Abstract
Abstract Multi-target tracking is mainly challenged by the nonlinearity present in the measurement equation and the difficulty in fast and accurate data association. To overcome these challenges, the present paper introduces a grid-based model in which the state captures target signal strengths on a known spatial grid (TSSG). This model leads to linear state and measurement equations, which bypass data association and can afford state estimation via sparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity of the novel model, two types of sparsity-cognizant TSSG-KF trackers are developed: one effects sparsity through ℓ 1-norm regularization, and the other invokes sparsity as an extra measurement. Iterative extended KF and Gauss-Newton algorithms are developed for reduced-complexity tracking, along with accurate error covariance updates for assessing performance of the resultant sparsity-aware state estimators. Based on TSSG state estimates, more informative target position and track estimates can be obtained in a follow-up step, ensuring that track association and position estimation errors do not propagate back into TSSG state estimates. The novel TSSG trackers do not require knowing the number of targets or their signal strengths and exhibit considerably lower complexity than the benchmark hidden Markov model filter, especially for a large number of targets. Numerical simulations demonstrate that sparsity-cognizant trackers enjoy improved root-mean-square error performance at reduced complexity when compared to their sparsity-agnostic counterparts. Comparison with the recently developed additive likelihood moment filter reveals the better performance of the proposed TSSG tracker.
Highlights
Target tracking research and development are of major importance and continuously expanding interest to a gamut of traditional and emerging applications, which include radar- and sonar-based systems, surveillance and habitat monitoring using distributed wireless sensors, collision avoidance modules envisioned for modern transportation systems, and mobile robot localization and navigation in static and dynamically changing environments, to name a few; see, e.g., [1,2] and references therein.At the core of long-standing research issues even for single-target tracking applications is the nonlinear dependence of the measurements on the desired state estimates, which challenges the performance of linearized Kalman filter (KF) trackers, including the extended (E)KF, the unscented (U)KF, and their iterative variants [1,2]
The present paper investigates the multi-target tracking problem, whereby the available measurements comprise the superposition of received target signal strengths of all targets in the sensor field of view
Given measurements y1:k and supposing that the number of targets M and their signal strengths {s(1), . . . , s(M)} are known, the maximum a posteriori (MAP) and minimum mean-square error (MMSE) optimal trackers can be derived from a hidden Markov model (HMM) filter implementing the recursions (7) derived from Bayes’ rule (cf. (34) and (35) in the Appendix), where fk( ji) is the transition probability as in (3)
Summary
Target tracking research and development are of major importance and continuously expanding interest to a gamut of traditional and emerging applications, which include radar- and sonar-based systems, surveillance and habitat monitoring using distributed wireless sensors, collision avoidance modules envisioned for modern transportation systems, and mobile robot localization and navigation in static and dynamically changing environments, to name a few; see, e.g., [1,2] and references therein. Comes from a sensor and comprises the superposition of received signal strengths emitted by or reflected from all targets in the sensor field of view This model considers the localization and tracking problems jointly and avoids the measurement-target association issue. Notwithstanding, thanks to the grid-based model, the measurements in (2) have become linear functions of the unknown xk, whose nonzero entries reveal the grid points where target signal strengths are present at time k. S(M)} are known, the maximum a posteriori (MAP) and minimum mean-square error (MMSE) optimal trackers can be derived from a hidden Markov model (HMM) filter implementing the recursions (7) derived from Bayes’ rule (cf (34) and (35) in the Appendix), where fk( ji) is the transition probability as in (3) These HMM recursions hinge on prior knowledge of the target-grid association {Gk(m)}Mm=0, which needs to be figured out among a total of (M +1)G−MG! The TSSG-KF tracker implemented by (8) to (10) is sparsity-agnostic, as it does not explicitly utilize the prior knowledge that xk is sparse
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