Patent ID: 7602331

Claim:
A method for estimating the range profile of a physical system that characterizes the location of scatterers in the physical system as designated by a plurality of range cells, comprising: transmitting an energy pulse waveform to the physical system, wherein a discrete-time version of the transmitted waveform is denoted as the column vector s=[s 0 s 1 . . . s N ] T having length N, where N is an integer; receiving a return signal produced by scattering of the transmitted waveform by the physical system as represented by the convolution of the transmitted waveform with the impulse response of the physical system, the received return signal being denoted in discrete notation at the l th range cell as: y ( l )= x T ( l ) s+v ( l ) for l=0, . . . , L+N−2, where x(l)=[x(l) x(l−1) . . . x(l−N+4] T is the portion of the range profile that the transmitted waveform s convolves with at delay l, v(l) is a sample of an additive noise signal, and L is the number of range cells of interest; computing an estimate {circumflex over (x)}(l) of the impulse response of the physical system and thereby the range profile as: {circumflex over (x)} ( l )= {tilde over (w)} H ( l ) y ( l ) where {tilde over (w)}(l) is a piecewise Minimum Mean-Square Error (MMSE) pulse compression filter; computing {tilde over (w)}(l) by combining M number of length-K filter segments corresponding to M number of length-K segments of the received signal y(l), and wherein the m th length-K filter segment {tilde over (w)} m (l) is computed as: w ~ m ⁡ ( ℓ ) = ( E ⁡ [ y ~ m ⁡ ( ℓ ) ⁢ y ~ m H ⁡ ( ℓ ) ] ) - 1 ⁢ E ⁡ [ 1 M ⁢ y ~ m ⁡ ( ℓ ) ⁢ x * ⁡ ( ℓ ) ] for m=0, 1, . . . , M−1, where {tilde over (y)} m (l) is the m th length-K segment of the N contiguous samples of the received signal y(l); and, combining the filter segments {tilde over (w)} m (l) in a manner corresponding to the segmentation of the received signal y(l) that approximates a range-dependent MMSE filter w(l) obtained by minimizing the MMSE cost function J ( l )= E[|x ( l )− w H ( l ) y ( l )| 2 ] for each individual range cell l=0, 1, . . . , L−1.