Angle measurement procedure for sparse uniform arrays

Abstract

This document describes techniques and systems for radar systems with an angle determination process for sparse uniform arrays. The described radar systems include a processor and an antenna that can receive electromagnetic energy reflected by an object in a surrounding environment. The antenna includes a one-dimensional (ID) or two-dimensional (2D) sparse array. The processor can use the received electromagnetic energy to determine a signal subspace associated with the object that includes an invariance equation. Using an estimated solution of the invariance equation, the processor determines a solution of the invariance equation. The solution of the invariance equation is used to determine an angular phase associated with the object. The processor can then use the angular phase to determine an angle associated with the object. In this way, the described angle determination process enables a radar system with a sparse array to efficiently determine an angle associated with an object without blind spots.

Description

BACKGROUND

[0001] Radar systems use antennas to transmit and receive electromagnetic (EM) signals for detecting and tracking objects. In automotive applications, radar antennas can include one-dimensional (ID) or two-dimensional (2D) arrays to measure azimuth and / or elevation angles associated with objects. Some radar systems use estimation of signal parameters via rotational invariant techniques (ESPRIT) or unitary ESPRIT to distinguish multiple objects in the same range-Doppler bin. However, angular resolution is typically proportional to the aperture size of the array. Sparse ID and 2D arrays can provide a large aperture, but some angle-finding processes, including unitary ESPRIT, can have one or more blind spots. SUMMARY

[0002] This document describes techniques and systems of radar systems with angle-finding processes for sparse uniform arrays. Despite using sparse antenna arrays, the described angle-finding processes enable example radar systems to efficiently process radar data to determine angles associated with objects without blind spots attributed to other angle-finding processes. In this way, the described radar systems and angle-finding processes can have comparable angular resolution at a lower cost and a lower level of complexity, even using fewer antenna elements than traditional radar systems. For example, a radar system includes a processor and an antenna that can receive electromagnetic energy reflected by one or more objects. The antenna includes a one-dimensional (ID) (e.g., linear) or two-dimensional (2D) sparse array of antenna elements. The processor can determine, using the electromagnetic energy received by the ID or 2D sparse array, a signal subspace associated with the one or more objects that includes an invariance equation. Using an estimated solution of the invariance equation, the processor determines a solution of the invariance equation. The solution of the invariance equation is used to determine an angular phase associated with the one or more objects. The processor can then determine angles associated with the one or more objects using the angular phase.

[0003] This document also describes methods performed by the systems summarized above and other configurations of radar systems set forth herein, as well as apparatuses for performing those methods.

[0004] This Summary introduces aspects that can be implemented in a radar system with an angle determination process for sparse uniform arrays, which will be further described below in the and accompanying drawings. This Summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended for determining the scope of the claimed subject matter. BRIEF DESCRIPTION OF DRAWINGS

[0005] Details of one or more aspects of a radar system with an angle determination process for sparse uniform arrays are described in this document in connection with the following drawings. Like numbers refer to like elements throughout:

[0006] Figure 1 An example environment in which a radar system with an angle determination process for sparse uniform arrays can be implemented is shown;

[0007] Figures 2-1 to 2-4 An example sparse uniform antenna array of a radar system with an angle determination process is shown;

[0008] Figure 3 An example environment in which a radar system uses an angle determination module to perform an angle determination process for sparse uniform arrays is shown;

[0009] Figure 4 An example flowchart of a radar system with an angle determination process for sparse uniform linear arrays is shown;

[0010] Figure 5 An example flowchart of a radar system with an angle determination process for sparse uniform 2D arrays is shown; and

[0011] Figure 6 An example method of a radar system with an angle determination process for sparse uniform arrays is shown. DETAILED DESCRIPTION

[0012] SUMMARY

[0013] A radar system can be configured as an important sensing technology that vehicle-based systems use to acquire information about the surrounding environment. For example, a vehicle-based system can use a radar system to detect objects in or near a roadway and rely on the radar system output to take action (e.g., reduce speed, change lanes) to avoid a collision if necessary.

[0014] Radar systems often include at least two antennas to transmit and receive EM radiation. Some automotive radar systems operate multiple-input and multiple-output (MIMO) radars to obtain reliable detection of objects. These systems can include receive antennas with one-dimensional (ID) or two-dimensional (2D) arrays of antenna elements to measure azimuth and / or elevation angles associated with objects. While a large aperture of the receive antennas in the azimuth direction and / or the elevation direction can improve angular resolution, the larger aperture can also increase the number of antenna elements and the cost of the radar system. Accordingly, some radar systems use sparse ID and / or 2D arrays to improve the angular resolution of the radar system without increasing the cost.

[0015] Radar systems can use various angle determination processes to estimate angles associated with objects. For example, a radar system can use ESPRIT techniques, which are super- resolution direction of arrival (DoA) estimation algorithms, to estimate angles associated with objects. Eigenvalue decomposition of the complex covariance matrix in ESPRIT techniques is often computationally inefficient, making them less suitable for automotive applications.

[0016] Other radar systems use a single ESPRIT algorithm that employs more efficient real- valued computations. For example, real-time embedded radar systems (e.g., automotive radar systems) can use single-ESPRIT as a super-resolution DoA estimation algorithm. Single-ESPRIT provides stable angle estimates for radar systems with dense uniform linear arrays (ULAs). If the radar system uses sparse uniform linear arrays, single-ESPRIT and potentially other angle determination processes can include computational blind spots for certain angles within the field of view of the radar system. For example, assume an object is located at a problematic angle. In this case, these radar systems often fail to detect the object, resulting in potentially unsafe driving conditions.

[0017] In contrast, this document describes techniques and systems for providing angle determination processes for sparse uniform linear arrays or sparse uniform 2-D arrays. For example, a radar system can include an antenna that can receive EM energy reflected by one or more objects. The antenna can include a ID or 2D subarray of antenna elements. The radar system can also include one or more processors that can determine a signal subspace associated with the one or more objects using invariance equations using the electromagnetic energy received by the ID or 2D sparse array. Using an estimated solution of the invariance equations, the processors determine a solution of the invariance equations. The solution of the invariance equations is used by the processors to determine an angular phase associated with the one or more objects. In this way, the described systems and techniques can reduce the number of antenna elements by using sparse arrays while avoiding blind spots that can occur when processing radar data from sparse arrays.

[0018] This is just one example of the techniques and systems described having a radar system for angle measurement procedures for sparse uniform linear arrays or sparse uniform 2-D arrays. Other examples and implementations are described in this document.

[0019] Operating Environment

[0020] Figure 1 An example environment 100 in which a radar system 102 having angle measurement procedures for sparse uniform arrays can be implemented is shown. In the depicted environment 100, the radar system 102 is mounted to or integrated within a vehicle 104. The radar system 102 can detect one or more objects 120 in a vicinity of the vehicle 104 in or on a roadway 118. Although shown as an automobile, the vehicle 104 can represent other types of automobiles or motorized vehicles (e.g., motorcycles, buses, tractors, semi-trailers), non-motorized vehicles (e.g., bicycles), rail vehicles (e.g., trains), watercraft (e.g., boats), aircraft (e.g., airplanes), or spacecraft (e.g., satellites). In general, a manufacturer can mount the radar system 102 to any mobile platform, including mobile machinery or robotic devices.

[0021] The radar system 102 can detect the objects 120 from any exterior surface of the vehicle 104. For example, a vehicle manufacturer can integrate the radar system 102 into a bumper, a side mirror, a headlight, a taillight, or any other interior or exterior location where the objects 120 need to be detected. In the depicted implementation, the radar system 102 is mounted on a front of the vehicle 104 and illuminates the objects 120. In some cases, the vehicle 104 includes multiple radar systems 102, such as a first radar system 102 and a second radar system 102, that provide a greater field of view.

[0022] In general, a vehicle manufacturer can design a location of one or more radar systems 102 to provide a particular field of view that encompasses a region of interest. Example fields of view include a 360-degree field of view, one or more 180-degree fields of view, one or more 90-degree fields of view, and the like, which can overlap or be combined into a field of view of a particular size.

[0023] The objects 120 are composed of one or more materials that reflect radar signals. Depending on the application, the objects 120 can represent targets of interest. In some cases, the objects 120 can be moving objects (e.g., another vehicle) or stationary objects (e.g., a roadside sign).

[0024] The radar system 102 transmits EM radiation by transmitting EM signals or waveforms via antenna elements. In the environment 100, the radar system 102 can detect and track the object 120 by transmitting and receiving one or more radar signals. For example, the radar system 102 can transmit EM signals between one hundred and four hundred gigahertz (GHz), between four and one hundred GHz, or between approximately seventy and eighty GHz.

[0025] The radar system 102 can include a transmitter 106 and at least one antenna for transmitting EM signals. The radar system 102 can also include a receiver 108 and at least one antenna for receiving reflected versions of EM signals. The transmitter 106 includes one or more components for transmitting EM signals. The receiver 108 includes one or more components for receiving reflected EM signals. The transmitter 106 and the receiver 108 can include a sparse linear or one-dimensional (ID) array of antenna elements and / or a sparse two-dimensional (2D) array of antenna elements. The use of sparse arrays improves the angular resolution of the radar system 102 without increasing the cost and computational complexity associated with additional antenna elements. The transmitter 106 and the receiver 108 can be incorporated together on the same integrated circuit (e.g., a transceiver integrated circuit) or separately on different integrated circuits.

[0026] The radar system 102 also includes one or more processors 110 (e.g., energy processing units) and a computer-readable storage medium (CRM) 112. The processor 110 can be a microprocessor or a system on a chip. The processor 110 can execute instructions stored in the CRM 112. For example, the processor 110 can process EM energy received by the receiver 108 and determine a location of the object 120 relative to the radar system 102 using an angular determination module 114. The processor 110 can also generate radar data for at least one automotive system. For example, the processor 110 can control an autonomous or semi-autonomous driving system of the vehicle 104 based on processed EM energy from the receiver 108.

[0027] The angle determination module 114 obtains the EM energy received by the receiver 108 and uses an angle determination process 116 to determine an azimuth angle and / or an elevation angle associated with the object 120. The angle determination module 114 and the angle determination process 116 can be implemented as instructions in the CRM 112, hardware, software, or a combination thereof executed by the processor 110. Although the receiver 108 includes a sparse ID or 2D array, the angle determination process 116 enables the radar system 102 to efficiently process radar data to determine angles associated with one or more objects 120 without blind spots. In this way, the radar system 102 and the angle determination process 116 can have comparable angular resolution at a lower cost and a lower level of complexity, even using fewer antenna elements than traditional radar systems.

[0028] The radar system 102 can determine a distance to the object 120 based on a time it takes for an EM signal to travel from the radar system 102 to the object 120 and back to the radar system 102 from the object 120. The radar system 102 can also use the angle determination module 114 and the angle determination process 116 to determine a location of the object 120 from an azimuth angle 128 and an elevation angle 130 based on a direction of one or more amplitude peaks in a reflected signal received by the radar system 102.

[0029] As an example, Figure 1 A vehicle 104 is shown traveling on a road 118. The radar system 102 detects an object 120 in front of the vehicle 104. The radar system 102 can define a coordinate system having an x-axis 122 (e.g., in a forward direction along the road 118), a y-axis 124 (e.g., perpendicular to the x-axis 122 and along a surface of the road 118), and a z-axis 126 (e.g., perpendicular to the surface of the road 118). The radar system 102 can locate the object 120 from an azimuth angle 128 and / or an elevation angle 130. The azimuth angle 128 can represent a horizontal angle from the x-axis 122 to the object 120. The elevation angle 130 can represent a vertical angle from the surface of the road 118 (e.g., a plane defined by the x-axis 122 and the y-axis 124) to the object 120.

[0030] The vehicle 104 can also include at least one automotive system that relies on data from the radar system 102, such as a driver assistance system, an autonomous driving system, or a semi-autonomous driving system. The radar system 102 can include an interface to interface with the data-reliant automotive system. For example, the processor 110 outputs radar data via the interface as signals based on the EM energy received by the receiver 108.

[0031] Generally, automotive systems use radar data provided by the radar system 102 to perform functions. For example, a driver assistance system can provide blind spot monitoring and generate an alert indicating a potential collision with an object 120 detected by the radar system 102. In such implementations, radar data from the radar system 102 indicates when changing lanes is safe or unsafe.

[0032] An autonomous driving system can move the vehicle 104 to a particular location on the road 118 while avoiding collisions with objects 120 detected by the radar system 102. Radar data provided by the radar system 102 can provide information about distances to objects 120 and locations of objects 110 to enable the autonomous driving system to perform emergency braking, perform a lane change, or adjust a speed of the vehicle 104.

[0033] Figures 2-1 to 2-4 An example sparse uniform antenna array of a radar system with an angular determination process is shown. For example, the radar system can be the radar system 102 of Figure 1 In the depicted implementation, the antennas 200-1, 200-2, 200-3, and 200-4 include transmitter arrays 202 and receiver arrays 204 that can correspond to the transmitters 106 and receivers 108 of Figure 1 FIG. 1, respectively.

[0034] The transmitter array 202 is a sparse uniform linear array that includes N T antenna elements 208 with a first spacing 210 di in a first direction (e.g., an azimuth direction), as shown in Figure 2-1 and Figure 2-3 or N T antenna elements 208 with a third spacing 214 d3 in a second direction (e.g., an elevation direction), as shown in Figure 2-4 The first spacing 210 and the third spacing 214 can be multiples of 0.5l, where l is a wavelength of the EM radiation transmitted. In the depicted implementation of Figure 2-1 The transmitter array 202-1 includes two antenna elements 208 (e.g., N T equals two). In Figure 2-3 and Figure 2-4 The transmitter arrays 202-3 and 202-4 include three antenna elements. As another example, the transmitter array 202 can include one antenna element 208, as depicted in Figure 2-2 In other implementations, the transmitter array 202 can also include additional or fewer antenna elements 208. As depicted in Figures 2-1 to 2-4 The transmitter array 202 can include antenna elements 208 in either the azimuth direction or the elevation direction.

[0035] The antenna elements 208 of the transmitter array 202 are separated by a uniform spacing (e.g., first spacing 210 or third spacing 214) in an azimuth direction or an elevation direction. For example, the antenna elements 208 can be spaced apart by 2.0λ in the azimuth direction (e.g., the first spacing 210 is equal to 2.0λ). In other implementations, the first spacing 210 or the third spacing 214 can have different values. For example, for the transmitter arrays 202-1 and 202-3, the first spacing 210 is equal to 4.0λ and 2.0λ, respectively. For the transmitter array 202-4, the third spacing 214 is equal to 2.0λ. As depicted in FIG. 2B, the transmitter array 202 can be a sparse uniform linear array (ULA) in the azimuth direction or the elevation direction. The transmitter array 202 can also be a sparse uniform 2D array in the azimuth direction and the elevation direction. Figures 2-1 to 2-4

[0036] The receiver array 204 is also a sparse uniform linear array that includes N R antenna elements 208 with a second spacing 212 d2 in a direction (e.g., the azimuth direction or the elevation direction). In the depicted implementation, the receiver array 204-1 includes four antenna elements 208 (e.g., N R is equal to four). In other implementations as shown in FIG. 2B, the receiver array 204 can also include additional or fewer antenna elements 208. Figure 2-1 Figure 2-2

[0037] In the depicted implementations, the antenna elements 208 of the receiver array 204 are separated by the second spacing 212 in the azimuth direction. For example, the antenna elements 208 can be spaced apart by 1.5λ in the azimuth direction. For the receiver arrays 204-1 and 204-2, the second spacing 212 is equal to 1.0λ, and for the receiver arrays 204-3 and 204-4, the second spacing 212 is equal to 1.5λ. In other words, the receiver arrays 204 in the depicted implementations are ULAs with sparsely spaced antenna elements 208. In other implementations, the second spacing 212 can have different values.

[0038] The receiver array 204 can also be a two-dimensional (2D) sparse uniform array that includes N antenna elements 208 in a first direction and M antenna elements in a second direction, where N is equal to or not equal to M. The antenna elements 208 of the 2D array are separated by the first spacing 210 in the first direction and the third spacing 214 in the second direction. For the 2D sparse uniform array, the first spacing 212 can be equal to or different from the third spacing 214. The antenna elements 208 of the 2D sparse array can be arranged in an approximately rectangular shape.

[0039] ​​​Antenna 200 supports a MIMO radar system and can rely on the sparse arrays of transmitter array 202 and receiver array 204 to match radar returns to corresponding signals. In other implementations, the radar system can operate as a conventional radar system that does not rely on dynamic MIMO techniques.

[0040] Radar system can generate a synthetic array 206 of antenna elements 208 with a minimum spacing equal to 0.5λ, allowing angle estimation by angle determination module 114 to cover -90 degrees to 90 degrees. Synthetic array 206 includes N T N R antenna elements 208. In Figure 2-1 In the depicted implementation, synthetic array 206-1 includes eight antenna elements 208 (e.g., 2x4). Antenna elements 208 of synthetic array 206-1 are spaced apart by a first spacing and a second spacing in one direction (e.g., azimuth direction). As another example, synthetic array 206-3 is a sparse array. The ID data vector can be converted to a 2D data matrix, which can be considered an equivalent sparse uniform 2D array with the second spacing 212 in a first direction (e.g., azimuth direction) and the first spacing 210 in a second direction (e.g., elevation direction). Angle determination module 114 can then use the angle determination process for sparse uniform 2D arrays detailed in Figure 5

[0041] In automotive applications, the number of antenna elements 208 in synthetic array 206 can be larger than the expected maximum number of objects 120 to be detected by radar system 102.

[0042] In the depicted implementation, transmitter array 202 and receiver array 204 are positioned in the azimuth direction. In other implementations, transmitter array 202 and receiver array 204 can be positioned in the elevation direction or another direction.

[0043] Transmitter array 202 and receiver array 204 can be planar arrays that provide high gain and low loss. Planar arrays are well suited for vehicle integration due to their small size. For example, antenna elements 208 can be slots etched or otherwise formed in a plated material on one surface of a PCB for substrate integrated waveguide (SIW) antennas. Antenna elements 208 can also be part of aperture antennas, microstrip antennas, or dipole antennas. For example, transmitter array 202 and receiver array 204 can include subarrays of patch elements (e.g., microstrip patch antenna subarrays) or dipole elements.

[0044] In the depicted implementation, both transmitter array 202 and receiver array 204 are sparse arrays. When objects 120 are at certain angles (e.g., ​Many radar systems that apply a conventional angle determination process are unable to determine a solution or have large estimation errors when k is a positive integer and d is the spacing between the antenna elements 208). To address these potential radar blind angles, the described radar system 102 uses an improved angle determination process that can robustly determine an angle associated with an object 120 at each angle within the field of view of the radar system 102.

[0045] Figure 3 An example environment 300 is shown in which a radar system performs an angle determination process for a sparse uniform array using an angle determination module 114. The radar system and angle determination process can be, for example, Figure 1 the radar system 102 and angle determination process 116 of

[0046] The radar system includes a ID or 2D sparse synthetic array (e.g., synthetic array 206). The angle determination module 114 can generate a sparse unitary matrix Q N 304 based on the number of antenna elements 208 in the synthetic array. The generation of the sparse unitary matrix 304 will be described in more detail with reference to Figure 4 and Figure 5 The generation of the sparse unitary matrix 304 will be described in more detail with reference to

[0047] The radar system transmits EM signals to detect objects. The EM signals are reflected by the objects 120. The radar system receives EM energy 302 associated with the reflected EM signals. The angle determination module 114 can use multiple data snapshots of the EM energy 302 to generate a data matrix X 306. The generation of the data matrix 306 will be described in more detail with reference to Figure 4 and Figure 5 The generation of the data matrix 306 will be described in more detail with reference to

[0048] The angle determination module 114 can then use an angle determination process 116 to determine a real-valued data matrix Y 308, a covariance matrix R cov 310, and an eigenvector matrix E s 312 based on the data matrix 306 and the sparse unitary matrix 304. The angle determination module 114 can use the real-valued data matrix 308, the covariance matrix 310, and the eigenvector matrix to determine at least one of an azimuth angle Θ AZ 128 or an elevation angle Θ EV 130 associated with the objects 120. The angle determination process 116 will be described in more detail with reference to Figure 4 and Figure 5 The angle determination process 116 will be described in more detail with reference to

[0049] Figure 4 An example flowchart of a radar system 102 with an angle determination process for a sparse uniform linear array is shown. Figure 4The radar system 102 can be, for example, Figure 1 The radar system 102 can generate a sparse ULA composite array (e.g., composite array 206-1 or 206-2). The radar system 102 also includes an angle determination module 114, which uses an angle determination process 116 to determine the DoA angle 420 associated with an object 120 in a first direction (e.g., azimuth direction).

[0050] Consider a radar system 102 comprising a uniform one-dimensional (1D) or linear composite array having N antenna elements 208. The antenna elements 208 of the composite array are uniformly spaced apart by a distance d.

[0051] At position 404, the angle measurement module 114 obtains the EM energy 402 received by the 1D synthesis array 206-1 or 206-2 and estimates the signal subspace. The angle measurement process 116 generates an N×N sparse unitary matrix Q. N When N is even (e.g., N = 2n, where...), When ), the sparse unitary matrix is ​​provided by equation (1):

[0052]

[0053] When N is odd (for example, N = 2n + 1, where When ), the sparse unitary matrix is ​​provided by equation (2):

[0054]

[0055] Among them I n It is an n×n identity matrix, J n It is an n×n commutative matrix, and 0 n It is an n×1 zero vector.

[0056] Angle measurement module 114 can use multiple data snapshots of EM energy 402 to generate beam vector x l Where l = 1, 2, ..., L, and L is the number of snapshots used in the angle determination process 116. The angle determination process 116 may use multiple data snapshots (e.g., L > 1), depending on the speed at which the radar data needs to be processed by the radar system 102 or the vehicle-based system. One or more beam vectors are each complex N×1 vectors.

[0057] Angle measurement module 114 uses angle measurement process 116 to generate data matrix X, which is an N×L matrix represented by equation (3):

[0058] X = [x1, x2, ..., x L (3)

[0059] The angle determination module 114 can perform a unitary transformation on the data matrix X to generate a real-valued data matrix 306 Y. The real-valued data matrix 406 is represented by equation (4):

[0060]

[0061] The angle determination module 114 can use the real-valued data matrix 406 to generate a covariance matrix 408 R cov . The covariance matrix 408 is represented by equation (5):

[0062]

[0063] Given that the number of objects 120 detected by the radar system 102 is P, the angle determination process 116 can generate an eigenvector matrix 410 E s . The eigenvector matrix 410, contains P eigenvectors corresponding to the P largest eigenvalues of the covariance matrix 408.

[0064] At 412, the angle determination module 114 can estimate the solution to the invariance equation. Consider that the angle determination process 116 generates the following matrices represented by equations (6) to (8):

[0065] J2= [0 N-1 I N-1 ] (6)

[0066]

[0067]

[0068] The angle determination module 114 compares the absolute values of several products involving the eigenvector matrix 410. Specifically, the angle determination module 114 can determine the estimate to the invariance equation based on a comparison of the determinants of K2 and K1 using equation (9):

[0069] |(K2E s ) H (K2E s )| > |(K1E s ) H (K1E s )| (9)

[0070] If the angle determination module 114 determines that equation (9) is true, the angle determination module 114 estimates the solution to the invariance equation as represented by equation (10):

[0071] K2E s Ψ ~ K1E s(10)

[0072] If the angle determination module 114 determines that equation (9) is not true, the angle determination module 114 estimates the solution of the invariance equation to be represented by equation (11):

[0073] K1E s Ψ≈K2E s (11)

[0074] At 414, the angle determination module 114 can solve the corresponding invariance equation and determine Ψ using a total least squares (TLS) or least squares (LS) method. Generally, the TLS method has higher accuracy than the LS method, but can have higher computational cost. If equation (9) is true, the angle determination module 114 can determine whether the conditions represented by equations (12) and (13) are true:

[0075] |(K2E s ) H (K2E s )|<σ (12)

[0076] |(K2E s ) H (K2E s )|<ρ|(K1E s ) H (K1E s )| (13)

[0077] where σ and ρ are first and second threshold parameters, respectively. The radar system 102 or the angle determination module 114 can tune the first and second threshold parameters based on dimensions of the synthetic array 206 and numerical specifications of the radar system 102 or vehicle-based systems that use radar data generated by the radar system 102. For example, the first threshold parameter σ can be approximately one percent (e.g., σ = 10- 2 ) and the second threshold parameter ρ can be approximately ten (e.g., ρ = 10).

[0078] If both conditions (12) and (13) are true, the angle determination module 114 can solve for Ψ using the TLS method. If either condition (12) or condition (13) is not true, the angle determination module 114 can solve for Ψ using the LS method. In other implementations, the angle determination module 114 can solve for Ψ using the TLS or LS method regardless of whether both conditions (12) and (13) are true.

[0079] If equation (9) is not true, the angle determination module 114 can determine whether the conditions represented by equations (14) and (15) are true:

[0080] |(K1E s ) H (K1E s )| < σ (14)

[0081] |(K1E s ) H (K1E s )| < p | (K2E s ) H (K2E s )| (15)

[0082] If both conditions (14) and (15) are true, the angle determination module 114 can solve for using the TLS method. If either condition (14) or condition (15) is not true, the angle determination module 114 can solve for using the LS method. In other implementations, the angle determination module 114 can solve for using the TLS or LS method regardless of whether both conditions (14) and (15) are true.

[0083] At 416, the angle determination module 114 can estimate a 1D angular phase (e.g., azimuthal phase) associated with the object 120. The angle determination module 114 can use equation (16) to compute the eigenvalue of the matrix:

[0084] where

[0085] If the invariance equation at operation 414 is represented by equation (10), the angle determination module 114 can determine the angular phase using equation (17). However, if the invariance equation at operation 414 is represented by equation (11), the angle determination module 114 can determine the angular phase using equation (18).

[0086] μ i = 2 cot -1 ω i , i = 1, 2,..., P (17)

[0087] μ i = 2 tan -1 ω i , i = 1, 2,..., P (18)

[0088] At 418, the angle determination module 114 can estimate a DoA angle 420 in the first direction (e.g., azimuthal direction) using the angular phase estimate. The angle determination process 116 can define a relationship between the angular phase and the DoA angle using equation (19):

[0089] where where λ is the wavelength of the emitted EM radiation. The angle determination module 114 can then estimate the DoA angle 420 using equation (20):

[0090] where

[0091] In this way, the angle determination process 116 enables the radar system 102 to process radar data to determine angles associated with the object 120 without blind spots. If the spacing of the antenna elements 208 is greater than 0.5λ (e.g., a sparse ULA), the angular phase μ i cannot equal positive or negative π (e.g., ± π) because the corresponding angle θ i results in a blind spot for the radar system 102 or large estimation errors at these angles. For example, if d equals λ, the radar system 102 cannot detect objects at positive or negative thirty degrees. In contrast, the angle determination process 116 is able to detect objects at every angle within the field of view of the synthetic array 206. The angle determination process 116 also uses the determinant analysis described above to estimate the solution to the invariance equation and adaptively choose between the TLS and LS methods to avoid numerical problems with small determinants.

[0092] Figure 5 An example flowchart 500 is shown that illustrates a radar system 102 with an angle determination process for a sparse uniform 2D array. Figure 5 The radar system 102 of equation (1) can be, for example, Figure 1 The radar system 102 of equation (1). The radar system 102 includes a sparse uniform 2D synthetic array (e.g., the synthetic array 206-4 or an equivalent 2D synthetic array associated with the synthetic array 206-3). The radar system 102 also includes an angle determination module 114 that uses an angle determination process 116 to determine DoA angles 520 (e.g., azimuth and elevation angles) associated with the object 120 in a first direction (e.g., an azimuth direction) and a second direction (e.g., an elevation direction).

[0093] Consider that the radar system 102 includes a two-dimensional (2D) uniform synthetic array. The 2D synthetic array includes N antenna elements 208 with a spacing d EL in a first direction (e.g., an elevation direction) and M antenna elements 208 with a spacing d AZ in a second direction (e.g., an azimuth direction). The antenna elements 208 of the synthetic array are uniformly spaced by a first distance d1 in the first direction and a second distance d2 in the second direction.

[0094] At 504, the angle estimation module 114 obtains the EM energy 502 received by the 2D synthetic array and estimates the signal subspace. The angle estimation process 116 generates an N x N sparse unitary matrix Q N and an M x M sparse unitary matrix Q M When N or M is even (e.g., N = 2n, where or M = 2m, where the sparse unitary matrices are provided by equations (21a) and (21b):

[0095]

[0096]

[0097] When N or M is odd (e.g., N = 2n + 1, where or M = 2m + 1, where the sparse unitary matrices are provided by equations (22a) and (22b):

[0098]

[0099]

[0100] where I n is an n x n identity matrix, I m is an m x m identity matrix, J n is an n x n exchange matrix, J m is an m x m exchange matrix, 0 n is an n x 1 zero vector, and 0 m is an m x 1 zero vector.

[0101] The angle estimation module 114 can use multiple data snapshots of the EM energy 502 to generate beam vectors X l where l = 1, 2,..., L, and L is the number of snapshots used by the angle estimation process 116. The angle estimation process 116 can use two or more data snapshots (e.g., L > 1), depending on the speed at which the radar system 102 or vehicle-based system requires radar data to be processed. The multiple beam vectors are each complex-valued N x M matrices.

[0102] The angle estimation module 114 uses the angle estimation process 116 to generate a data matrix X, which is an NM x L matrix represented by equation (23):

[0103] X = [vector (X1), vector (X2),..., vector (X L )] (23)

[0104] The angle determination module 116 can perform a unitary transformation on the data matrix X to generate a real-valued data matrix 506 (Y). The real-valued data matrix 506 is represented by equation (24):

[0105]

[0106] The angle determination module 114 can use the real-valued data matrix 506 to generate a covariance matrix 508 (R cov ). The covariance matrix 508 is represented by equation (25):

[0107]

[0108] Given that the number of objects 120 detected by the radar system 102 is P, the angle determination process 116 can generate an eigenvector matrix 410 (E s ). The eigenvector matrix 510, contains P eigenvectors corresponding to the P largest eigenvalues of the covariance matrix 508.

[0109] At 512, the angle determination module 114 can estimate a solution to the invariance equation. Consider that the angle determination process 116 generates the following matrices represented by equations (26) to (30) for a first dimension (e.g., an elevation dimension):

[0110] J2= [0 N-1 I N-1 ] (26)

[0111]

[0112]

[0113]

[0114]

[0115] The angle determination module 114 compares the absolute values of several products involving the eigenvector matrix 510. Specifically, the angle determination module 114 can use equation (31) to determine an estimate to the invariance equation:

[0116] |(K μ2 E s ) H (K μ2 E s )|>|(K μ1 E s ) H (K μ1 E s )| (31)

[0117] If the angle determination module 114 determines that equation (31) is true, the angle determination module 114 estimates the solution to the invariance equation as represented by equation (32):

[0118] K μ2 E s Ψ μ ≈K μ1 E s (32)

[0119] If the angle determination module 114 determines that equation (31) is not true, the angle determination module 114 estimates the solution to the invariance equation as represented by equation (33):

[0120] K μ1 E s Ψ μ ≈K μ2 E s (33)

[0121] Consider that the angle determination process 116 generates the following matrices represented by equations (34) through (38) for the second dimension (e.g., the azimuthal dimension):

[0122] J4 = [0 M-1 I M-1 ] (34)

[0123]

[0124]

[0125]

[0126]

[0127] The angle determination module 114 compares the absolute values of several products involving the eigenvector matrix 510. Specifically, the angle determination module 114 can use equation (39) to determine an estimate of the invariance equation:

[0128] |(K v2 E s ) H (K v2 E s )|>|(K v1 E s ) H (K v1 E s )| (39)

[0129] If the angle determination module 114 determines that equation (39) is true, the angle determination module 114 estimates the solution to the invariance equation as represented by equation (40):

[0130] K v 2E s Ψ v ≈K v1 E s (40)

[0131] If the angle determination module 114 determines that equation (39) is not true, the angle determination module 114 estimates the solution to the invariance equation to be represented by equation (41):

[0132] K v1 E s Ψ v ≈K v2 E s (41)

[0133] At 514, the angle determination module 114 can solve the corresponding invariance equation using a total least squares (TLS) or least squares (LS) method and determine μ If equation (31) is true, the angle determination module 114 can determine whether the conditions represented by equations (42) and (43) are true:

[0134] |(K μ2 E s ) H (K μ2 E s )|<σ μ (42)

[0135] |(K μ2 E s ) H (K μ2 E s )|<ρ μ |(K μ1 E s ) H (K μ1 E s )| (43)

[0136] where σ μ and p μ are a first threshold parameter and a second threshold parameter, respectively. The radar system 102 or the angle determination module 114 can adjust the first threshold parameter and the second threshold parameter based on dimensions of the synthetic array and numerical specifications of the radar system 102 or a vehicle-based system that uses radar data generated by the radar system 102. For example, the first threshold parameter σ μ may be approximately one percent (e.g., σ μ = 10- 2 ) and the second threshold parameter p μmay be approximately ten (e.g., p μ = 10).

[0137] If both conditions (42) and (43) are true, the angle determination module 114 can solve for Ψ μ using the TLS method. If either condition (42) or condition (43) is not true, the angle determination module 114 can solve for Ψ μ using the LS method.

[0138] If equation (31) is not true, the angle determination module 114 can determine whether conditions represented by equations (44) and (45) are true:

[0139] |(K μ1 E s ) H (K μ1 E s )| < σ μ (44)

[0140] |(K μ1 E s ) H (K μ1 E s )| < p μ |(K μ2 E s ) H (K μ2 E s )| (45)

[0141] If both conditions (44) and (45) are true, the angle determination module 114 can solve for Ψ μ using the TLS method. If either condition (44) or condition (45) is not true, the angle determination module 114 can solve for Ψ μ using the LS method.

[0142] The angle determination module 114 can also solve the corresponding invariance equations and determine Ψ υ using a total least squares (TLS) or least squares (LS) method. If equation (39) is true, the angle determination module 114 can determine whether conditions represented by equations (46) and (47) are true:

[0143] |(K v2 E s ) H (K v2 E s )| < σ v (46)

[0144] |(K v2 E s) H (K v2 E s )|<ρ v |(K v1 E s ) H(K v1 E s )| (47)

[0145] where σ v and ρ v are first and second threshold parameters, respectively. The radar system 102 or the angle determination module 114 can adjust the first and second threshold parameters based on dimensions of the synthetic array and numerical specifications of the radar system 102 or vehicle-based systems that use radar data generated by the radar system 102. For example, the first threshold parameter σ v may be approximately one percent (e.g., σ v = 10 -2 ) and the second threshold parameter ρ v may be approximately ten (e.g., ρ v = 10).

[0146] If both conditions (46) and (47) are true, the angle determination module 114 can solve for Ψ υ using the TLS method. If either condition (46) or condition (47) is not true, the angle determination module 114 can solve for Ψ υ using the LS method.

[0147] If equation (39) is not true, the angle determination module 114 can determine whether conditions represented by equations (48) and (49) are true:

[0148] |(K v1 E s ) H (K v1 E s ) |<σ v (48)

[0149] |(K v1 E s ) H (K v1 E s )|<ρ v |(K v2 E s ) H (K v2 E s )| (49)

[0150] If both conditions (48) and (49) are true, then the angle measurement module 114 can use the TLS method to solve for Ψ. υ If condition (48) or condition (49) is not true, then the angle measurement module 114 can use the LS method to solve for Ψ. υ .

[0151] At position 516, angle measurement module 114 can estimate the 2D angular phase (e.g., azimuth and elevation phases) associated with object 120. Angle measurement module 114 can use equation (50) to calculate the complex-valued P×P matrix Ψ. μ +jΨ v Eigenvalues:

[0152] Ψ μ +jΨ v =TΩT -1 in

[0153] For the first dimension (e.g., the elevation dimension), if the invariant equation at operation 514 is represented by equation (32), then the angle measuring module 114 can use equation (51) to determine the elevation angle phase. However, if the invariant equation at operation 514 is represented by equation (33), then the angle measuring module 114 can use equation (52) to determine the elevation angle phase.

[0154] μ i =2cot -1 (Re{ω i}), i = 1, 2, ..., P (51)

[0155] v i =2tan- 1 (Im{ω i}), i = 1, 2, ... P (52)

[0156] For the second dimension (e.g., the azimuth dimension), if the invariant equation at operation 514 is represented by equation (40), then the angle measuring module 114 can use equation (53) to determine the azimuth phase. However, if the invariant equation at operation 514 is represented by equation (41), then the angle measuring module 114 can use equation (54) to determine the azimuth phase.

[0157] v i =2cot -1 (Im{ω i}), i = 1, 2, ..., P (53)

[0158] v i =2tan -1(Im{ωi}), i=1, 2,..., p (54)

[0159] At 518, the angle measurement module 114 can use angular phase estimation to estimate the DoA angle 520 in a first direction (e.g., elevation direction) and a second direction (e.g., azimuth direction). The angle measurement process 116 can define the angular phase (e.g., elevation phase μ) using equations (55) and (56). i and azimuth phase ν i ) and DoA angle (e.g., elevation angle) and azimuth The relationship between )

[0160] in

[0161] in Where λ is the wavelength of the emitted EM radiation. The angle measurement module 114 can then use equations (57) and (58) to estimate the DoA angle 520:

[0162] in

[0163] in

[0164] In this way, the angle measurement module 114 can determine the azimuth and elevation angles associated with the object 120 with relatively low processing complexity and cost. Furthermore, the angle measurement process 116 avoids computational blind spots when detecting the object 120.

[0165] Example Method

[0166] Figure 6 An example method 600 for a radar system 102 with an angle determination process for a sparse uniform array is shown. Method 600 is shown as a plurality of operations (or actions) performed, but is not necessarily limited to the order or combination of operations shown herein. Furthermore, any one or more of the operations may be repeated, combined, or recombined to provide other methods. References may be made in the various sections discussed below. Figure 1 Environment 100 and Figures 1 to 5 The entities detailed herein are for illustrative purposes only. This technique is not limited to being performed by one or more entities.

[0167] At 602, the radar system's antenna receives EM energy reflected by one or more objects. For example, the antenna 200 of radar system 102 can receive EM energy reflected by one or more objects 120.

[0168] At 604, a signal subspace associated with one or more objects is determined using EM energy received by the ID or 2D sparse uniform array. The signal subspace includes an invariance equation. For example, the angle determination module 114 can use the angle determination process 116 to determine a signal subspace associated with one or more objects 120. The angle determination module 114 can use EM energy received by the ID or 2D sparse uniform array (e.g., the synthetic array 206). The determination of the signal subspace can include determining the real-valued data matrix 406 or 506, the covariance matrix 408 or 508, and the eigenvector matrix 410 or 510 used to define the invariance equation.

[0169] At 606, an estimated solution to the invariance equation is determined. For example, the angle determination module 114 can use the angle determination process 116 to determine an estimated solution to the invariance equation. The estimated solution can determine a first determinant value and a second determinant value using the eigenvector matrix 410 or 510 and the real and imaginary parts of the sparse unitary matrix. Based on a comparison of the first determinant value to the second determinant value as described with reference to Figure 4 and Figure 5 the angle determination module 114 can determine the estimated solution to the invariance equation using the eigenvector matrix.

[0170] At 608, a solution to the invariance equation is determined using the estimated solution to the invariance equation. For example, the angle determination module 114 can use the angle determination process 116 to determine a solution to the invariance equation. As described with reference to Figure 4 and Figure 5 the angle determination module 114 can compare the first determinant or the second determinant to the first threshold and the second threshold and determine whether to use the TLS or LS method to solve the invariance equation.

[0171] At 610, an angular phase associated with one or more objects is determined using the solution to the invariance equation. For example, the angle determination module 114 can use the angle determination process 116 to determine an angular phase associated with the objects 120 as described with reference to Figure 4 and Figure 5 .

[0172] At 612, an angle associated with one or more objects is determined using the angular phase associated with the one or more objects. For example, the angle determination module 114 can use the angle determination process 116 to determine an azimuth angle and / or an elevation angle associated with the objects 120 as described with reference to Figure 4 and Figure 5 .

[0173] Example

[0174] Examples are provided in the following sections.

[0175] Example 1 : A radar system comprising: an antenna configured to receive electromagnetic (EM) energy reflected by one or more objects, the antenna comprising a one-dimensional (ID) or two-dimensional (2D) sparse uniform array of antenna elements; and one or more processors configured to: determine, using the EM energy received by the ID or 2D sparse uniform array, a signal subspace associated with the one or more objects, the signal subspace comprising an invariance equation; determine an estimated solution to the invariance equation; determine a solution to the invariance equation using the estimated solution to the invariance equation; determine an angular phase associated with the one or more objects using the solution to the invariance equation; and determine an angle associated with the one or more objects using the angular phase associated with the one or more objects.

[0176] Example 2: The radar system of Example 1, wherein: the ID sparse uniform array comprises a uniform linear array positioned in an azimuth direction; and the angle associated with the one or more objects comprises an azimuth angle associated with the one or more objects.

[0177] Example 3: The radar system of Example 1 or 2, wherein: the 2D sparse uniform array is positioned in an elevation direction and an azimuth direction; and the angle associated with the one or more objects comprises an elevation angle and an azimuth angle associated with the one or more objects.

[0178] Example 4: The radar system of any of the preceding examples, wherein the antenna elements of the ID or 2D sparse uniform array are at least one of: uniformly spaced apart by a first distance in the azimuth direction, or uniformly spaced apart by a second distance in the elevation direction.

[0179] Example 5: The radar system of Example 4, wherein the first distance and the second distance are a first positive integer and a second positive integer of one-half of a wavelength of the EM energy.

[0180] Example 6: The radar system of any of the preceding examples, wherein the angle associated with the one or more objects is determined without one or more blind spots within a field of view of the ID or 2D sparse uniform array.

[0181] Example 7: The radar system of any of the preceding examples, wherein, in determining the signal subspace associated with the one or more objects, the one or more processors are configured to: generate a beam vector for each of a plurality of data snapshots of EM energy received by the ID or 2D sparse array; generate a data matrix using the beam vector for each of the plurality of data snapshots; generate a real-valued data matrix using the data matrix; determine a covariance matrix using the real-valued data matrix; and determine an eigenvector matrix using the covariance matrix, the eigenvector matrix including a first number of eigenvectors corresponding to a first number of largest eigenvalues of the covariance matrix, the first number equaling a second number of the one or more objects detected by the radar system.

[0182] Example 8: The radar system of Example 7, wherein, in determining the estimated solution to the invariance equation, the one or more processors are configured to: determine a first determinant value using the real part of the sparse unitary matrix and the eigenvector matrix; determine a second determinant value using the imaginary part of the sparse unitary matrix and the eigenvector matrix; determine whether the first determinant value is greater than or not greater than the second determinant value; and in response to the second determinant value being greater than the first determinant value, determine the estimated solution to the invariance equation as a product of the real part of the sparse unitary matrix and the eigenvector matrix; or in response to the second determinant value not being greater than the first determinant value, determine the estimated solution to the invariance equation as a product of the imaginary part of the sparse unitary matrix and the eigenvector matrix.

[0183] Example 9: The radar system of Example 8, wherein, in determining the solution to the invariance equation, the one or more processors are configured to: in response to the second determinant value being greater than the first determinant value: determine whether a first condition is satisfied, the first condition being whether the second determinant value is less than a first threshold value; determine whether a second condition is satisfied, the second condition being whether the second determinant value is less than a product of a second threshold value and the first determinant value; and in response to both the first condition and the second condition being satisfied, solve the invariance equation using a total least squares method; or in response to either the first condition or the second condition not being satisfied, solve the invariance equation using a least squares method; and in response to the second determinant value not being greater than the first determinant value: determine whether a third condition is satisfied, the third condition being whether the first determinant value is less than the first threshold value; determine whether a fourth condition is satisfied, the fourth condition being whether the first determinant value is less than a product of a second threshold value and the second determinant value; and in response to both the third condition and the fourth condition being satisfied, solve the invariance equation using the total least squares method; or in response to either the third condition or the fourth condition not being satisfied, solve the invariance equation using the least squares method.

[0184] Example 10: The radar system of example 9, wherein in determining the angular phase associated with the one or more objects, the one or more processors are configured to: determine an eigenvalue of the solution of the invariance equation; and in response to the second determinant value being greater than the first determinant value, determine the angular phase as an inverse cotangent of the eigenvalue of the solution of the invariance equation; or in response to the second determinant value not being greater than the first determinant value, determine the angular phase as an inverse tangent of the eigenvalue of the solution of the invariance equation.

[0185] Example 11 : The radar system of example 10, wherein the angle associated with the one or more objects is a function of: the angular phase associated with the one or more objects, a wavelength of the EM energy, and a distance between the antenna elements of the ID or 2D sparse uniform array.

[0186] Example 12: The radar system of any of the preceding examples, wherein the angle associated with the one or more objects is determined using an Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) process.

[0187] Example 13: The radar system of any of the preceding examples, wherein the radar system is configured to be mounted on an automobile.

[0188] Example 14: A method comprising: receiving, by an antenna of a radar system, electromagnetic (EM) energy reflected by one or more objects; determining, using the EM energy received by a one-dimensional (ID) or two-dimensional (2D) sparse uniform array of antenna elements, a signal subspace associated with the one or more objects, the signal subspace comprising an invariance equation; determining an estimated solution of the invariance equation; determining a solution of the invariance equation using the estimated solution of the invariance equation; determining an angular phase associated with the one or more objects using the solution of the invariance equation; and determining an angle associated with the one or more objects using the angular phase associated with the one or more objects.

[0189] Example 15: The method of example 14, wherein determining the signal subspace associated with the one or more objects comprises: generating a beam vector for each of a plurality of data snapshots of the EM energy received by the ID or 2D sparse uniform array; generating a data matrix using the beam vector for each of the plurality of data snapshots; generating a real-valued data matrix using the data matrix; determining a covariance matrix using the real-valued data matrix; and determining an eigenvector matrix using the covariance matrix, the eigenvector matrix comprising a first number of eigenvectors corresponding to a first number of largest eigenvalues of the covariance matrix, the first number being equal to a second number of the one or more objects detected by the radar system.

[0190] Example 16: The method of example 15, wherein determining the estimated solution to the invariance equation comprises: determining a first determinant value using the real part of the sparse unitary matrix and the eigenvector matrix; determining a second determinant value using the imaginary part of the sparse unitary matrix and the eigenvector matrix; determining whether the first determinant value is greater than or not greater than the second determinant value; and in response to the second determinant value being greater than the first determinant value, determining the estimated solution to the invariance equation as a product of the real part of the sparse unitary matrix and the eigenvector matrix; or in response to the second determinant value being not greater than the first determinant value, determining the estimated solution to the invariance equation as a product of the imaginary part of the sparse unitary matrix and the eigenvector matrix.

[0191] Example 17: The method of example 16, wherein determining the solution to the invariance equation comprises: in response to the second determinant value being greater than the first determinant value: determining whether a first condition is satisfied, the first condition being whether the second determinant value is less than a first threshold value; determining whether a second condition is satisfied, the second condition being whether the second determinant value is less than a product of a second threshold value and the first determinant value; and in response to both the first condition and the second condition being satisfied, solving the invariance equation using a full least squares method; or in response to either the first condition or the second condition not being satisfied, solving the invariance equation using a least squares method; and in response to the second determinant value being not greater than the first determinant value: determining whether a third condition is satisfied, the third condition being whether the first determinant value is less than the first threshold value; determining whether a fourth condition is satisfied, the fourth condition being whether the first determinant value is less than a product of the second threshold value and the second determinant value; and in response to both the third condition and the fourth condition being satisfied, solving the invariance equation using the full least squares method; or in response to either the third condition or the fourth condition not being satisfied, solving the invariance equation using the least squares method.

[0192] Example 18: The method of example 17, wherein determining the angular phase associated with the one or more objects comprises: determining an eigenvalue of the solution to the invariance equation; and in response to the second determinant value being greater than the first determinant value, determining the angular phase as an arc cotangent of the eigenvalue of the solution to the invariance equation; or in response to the second determinant value being not greater than the first determinant value, determining the angular phase as an arc tangent of the eigenvalue of the solution to the invariance equation.

[0193] Example 19: The method of example 18, wherein the angle associated with the one or more objects is a function of: the angular phase associated with the one or more objects, a wavelength of the EM energy, and a distance between the antenna elements of the ID or 2D sparse uniform array.

[0194] Example 20: The method of any one of examples 14-19, wherein: the ID sparse uniform array comprises a uniform linear array positioned in an azimuthal direction; and the angle associated with the one or more objects comprises an azimuthal angle associated with the one or more objects.

[0195] Example 21 : The method of any one of Examples 14 to 20, wherein: the 2D sparse uniform array is positioned in an elevation direction and an azimuth direction; and the angles associated with the one or more objects comprise an elevation and an azimuth associated with the one or more objects.

[0196] Example 22: The method of any one of Examples 14 to 21, wherein the antenna elements of the ID or 2D sparse uniform array are at least one of: uniformly spaced apart by a first distance in an azimuth direction, or uniformly spaced apart by a second distance in an elevation direction.

[0197] Example 23: The method of Example 22, wherein the first distance and the second distance are first and second positive integers of one-half of a wavelength of the EM energy.

[0198] Example 24: The method of any one of Examples 14 to 23, wherein the angles associated with the one or more objects are determined without one or more blind spots within a field of view of the ID or 2D sparse uniform array.

[0199] Example 25: The method of any one of Examples 14 to 24, wherein the angles associated with the one or more objects are determined using an Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) process.

[0200] Example 26: The method of any one of Examples 14 to 25, wherein the radar system is configured for installation on an automobile.

[0201] Example 27: A radar system comprising: an antenna configured to receive electromagnetic (EM) energy reflected by one or more objects, the antenna comprising a one-dimensional (ID) or two-dimensional (2D) sparse uniform array of antenna elements; and one or more processors configured for performing the method of any one of Examples 14 to 26.

[0202] Example 28: A computer-readable storage medium comprising computer- executable instructions that, when executed, cause a processor of a radar system to perform the method of any one of Examples 14 to 26.

[0203] Example 29: A computer-readable storage medium comprising computer- executable instructions that, when executed, cause a processor of a radar system to: receive, by an antenna of the radar system, electromagnetic (EM) energy reflected by one or more objects; determine, using the EM energy received by a one-dimensional (ID) or two- dimensional (2D) sparse uniform array of antenna elements, a signal subspace associated with the one or more objects, the signal subspace comprising an invariance equation; determine an estimated solution to the invariance equation; determine a solution to the invariance equation using the estimated solution to the invariance equation; determine an angular phase associated with the one or more objects using the solution to the invariance equation; and determine an angle associated with the one or more objects using the angular phase associated with the one or more objects.

[0204] CONCLUSION

[0205] While various embodiments of the present disclosure have been described and illustrated in the foregoing description and shown in the accompanying drawings, it will be understood that the present disclosure is not limited to the only embodiments described and illustrated herein, but can be practiced with various modifications and alterations within the scope of the claims that follow. It will be apparent from the foregoing description that various changes can be made without departing from the spirit and scope of the present disclosure as defined by the following claims.

Claims

1. A radar system, comprising: an antenna configured to receive electromagnetic (EM) energy reflected by one or more objects, the antenna comprising a one-dimensional (ID) or two-dimensional (2D) sparse uniform array of antenna elements; and one or more processors configured to: determine, using the EM energy received by the ID or 2D sparse uniform array, a signal subspace associated with the one or more objects, the signal subspace comprising an invariance equation, wherein in determining the signal subspace associated with the one or more objects: generate a beam vector for each of a plurality of data snapshots of the EM energy received by the ID or 2D sparse uniform array; generate a data matrix using the beam vector for each of the plurality of data snapshots; generate a real-valued data matrix using the data matrix; determine a covariance matrix using the real-valued data matrix; and determine an eigenvector matrix using the covariance matrix, the eigenvector matrix comprising a first number of eigenvectors corresponding to a first number of largest eigenvalues of the covariance matrix, the first number being equal to a second number of the one or more objects detected by the radar system; determine an estimated solution to the invariance equation, wherein in determining the estimated solution to the invariance equation: determine a first determinant value using a real part of a sparse unitary matrix and the eigenvector matrix; determine a second determinant value using an imaginary part of the sparse unitary matrix and the eigenvector matrix; determine whether the first determinant value is greater than or not greater than the second determinant value; and in response to the second determinant value being greater than the first determinant value, determine the estimated solution to the invariance equation as a product of the real part of the sparse unitary matrix and the eigenvector matrix; or in response to the second determinant value being not greater than the first determinant value, determine the estimated solution to the invariance equation as a product of the imaginary part of the sparse unitary matrix and the eigenvector matrix; determine a solution to the invariance equation using the estimated solution to the invariance equation, wherein in determining the solution to the invariance equation: in response to the second determinant value being greater than the first determinant value: determine whether a first condition is satisfied, the first condition being whether the second determinant is less than a first threshold value; determine whether a second condition is satisfied, the second condition being whether the second determinant is less than a product of a second threshold value and the first determinant value; and in response to both the first condition and the second condition being satisfied, solve the invariance equation using a full least squares method; or in response to either the first condition or the second condition not being satisfied, solve the invariance equation using a least squares method; and in response to the second determinant value being not greater than the first determinant value: determine whether a third condition is satisfied, the third condition being whether the first determinant is less than the first threshold value; determine whether a fourth condition is satisfied, the fourth condition being whether the first determinant is less than a product of the second threshold value and the second determinant value; and solving the invariance equation using the total least squares method in response to both the third condition and the fourth condition being satisfied; or solving the invariance equation using the least squares method in response to either the third condition or the fourth condition not being satisfied; determining an angular phase associated with the one or more objects using the solution of the invariance equation; and determining an angle associated with the one or more objects using the angular phase associated with the one or more objects.

2. The radar system of claim 1, wherein: the ID sparse uniform array comprises a uniform linear array positioned in an azimuth direction; and the angle associated with the one or more objects comprises an azimuth angle associated with the one or more objects.

3. The radar system of claim 1, wherein: the 2D sparse uniform array is positioned in an elevation direction and an azimuth direction; and the angle associated with the one or more objects comprises an elevation angle and an azimuth angle associated with the one or more objects.

4. The radar system of claim 1, wherein, the antenna elements of the ID or 2D sparse uniform array are at least one of uniformly spaced apart by a first distance in an azimuth direction or uniformly spaced apart by a second distance in an elevation direction.

5. The radar system of claim 4, wherein, the first distance and the second distance are first and second positive integers of one half of a wavelength of the EM energy.

6. The radar system of claim 1, wherein, the angle associated with the one or more objects is determined without one or more blind spots within a field of view of the ID or 2D sparse uniform array.

7. The radar system of claim 1, wherein, in determining the angular phase associated with the one or more objects, the one or more processors are configured to: determine an eigenvalue of the solution of the invariance equation; and in response to the second determinant value being greater than the first determinant value, determine the angular phase as an inverse cotangent of the eigenvalue of the solution of the invariance equation; or in response to the second determinant value not being greater than the first determinant value, determine the angular phase as an inverse tangent of the eigenvalue of the solution of the invariance equation.

8. The radar system of claim 7, wherein, the angle associated with the one or more objects is a function of the angular phase associated with the one or more objects, a wavelength of the EM energy, and a distance between the antenna elements of the ID or 2D sparse uniform array.

9. The radar system of claim 1, wherein, the angle associated with the one or more objects is determined using an Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) process.

10. The radar system of claim 1, wherein, the radar system is configured to be installed on an automobile.

11. A method for a radar system, the method comprising: receiving, by an antenna of the radar system, electromagnetic (EM) energy reflected by one or more objects; determining, using the EM energy received by a one-dimensional (ID) or two-dimensional (2D) sparse uniform array of antenna elements, a signal subspace associated with the one or more objects, the signal subspace comprising an invariance equation, wherein determining the signal subspace associated with the one or more objects comprises: generating a beam vector for each of a plurality of data snapshots of the EM energy received by the 1D or 2D sparse uniform array; generating a data matrix using the beam vector for each of the plurality of data snapshots; generating a real-valued data matrix using the data matrix; determining a covariance matrix using the real-valued data matrix; and determining an eigenvector matrix using the covariance matrix, the eigenvector matrix including a first number of eigenvectors corresponding to a first number of largest eigenvalues of the covariance matrix, the first number equal to a second number of the one or more objects detected by the radar system; determining an estimated solution to the invariance equation, wherein determining the estimated solution to the invariance equation includes: determining a first determinant value using a real part of a sparse unitary matrix and the eigenvector matrix; determining a second determinant value using an imaginary part of the sparse unitary matrix and the eigenvector matrix; determining whether the first determinant value is greater than or not greater than the second determinant value; and in response to the second determinant value being greater than the first determinant value, determining the estimated solution to the invariance equation as a product of the real part of the sparse unitary matrix and the eigenvector matrix; or in response to the second determinant value being not greater than the first determinant value, determining the estimated solution to the invariance equation as a product of the imaginary part of the sparse unitary matrix and the eigenvector matrix; determining a solution to the invariance equation using the estimated solution to the invariance equation, wherein determining the solution to the invariance equation includes: in response to the second determinant value being greater than the first determinant value: determining whether a first condition is satisfied, the first condition being whether the second determinant is less than a first threshold value; determining whether a second condition is satisfied, the second condition being whether the second determinant is less than a product of a second threshold value and the first determinant; and in response to both the first condition and the second condition being satisfied, solving the invariance equation using a full least squares method; or in response to either the first condition or the second condition not being satisfied, solving the invariance equation using a least squares method; and in response to the second determinant value being not greater than the first determinant value: determining whether a third condition is satisfied, the third condition being whether the first determinant is less than the first threshold value; determining whether a fourth condition is satisfied, the fourth condition being whether the first determinant is less than a product of the second threshold value and the second determinant; and in response to both the third condition and the fourth condition being satisfied, solving the invariance equation using the full least squares method; or in response to either the third condition or the fourth condition not being satisfied, solving the invariance equation using the least squares method; determining an angular phase associated with the one or more objects using the solution to the invariance equation; and determining an angle associated with the one or more objects using the angular phase associated with the one or more objects.

12. The method of claim 11, wherein, determining the angular phase associated with the one or more objects includes: determining an eigenvalue of the solution of the invariance equation; and determining the angle phase as an inverse tangent of the eigenvalue of the solution of the invariance equation in response to the second determinant value being greater than the first determinant value; or determining the angle phase as an inverse tangent of the eigenvalue of the solution of the invariance equation in response to the second determinant value not being greater than the first determinant value.

13. The method of claim 12, wherein, The angle associated with the one or more objects is a function of the angle phase associated with the one or more objects, a wavelength of the EM energy, and a distance between the antenna elements of the ID or 2D sparse uniform array.

14. A computer-readable storage medium comprising computer-executable instructions that, when executed, cause a processor of a radar system to: receive, by an antenna of a radar system, electromagnetic (EM) energy reflected by one or more objects; determine, using the EM energy received by a one-dimensional (ID) or two-dimensional (2D) sparse uniform array of antenna elements, a signal subspace associated with the one or more objects, the signal subspace comprising an invariance equation, wherein determining the signal subspace associated with the one or more objects: generate a beam vector for each of a plurality of data snapshots of the EM energy received by the ID or 2D sparse uniform array; generate a data matrix using the beam vector for each of the plurality of data snapshots; generate a real-valued data matrix using the data matrix; determine a covariance matrix using the real-valued data matrix; and determine an eigenvector matrix using the covariance matrix, the eigenvector matrix comprising a first number of eigenvectors corresponding to a first number of largest eigenvalues of the covariance matrix, the first number being equal to a second number of the one or more objects detected by the radar system; determine an estimated solution of the invariance equation, wherein determining the estimated solution of the invariance equation: determine a first determinant value using a real part of a sparse unitary matrix and the eigenvector matrix; determine a second determinant value using an imaginary part of the sparse unitary matrix and the eigenvector matrix; determine whether the first determinant value is greater than or not greater than the second determinant value; and determine the estimated solution of the invariance equation as a product of the real part of the sparse unitary matrix and the eigenvector matrix in response to the second determinant value being greater than the first determinant value; or determine the estimated solution of the invariance equation as a product of the imaginary part of the sparse unitary matrix and the eigenvector matrix in response to the second determinant value not being greater than the first determinant value; determine a solution of the invariance equation using the estimated solution of the invariance equation, wherein determining the solution of the invariance equation: in response to the second determinant value being greater than the first determinant value: determine whether a first condition is satisfied, the first condition being whether the second determinant is less than a first threshold value; ​ determining whether a second condition is satisfied, the second condition being whether the second determinant is less than a product of a second threshold and the first determinant; and in response to both the first condition and the second condition being satisfied, solving the invariance equation using a full least squares method; or in response to either the first condition or the second condition not being satisfied, solving the invariance equation using a least squares method; and in response to the second determinant value not being greater than the first determinant value: determining whether a third condition is satisfied, the third condition being whether the first determinant is less than the first threshold; determining whether a fourth condition is satisfied, the fourth condition being whether the first determinant is less than a product of the second threshold and the second determinant; and in response to both the third condition and the fourth condition being satisfied, solving the invariance equation using the full least squares method; or in response to either the third condition or the fourth condition not being satisfied, solving the invariance equation using the least squares method; determining an angular phase associated with the one or more objects using the solution of the invariance equation; and determining an angle associated with the one or more objects using the angular phase associated with the one or more objects.

Images