Abstract
The error bound is a typical measure of the limiting performance of all filters for the given sensor measurement setting. This is of practical importance in guiding the design and management of sensors to improve target tracking performance. Within the random finite set (RFS) framework, an error bound for joint detection and estimation (JDE) of multiple targets using a single sensor with clutter and missed detection is developed by using multi-Bernoulli or Poisson approximation to multi-target Bayes recursion. Here, JDE refers to jointly estimating the number and states of targets from a sequence of sensor measurements. In order to obtain the results of this paper, all detectors and estimators are restricted to maximum a posteriori (MAP) detectors and unbiased estimators, and the second-order optimal sub-pattern assignment (OSPA) distance is used to measure the error metric between the true and estimated state sets. The simulation results show that clutter density and detection probability have significant impact on the error bound, and the effectiveness of the proposed bound is verified by indicating the performance limitations of the single-sensor probability hypothesis density (PHD) and cardinalized PHD (CPHD) filters for various clutter densities and detection probabilities.
Highlights
The problem of joint detection and estimation (JDE) of multiple targets arises from many applications in surveillance and defense [1], where the number of targets is unknown and the sensor may receive measurements generated randomly from either targets or clutters
This paper proposes an random finite set (RFS)-based single-sensor multi-target JDE error bound when clutter and missed detection may simultaneously exist in the sensor
The simulation results show that clutter density and detection probability have significant impacts on the proposed bound, and the effectiveness of the proposed bound is verified by indicating the performance limitations of the single-sensor probability hypothesis density (PHD) [4] and cardinalized PHD (CPHD) [5] filters for various clutter densities and detection probabilities
Summary
The problem of joint detection and estimation (JDE) of multiple targets arises from many applications in surveillance and defense [1], where the number of targets is unknown and the sensor may receive measurements generated randomly from either targets or clutters. The CRLB was extended to the cases in which clutter or missed detection was present in the sensor [12,13,14,15] These CRLBs [12,13,14,15] could barely be applied to such a JDE problem, since CRLB only considers the estimation error of a target state, but not the detection error of the target number Tong et al presented a recursive form of a single-sensor single-target error bound based on CRLB when only missed detection, but not clutter, exists [17] and extended the result of [17] to the single-sensor multi-target case with the more rigorous restriction that neither clutter nor missed detection exists [18]. This paper proposes an RFS-based single-sensor multi-target JDE error bound when clutter and missed detection may simultaneously exist in the sensor. Relevant mathematical proofs are provided in Appendices A and B
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