RESUMEN
Handling the challenge of missing measurements in nonlinear systems is a difficult problem in various scientific and engineering fields. Missing measurements, which can arise from technical faults during observation, diffusion channel shrinking, or the loss of specific metrics, can bring many challenges when estimating the state of nonlinear systems. To tackle this issue, this paper proposes a technique that utilizes a robust cubature Kalman filter (RCKF) by integrating Huber's M-estimation theory with the standard conventional cubature Kalman filter (CKF). Although a CKF is often used for solving nonlinear filtering problems, its effectiveness might be limited due to a lack of knowledge regarding the nonlinear model of the state and noise-related statistical information. In contrast, the RCKF demonstrates an ability to mitigate performance degradation and discretization issues related to track curves by leveraging covariance matrix predictions for state estimation and output control amidst dynamic disruption errors-even when noise statistics deviate from prior assumptions. The performance of extended Kalman filters (EKFs), unscented Kalman filters (UKFs), CKFs, and RCKFs was compared and evaluated using two numerical examples involving the Univariate Non-stationary Growth Model (UNGM) and bearing-only tracking (BOT). The numerical experiments demonstrated that the RCKF outperformed the EKF, EnKF, and CKF in effectively handling anomaly errors. Specifically, in the UNGM example, the RCKF achieved a significantly lower ARMSE (4.83) and ANCI (3.27)-similar outcomes were observed in the BOT example.
RESUMEN
This paper considers the binary Gaussian distribution robust hypothesis testing under aBayesian optimal criterion in the wireless sensor network (WSN). The distribution covariance matrixunder each hypothesis is known, while the distribution mean vector under each hypothesis driftsin an ellipsoidal uncertainty set. Because of the limited bandwidth and energy, we aim at seeking asubset of p out of m sensors such that the best detection performance is achieved. In this setup, theminimax robust sensor selection problem is proposed to deal with the uncertainties of distributionmeans. Following a popular method, minimizing the maximum overall error probability with respectto the selection matrix can be approximated by maximizing the minimum Chernoff distance betweenthe distributions of the selected measurements under null hypothesis and alternative hypothesis tobe detected. Then, we utilize Danskin's theorem to compute the gradient of the objective functionof the converted maximization problem, and apply the orthogonal constraint-preserving gradientalgorithm (OCPGA) to solve the relaxed maximization problem without 0/1 constraints. It is shownthat the OCPGA can obtain a stationary point of the relaxed problem. Meanwhile, we provide thecomputational complexity of the OCPGA, which is much lower than that of the existing greedyalgorithm. Finally, numerical simulations illustrate that, after the same projection and refinementphases, the OCPGA-based method can obtain better solutions than the greedy algorithm-basedmethod but with up to 48.72% shorter runtimes. Particularly, for small-scale problems, the OCPGA-based method is able to attain the globally optimal solution.
RESUMEN
This paper proposes a new distributed Kalman filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices.