Subspace Track-before-Detect for Passive Multi-Target Tracking with Unknown Emitted Signals

Abstract

Passive multi-target tracking (MTT) aims to infer the time-varying kinematic and activity states of an unknown number of sources that emit unknown and possibly nonstationary signals, using only noisy mixtures of these signals observed at sensors. Track-before-detect (TBD) methods improve noise robustness by evaluating multi-target hypotheses directly on raw sensor data, without relying on a preceding detection stage. However, existing TBD likelihoods typically assume that the contribution of each active target to the observation is determined solely by its kinematic state. This assumption does not hold in passive sensing scenarios, where the observed mixtures also depend on unknown and possibly nonstationary source signals. To address this issue, we propose subspace TBD, a passive multi-target TBD method that employs a source-signal-insensitive likelihood derived from the complex spherical Student's $t$ (cST) distribution. Instead of explicitly modeling or estimating the nuisance source signals, the method represents each multi-target hypothesis by the subspace spanned by source steering vectors. The cST likelihood then evaluates how well the normalized multichannel mixtures align with this subspace. We conducted acoustic MTT simulations with two moving speakers in noisy, reverberant environments, comparing the proposed method with a baseline consisting of steered response power with phase transform (SRP-PHAT) followed by a sequential Monte Carlo implementation of the generalized labeled multi-Bernoulli filter (SMC-GLMB). The proposed method achieved lower mean optimal subpattern assignment (OSPA) values in all tested conditions.