Accurate location sonar and radar

Claim 2

In a radar or sonar system a method of estimation of sources of stationary random processes with an array of detectors (labelled with i from 1 to I), comprising the steps of: (a) subdividing the region containing said sources into annular segments from the center of said array and further subdividing each of said annular segments into volume elements (labelled p from 1 to P) of diameter less than the resolution of said array so the sources within each element may be represented by a single source; (b) forming an I by P matrix C(w) with the i,p element equal to Qipexp[jwSip] where Qip is the attenuation between the pth source and the ith array detector and Sip is the propagation delay between the pth source and the ith array detector; (c) computing a P by I matrix D(w) equal to [C(w)*C(w)].sup.˜ C(w)* with * denoting the transpose and .sup.˜ denoting the inverse of a matrix; (d) time sampling the energy received from said sources by each of said array detectors and Fourier transforming said samples to form an I component vector Z(w); and (e) matrix multiplying D(w)Z(w) to yield a P component vector Y(w) which are the power spectrum estimates for the P sources.

Claim 3

The method of claim 1, comprising the further steps of: (a) conditioning said matrix D(w) by using a singular value decomposition, replacing all singular values less than a selected fraction of the maximum singular value with zeroes in the diagonal matrix of the decomposition, and truncating the multiplying matrices corresponding to said replacing.

Claim 4

In a radar or sonar system a method of estimation of scatterers near an array of detectors (labelled i from 1 to I) by detection of the scattering of an energy pulse transmitted towards said scatterers, comprising the steps of: (a) subdividing the region containing said scatterers into annular segments from the center of said array and further subdividing each of said annular segments into volume elements (labelled p from 1 to P) of diameter less than the resolution of said array so that the scatters within each element may be represented by a single scatterer; (b) selecting one of said annular segments and a Doppler frequency Wl relative to the center of said array; (c) selecting K sampling labelled Tk from T1 to TK in the time interval [s, t] where s corresponds to the time said energy pulse would arrive at the center of said array if reflected from the near face of said selected annular segment and t corresponds to the time said energy pulse would arrive at the center of said array if reflected from the far face of said annular segment; (d) forming an IK by P matrix C for said selected segment and said selected Doppler frequency Wl, said matrix elements labelled by ik and p and equal to QipF(Tk=Sip) exp [jWiplTk] where F(.) is the complex envelope of said transmitted energy pulse, Sip is the propagation delay between said ith detector and pth scatterer, Wipl is the lth array center Doppler frequency adjusted to the ith detector and pth scatterer, Qip is the attenuation from the ith detector to the pth scatterer including the attentuation resulting from the transmit energy pulse beam pattern; (e) computing a P by IK matrix D so Re{CD} is the identity matrix; (f) transmitting said energy pulse from said array towards said scatterers; (g) time sampling at said times Tk the energy scattered from said pulse by said scatterers and received by said detectors; and (h) matrix multiplying said matrix D times the vector formed from concatenating the signals received by said I detectors at said K sampling times and summed over said P representative scatterers, thereby forming the estimation for said P representative scatterers in said selected annulus annular segment at said Doppler frequency and an estimation of said scatterers.

Claim 5

In a radar or sonar system a method of estimation of scatterers near an array of detectors (labelled i from 1 to I) by detection of the scattering of an energy pulse transmitted towards said scatterers, comprising the steps of: (a) subdividing the region containing said scatterers into annular segments from the center of said array and further subdividing each of said annular segments into volume elements (labelled p from 1 to P) of diameter less than the resolution of said array so that the scatters within each element may be represented by a single scatterer; (b) selecting one of said annular segments and a Doppler frequency Wl relative to the center of said array; (c) selecting K sampling labelled Tk from T1 to TK in the time interval [s, t] where s corresponds to the time said energy pulse would arrive at the center of said array if reflected from the near face of said selected annular segment and t corresponds to the time said energy pulse would arrive at the center of said array if reflected from the far face of said annular segment; (d) forming an IK by P matrix C for said selected segment and said selected Doppler frequency Wl, said matrix elements labelled by ik and p and equal to QipF(Tk=Sip) exp [jWiplTk] where F(.) is the complex envelope of said transmitted energy pulse, Sip is the propagation delay between said ith detector and pth scatterer, Wipl is the lth array center Doppler frequency adjusted to the ith detector and pth scatterer, Qip is the attenuation from the ith detector to the pth scatterer including the attentuation resulting from the transmit energy pulse beam pattern; (e) computing a P by IK matrix D so Re{CD} is the identity matrix; (f) transmitting said energy pulse from said array towards said scatterers; (g) time sampling at said times Tk the energy scattered from said pulse by said scatterers and received by said detectors; and (h) matrix multiplying said matrix D times the vector formed from concatenating the signals received by said I detectors at said K sampling times and summed over said P representative scatterers, thereby forming the estimation for said P representative scatterers in said selected annulus annular segment at said Doppler frequency and an estimation of said scatterers.

Claim 6

The method of claim 3, wherein: (a) said computing matrix D includes separating said matrix C into real and imaginary parts, forming a IK by 2P real matrix M by joining Re{C} with -Im{C}, and setting D equal to [M*M].sup.˜ M* with * denoting the transpose and .sup.˜ denoting the inverse of a matrix, whereby D is a real 2P by IK matrix and the estimation for the P representative scatterers has 2P real components which are the real and imaginary parts of a P component complex estimation.

Claim 7

The method of claim 4, comprising the further step of: (a) conditioning said matrix D by using a singular value decomposition, replacing all singular values less than a selected fraction of the maximum singular value with zeroes in the diagonal matrix of the decomposition, and truncating the multiplying matrices corresponding to said replacing.

Claim 8

The method of claim 5, comprising the further steps of: (a) repeating said estimation for other of said annular segments.

Claim 9

The method of claim 4, comprising the further steps of: (a) repeating said estimation for other of said annular segments.

Claim 10

The method of claim 3, comprising the further step of: (a) conditioning said matrix D by using a singular value decomposition, replacing all singular values less than a selected fraction of the maximum singular value with zeroes in the diagonal matrix of the decomposition, and truncating the multiplying matrices corresponding to said replacing.

Claim 11

The method of claim 8, comprising the further steps of: (a) repeating said estimation for other of said annular segments.

Claim 12

The method of claim 3, comprising the further steps of: (a) repeating said estimation for other of said annular segments.

Claim 13

The method of claim 3, comprising the further steps of: (a) repeating said formation of matrix C for each of a selected set of Doppler frequencies, Wl from W1 to WL; and (b) summing all of such matrices C to form matrix C+, and using C+ to compute D.