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This paper proposes a general framework solution of Gaussian filter (GF) for both linear and nonlinear dynamic systems with correlated noises at the same epoch. Detailed discussions and simulation comparisons with existing Gaussian approximation recursive filter and existing de-correlating GF are provided, which show advantages of estimation accuracy of the proposed method in some applications. [ABSTRACT FROM AUTHOR]

This paper addresses the state estimation problem for dynamic systems subject to uncertain constraints, i.e., all possible constraints are described by a finite set, and only one constraint is satisfied at each moment. For this typical hybrid system estimation problem with coupled discrete constraint modes and continuous states, we design a mode separability-based state estimation (MSSE) framework. Based on the measurement model over a window, the hypothesis testing is performed to detect whether the mode changes firstly. Then the maximum-likelihood criterion is used to estimate the mode change sequence once detecting the change. Next, to consider the possible impact of the decided modes on the state estimation, a metric of mode separability is proposed to evaluate the separability of the recognized modes, and two different state estimation methods are introduced. Specifically, if the recognized modes are separable from the others, the state estimates are obtained by a recursive mode-based constraint Kalman filter (MCKF) which is proved that the estimation error is bounded in mean square. Otherwise, the estimation results output the fused state estimates (FSE) of the inseparable modes. Finally, simulation results of road-constrained vehicle tracking are provided to demonstrate the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]