Aiming at the problem of multiple-source direction of arrival (DOA) tracking in impulse noise, this paper models the impulse noise by using the symmetric α stable (SαS) distribution, and proposes a DOA tracking algorithm based on the Unscented Transform Multi-target Multi-Bernoulli (UT-MeMBer) filter framework. In order to overcome the problem of particle decay in particle filtering, UT is adopted to select a group of sigma points with different weights to make them close to the posterior probability density of the state. Since the α stable distribution does not have finite covariance, the Fractional Lower Order Moment (FLOM) matrix of the received array data is employed to replace the covariance matrix to formulate a MUSIC spatial spectra in the MeMBer filter. Further exponential weighting is used to enhance the weight of particles at high likelihood area and obtain a better resampling. Compared with the PASTD algorithm and the MeMBer DOA filter algorithm, the simulation results show that the proposed algorithm can more effectively solve the issue that the DOA and number of target are time-varying. In addition, we present the Sequential Monte Carlo (SMC) implementation of the UT-MeMBer algorithm.

To address the challenge of simultaneous localization and mapping (SLAM) in the presence of heavy-tailed noise, this papper introduces a robust probability hypothesis density (PHD) SLAM algorithm. This algorithm models measurement noise using the Student's t-distribution, which better captures the heavy-tailed nature of the noise. Since the prior density is assumed to be Gaussian mixture form, the posterior density is no longer Gaussian mixture form after the likelihood update of the t-distribution. A variational Bayesian approach is employed to ensure computable multi-target densities during filtering, minimizing the Kullback-Leibler divergence to obtain an approximate solution for the new marginal likelihood function. Then a new closed-form recursion of PHD-SLAM is derived by using t-distribution. Simulation results and real-world validations demonstrate that the proposed algorithm outperforms PHD-SLAM 1.0 and PHD-SLAM 2.0 in terms of both localization and mapping accuracy while maintaining computational efficiency in SLAM scenarios affected by heavy-tailed noise.