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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]

In this paper, a computationally efficient algorithm for Bayesian joint change point detection (CPD) in multiple time series is presented. The data generation model includes a number of change configurations (CC), each affecting a unique subset of the time series, which introduces correlation between the positions of change points (CPs) in the monitored time series. The inference objective is to identify joint changes and the associated CC. The algorithm consists of two stages: First, a univariate CPD algorithm is applied separately to each of the involved time series. The outcomes of this step are maximum a posteriori (MAP) detected CPs and posterior distributions of CPs conditioned on the MAP CPs. These outcomes are used in combination to approximate the posterior for the CCs. In the second algorithm stage, dynamic programming is used to find the maxima of this approximate CC posterior. The algorithm is applied to synthetic data, and it is shown to be both significantly faster and more accurate compared to a previously proposed algorithm designed to solve similar problems. Also, the initial algorithm is extended with steps from the maximization–maximization algorithm, which allows the hyperparameters of the data generation model to be estimated jointly with the CCs, and we show that these estimates coincide with estimates obtained from a Markov chain Monte Carlo algorithm. [ABSTRACT FROM AUTHOR]

Conventional direction-of-arrival (DOA) estimation methods are sensitive to outlier measurements. Therefore, their performance may degrade substantially in the presence of impulsive noise. In this paper, we address the problem of DOA estimation in additive outliers from the perspective of sparse Bayesian learning (SBL). A Bayes-optimal algorithm is devised for robust DOA estimation, which can achieve excellent performance in terms of resolution and accuracy. To reduce the computational complexity of the SBL scheme, a fast alternating algorithm is also developed. New grid-refining procedures are further introduced into these two proposed algorithms to efficiently fix the off-grid gap. As our solutions do not require the prior knowledge of the number of sources and can resolve highly correlated or coherent sources, it is expected that they have higher applicability. Simulation results verify the outlier-robust performance of the SBL approach. [ABSTRACT FROM AUTHOR]