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Summary: In this paper, we propose a new framework of particle filtering that adopts the minimax strategy. In the approach, we minimize a maximized risk, and the process of the risk maximization is reflected when computing the weights of particles. This scheme results in the significantly reduced variance of the weights of particles that enables the robustness against the degeneracy problem, and we can obtain improved quality of particles. The proposed approach is robust against environmentally adverse scenarios, particularly when the state of a target is highly maneuvering. Furthermore, we can reduce the computational complexity by avoiding the computation of a complex joint probability density function. We investigate the new method by comparing its performance to that of standard particle filtering and verify its effectiveness through experiments. The employed strategy can be adopted for any other variants of particle filtering to enhance tracking performance. [ABSTRACT FROM AUTHOR]

While inter-symbol interference is not of concern, inter-carrier interference that is caused by carrier frequency offset (CFO) is more concerned in orthogonal frequency division multiplexing (OFDM) systems. The estimation of channel impulse response (CIR) is another important parameter of interest in the system. Recently, a number of approaches for the joint estimation of CFO and CIR in OFDM systems have been proposed in the literature, and most of them are traditional maximum-likelihood-based approaches. In this paper, we propose a number of mixture cost-reference particle filtering (CRPF) approaches for joint estimation of CIR and CFO, and a couple of them can be applied without the knowledge of both state and measurement noise statistics. Conventional least mean squares algorithm or recursive least squares algorithm is jointly employed with recently developed CRPF for nonlinear and multiple parameters estimation in OFDM systems. The computer simulation results show that mixture CRPFs are more robust against particle impoverishment (PI) problem than standard mixture particle filtering (PF) and mixture regularized PF (RPF) approaches although RPF was particularly developed to tackle the PI problem. In this paper, we investigate a number of mixture PF approaches including ones that do not need the information of noise statistics for the joint estimation of CFO and channel in OFDM systems. [ABSTRACT FROM PUBLISHER]

We provide a tutorial for a number of variants of the extended Kalman filter (EKF). In these methods, so called, sigma points are employed to tackle the nonlinearity of problems. The sigma points exactly represent the mean and the variance of the state distribution function in a dynamic state equation. The initially developed EKF variant, that is, unscented Kalman filter (UKF) (also called sigma point Kalman filter) shows enhanced performance compared with that of conventional EKF in the literature. Another variant, which is not well known, is central difference Kalman filter (CDKF) whose way to approximate the nonlinearity is based on the Sterling's polynomial interpolation formula instead of the Taylor series. Endeavor to reduce the computational load resulted in the development of square root versions of both UKF and CDKF, that is, square root unscented Kalman filter and square root central difference Kalman filter (SR-CDKF). These SR-versions are supposed to be numerically more stable than their original versions because the state covariance is guaranteed to be positive definite by avoiding the step of matrix decomposition. In this paper, we provide the step-by-step algorithms of above-mentioned EKF variants with their pros and cons. We apply these filtering methods to a number of problems in various disciplines for performance assessment in terms of both mean squared error (MSE) and processing speed. Furthermore, we show how to optimize the filters in terms of MSE performance depending on diverse scenarios. According to simulation results, CDKF and SR-CDKF show the best MSE performance in most scenarios; particularly, SR-CDKF shows faster processing speed than that of CDKF. Therefore, we justify that SR-CDKF is the most efficient and the best approach among the Kalman variants including the EKF for various nonlinear problems. The motivation of this paper targets at the contribution to the disseminative usage of the Kalman variants approaches, particularly, SR-CDKF taking advantage of its estimating performance and high processing speed. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]