An SVD approach for data compression in emitter location systems

Abstract

In classical TDOA/FDOA emitter location methods, pairs of sensors share the received data to compute the CAF and extract the ML estimates of TDOA/FDOA. The TDOA/FDOA estimates are then transmitted to a common site where they are used to estimate the emitter location. In some recent methods, it has been proposed that rather than sending the TDOA/FDOA estimates, it is better to send the entire CAFs to the common site. Thus, it is desirable to use some methods to compress the CAFs. In this paper, we will propose an SVD (Singular Value Decomposition) approach for CAF data compression. We will see that SVD approach is a beneficial method for data compression and also it is a strong tool for denoising. Simulation results show that by applying SVD Data Compression it is possible to perform accurate location estimation in spite of the fact that we transmit fewer bits. Also for smaller compression ratio, we even achieve an improvement in performance of location estimation compared to the case that we do not compress the data at all and that is because of the denoising effect of the SVD.

Distributed computation for direct position determination emitter location

“…By truncating the above summation to k < r 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 [10,17]. Thus, from a data compression viewpoint we can think of X k as a minimum mean square error (MSE) distortion version of X.…”

“…Now, we can write one of the received signals in terms of the other one: s 2 (t) = α 2 α 1 e jω c τ 12 e −jω 1 τ 12 e −jω 12 tŝ 1 (t + τ 12 ) s 2 (t) = G 12 e −jω 12 tŝ 1 (t + τ 12 ) G 12 = α 2 α 1 e jω c τ 12 e −jω 1 τ 12 (10) where τ 12 = (τ 1 − τ 2 ) is the TDOA and ω 12 = (ω 1 − ω 2 ) is the FDOA. The CAF between these two signals can be written as being proportional to the AAF of the first signal as…”

“…Furthermore, to reduce the transmission requirement for CAF-sharing, we propose to apply data compression methods tailored to exploit CAF properties, such as the preliminary approaches developed in [8][9][10]. In this paper we expand our earlier results by discussing the communication and computation structures needed to support this method.…”