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The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multitarget tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a Second-Order PHD (SO-PHD) filter, propagating the second-order moment (i.e., variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modeling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. This paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multiobject filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters. [ABSTRACT FROM PUBLISHER]

This paper is devoted to the terrain aided navigation (TAN) systems based on the state estimation algorithms. In particular, the emphasis is laid on the design of the Bayesian Rao–Blackwellized point-mass filter for nonlinear state-space models of a specific structure typically used in the terrain aided navigation. The proposed filter preserves advantages of the point-mass filter, including the high estimation accuracy, robust initialization, deterministic nature of the algorithm, and predictable computational complexity, while the computational complexity is significantly reduced. The performance of the Rao–Blackwellized point-mass filter is illustrated using a simulated numerical example and a TAN system based on the real data. [ABSTRACT FROM AUTHOR]