), wherein the phase offset associated with each of the calibration antennas other than a first calibration antenna of the calibration antennas is calculated relative to the phase offset of the first calibration antenna of the calibration antennas and any calibration antennas located between the calibration antenna and the first calibration antenna.

[0119] (8) The method of (7), wherein the phase offset of the first calibration antenna of the calibration antenna is zero.

[0120] (9) calculating the phase offset of a given one of the calibration antennas other than the first calibration antenna of the calibration antennas; identifying a subset of the plurality of phased array antennas based on a weighting factor associated with each of the phased array antennas in the subset, the given calibration antenna and the first calibration antenna, or another calibration antenna adjacent to and between the given calibration antenna and the first calibration antenna; transmitting a signal from each of the phased array antennas in the subset, measuring the transmission phase at the given calibration antenna and the first or adjacent calibration antenna, and calculating a transmission phase difference value for each of the phased array antennas in the subset by subtracting the corresponding transmission phase measured at the given calibration antenna and the corresponding transmission phase measured at the first or adjacent calibration antenna; and calculating a phase offset for the given calibration antenna based on a weighted average of the transmit phase difference values ​​associated with the phased array antennas in the subset.

[0121] (10) adjusting each measured transmit phase and each measured receive phase by a phase offset associated with a corresponding one of the calibration antennas; 9. The method of claim 8, comprising adding to each measured transmit phase and each measured receive phase the calculated phase offset of the corresponding one of the calibration antennas and the calculated phase offsets of any and all calibration antennas located between the corresponding one of the calibration antennas and the first calibration antenna.

[0122] (11) A radar calibration method, comprising: for each of a plurality of radar assemblies each including a first antenna and a plurality of phased array antennas; transmitting a signal from the first antenna to each of a plurality of phased array antennas and measuring a received phase of the signal as it is received at each of the plurality of phased array antennas; receiving, at the first antenna, a signal transmitted from each of the plurality of phased array antennas and measuring a transmission phase for each signal transmitted by the plurality of phased array antennas as received at the first antenna; calculating a transmission channel phase correction for each of the plurality of phased array antennas based on the corresponding transmission phase measurement of each of the plurality of phased array antennas adjusted by a loopback phase value corresponding to the radar assembly in which each individual phased array is located; calculating a receive channel phase correction for each of the plurality of phased array antennas based on the corresponding receive phase measurement of each of the plurality of phased array antennas adjusted by the loopback phase value corresponding to the radar assembly in which each individual phased array is located; and calibrating the plurality of phased array antennas during radar operation based on the transmit and receive channel phase corrections.

[0123] (12) The plurality of phased array antennas in each of the plurality of radar assemblies are linearly aligned; 12. The method of claim 11, wherein the plurality of radar assemblies are linearly aligned.

[0124] (13) The method according to (11), wherein the first antenna is a field probe.

[0125] (14) The method of (11), further comprising measuring the loopback phase for each of the plurality of radar assemblies during the radar calibration.

[0126] (15) calculating the transmission channel phase corrections for each of the plurality of phased array antennas based on the corresponding transmission phase measurements of each of the plurality of phased array antennas includes adjusting each transmission phase measurement by at least one predetermined phase constant; 12. The method of claim 11, wherein calculating the receive channel phase corrections for each of the plurality of phased array antennas based on the corresponding receive phase measurements of each of the plurality of phased array antennas comprises adjusting each receive phase measurement by the at least one predetermined phase constant.

[0127] (16) The method of (15), wherein the at least one predetermined phase constant is a free-space phase value associated with each of the plurality of phased array antennas and the corresponding first antenna.

[0128] (17) calculating an inter-radar assembly transmission phase offset for each of the plurality of radar assemblies; calculating an inter-radar assembly receive phase offset for each of the plurality of radar assemblies; calculating an internal transmission phase offset for each of the plurality of phased array antennas by adjusting the transmission channel phase correction of each of the plurality of phased array antennas by the inter-radar assembly transmission phase offset calculated for the corresponding radar assembly in which each of the plurality of phased array antennas is located; calculating an internal receive phase offset for each of the plurality of phased array antennas by adjusting the receive channel phase correction of each of the plurality of phased array antennas by the inter-radar assembly receive phase offset calculated for the corresponding radar assembly in which each of the plurality of phased array antennas is located; storing the internal transmit phase offset for each of the plurality of phased array antennas and the internal receive phase offset for each of the plurality of phased array antennas; 12. The method of claim 11, further comprising: calibrating each of the phased array antennas during radar operation based on a corresponding internal transmit phase offset and a total internal receive phase offset.

[0129] (18) calculating the inter-radar assembly transmit phase offset and the inter-radar assembly receive phase offset for each of the plurality of radar assemblies, measuring transmit and receive calibration phases for each of the plurality of radar assemblies; measuring the transmit and receive cross phase for each pair of radar assemblies; calculating an inter-radar assembly transmission phase for each pair of radar assemblies, the inter-radar assembly transmission phase for a given radar assembly pair being correlated with a loopback phase, a transmission calibration phase, a transmission crossover phase, and at least one predetermined phase constant; calculating an inter-radar assembly receive phase for each pair of radar assemblies, the inter-radar assembly receive phase for a given radar assembly pair being correlated with a loopback phase, a receive calibration phase, a receive crossover phase, and at least one predetermined phase constant; calculating an angular average for each pair of radar assemblies as a function of the inter-radar assembly transmit phase and the inter-radar assembly receive phase calculated for each pair of radar assemblies; calculating the inter-radar assembly transmit phase offset and the inter-radar assembly receive phase offset for each of the plurality of radar assemblies as a function of the angular average for each pair of the radar assemblies.

[0130] (19) the inter-radar assembly transmission phase offset for a given one of the plurality of radar assemblies is equal to an inter-radar assembly transmission value for the given radar assembly and an inter-radar assembly transmission value for a reference radar assembly; 19. The method of claim 18, wherein the inter-radar assembly receive phase offset for the given one of the plurality of radar assemblies is equal to an inter-radar assembly receive value for the given radar assembly and an inter-radar assembly receive value for the reference radar assembly.

[0131] (20) The plurality of phased array antennas in each of the plurality of radar assemblies are linearly aligned; 19. The method of claim 18, wherein the plurality of radar assemblies are linearly aligned.

[0132] (21) The method of (20), wherein the loopback phase is correlated with the loopback phase of a corresponding one of the radar assemblies and the loopback phase of a reference radar assembly.

[0133] (22) The method of (21), wherein the reference radar assembly is the radar assembly physically located at the center of the plurality of linearly aligned radar assemblies.

[0134] (23) The method of (18), wherein the transmit cross phase and the receive cross phase are correlated with signals transmitted and received between adjacent radar assemblies.

[0135] (24) The method of (23), wherein the plurality of radar assemblies are linearly aligned with one another and the adjacent radar assemblies are directly adjacent to one another.

[0136] (25) the transmit calibration phase is correlated with signal measurements made at a first antenna based on signals transmitted by first and second phased array antennas of the plurality of phased array antennas in the given radar assembly; 19. The method of claim 18, wherein the receive calibration phase is correlated with signal measurements made at first and second phased array antennas of the plurality of phased array antennas in the given radar assembly based on a signal transmitted by the first antenna in the given radar assembly.

[0137] (26) The plurality of phased array antennas in each of the plurality of radar assemblies are linearly aligned with respect to one another; the plurality of radar assemblies are linearly aligned with respect to one another; the first one of the phased array antennas is located at a first end of the linearly aligned phased array antenna in the given radar assembly; 26. The method of claim 25, wherein the second one of the phased array antennas is located at an opposite end of the linearly aligned phased array antenna within the given radar assembly.

Claims

1. 1. A radar calibration method comprising: transmitting a signal from each of a plurality of phased array antennas and measuring a transmission phase of each transmitted signal as it is received at one or more calibration antennas, one transmission phase being measured for each phased array antenna-calibration antenna combination; receiving a signal at each of the plurality of phased array antennas from each of the one or more calibration antennas and measuring a receive phase for each received signal at each of the plurality of phased array antennas, one receive phase being measured for each phased array antenna-calibration antenna combination; adjusting each measured transmit phase and each measured receive phase by a phase offset associated with a corresponding one of the one or more calibration antennas, wherein the phase offset associated with each one of the one or more calibration antennas is greater than or equal to zero, and the phase offset associated with each of the calibration antennas other than a first calibration antenna of the calibration antennas is calculated relative to the phase offset of the first calibration antenna of the calibration antennas and any calibration antennas located between the calibration antenna and the first calibration antenna; calculating a single transmit phase correction for each of the plurality of phased array antennas, the single transmit phase correction for a given one of the phased array antennas being based on a weighted average of the adjusted and measured transmit phases associated with the given one of the phased array antennas and the one or more calibration antennas relative to a number of the calibration antennas; calculating a single receive phase correction for each of the plurality of phased array antennas, the single receive phase correction for a given one of the phased array antennas being based on a weighted average of the adjusted and measured receive phases associated with the given one of the phased array antennas and the one or more calibration antennas relative to a number of the calibration antennas; storing the single transmit phase correction for each of the plurality of phased array antennas and the single receive phase correction for each of the plurality of phased array antennas to adjust the transmit phases and the receive phases of the plurality of phased array antennas during radar operation; calculating the phase offset of a given one of the calibration antennas other than the first one of the calibration antennas; identifying a subset of the plurality of phased array antennas based on a weighting factor associated with each of the phased array antennas in the subset, the given calibration antenna and the first calibration antenna, or another calibration antenna adjacent to and between the given calibration antenna and the first calibration antenna; transmitting a signal from each of the phased array antennas in the subset, measuring the transmission phase at the given calibration antenna and the first or adjacent calibration antenna, and calculating a transmission phase difference value for each of the phased array antennas in the subset by subtracting the corresponding transmission phase measured at the given calibration antenna and the corresponding transmission phase measured at the first or adjacent calibration antenna; and calculating a phase offset for the given calibration antenna based on a weighted average of the transmission phase difference values ​​associated with the phased array antennas in the subset relative to the number of calibration antennas.

2. measuring a free space phase offset for each phased array antenna-calibration antenna pair; 10. The method of claim 1, further comprising: adjusting the measured transmit phase for each phased array antenna-calibration antenna pair; and adjusting the measured receive phase for each phased array antenna-calibration antenna pair by the measured free-space phase offset for the corresponding phased array antenna-calibration antenna pair.

3. The method of claim 1 , wherein the plurality of phased array antennas are linearly aligned with respect to each other.

4. The method of claim 3 , wherein the one or more calibration antennas are embedded in a surface of a radar reflector.

5. The method of claim 4 , wherein the number of calibration antennas is greater than one, and the calibration antennas are spaced apart from the plurality of phased array antennas.

6. The method of claim 5 , wherein the calibration antenna is linearly aligned and uniformly distributed with respect to the plurality of phased array antennas.

7. The method of claim 1 , wherein the phase offset of the first of the calibration antennas is zero.

8. adjusting each measured transmit phase and each measured receive phase by a phase offset associated with a corresponding one of the calibration antennas; 8. The method of claim 7, comprising adding to each measured transmit phase and each measured receive phase the calculated phase offset of the corresponding one of the calibration antennas and the calculated phase offsets of any and all calibration antennas located between the corresponding one of the calibration antennas and the first calibration antenna.

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