The Recursive Form of Error Bounds for RFS State and Observation with Pd<1

TL;DR

This paper introduces a recursive performance bound for target state estimation using finite set statistics, accommodating detection probabilities less than one and target appearance/disappearance, applicable to both linear and nonlinear scenarios.

Contribution

It presents the first recursive bound for RFS-based target tracking that handles detection probability less than one and dynamic target existence, extending previous bounds.

Findings

The bound aligns with existing results when detection probability is one.

The bound is more general, applicable to both linear and nonlinear models.

Validation through applications confirms the theoretical advantages.

Abstract

In the target tracking and its engineering applications, recursive state estimation of the target is of fundamental importance. This paper presents a recursive performance bound for dynamic estimation and filtering problem, in the framework of the finite set statistics for the first time. The number of tracking algorithms with set-valued observations and state of targets is increased sharply recently. Nevertheless, the bound for these algorithms has not been fully discussed. Treating the measurement as set, this bound can be applied when the probability of detection is less than unity. Moreover, the state is treated as set, which is singleton or empty with certain probability and accounts for the appearance and the disappearance of the targets. When the existence of the target state is certain, our bound is as same as the most accurate results of the bound with probability of detection is less than unity in the framework of random vector statistics. When the uncertainty is taken into account, both linear and non-linear applications are presented to confirm the theory and reveal this bound is more general than previous bounds in the framework of random vector statistics.In fact, the collection of such measurements could be treated as a random finite set (RFS).