In this paper, a new Gaussian sum (GS) filter with shifted Rayleigh filter (SRF) as proposal has been developed for the bearings-only tracking (BOT) problem. The proposed filter estimates the prior and posterior probability density functions as weighted sum of several Gaussian densities, where the individual Gaussian densities are generated from the SRF. Performance of the proposed filter on the BOT problem is compared with the SRF, the GS sparse-grid Gauss–Hermite filter, and other available GS and quadrature-based filters. Performance of filters is compared in terms of a root-mean-square error (RMSE), track divergence, and computational time. The effect of initial uncertainty, measurement noise covariance, and sampling time on filtering accuracy are also studied. Finally, RMSEs of all the filters are evaluated in comparison with the Cramer–Rao lower bound. From simulation results, it is observed that the performance of the proposed GS-SRF is superior to all other nonlinear filters considered.

In this paper, a new method termed as new sigma point Kalman filter (NSKF), is proposed for generating sigma points and weights for estimating the states of a stochastic nonlinear dynamic system. The sigma points and their corresponding weights are generated such that the points nearer to the mean (in inner product sense) have a higher probability of occurrence, and the mean vector and covariance matrix are matched exactly. Performance of the new algorithm is compared with the existing unscented Kalman filter (UKF), the cubature Kalman filter (CKF), the cubature quadrature Kalman filter (CQKF) and higher order unscented filter (HOUF) for two different problems. Comparison is done by calculating the root mean square error (RMSE), relative computational time and track-loss. From simulation results, it can be concluded that the proposed algorithm performs with superior estimation accuracy when compared to the UKF, CKF, CQKF and HOUF.

Very often, a measurement is transmitted through network systems before it is available for filtering. The network systems, designed with several communication channels, are prone to cyber-attacks. The cyber-attack often injects false data to alter the original measurement. This article develops a modified Bayesian approximation filtering method for nonlinear filtering with measurements altered due to cyber-attack. The proposed development is within the scope of nonlinear Gaussian filtering. It considers the false data to have either additive or multiplicative effect over the original measurement. Subsequently, two modified measurement models are introduced to model the possibility of false data stochastically. Then, the traditional nonlinear Gaussian filtering method is redesigned for the modified measurement models to deal with the false data attack. The proposed modification is applicable to any of the existing nonlinear Gaussian filters, such as extended Kalman filter, unscented Kalman filter, cubature Kalman filter, and Gauss–Hermite filter. The simulation results show an enhanced estimation accuracy for the proposed modification over the traditional nonlinear Gaussian filtering in the presence of false data.

In this paper, angles-only target tracking (AoT) problem is investigated in the non Gaussian environment. Since the conventional minimum mean square error criterion based estimators tend to give poor accuracy in the presence of large outliers or impulsive noises in measurement, a maximum correntropy criterion (MCC) based framework is presented. Accordingly, three new estimation algorithms are developed for AoT problems based on the conventional sigma point filters, termed as MC-UKF-CK, MC-NSKF-GK and MC-NSKF-CK. Here MC-NSKF-GK represents the maximum correntropy new sigma point Kalman filter realized using Gaussian kernel and MC-NSKF-CK represents realization using Cauchy kernel. Similarly, based on the unscented Kalman filter, MC-UKF-CK has been developed. The performance of all these estimators is evaluated in terms of root-mean-square error (RMSE) in position and % track loss. The simulations were carried out for 2D as well as 3D AoT scenarios and it was inferred that, the developed algorithms performed with improved estimation accuracy than the conventional ones, in the presence of non Gaussian measurement noise.