Data compression using SVD and Fisher information for radar emitter location

Abstract

This paper presents a data compression method that can achieve a very large compression ratio for radar pulse trains that are to be used for time-difference-of-arrival/frequency-difference-ofarrival (TDOA/FDOA) multiple-platform emitter location; this method exploits pulse-to-pulse redundancy to get a compression ratio much higher than possible using standard compression methods. We show how to use (i) the ability of the singular value decomposition (SVD) to exploit redundancy between radar pulses, and (ii) a Fisher information-based distortion criterion to enable elimination of pulses that are negligible to the FDOA estimation tasks. To enable the SVD to effectively remove the redundancy it is necessary to first optimally gate the pulses and place them in the rows of a matrix and then align the pulses to arrive at a matrix that is close to having rank of one. Finally, we suggest reasonable coding schemes for the information to be sent and assess the achievable compression level.The Fisher information-based removal of pulses is shown to have negligible impact on the FDOA accuracy but does degrade the TDOA accuracy from that achievable using the SVD-based compression without pulse elimination. However, we demonstrate that the SVD method includes an inherent denoising effect (common in SVD-based signal processing) that provides an improvement in TDOA accuracy over the case of no compression processing; thus, the overall impact on TDOA/FDOA accuracy is negligible while providing compression ratios up to 100:1 for typical radar signals.

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“…Besides, every matrix is guaranteed to have a SVD and, due to its properties, this is a technique that has been widely used for data compression. 58 Based on all of the above, we use the rank-h SVD of the input matrix X to obtain the weights of the first layer. As mentioned, the full SVD of X is a factorization of the matrix of the form:…”

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“…r is the number of non-zero singular values, is the ith left singular vector and is Hermitian of the ith right singular vector. By truncating the above summation to terms, we get a rank-k matrix X k that approximates X better than any other rank-k matrix in the least square error sense [16], [17], [18]. This is the main idea of SVD data compression.…”

“…The effect of the noise on the singular values is spread across all the singular values but, as mentioned before, most of the data is concentrated in the first few singular vectors and values. Thus, by SVD truncation we reduce the noise and equivalently we increase the signal to noise ratio (SNR) [18].…”

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