High resolution and computationally efficient radar techniques
Methods, systems, computer-readable media, and apparatuses for determining one or more attributes of at least one target based on eigenspace analysis of radar signals are presented. In some embodiments, a subset of eigenvectors to use for forming a signal or noise subspace is identified based on principal component analysis. In some embodiments, the subset of eigenvectors is identified based on estimating the total number of targets using a discrete Fourier transform (DFT) or other spectral analysis technique. In some embodiments, a DFT is used to identify areas of interest in which to perform eigenspace analysis. In some embodiments, a DFT is used to estimate one attribute of a target, and eigenspace analysis is performed to estimate a different attribute of the target, with the results being combined to generate a multi-dimensional representation of a field of view.
1. An apparatus comprising:
a signal generator configured to generate a radar signal;
at least one transmit antenna configured to transmit the radar signal;
a plurality of antennas configured to receive a reflected radar signal, wherein each antenna of the plurality of antennas is configured to generate a respective received signal in response to the reflected radar signal; and
one or more processors configured to:
generate a signal array as a digital representation of the received signals;
calculate a covariance matrix using the signal array;
determine a set of eigenvectors of the covariance matrix, wherein the set of eigenvectors is a subset of all eigenvectors of the covariance matrix, each eigenvector of the set of eigenvectors corresponding to a different target among a set of targets, and wherein to determine the set of eigenvectors, the one or more processors are configured to identify each eigenvector of the set of eigenvectors one at a time, through an iterative process in which a corresponding candidate eigenvector initialized with random values is refined until the candidate eigenvector converges to a final eigenvector representing a principal component; and
determine one or more attributes of at least one target among the set of targets based on the set of eigenvectors.
2. The apparatus of claim 1 , wherein to identify each eigenvector, the one or more processors are configured to:
generate a candidate eigenvector that, if included in the set of eigenvectors, forms an orthonormal basis; and
iteratively refine the candidate eigenvector by:
generating a next candidate eigenvector;
calculating a similarity metric whose value indicates a degree of similarity between the candidate eigenvector and the next candidate eigenvector;
determining that the candidate eigenvector and the next candidate eigenvector are dissimilar based on comparing the value of the similarity metric to a threshold; and
replacing the candidate eigenvector with the next candidate eigenvector based on determining that the candidate eigenvector and the next candidate eigenvector are dissimilar.
3. The apparatus of claim 1 , wherein to identify each eigenvector, the one or more processors are configured to:
generate a candidate eigenvector that, if included in the set of eigenvectors, forms an orthonormal basis; and
iteratively refine the candidate eigenvector by:
generating a next candidate eigenvector;
calculating a similarity metric whose value indicates a degree of similarity between the candidate eigenvector and the next candidate eigenvector;
determining that the candidate eigenvector and the next candidate eigenvector are similar based on comparing the value of the similarity metric to a threshold; and
identifying the next candidate eigenvector as being an eigenvector of the set of eigenvectors based on determining that the candidate eigenvector and the next candidate eigenvector are similar.
4. The apparatus of claim 1 , wherein to determine the one or more attributes of the at least one target, the one or more processors are configured to:
form a signal subspace using the set of eigenvectors;
project tones of different frequencies onto the signal subspace; and
generate a pseudo spectrum based on the projected tones.
5. The apparatus of claim 4 , wherein the one or more processors are configured to determine the one or more attributes based on the pseudo spectrum.
6. The apparatus of claim 1 , wherein the one or more attributes comprise at least one of a distance of the at least one target and a direction of arrival of the at least one target.
7. A method comprising:
transmitting a radar signal;
receiving, by a plurality of antennas, a reflected radar signal, wherein each antenna of the plurality of antennas is configured to generate a respective received signal in response to the reflected radar signal;
generating a signal array as a digital representation of the received signals;
calculating a covariance matrix using the signal array;
determining a set of eigenvectors of the covariance matrix, wherein the set of eigenvectors is a subset of all eigenvectors of the covariance matrix, each eigenvector of the set of eigenvectors corresponding to a different target among a set of targets, and wherein the determining of the set of eigenvectors comprises identifying each eigenvector of the set of eigenvectors one at a time, through an iterative process in which a corresponding candidate eigenvector initialized with random values is refined until the candidate eigenvector converges to a final eigenvector representing a principal component; and
determining one or more attributes of at least one target among the set of targets based on the set of eigenvectors.
8. The method of claim 7 , wherein the identifying of each eigenvector comprises:
generating a candidate eigenvector that, if included in the set of eigenvectors, forms an orthonormal basis; and
iteratively refining the candidate eigenvector by:
generating a next candidate eigenvector;
calculating a similarity metric whose value indicates a degree of similarity between the candidate eigenvector and the next candidate eigenvector;
determining that the candidate eigenvector and the next candidate eigenvector are dissimilar based on comparing the value of the similarity metric to a threshold; and
replacing the candidate eigenvector with the next candidate eigenvector based on determining that the candidate eigenvector and the next candidate eigenvector are dissimilar.
9. The method of claim 7 , wherein the identifying of each eigenvector comprises:
generating a candidate eigenvector that, if included in the set of eigenvectors, forms an orthonormal basis; and
iteratively refining the candidate eigenvector by:
generating a next candidate eigenvector;
calculating a similarity metric whose value indicates a degree of similarity between the candidate eigenvector and the next candidate eigenvector;
determining that the candidate eigenvector and the next candidate eigenvector are similar based on comparing the value of the similarity metric to a threshold; and
identifying the next candidate eigenvector as being an eigenvector of the set of eigenvectors based on determining that the candidate eigenvector and the next candidate eigenvector are similar.
10. The method of claim 7 , wherein determining the one or more attributes of the at least one target comprises:
forming a signal subspace using the set of eigenvectors;
projecting tones of different frequencies onto the signal subspace; and
generating a pseudo spectrum based on the projected tones.
11. The method of claim 10 , wherein the one or more attributes are determined based on the pseudo spectrum.
12. The method of claim 7 , wherein the one or more attributes comprise at least one of a distance of the at least one target and a direction of arrival of the at least one target.