Motion parameter estimation of multiple ground moving targets in multi-static passive radar systems

Abstract

Multi-static passive radar (MPR) systems typically use narrowband signals and operate under weak signal conditions, making them difficult to reliably estimate motion parameters of ground moving targets. On the other hand, the availability of multiple spatially separated illuminators of opportunity provides a means to achieve multi-static diversity and overall signal enhancement. In this paper, we consider the problem of estimating motion parameters, including velocity and acceleration, of multiple closely located ground moving targets in a typical MPR platform with focus on weak signal conditions, where traditional time-frequency analysis-based methods become unreliable or infeasible. The underlying problem is reformulated as a sparse signal reconstruction problem in a discretized parameter search space. While the different bistatic links have distinct Doppler signatures, they share the same set of motion parameters of the ground moving targets. Therefore, such motion parameters act as a common sparse support to enable the exploitation of group sparsity-based methods for robust motion parameter estimation. This provides a means of combining signal energy from all available illuminators of opportunity and, thereby, obtaining a reliable estimation even when each individual signal is weak. Because the maximum likelihood (ML) estimation of motion parameters involves a multi-dimensional search and its performance is sensitive to target position errors, we also propose a technique that decouples the target motion parameters, yielding a two-step process that sequentially estimates the acceleration and velocity vectors with a reduced dimensionality of the parameter search space. We compare the performance of the sequential method against the ML estimation with the consideration of imperfect knowledge of the initial target positions. The Cramér-Rao bound (CRB) of the underlying parameter estimation problem is derived for a general multiple-target scenario in an MPR system. Simulation results are provided to compare the performance of the sparse signal reconstruction-based methods against the traditional time-frequency-based methods as well as the CRB.

Cramer-Rao type bounds for sparsity-aware multi-target tracking in multi-static passive radar

“…k,i is the reflection coefficient corresponding to the ith target, m = 0, · · · , M − 1 represent the discrete-time instants sampled at a rate of F s Hz over the kth interval, and f (r) k,i is the bistatic Doppler frequency given as [13,14] f (r)…”

“…Since the unknown variables under consideration are the target state vectors, the first term in (14) vanishes to zero because the covariance matrix is independent of the target state vectors. As such, substituting for the values of the mean vector μ (r) k and the covariance matrix C, we obtain…”

Group sparsity based multi-target tracking in multi-static passive radar systems using Doppler-only measurements

“…Unlike [19][20][21], where entire raw measurement vectors corresponding to each bistatic link are assumed available at the fusion center, it is not possible to directly combine these scalar Doppler-shift measurements across different bistatic links deploying the fuse-before-track approach. Therefore, the existing tracking methods rely on the sub-optimal track-before-fuse schemes.…”

Long Coherent Integration in Passive Radar Systems Using Super-Resolution Sparse Bayesian Learning

“…Comparatively, in a multi-target case the superposition of chirps and the coupling of the RM and DFM effects make the overall compensation routine very challenging. In the radar literature, the multi-target scenario has been often considered in conjunction with the simplified assumptions that: a) only linear RM is present [1], [2], b) only DFM is present [17], [18], c) RM-DFM coupling is not accounted for [9], or d) successive target RM and DFM compensation, detection, and cancellation is enabled by model-based CLEAN-like schemes [3], [6], [7], [19], [20]. The CLEAN-type algorithms aim to successively detect and remove the contributions of the strong targets from the received signal such that to allow for detecting any weaker targets.…”

“…Moreover, in our case the parameter space is not discretized and the variational Bayesian (VB) framework is used to construct an analytical approximation to the posterior distribution while in [23] a numerical approximation is employed. A sparsity-driven approach was also considered in [17] in the context of estimating the parameters of multiple closely spaced and migrating targets. Nevertheless, the work in [17] assumes a passive multistatic SAR geometry and only accounts for the target DFM.…”