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This note presents new results on the design of the process noise covariance matrix in Kalman filtering. The proposed design belongs to the realm of worst case methods: the optimal covariance is sought such as to maximize an upper bound on the estimation error matrix under a total budget constraint. Optimality conditions are derived along with a numerical algorithm for iterative approximation of the optimal solution. The optimal solution features a few time points and the associated covariances. Broadly speaking, the process noise is only “active” at the time points that enhance its controllability. The importance of the method is that it bounds from above the performance of any Kalman filter with a different design. Monte Carlo simulations on a double harmonic system numerical example illustrate the good convergence, performance, and low sensitivity to initial guesses of the proposed method. Moreover, in terms of estimation accuracy, the Kalman filter with the optimal design outperforms a robust $H_2$ filter designed to cope with an equivalent uncertainty. [ABSTRACT FROM AUTHOR]

In this paper, we present the globally optimal distributed Kalman filtering fusion with singular covariances of filtering errors and measurement noises. The following facts motivate us to consider the problem. First, the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms. However, it can not be guaranteed to exist in practice. For example, when state estimation for a given dynamic system is subject to state equality constraints, the estimation error covariance matrices must be singular. Second, the proposed fused state estimate is still exactly the same as the centralized Kalman filtering using all sensor raw measurements. [ABSTRACT FROM AUTHOR]

This technical note studies some of the challenging issues on moving horizon state estimation for networked control systems in the presence of multiple packet dropouts in both sensor-to-controller and controller-to-actuator channels, which both situations are modeled by two mutually independent stochastic variables satisfying the Bernoulli binary distribution. Compared with standard Kalman filter, this study proposes a novel moving horizon estimator to deal with the uncertainties induced from the multiple packet dropouts, which has a larger degree of freedom to obtain better behavior by tuning the weight parameters. A sufficient condition for the convergence of the norm of the average estimation error is also presented to guarantee the performance of the estimator. Finally, a real-time simulation experiment is presented to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]