Initial orbit determination using angular velocity and angular acceleration measurements

Abstract

The present disclosure provides a system and method for directly measuring the angular velocity and angular acceleration of a space object and using the measured angular velocity and angular acceleration as inputs to a new, unique algorithm for initial orbit determination. Sensors measuring the location and time of a light event can be used to generate a virtual rate trail image for space object identification. The right ascension and declination of a space object event versus time can be fitted to a polynomial or spline to determine the associated angle, angular rate, and angular acceleration of the space object. A new, unique initial orbit algorithm can then be applied to estimate the orbital elements of the space object.

Description

[Technical Field]

[0001] (Related Applications) This non-provisional patent application claims the benefit of priority, as to all common subject matter, to an earlier-filed U.S. Provisional Patent Application No. 63 / 389,538, filed July 15, 2022, entitled "INITIAL ORBIT DETERMINATION USING ANGULAR VELOCITY AND ANGULAR ACCELERATION MEASUREMENTS." The identified earlier-filed provisional patent application is incorporated herein by reference in its entirety.

[0002] (Field) FIELD OF THE DISCLOSURE Embodiments of the present disclosure relate to initial orbit determination (IOD), and more particularly, to IOD using measured angular rate and measured angular acceleration as inputs. [Background technology]

[0003] Typically, a standard orbit requires six parameters to be accounted for: eccentricity, semimajor axis, inclination, longitude of ascending node, argument of periapsis, and true anomaly. These parameters can be determined by making measurements of the orbiting object over time and utilizing an orbit determination algorithm to estimate the orbit. Standard methods involve multiple sensors to measure positions at various times, calculating physical model trajectories, projecting potential orbits, and converging on an estimated orbit. These typical methods generally require a relatively long time (e.g., minutes or hours) to obtain an initial estimate of the object's orbit.

[0004] Traditionally, various IOD approaches have been implemented with relatively similar results. One class of traditional IOD techniques is to collect multiple observations over a relatively long period of time (e.g., Gooding's method). Trial orbital path generation can be integrated over time for comparison with the observation data. The trial orbit is repeated until the midpoint observations match the measured azimuth and elevation angles during the time of collection for the midpoint observations. Once the observations and trial orbit are aligned, an accurate initial orbit is determined. However, any changes in the satellite's orbital parameters during the collection period will result in inaccurate results.

[0005] A second exemplary IOD calculation method, typically called Laplace's method, uses three separate observations and numerically estimates the angular velocity and angular acceleration at the intermediate observations. A problem associated with this method is that the angular velocity and angular acceleration of both the observer and the target can change dramatically between observations. If the time between successive observations is too short, errors in the angular measurements will lead to inaccurate numerical derivatives of the angular velocity and angular acceleration. If the time between successive observations is too long, the angular velocity and angular acceleration of the observer and target objects may change too much for accurate estimates to be made for the intermediate observations. Object motion may have significant third derivatives (changes in angular acceleration), which makes the numerical estimate inaccurate.

[0006] Currently, more and more satellites and more and more space debris are being placed in orbit. This causes clutter on the satellites. This clutter must be tracked to avoid potential collisions. When a satellite is moved by commanded or uncommanded forces, a new orbit update must be performed. The longer it takes to determine a new orbit, the higher the chance that a collision will occur. Therefore, it is necessary to develop new techniques for IOD that are fast and accurate.

[0007] There are currently plans to send more satellites into lunar orbit. These moon / Earth orbits may be non-conventional and may vary due to commanded and uncommanded forces (e.g., relatively strong solar radiation pressure). It is necessary to accurately track these orbital changes in order to take corrective measures.

[0008] What is needed is a system and method that quickly and accurately performs IOD. Summary of the Invention [Means for solving the problem]

[0009] Embodiments of the present invention solve the above-referenced problems by providing a system and method that directly measures angular velocity and angular acceleration and uses the measured angular velocity and angular acceleration as inputs to a new and unique algorithm for IOD.

[0010] A first embodiment is directed to a method for determining a trajectory of an object, the method including: acquiring, by a sensor, data indicative of a plurality of objects in a trajectory, the data indicative of angular velocities and angular accelerations of an object among the plurality of objects; identifying the object from the data; measuring the angular velocities and angular accelerations from the data; determining an initial trajectory of the object using the angular velocities and angular accelerations; and estimating orbital elements from the initial trajectory of the object.

[0011] A second embodiment is directed to one or more non-transitory computer-readable media storing computer-executable instructions that, when executed by at least one processor, implement a method for determining a trajectory of an object. The method includes acquiring, by a sensor, data indicative of a plurality of objects in a trajectory, the data indicative of an angular velocity and an angular acceleration of an object among the plurality of objects; identifying the object from the data by generating a virtual rate track image comprising a virtual rate track of each object among the plurality of objects in the virtual rate track image, mapping the virtual rate tracks to locations in a field of view, identifying the plurality of objects based on their locations in the field of view, and identifying the object from the plurality of objects based on a comparison of the virtual rate tracks; determining the angular velocity and angular acceleration of the object from the virtual rate track; determining an initial trajectory of the object using the angular velocity and angular acceleration; and estimating orbital elements from the initial trajectory of the object.

[0012] A third embodiment is directed to one or more non-transitory computer-readable media storing computer-executable instructions that, when executed by at least one processor, implement a method for determining an orbit of an object. The method includes acquiring, by a sensor, data indicative of a plurality of objects in an orbit, the data indicative of angular velocities and angular accelerations of objects among the plurality of objects, identifying the object from the data, measuring the angular velocities and angular accelerations from the data, determining an initial orbit of the object by fitting an orbital ephemeris to the data, and determining an orbit of the object using the initial orbit as a starting solution for an orbit determination algorithm.

[0013] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Other aspects and advantages of the present invention will be apparent from the following Detailed Description of the embodiments and the accompanying drawing figures. [Brief explanation of the drawings]

[0014] Embodiments of the present invention are described in detail below with reference to the accompanying drawing figures.

[0015] [Figure 1] FIG. 1 depicts an exemplary prior art method of IOD.

[0016] [Figure 2A] 2A and 2B depict an example embodiment that uses angular velocity and angular acceleration to determine the initial state vector. [Figure 2B] 2A and 2B depict an example embodiment that uses angular velocity and angular acceleration to determine the initial state vector.

[0017] [Figure 3] FIG. 3 depicts an exemplary sensor for measuring angular velocity and angular acceleration.

[0018] [Figure 4] FIG. 4 depicts an embodiment of a photon-counting imager versus framing sensor imaging.

[0019] [Figure 5] FIG. 5 depicts an exemplary satellite detection by an event-based sensing system.

[0020] [Figure 6] FIG. 6 depicts an embodiment of a system comprising a telescope and a Ronchi filter for measuring angular velocity and angular acceleration.

[0021] [Figure 7] FIG. 7 depicts an embodiment utilizing color sensors and filters for independent measurement of two-dimensional motion and luminance.

[0022] [Figure 8] FIG. 8 depicts an exemplary process for the IOD.

[0023] [Figure 9] FIG. 9 depicts an exemplary process for calibrating a sensor for an IOD. [Figure 9-1] FIG. 9 depicts an exemplary process for calibrating a sensor for an IOD.

[0024] [Figure 10] FIG. 10 depicts a hardware system for an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0025] The drawing figures do not limit the invention to the specific embodiments disclosed and described herein. The drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the invention.

[0026] The following detailed description refers to the accompanying drawings that illustrate specific embodiments in which the invention may be practiced. The embodiments are intended to describe aspects of the invention in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized, and changes may be made without departing from the scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense. The scope of the present invention is defined only by the appended claims, along with the full scope of equivalents to which such claims are entitled.

[0027] In this description, a reference to "one embodiment," "an embodiment," or "embodiments" means that the referenced feature or features are included in at least one embodiment of the technology. Separate references to "one embodiment," "an embodiment," or "embodiments" in this description do not necessarily refer to the same embodiment, nor are they mutually exclusive, unless so stated and / or would be readily apparent to one of ordinary skill in the art from the description. For example, features, structures, acts, etc. described in one embodiment may also be included in other embodiments, but are not necessarily included. Thus, the technology may include various combinations and / or integrations of the embodiments described herein.

[0028] Generally, embodiments of the present disclosure are directed to systems and methods for quickly and accurately performing initial orbit determination (IOD). In some embodiments, sensors are used to measure angular velocity and angular acceleration, which are used as inputs to a new and unique orbit determination algorithm. Optical sensors may be used to make a single optical measurement of the sky comprising the object. Utilizing optical sensors in conjunction with new techniques for object detection and orbit determination enables the conversion of object track data comprising time-tagged pixel illumination and / or photon position data into angular position, angular velocity, and angular acceleration data that can be used to generate an initial object state vector. The systems and methods described herein may quickly and accurately provide initial orbit solutions as a starting point for estimating the orbit of a new maneuvered space object.

[0029] Generally, an orbit is described in terms of six parameters (i.e., eccentricity, semimajor axis, inclination, longitude of ascending node, argument of periapsis, and true anomaly). Typically, two angles are measured. These six parameters must be known to describe an orbit. Therefore, the object must be tracked to obtain enough information to calculate these parameters. Tracking to obtain enough information to accurately estimate the orbit of a space object can take minutes or hours. The only requirement is that the observer's motion and gravitational potential along the line of sight be known.

[0030] Typically, angular rate and angular acceleration are calculated from fixed angular measurements. Therefore, angular rate and angular acceleration are coupled to position measurements. As a result, errors in the position measurements are magnified in the angular rate and angular acceleration calculations. Furthermore, these parameters are coupled in the covariance matrix of current orbit determination methods, further complicating error minimization and noise reduction. Utilizing the sensors described herein, angular rate and angular acceleration are measured directly, allowing the angular rate and angular acceleration to be decoupled from the position measurements of a space object. Using angular rate and angular acceleration derived directly from the measurements as inputs to an initial orbit determination algorithm allows the orbit of a space object to be determined more quickly and accurately than typical standard methods.

[0031] In some embodiments, the space object may be any object in orbit around any other object (e.g., a planet, a star, a satellite, a missile, space debris, and an unknown object). Furthermore, measurements may be made from an observer that may be located on the Earth or any other object in orbit. In this manner, the orbit of any object may be determined from any other object. Thus, whether any two or more orbits intersect may be determined. Furthermore, locations where orbits may intersect with locations on the Earth or any other planet or satellite may be quickly and accurately determined. Any circular, elliptical, parabolic, or hyperbolic orbit may be quickly and accurately estimated. Similarly, any irregular orbit or unknown trajectory around a celestial body, including the Moon, or comprising a two-body problem, a three-body problem, or more, may be estimated. Furthermore, any standard altitude orbit (i.e., low Earth orbit (LEO), medium Earth orbit (MEO), highly elliptical orbit (HEO), geosynchronous orbit (GEO)) may be estimated using the systems and methods described herein.

[0032] In some embodiments, non-traditional orbits can be estimated using the systems and methods described herein. Currently, there is a new effort to extend orbits to the Moon and other planets. This results in non-traditional orbits that do not follow the two-body convention. This creates new uncertainties for space objects. The methods and systems described herein can also estimate these non-traditional orbits (e.g., lunar orbits, L2 regions, Earth-Moon orbits, orbital transfers, near-linear halos).

[0033] In general, an orbit can be determined from measurement data using an orbit estimation algorithm. Typically, a state vector is determined using the parameters illustrated in Figure 1. For example, a conventional method for IOD is shown in Figure 1. Figure 1 illustrates a distance estimation algorithm known as Laplace's method 102.

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[0034] Laplace's method 102 has its drawbacks. It is currently the least accepted method of IOD.

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[0035] A more accepted method is Gooding's method 104. Gooding's method 104 involves collecting multiple observations over a relatively long period of time. Trial orbital path generation can be integrated over time for comparison with the observation data. The trial orbit is repeated until the midpoint observations match the azimuth and elevation angles measured during the time of collection for the midpoint observations. Once the observations and trial orbit are aligned, an accurate initial orbit is determined. However, any changes in the satellite's orbital parameters during the collection period will result in inaccurate results.

[0036] The application of new sensors can allow angular velocity and angular acceleration to be measured rather than calculated. Measuring angular velocity and angular acceleration decouples them from position measurements. These independent measurements add two terms that previously needed to be calculated through successive measurements of fixed angles. Because angle, angular velocity, and angular acceleration can be measured simultaneously, the time to converge on an estimated initial state vector, and therefore an estimated trajectory, is reduced relative to previous methods. Figures 2A and 2B depict an example embodiment that uses adapted angle, angular rate, and angular acceleration values to determine the initial state vector.

[0037] 2A and 2B depict an embodiment of the free-body diagram and calculations required in a typical method to determine distance and distance rate from measured angular velocity and angular acceleration from an Earth-based observer (FIG. 2A) and a space-based observer (FIG. 2B). Note that in the embodiments described herein, angular velocity and angular acceleration do not need to be estimated numerically. This reduces the calculations, leaving a single nonlinear equation for calculating distance and distance rate as shown below and derived in FIG. 2B.

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[0038] Thus, an initial target state vector for the orbiting object can be determined. Similarly, any IOD method can be adapted to include input of measured angular velocity and angular acceleration and parameters determined therefrom (e.g., range and range rate). Using these measured values decouples the angular acceleration and angular velocity from the position measurements in the initial state vector. The initial state vector can then be used as input to an orbit determination algorithm, such as a Kalman filter (KF), an extended Kalman filter (EKF), a batch filter, etc., as described in the embodiments below. Using the measured angular rates in the calculation of the initial state vector as a starting point for an exemplary EKF amplifies the EKF to converge to a solution much more quickly (in some embodiments, an order of magnitude faster than conventional methods).

[0039] FIG. 3 depicts an example collection of sensors 300 that may be used in the embodiments described herein. Ideally, a sensor that detects not only the arrival time and spatial location on the focal plane of each light event, but also wavelength and / or polarization, would provide information to greatly increase the accuracy and reliability of measurements, thereby enabling rapid and accurate IOD. Currently, there is a trade-off between measuring spatially and temporally with respect to framing sensors. When high-speed imaging is used, the location of an object contains error because a relatively small number of photons indicating the object's location are received. Similarly, to obtain more information about the object's location, the exposure time must be increased. The methods and systems described herein can decouple the temporal and spatial components using a sensor system, along with the methods for capture described herein.

[0040] Generally, the coordinates X and Y described herein are coordinates on the focal planes of various sensors. Additionally, time (T) is used in conjunction with the X and Y coordinates to generally describe the X and Y location of a light event or event at time T, where the light event comprises pixel illumination from a space object or photon collision detection. Furthermore, "light" can be electromagnetic radiation of any wavelength. The techniques and detectors described herein are effective for light reflected from or emitted by a space object from either artificial or natural sources. Depending on the detector, single-photon or light-change event-based camera detectors as described herein can be used from extreme ultraviolet (or even X-ray) to long-wave infrared. Thus, light wavelength bands from 100 angstroms to 10 microns or wider can be detected. For example, the techniques described herein may be effective for ultraviolet light from the sun reflected from any space object, ultraviolet light emitted from thrusters on a space object, artificial lights (such as LEDs) on a space object, natural visible light from the sun reflected from a space object, lasers illuminating a space object, infrared radiation emitted by the heat of a space object, etc.

[0041] In some embodiments, an image photon counter (IPC) may be used. An exemplary microchannel plate (MCP) 302 delay line detector may be used. The MCP 302 delay line detector may asynchronously detect photon positions in X and Y and store the corresponding time T associated with each photon collision event while maintaining continuous spatial resolution. Similarly, a single-photon avalanche diode array (SPAD) 304 may asynchronously detect individual photons in X and Y and accurately measure the corresponding time of collision. The SPAD 304 may be limited in spatial resolution by pixel counting; however, each pixel is independent. The independent operation of each pixel allows for simultaneous detection of photons across the focal plane. IPC sensors are discussed in more detail below.

[0042] In some embodiments, an event-based sensor may be used, which may be an event-based camera (EBC) 306. The exemplary EBC 306 illustrated is a neuromorphic camera. Asynchronous X, Y, P (polarity changes), and time may be detected. Spatial resolution may be defined by pixel count. For the event-based sensors described herein, light changes above a minimum threshold can be detected. This qualifies the data by not collecting data from all pixels simultaneously, but only generating data when a light illumination change is detected.

[0043] In some embodiments, a charge-coupled device (CCD, not shown) or a complementary metal-oxide semiconductor (CMOS) 308 may be used. CCD and CMOS 308 are framing cameras that offer the trade-off between spatial accuracy and timing accuracy described above. In some embodiments, a high frame rate in low light conditions must be used. Therefore, there may be a penalty for high data volume.

[0044] The sensors shown in Figure 3 are exemplary only. Any sensors that collect information indicative of position, angular velocity, and angular acceleration may be used. Additionally, various sensors may be used in combination. The sensors described above are further described in the following embodiments for detecting angular velocity and angular acceleration.

[0045] The IPC and EBC 306 may allow angular rates and angular accelerations to be measured. Furthermore, the data collected by these sensors can be transformed without distortion into any fixed or co-moving coordinate system. Therefore, any measurement can be used with any relatively fixed object or between multiple relatively fixed objects and / or between multiple moving objects.

[0046] Additionally, frame sensor imaging, such as from a charge-coupled device (CCD), can collect photon data. However, photon data can be susceptible to errors of up to + / - 1 electron in low-light conditions. Therefore, even in low-light conditions, it is not possible to reliably collect information about individual photons striking the frame. This results in photons from the object being smeared across the focal plane, diluted, and mixed with diffuse background light and starlight. Tracking on the CCD output provides only angular position and time data from multiple measurements.

[0047] FIG. 4 depicts an exemplary comparison between an IPC (e.g., MCP 302 and SPAD 304) and a framing sensor (e.g., CCD, CMOS 308). The IPC can collect X, Y, and time information by performing vibration measurements on a membrane 402. For example, a photon 404 can strike the membrane and cause a vibration or sound wave across the membrane 402 to a membrane sensor 406 located at the edge 408 of the membrane 402. The membrane sensor 406 can detect the vibration at different times. Knowing the propagation speed of the vibration through the membrane 402 provides the precise location and time at which the photon 404 struck the membrane 402. Thus, the location and time data of the photon strike are known. The time-tagged photon list data can be projected onto a plane 410 in position-time three-dimensional space, as shown in FIG. 4, where all photon events from a space object wake 414 fall into a single virtual pixel 412. IPC allows for rate tracking in software after the data is collected, rather than during collection as with CCD. As shown, observation is continuous data collection. For IPC, the observation is each photon that strikes the membrane 402. From continuous data collection of object motion, higher-order derivatives of angular motion can be derived throughout the space object wake 414. With CCD, the tracking rate of the time-delay integration / quadrature transfer array must be known during observation or mechanical rate tracking. With IPC, movies with arbitrary time resolution can be created using IPC data. This enhances moving object detection, as a variable motion rate can be applied so that the motion of sky objects (e.g., stars) can be obscured, while the motion of the object to be detected is enhanced. Furthermore, through these same methods, multiple objects with different arbitrary velocities can be detected in the same dataset.

[0048] Using the focal plane measurements (e.g., X and Y measurements) along with the precise time of the measurements, the angular velocity and angular acceleration relative to the observer can be determined using the calculations presented in Figures 2A-2B. Once data is collected and the angular velocity and angular acceleration are determined from the collected data, the angular velocity and angular acceleration can be used to calculate an initial state vector using the modified Laplacian described above, which can then be used as input to an orbit determination algorithm (e.g., Extended Kalman Filter (EKF), Gooding's method). This provides a fast and efficient way to determine IOD when noise is present in the measurements.

[0049] Alternatively, in some embodiments, other sensors and techniques can be used to acquire angular velocity and angular acceleration data of an object. FIG. 5, for example, depicts an example scatter plot 500 generated from data collected by the EBC 306. In some embodiments, the EBC 306 can be used for object detection. The EBC 306 can record light level changes of pixels with high temporal resolution. The EBC 306 can detect light changes above a threshold amount in each pixel and create a timestamp for each light change event. Thus, any change in the field of view is recorded along with a very precise time that the change occurred. Because each pixel records data only when a change is detected, the amount of data and processing is reduced compared to a frame-based camera, where all frames are recorded simultaneously. This allows each pixel to operate independently of other pixels.

[0050] Enabling the EBC 306 to collect data on a portion of the sky provides data that can be visualized in the exemplary scatter plot 500 of Figure 5. The pixel variations are clearly shown, with various stars 502 appearing as small lines caused by the Earth's rotation and satellites 504 being lines of different lengths caused by the satellite's orbit. These lines are generated by the continuously detected light variations over each individual pixel and the associated time data. Thus, the angular rate and angular acceleration of an object can be determined directly from the data acquired by the EBC 306.

[0051] 6 depicts an embodiment for detecting intensity variations of an object as it moves through an orbit. In the arrangement shown, light from the object is magnified by a telescope 602 and then transmitted through a system of lenses 604 and Ronchi filters 606. The Ronchi filters 606 may have various slit widths to match tangential plane angular motion. Thus, as the object moves across the focal plane, the light intensity from the object passing through the Ronchi filters 606 indicates the angular velocity of the object.

[0052] The Ronchi filter 606 must have a variable slit pattern to match the angular displacement of the ray 608. Due to the tangential projection of the image on the focal plane, the spacing and width of the bars of the Ronchi filter 606 should increase toward the edge of the field of view. This provides an aperture in the Ronchi filter 606 that represents a constant angular displacement. Therefore, angular velocity is measured directly without compensation for the ray displacement angle, completely decoupled from the fixed angular measurement.

[0053] As an object moves across the focal plane, a low spatial resolution, high temporal resolution sensor 610 can be used to accurately detect light event arrival times and the light intensity of the light and dark bars as they change on the screen, as shown in process 612. The frequency of the changes in intensity 614 can be measured by spectral analysis. The intensity frequency can indicate angular velocity, and the changes in intensity can indicate angular acceleration. Thus, angular velocity and angular acceleration can be determined by spectral analysis. The uncertainty and covariance of angular velocity and angular acceleration are decoupled from the absolute angle measurements.

[0054] FIG. 7 depicts an embodiment utilizing color filters to encode x and y motion and intensity. In some embodiments, three filters 702 may be used to block light frequencies, as shown for the motion encoding of each X and Y component. In an exemplary embodiment, a magenta filter 704 blocks green light and allows red and blue to pass, a yellow filter 706 blocks blue light and allows green and red to pass, and a blue-green filter (not shown) blocks red light and passes green and blue. In some embodiments, a combination of magenta and yellow Ronchi filters encodes X and Y motion across a diffraction grating on a monochromatic focal plane. A blue-green-red camera may be used to detect the different color outputs. In block 708, blue represents the component of X motion, green represents the component of Y motion, and red represents the intensity change over time. This allows angular motion-intensity encoding to be performed using one telescope instead of three.

[0055] In some embodiments, additional algorithms (e.g., machine learning algorithms) can be applied to improve the fidelity of object detection and results. For example, a convolutional neural network (CNN) can be trained to characterize orbiting objects against the sky. Based on the time of exposure and the length of the track, the orbit type and possibly the satellite type can be characterized by the CNN. Any artificial intelligence (AI) or statistical algorithm can be used to further enhance object detection.

[0056] 8 depicts an exemplary method of determining an initial orbit, generally referenced by the numeral 800. In step 802, a sensor receives light from the sky, including an orbiting object as described in the above embodiments. The sensor may be any IPC, EBC, telescope sensor arrangement as described above, and / or any other arrangement and combination that may be capable of detecting angular velocity and angular acceleration.

[0057] In step 804, the sensor processes the received light as described in the above embodiments. Depending on the sensor being used, the processing may vary. Here, the sensor may detect light events including frequency fluctuations, intensity fluctuations, illumination changes, and individual photons coupled with precise time measurements to accurately determine the angular position, angular velocity, and angular acceleration of the detected orbital object.

[0058] In step 806, angular velocity and angular acceleration may be determined from the received data. The received data collected by the sensor may be indicative of angular velocity and angular acceleration, but the data may be time and position data of photons, rate of change of frequency, rate of change of intensity, etc., as described above. A curve may be fitted to the data indicative of angular velocity and angular acceleration. The angular velocity and angular acceleration may be determined from the curve fit. In some embodiments, right ascension and declination may be determined.

[0059] In step 808, the angular velocity and angular acceleration may be input into the algorithm described above (e.g., a modified Laplace) to determine the range and range rate between the target object and the observer. Additionally, an initial state vector may be determined using the range and range rate. The IOD is determined more quickly than current methods by inputting the angular velocity and angular acceleration into the range and range rate equations described in FIGS. 2A and 2B. The initial state vector may then be used in the EKF or batch algorithm in step 810. When noise is present in the real-world measurements, the decoupled system described above results in convergence to an accurate trajectory at least an order of magnitude faster than current methods.

[0060] Figure 9 depicts a more complete process of utilizing the sensor and algorithms to calibrate the sensor, employ the IOD process described above, and use the IOD output for orbit determination. In some embodiments, sophisticated calibration may be necessary or useful in providing an efficient IOD. The calibration process may include a list-based process for generating a dynamic model of the sensor field of view. In some embodiments, the data may be adjusted for calculations in a preprocessing stage. In some embodiments, the sensor data may not be correct for astronomical coordinate calculations. For example, X and Y data related to the focal plane, angular rate, angular acceleration, etc. may be scaled based on sensor or telescope parameters. Rescaling the data may be used to generate pseudo-X', Y' and produce a round central focal plane image. The data may be adjusted, divided into 1-second time segments, and saved as Flexible Image Transport System (FITS) images. Multiple images may then be analyzed and solved for the astronomical coordinate system. In some embodiments, this process may be performed by a third party, such as astronomy.net. The process is described in detail below.

[0061] Step 902 may begin a preprocessing routine to collect star data and create a corrected star data space. In step 902, stars moving across the sky may be detected, and their velocity across the focal planes vx, vy as described above may be determined in pixel coordinates. In some embodiments, the best instrument placement for capturing the object may be determined. The best setting may be sensor-specific. For example, the best setting may be a fixed telescope orientation. Thus, the sky will effectively move past the field of view of the telescope and sensor. Thus, the star will trace a path across the field of view like an object in orbit. In some embodiments, it may be better to move or rotate the telescope along with the star, so that the star appears stationary in the field of view and the only perceived movement is that of the orbiting object. Furthermore, the telescope and sensor are positioned to detect a desired portion of the sky with an orbiting object with a known location that can later be compared. For the exemplary process described herein, the telescope is stationary and corrections are made for the relative motion of the space object.

[0062] A set of data may be received by a sensor. The sensor may be operated to receive light from the sky and detect any luminous objects in a desired location. The light is collected by the sensor. The sensor may be any of the sensors described above, and the light may be collected by any of the systems and methods described above associated with the sensor.

[0063] In step 904, the virtual image (2D histogram) of the event may be projected into a star motion correction space for star tracking that includes aberrations due to the Earth's rotation and the Earth's relative velocity. The star motion correction space may be defined by X' = x + vx × t, Y' = y + vy × t.

[0064] In step 906, astrometric processing pass 1 begins. In step 906, point sources are selected in the virtual image and tabulated for identification and classification. The list-based approach described herein provides tracking data in a manner that does not distort the data. Tracking data is added to a list as it becomes increasingly refined, as described in more detail below.

[0065] In step 908, a point source solution is realized. The list of point source data can be submitted to an online database, such as astronomy.net, for processing. The astrometric solution is provided in X', Y' space.

[0066] In step 910, all events may be transformed into RA and DEC data coordinates using the solution in X', Y' space. All events are then labeled with RA and DEC data.

[0067] In step 912, a search in the GAIA catalog may be performed for an associated star in the virtual image area of the sky. In step 914, the GAIA star is assigned to the source object in the virtual image. In step 916, the GAIA catalog coordinates are corrected for aberration data based on the Earth's velocity. In step 918, all events associated with the image source are labeled with the corrected GAIA coordinates.

[0068] Astrometric processing pass 2 begins at step 920. In step 920, a 17-parameter time-dependent dynamic model of the astrometric tangent plane is then fitted to map each event's x, y, and time to RA and DEC. The mapping provides each event with an x, y, and timestamp and a conversion to RA and DEC. Additionally, optical barrel corrections may be performed to correct for spherical mapping. A simultaneous fit is performed for space objects. This process defines how the field of view is moving across the sky relative to the sensor mount, which rotates with the Earth. Pixel coordinates may be fixed to right ascension and time. The list process continues to add increasingly refined data to the list, rather than warping the data to fit the mapping. This dynamic model fit is used to confirm the data and label the data as a pass 2 RA and DEC position in the sky. This allows for rapid conversion between X, Y, and time and RA, DEC, and time. In step 922, all events are labelled using the results of the pass 2 tangent plane motion fit.

[0069] Pass 3 astrometric processing begins in step 924. In step 924, the RA and DEC residuals for all events that can be associated with stars in the GAIA catalog can be plotted. In step 926, a spline fit can be generated for the RA and DEC corrections in time. This can be used to correct the data for unmodeled inputs such as telescope mount jitter. In step 928, all events can be corrected using pass 3 corrections. These corrections provide real event location data indicating their location in the sky. At this point, all events can be labeled as stars or objects (e.g., satellites, meteorites, missiles, etc.).

[0070] In step 930, space object event identification may begin as described in the above embodiments. In step 930, the x and y pixel velocities of the object may be determined from the sensor data. Once the x and y pixel velocities are identified, a virtual rate wake image may be generated in step 932 to identify the source. The virtual rate wake image may show the x and y velocities of the source over time, and events associated with the source may be tracked over time in step 934. Sources of light impingement may be compared to identify the object based on the rate wakes as described in the above embodiments.

[0071] The IOD process described above may begin in step 936. In step 936, the RA and DEC of the space object may be fitted to polynomials and splines. The intermediate time of the space object event set may be determined, and the angle, angular rate, and angular acceleration at that time may be determined in step 938.

[0072] An IOD algorithm may be applied in step 940. In step 940, range and range rate may be calculated using the measured angular velocity and angular acceleration. Additionally, other orbital elements may be calculated from the IOD. In some embodiments, the other orbital elements may be those necessary to describe the orbit as shown in FIGS. 2A and 2B and described in detail above.

[0073] In step 942, an extension of the IOD, referred to herein as IOD+, may be added. In step 942, an exemplary Levenberg-Marquardt algorithm may be used in conjunction with the IOD to fit the orbital ephemeris to the event data. The orbital ephemeris may be used as a starting point solution for orbit determination. This provides a better starting point in a faster time than current standard methods of orbit determination.

[0074] In step 944, typical orbit determination techniques may be used to estimate the orbit of the space object using the origin solution.

[0075] FIG. 10 depicts an exemplary hardware platform 1000 for an embodiment of the present invention. The computer 1002 may be a desktop computer, a laptop computer, a server computer, a mobile device such as a smartphone or tablet, or a general-purpose or special-purpose computing device of any other form factor. For illustrative purposes, several components are depicted with the computer 1002. In some embodiments, certain components may be arranged differently or may not be present. Additional components may also be present. A system bus 1004 is included in the computer 1002, allowing other components of the computer 1002 to communicate with each other. In some embodiments, there may be multiple buses, or components may communicate directly with each other. A central processing unit (CPU) 1006, as well as one or more random access memory (RAM) modules 1008, are connected to the system bus 1004. A graphics card 1010 is also attached to the system bus 1004. In some embodiments, the graphics card 1010 may not be a physically separate card but rather may be integrated into the motherboard or the CPU 1006. In some embodiments, the graphics card 1010 has a separate graphics processing unit (GPU) 1012, which can be used for graphics processing or for general-purpose computing (GPGPU). GPU memory 1014 is also on the graphics card 1010. A display 1016 for user interaction is connected (directly or indirectly) to the graphics card 1010. In some embodiments, there is no display, while in others, a display is integrated into the computer 1002. Similarly, peripherals such as a keyboard 1018 and a mouse 1020 are connected to the system bus 1004. Like the display 1016, these peripherals may or may not be integrated into the computer 1002.A local storage device 1022 is also connected to the system bus 1004 and may be any form of computer-readable media that may be internally installed within computer 1002 or externally and removably installed.

[0076] Computer-readable media includes both volatile and nonvolatile media, removable and non-removable media, and contemplates media that is readable by a database. For example, computer-readable media includes (but is not limited to) RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVDs), holographic media or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage, and other magnetic storage devices. These technologies can store data temporarily or permanently. However, unless expressly specified otherwise, the term "computer-readable media" should not be interpreted to include physical but transitory forms of signal transmission, such as radio broadcasts or electrical signals over wires. Examples of stored information include computer-usable instructions, data structures, program modules, and other data representations.

[0077] Finally, a network interface card (NIC) 1024 is also attached to the system bus 1004 and enables the computer 1002 to communicate over a network, such as network 1026. The NIC 1024 can be any form of network interface known in the art, such as Ethernet, ATM, fiber, Bluetooth, or Wi-Fi (i.e., the IEEE 802.11 family of standards). The NIC 1024 connects the computer 1002 to a local network 1026, which may include one or more other computers, such as computer 1028, and network storage devices, such as data store 1030. In general, a data store, such as data store 1030, may be any repository in which information can be stored and retrieved as needed. Examples of data stores include relational or object-oriented databases, spreadsheets, file systems, flat files, directory services such as LDAP and Active Directory, or email storage systems. A data store may be accessible through a complex API (e.g., a structured query language, etc.), a simple API that provides only read, write, and seek operations, or any level of complexity in between. Some data stores may additionally provide management functions for the data sets stored therein, such as backup or versioning. A data store may be local to a single computer, such as computer 1028, accessible over a local network, such as local network 1026, or remotely accessible via the Internet 1032. The local network 1026 is in turn connected to the Internet 1032, which connects many networks, such as the local network 1026, remote network 1034, or directly attached computers, such as computer 1036. In some embodiments, the computer 1002 itself can be directly connected to the Internet 1032.

[0078] In some aspects, techniques described herein relate to a method of determining a trajectory of an object, the method including: acquiring, by a sensor, data indicative of a plurality of objects in the trajectory, the data indicative of angular velocities and angular accelerations of an object among the plurality of objects; identifying the object from the data; measuring the angular velocities and angular accelerations from the data; determining an initial trajectory of the object using the angular velocities and angular accelerations; and estimating orbital elements from the initial trajectory of the object.

[0079] In some aspects, the method further includes determining locations of light impingement on pixels of the sensor, where the locations of light impingement indicate relative locations of multiple objects within the field of view; generating a virtual rate wake image of the locations of light impingement over time; and identifying the objects and associated angles, angular velocities, and angular accelerations from the virtual rate wake image.

[0080] In some aspects, the techniques described herein relate to methods in which the sensor is an event-based camera and the data indicates changes in light intensity at each pixel of the event-based camera.

[0081] In some aspects, the techniques described herein relate to methods in which the sensor is an image photon counter and the data indicates the time and location of photon impingement on the sensor.

[0082] In some aspects, the techniques described herein relate to methods in which the sensor is a color sensor and the incident light is filtered to indicate components of angular velocity and angular acceleration.

[0083] In some aspects, the techniques described herein relate to methods in which the sensor is an Earth-based sensor or a space-based sensor.

[0084] In some aspects, the techniques described herein relate to one or more non-transitory computer-readable media storing computer-executable instructions that, when executed by at least one processor, implement a method for determining a trajectory of an object. The method includes acquiring, by a sensor, data indicative of a plurality of objects in a trajectory, the data indicative of an angular velocity and an angular acceleration of an object among the plurality of objects; identifying the object from the data by generating a virtual rate trail image including a virtual rate trail of each object among the plurality of objects in the virtual rate trail image, mapping the virtual rate trail to a location within a field of view, identifying the plurality of objects based on their locations within the field of view, and identifying the object from the plurality of objects based on a comparison of the virtual rate trails; determining the angular velocity and angular acceleration of the object from the virtual rate trail; determining an initial trajectory of the object using the angular velocity and angular acceleration; and estimating orbital elements from the initial trajectory of the object.

[0085] In some aspects, the techniques described herein relate to media where the method further includes determining an initial state vector including a range and a range rate of the object determined from the angular velocity and angular acceleration.

[0086] In some aspects, the techniques described herein relate to a medium that further includes determining an initial orbit of the object by fitting an orbital ephemeris to the data, and determining an orbit of the object using the initial orbit as a starting solution.

[0087] In some aspects, the techniques described herein relate to a medium in which an orbital ephemeris is fitted to the data using the Levenberg-Marquardt algorithm.

[0088] In some aspects, the techniques described herein relate to a medium in which the sensor is one of a microchannel plate delay line detector, an event-based camera, a single-photon avalanche diode array, or a complementary metal-oxide semiconductor.

[0089] In some aspects, the techniques described herein relate to media in which angular velocity, angular acceleration, and associated angles are determined at intermediate times in the data.

[0090] In some aspects, the techniques described herein relate to a medium in which the sensor is located in space.

[0091] In some aspects, the techniques described herein relate to one or more non-transitory computer-readable media storing computer-executable instructions that, when executed by at least one processor, implement a method for determining an orbit of an object. The method includes acquiring, by a sensor, data indicative of multiple objects in an orbit, the data indicative of angular velocity and angular acceleration of an object among the multiple objects, identifying the object from the data, measuring the angular velocity and angular acceleration from the data, determining an initial orbit of the object by fitting an orbital ephemeris to the data, and determining the orbit of the object using the initial orbit as a starting point solution for an orbit determination algorithm.

[0092] In some aspects, the techniques described herein relate to a medium in which the sensor is one of a microchannel plate delay line detector, an event-based camera, a single-photon avalanche diode array, or a complementary metal-oxide semiconductor.

[0093] In some aspects, the techniques described herein relate to media where the method further includes determining x and y pixel velocities of the object on the sensor.

[0094] In some aspects, the techniques described herein relate to a medium in which identifying an object from data includes generating a virtual rate track image from x and y pixel velocities, the virtual rate track image including a virtual rate track for each object among a plurality of objects in the virtual rate track image; mapping the virtual rate tracks to locations within the field of view; and comparing each rate track among the virtual rate tracks to determine a rate track corresponding to the object.

[0095] In some aspects, the techniques described herein relate to media in which angular velocity, angular acceleration, and associated angles are determined at intermediate times in the data.

[0096] In some aspects, the techniques described herein relate to a medium in which an orbital ephemeris is fitted to the data using the Levenberg-Marquardt algorithm.

[0097] Although the present invention has been described with reference to the embodiments illustrated in the accompanying drawing figures, it should be noted that equivalents may be employed and substitutions may be made herein without departing from the scope of the invention as recited in the claims.

[0098] Having thus described various embodiments of the present disclosure, what is claimed as new and desired to be protected by Letters Patent is, among other things:

Claims

1. A method for determining the trajectory of an object, wherein the method is: The method involves acquiring data from a sensor that indicates multiple objects in a trajectory, wherein the data indicates the angular velocity and angular acceleration of one of the multiple objects. Detecting the location of a light event on a pixel of the sensor (804), wherein the location of the light event indicates the relative location of the plurality of objects in the field of view, Tracking the aforementioned multiple objects over time, Identifying the object from the aforementioned tracking, Determining the angular velocity and angular acceleration of the object from the aforementioned tracking (806), Using the angular velocity and angular acceleration, determine the initial trajectory of the object (808), Estimating the orbital elements from the initial trajectory of the object Methods that include...

2. (932) To generate a virtual track image of the location of the optical event over time, From the virtual track image, the object and its associated angle, angular velocity, and angular acceleration are identified. The method according to claim 1, further comprising:

3. The aforementioned sensor is an event-based camera (306), The method according to claim 2, wherein the data shows the change in luminosity at each pixel of the event-based camera (306).

4. The method according to claim 2, wherein the sensor is an image photon counter, and the data indicates the time and location of a photon collision with the sensor.

5. The method according to claim 1, wherein the sensor is a color sensor and the incident light is filtered to show components of the angular velocity and the angular acceleration.

6. The method according to claim 1, wherein the sensor is an Earth-based sensor.

7. The method according to claim 1, wherein the sensor is a space-based sensor.

8. One or more non-transient computer-readable media storing computer-executable instructions, wherein, when executed by at least one processor, the computer-executable instructions perform a method for determining the trajectory of an object, and the method The method involves acquiring data from a sensor that indicates multiple objects in a trajectory, wherein the data indicates the angular velocity and angular acceleration of one of the multiple objects. Identifying the object from the aforementioned data, (806) measuring the angular velocity and angular acceleration from the aforementioned data, The initial trajectory of the object is determined by fitting the trajectory ephemeris to the aforementioned data (942), (944) Using the initial trajectory as a starting point solution for the trajectory determination algorithm to determine the trajectory of the object. One or more non-transient computer-readable media, including [the specified text].

9. The medium according to claim 8, wherein the sensor is one of a microchannel plate delay line detector (302), an event-based camera (306), a single-photon avalanche diode array (304), or a complementary metal oxide semiconductor (308).

10. The method further comprises determining the x and y pixel velocities of the object on the sensor (930), according to claim 9.

11. Identifying the object from the aforementioned data is (932) A virtual velocity track image is generated from the x and y pixel velocities, wherein the virtual velocity track image comprises the virtual velocity track of each of the multiple objects in the virtual velocity track image. The aforementioned virtual trajectory is mapped to a location within the field of view, The process involves comparing each of the aforementioned virtual rate tracks to determine the rate track corresponding to the object. The medium according to claim 10, including the following:

12. The medium according to claim 11, wherein the angular velocity, the angular acceleration, and the associated angle are determined at an intermediate time of the data.

13. The medium according to claim 12, wherein the orbital ephemeris is fitted to the data using the Levenberg-Marquardt algorithm (942).

14. The method described above is: To fit the curve to the aforementioned data, The angular velocity and angular acceleration are determined from the curve. A non-transient computer-readable medium according to claim 8, further comprising:

15. Further comprising filtering the incident light through at least one filter, The first filter is a reddish-purple filter (704), The second filter is the yellow filter (706), The method according to claim 5, wherein the third filter is a blue-green filter.

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