Abstract The invention relates generally to the field of signal processing for signal reception and parameter estimation. The invention has many applications such as frequency estimation and filtering, and array data processing, etc. For convenience, only applications of this invention to sensor array processing are described herein. The array processing problem addressed is that of signal parameter and waveform estimation utilizing data collected by an array of sensors. Unique to this invention is that the sensor array geometry and individual sensor characteristics need not be known. Also, the invention provides substantial advantages in computations and storage over prior methods. However, the sensors must occur in pairs such that the paired elements are identical except for a displacement which is the same for all pairs. These element pairs define two subarrays which are identical except for a fixed known displacement. The signals must also have a particular structure which in direction-of-arrival estimation applications manifests itself in the requirement that the wavefronts impinging on the sensor array be planar. Once the number of signals and their parameters are estimated, the array configuration can be determined and the signals individually extracted. The invention is applicable in the context of array data processing to a number of areas including cellular mobile communications, space antennas, sonobuoys, towed arrays of acoustic sensors, and structural analysis.
A method of locating signal sources and estimating source parameters comprising the following steps: (a) providing an array of groups of signal sensor pairs, the sensors in each pair in each group being identical except for a fixed displacement which may differ from group to group, thereby defining two subarrays (X and Y) in each group, (b) obtaining signal measurements with the sensor array so configured, (c) determining from said signal measurements the auto-covariance matrix R xx of the X subarray in each group and the cross-covariance matrix R xy between the X and Y subarrays in each group, (d) determining the smallest eigenvalue of the covariance matrix, (e) subtracting said smallest eigenvalue from each element of the principal diagonal of the covariance matrix R xx and obtaining a difference C xx , (f) determining the generalized eigenvalues of the matrix pair (C xx , R xy ), and (g) locating the generalized eigenvalues which lie on a unit circle, the number of which corresponding to the number of sources and the locations of which corresponding to the parameter estimates.
Claim 2
Independent Claim
180 words
A method of locating signal sources and estimating source parameters comprising the following steps: (a) providing an array of groups of signal sensor pairs, the sensors in each pair in each group being identical except for a fixed displacement which may differ from group to group, thereby defining two subarrays (X and Y) in each group, (b) obtaining signal measurements with the sensor array so configured, (c) determining from said signal measurements the auto-covariance matrix R xx of the X subarray in each group and the cross-covariance matrix R xy between the X and Y subarrays in each group, (d) determining the smallest eigenvalue of the covariance matrix, (e) subtracting said smallest eigenvalue from each element of the principal diagonal of the covariance matrix R xx and obtaining a difference C xx , (f) determining the generalized eigenvalues of the matrix pair (C xx , R xy ), and (g) locating the generalized eigenvalues which lie on a unit circle, the number of which corresponding to the number of sources and the locations of which corresponding to the parameter estimates.
Claim 3
Dependent Claim
40 words
The method as defined by claim 1 and further including the steps of: (a) varifying specific signal reception by determining array response (direction) vectors using the generalized eigenvectors, and (b) estimating the array geometry from the said array response vectors.
Claim 4
Dependent Claim
115 words
The method as defined in claim 1 with variations to improve numerical characteristics using generalized singular value decompositions of data matrices instead of generalized eigendecomposition of covariance matrices by: (a) forming data matrices X and Y from the data from the subarrays in each group, (b) computing the generalized singular vectors of the matrix pair (X,Y) yielding X=U X Σ X V* and Y=U Y Σ Y V*, (c) computing the eigenvalues of Σ X -1 U X *U Y Σ Y and (d) locating those eigenvalues which lie on or near the unit circle, the number of which corresponding to the number of sources and the locations of which corresponding to the parameter estimates.