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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]

Standard Kalman filter adopts constant covariance of measurement noise. When statistical characteristics of measurement noise changes, estimation error increases, which results in filtering divergence. An adaptive federated Kalman filter was proposed with fuzzy adaptive Kalman filter but not Kalman filter in the subsystem of federated Kalman filter, and the weighted coefficient of covariance matrix was adjusted by fuzzy inference algorithm real-timely. It made the measurement noise of the dynamic equation close to the truth level. When it is applied to multi-sensor attitude determination systems, simulation results demonstrate the true effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Optimal filters for nonlinear systems are in general difficult to derive or implement. The common approach is to use approximate solutions such as extended Kalman filters, ensemble filters or particle filters. However, no optimality properties can be guaranteed by these approximations, and even the stability of the estimation error cannot often be ensured. Another relevant issue is that, in most practical situations, the system whose variables have to be estimated is not known, and a two-step procedure is adopted, based on model identification from data and filter design from the identified model. However, the designed filter may display large performance deteriorations in the case of modeling errors. In this paper, a new approach overcoming these issues is proposed, allowing the design of optimal filters for nonlinear systems in both the cases of known and unknown system. The approach is based on the direct filter design from a set of data generated by the system. Either experimental or simulated data can be used for design. A bound on the number of data necessary to ensure a given filter accuracy is also provided, showing that the proposed approach is not affected by the curse of dimensionality. [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]