Radar system with sequential two-dimensional angle estimation
This document describes techniques and systems of a radar system with sequential two-dimensional (2D) angle estimation. The radar system can efficiently estimate angles in two dimensions for detections. 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 2D array that includes antenna elements positioned in a first dimension and a second dimension. The processor can determine, using electromagnetic energy received by the 2D array, first angles in the first dimension associated with a detection of the one or more objects. The processor can then steer the 2D array to the first angle to generate a steered 1D array for each first angle. Using the steered 1D array, the processor can determine second angles associated with the first angle for the detection.
1. A radar system comprising:
an antenna configured to receive electromagnetic (EM) energy reflected by one or more objects, the antenna comprising a two-dimensional (2D) array that includes at least four antenna elements positioned in a first dimension and a second dimension; and
one or more processors configured to:
determine, using the EM energy received at the antenna, first angles associated with one or more detections of the one or more objects, the first angles being in the first dimension;
for each respective first angle of the first angles:
steer the 2D array to the respective first angle to generate a steered 1D array by:
projecting the 2D array onto a subspace formed by a first-dimension steering vector associated with the respective first angle,
determining a projection matrix associated with the subspace formed by the first-dimension steering vector, and
determining second-dimension information associated with the respective first angle based on the projection matrix associated with the subspace formed by the first-dimension steering vector, the second-dimension information being used to determine the second angles associated with the respective first angle; and
determine, based on the steered 1D array, second angles associated with the one or more detections, the second angles being in the second dimension and associated with the respective first angle.
2. The radar system of claim 1 , wherein the one or more processors are configured to steer the 2D array to the respective first angle to generate the steered 1D array by:
determining an interference subspace associated with the respective first angle;
estimating a signal power associated with the first angles and a noise power; and
determining an inverse of an interference covariance matrix associated with the respective first angle using a Woodbury matrix identity to determine second-dimension information associated with the respective first angle, the second-dimension information being used to determine the second angles associated with the respective first angle.
3. The radar system of claim 1 , wherein the one or more processors are configured to steer the 2D array to the respective first angle and to determine the second angles associated with the respective first angle for each respective first angle of the first angles in parallel.
4. The radar system of claim 1 , wherein the one or more processors are configured to steer the 2D array to the respective first angle and to determine the second angles associated with the respective first angle for each respective first angle of the first angles sequentially.
5. The radar system of claim 1 , wherein:
the antenna further comprises an additional one-dimensional (1D) array including additional antenna elements not encompassed by the 2D array and positioned in the first dimension; and
the one or more processors are configured to determine the first angles associated with the one or more detections using the EM energy received at the additional 1D array.
6. The radar system of claim 5 , wherein the additional 1D array is a uniform linear array.
7. The radar system of claim 5 , wherein:
the additional antenna elements of the additional 1D array are concatenated with a subset of the antenna elements of the 2D array to form a concatenated 1D array; and
the first angles associated with the one or more detections are determined using the EM energy received at the concatenated 1D array.
8. The radar system of claim 1 , wherein the one or more processors are configured to:
determine the first angles using at least one of an Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), a Multiple Signal Classification (MUSIC), or a non-linear least squares (NLS) based function; and
determine the second angles using at least one of a phase compare, fast Fourier transform (FFT), or NLS based function.
9. The radar system of claim 1 , wherein the antenna elements of the 2D array are not vertically aligned.
10. The radar system of claim 1 , wherein the one or more processors are configured to determine the first angles associated with the one or more detections using the EM energy received at a subset of the antenna elements of the 2D array, the subset of the antenna elements positioned in the first dimension.
11. The radar system of claim 1 , wherein the antenna elements of the 2D array are positioned in an azimuth direction and an elevation direction.
12. The radar system of claim 1 , wherein the antenna elements of the 2D array are uniformly spaced apart by a first distance in the first dimension and a second distance in the second dimension, the first distance being equal to or different than the second distance.
13. The radar system of claim 1 , wherein the second dimension is orthogonal to the first dimension.
14. The radar system of claim 1 , wherein the second dimension is not orthogonal to the first dimension.
15. The radar system of claim 1 , wherein the radar system is configured to be installed on an automobile.
16. Non-transitory computer-readable storage media 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 two-dimensional (2D) array of the antenna, first angles associated with one or more detections of one or more objects, the 2D array comprising at least four antenna elements positioned in a first dimension and a second dimension, the first angles being in the first dimension; for each respective first angle of the first angles: steer the 2D array to the respective first angle to generate a steered 1D array by projecting the 2D array onto a subspace formed by a first-dimension steering vector associated with the respective first angle, determining a projection matrix associated with the subspace formed by the first-dimension steering vector, and determining second-dimension information associated with the respective first angle based on the projection matrix associated with the subspace formed by the first-dimension steering vector, the second-dimension information being used to determine the second angles associated with the respective first angle; and determine, based on the steered 1D array, second angles associated with the one or more detections, the second angles being in the second dimension and associated with the respective first angle.
17. The non-transitory computer-readable storage media of claim 16 , wherein the computer-readable storage media comprising additional computer-executable instructions that, when executed, cause the processor to steer the 2D array to the respective first angle to generate the steered 1D array by: determining an interference subspace associated with the respective first angle; estimating a signal power associated with the first angles and a noise power; and determining an inverse of an interference covariance matrix associated with the respective first angle using a Woodbury matrix identity to determine second-dimension information associated with the respective first angle, the second-dimension information being used to determine the second angles associated with the respective first angle.
18. 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 two-dimensional (2D) array of the antenna, first angles associated with one or more detections of one or more objects, the 2D array comprising at least four antenna elements positioned in a first dimension and a second dimension, the first angles being in the first dimension;
for each respective first angle of the first angles:
steering the 2D array to the respective first angle to generate a steered 1D array by:
projecting the 2D array onto a subspace formed by a first-dimension steering vector associated with the respective first angle,
determining a projection matrix associated with the subspace formed by the first-dimension steering vector, and determining second-dimension information associated with the respective first angle based on the projection matrix associated with the subspace formed by the first-dimension steering vector, the second-dimension information being used to determine the second angles associated with the respective first angle; and
determining, based on the steered 1D array, second angles associated with the one or more detections, the second angles being in the second dimension and associated with the respective first angle.