Joint detection and estimation error bounds for an unresolved target-group using single or multiple sensors

According to random finite set (RFS) and information inequality, the paper derives the joint detection and estimation (JDE) error bounds of an unresolved target-group using single and multiple sensors in the presence of missed detection and clutter.Relevant mathematical proofs of these conclusions are presented in the appendices.Examples 1 and 2 show variation of the bounds with probability of detection and clutter density. Example 3 verifies the effectiveness of the bounds by indicating the performance limitations of a UCPHD filter.The error bounds provide important indications of the performance limitations for existing unresolved target-group JDE approaches. Joint detection and estimation (JDE) of a target refers to determining the existence of the target and estimating the state of the target, if the target exists. This paper studies the error bounds for JDE of an unresolved target-group in the presence of clutter and missed detection using the random finite set (RFS) framework. We define a meaningful distance error for JDE of the unresolved target-group by modeling the state as a Bernoulli RFS. We derive the single and multiple sensor bounds on the distance error for an unresolved target-group observation model, which is based on the concept of the continuous individual target number. Maximum a posterior (MAP) detection criteria and unbiased estimation criteria are used in deriving the bounds. Examples 1 and 2 show the variation of the bounds with the probability of detection and clutter density for single and multiple sensors. Example 3 verifies the effectiveness of the bounds by indicating the performance limitations of an unresolved target-group cardinalized probability hypothesis density (UCPHD) filter.

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