Sparse Signal Reconstruction for Track-Before-Detect

Abstract

Accurately tracking an unknown and time-varying number of objects in complex environments is a challenging problem in radar and sonar sensing. The track-before-detect (TkBD) paradigm aims to avoid a detection stage by operating directly on sensor data to prevent information loss. This paper introduces a novel TkBD method based on a superpositional signal model adopted from the sparse signal reconstruction literature. The resulting TkBD measurement model accounts for sensor data correlations, amplitude fluctuations, and unknown measurement noise variance. By retaining relative phase information in complex-valued sensor data, the proposed measurement model supports phase-coherent processing directly within the TkBD method. It also enables the accurate representation of the physics of the data-generating process in the statistical model used for TkBD, including the complex acoustic wavefields used in matched-field processing. To accommodate measurements from multiple sensors or frequencies, we introduce a general multi-snapshot, multi-dictionary formulation of this model. The proposed statistical model is suitable for a wide range of problems in active and passive radar, active and passive sonar, as well as integrated sensing and communication systems. Based on a factor graph representation of the proposed model, a scalable belief propagation (BP) method is developed to perform efficient Bayesian inference. Experimental results obtained with both synthetic radar data and real acoustic data for matched-field processing demonstrate that the proposed method outperforms state-of-the-art conventional multiobject tracking (MOT) methods.