Posterior Cramér-Rao bounds for target tracking
In this chapter, we present a review of recent developments in the calculation of estimation error performance bounds for target tracking. We concentrate on the posterior Cramér-Rao bound (PCRB), which is computationally the simplest of a general class of lower bounds. We present full details of an efficient recursive formula for the PCRB for the general non-linear filtering problem, and of PCRB methodologies in cluttered environments (i.e. in which there can be missed detections and spurious false measurements). In such environments, the measurement origin uncertainty is shown to manifest itself as an information reduction factor that degrades tracking performance according to the severity of the clutter. A tutorial of the key PCRB methodologies in cluttered environments is provided, and via simulations, PCRBs are calculated for a scenario in which a single target is tracked using measurements generated by a stationary radar. The PCRBs are compared to the performance of an extended Kalman filter, and the results demonstrate the efficacy of the PCRB as an efficient theoretical predictor of the capability of the tracker. We also present a discussion of applications that would benefit greatly from the development of a PCRB methodology. These applications include sensor scheduling in passive coherent location networks; and performance assessment of algorithms designed for image fusion, data assimilation for meteorology/oceanography, simultaneous localization and mapping and quantum estimation.
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