In the Kalman filter (KF), the estimated state is a linear combination of the one-step prediction and measurement. The two combination weights depend on the prediction mean-square error matrix and the covariances matrix of measurement noise (CMMN), respectively. When the measurement noise values are small (large), the corresponding measurement is close to (far from) the real value, and the weight should be large (small). If there is non-Gaussian measurement noise, especially heavy-tailed noise, most of the noise values are small, and a few of them are large. The occasional impulses cause the overall noise variance to be much greater than the noise without impulses. Since the overall CMMN is adopted in the KF, its performance will deteriorate. In this article, we divide the measurement noise into two parts: 1) the background noise with small variance and 2) the impulse noise with large variance. Then, we use the expectation–maximization algorithm to dynamically calculate the parameters and propose a new KF algorithm to process them separately, which is called background-impulse KF (BIKF). It can dynamically determine whether there is an impulse and eliminate its impact as much as possible. Compared with the recent maximum correntropy criterion and minimum error entropy criterion-based KFs, simulations show that the proposed BIKF works better than them with lower computational complexity.

Dynamic area coverage is widely used in military and civil fields. Improving coverage efficiency is an important research direction for multi-agent dynamic area coverage. In this paper, we focus on the non-optimal coverage problem of free dynamic area coverage algorithms. We propose a distributed dynamic area coverage algorithm based on reinforcement learning and a γ-information map. The γ-information map can transform the continuous dynamic coverage process into a discrete γ point traversal process, while ensuring no-hole coverage. When agent communication covers the whole target area, agents can obtain the global optimal coverage strategy by learning the whole dynamic coverage process. In the event that communication does not cover the whole target area, agents can obtain a local optimal coverage strategy; in addition, agents can use the proposed algorithm to obtain a global optimal coverage path through off-line planning. Simulation results demonstrate that the required time for area coverage with the proposed algorithm is close to the optimal value, and the performance of the proposed algorithm is significantly better than the distributed anti-flocking Algorithms for dynamic area coverage.

Traditional interacting multiple model Kalman filter (IMM-KF) was derived for linear discrete time system with Markovian coefficients and it works well under Gaussian noise. In practice, when the system is affected by the impulsive noise, the performance of the traditional IMM-KF model becomes poor. Then, maximum correntropy Kalman filter (MCKF) which has advantages in dealing with non-Gaussian noise was proposed. However, the performance of traditional MCKF becomes poor when the motion state is not single. In this paper, we propose a new algorithm called interacting multiple model based on maximum correntropy Kalman filter (IMM-MCKF) by combining interacting multiple model (IMM) with MCKF to deal with the impulsive noise. Also, the traditional MCKF works poorly when the kernel bandwidth is small, we made a further improvement by changing the kernel. Simulation examples are given to demonstrate the effectiveness of the new algorithms.

Trajectory reconstruction (TR) plays an important role in practical applications. The data collected for TR are often contaminated with non-Gaussian noise due to environmental factors, which reduces the accuracy of TR. This study proposes a novel method to suppress the effects of non-Gaussian measurement noise. The method consists of two steps: decomposing the measurement noise and performing a weighted fusion of the relevant states. In the first step, the measurement noise is decomposed into a weighted combination of multiple Gaussian distributions using the Gaussian mixture model. In the second step, the interacting multiple model is employed to perform the weighted fusion of the relevant states. The main idea of the proposed method is to transform the state estimation problem from a non-Gaussian and nonlinear case into a state estimation problem in the nonlinear and Gaussian case. Based on this idea, a new unscented Kalman filter and an unscented Rauch–Tung–Striebel smoother framework are developed. The TR simulations and experiments are conducted for an underwater unmanned vehicle to verify the effectiveness and superiority of the proposed algorithms. The results demonstrate that the performance of the proposed algorithms is significantly better than that of the prominent existing algorithms, especially in the presence of non-Gaussian noise.