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This article considers the filtering problem with nonlinear measurements. We propose a new enabling variational inference model for approximating measurement likelihood, which is constructed by a linear Gaussian regression process. The resulting filter is referred to as the new enabling variational inference filter (NEVIF). In variational inference framework, the NEVIF obtains the variational posterior of state by minimizing the Kullback–Leibler divergence between the variational distribution and the true posterior. Then, the accuracy improvement and robustness of the NEVIF compared with the traditional methods are analyzed. Furthermore, an evaluation rule called the filtering evidence lower bound is developed to analyze the estimation accuracy performance of filters. Finally, the efficiency and superiority of the proposed filters compared with some existing filters are shown in numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with application of expectation maximization (EM) algorithm for deriving an adaptive version of divided difference filter for joint state estimation and multiplicative parameter identification of nonlinear system with the colored measurement noise. Owing to the fact that there exist a mutual coupling and interaction of state and parameter on each other, it requires a joint or simultaneous estimation of both state and parameter by a mutual iteration, and justly, EM iterates Expectation (E-)step and Maximization (M-)step to meet such requirement. Firstly, E-step involves state filtering and smoothing issues under knowing the previous parameter identification results, which is well solved by resorting to the Gaussian approximation with a trade-off between accuracy and complexity. Further, such Gaussian approximation estimators are applied for evaluating the condition expectation of complete-data likelihood function, nonlinearly characterized by the multiplicative parameter needed to be optimized. Secondly, M-step deals with the maximization of the condition expectation by directly making its derivative as zero to obtain the current general parameter identification equation as the nonlinear integral. Thirdly, by iteratively operating E-step and M-step, an adaptive divided difference filter is proposed for joint state estimation and parameter identification by using the second-order Stirling interpolation to compute the associated nonlinear integral. Finally, the robust performance of the EM-based adaptive version of divided difference filter to the unknown or time-varying multiplicative parameter, as compared with the standard augmentation method, is demonstrated by a maneuvering target tracking example. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The highly accurate state estimation of nonlinear systems is needed in many different application fields. In many existing nonlinear filters, the uncompensated nonlinear approximation error and widely used numerical sampling methods both seriously affect the estimation accuracy and numerical stability. In this paper, based on the variational Bayesian framework, a novel iterative nonlinear filter consisting of forward modeling and inverse estimation is proposed. In the forward modeling stage, a linear Gaussian regression process with distributed variational parameters (VPs) is designed to fit the whole nonlinear measurement likelihood. The distributed VPs consider both first and second moments information, so as to compensate for approximation error from the whole likelihood perspective, instead of only the nonlinear function approximation, which can further improve the accuracy of Bayesian posterior update. In the linear Gaussian regression process, the original nonlinear measurement function (NMF) is just viewed as a prior and no longer directly participates in the modeling of the measurement likelihood. Hence, in the inverse estimation stage, when maximizing the evidence lower bound to update the posteriors of the state and VPs, we can obtain closed‐form solutions without numerical sampling methods to approximate the integral of NMF required in many existing methods, which can guarantee numerical stability. Moreover, to avoid the random setting of hyperparameters and to block the propagation of the accumulated error, we propose two rules, estimation and lower bound consistencies, to conduct the hyperparameters' initialization at the beginning of iteration at each sampling time and also derive an optimization method to update hyperparameters during iteration. Finally, the performance of our proposed method is demonstrated in the nonlinear orbital estimation problems. [ABSTRACT FROM AUTHOR]

Summary: This article is concentrated on the particle filtering problem for nonlinear systems with nonlinear equality constraints. Considering the constraint information incorporated into filters can improve the state estimation accuracy, we propose an adaptive constrained particle filter via constrained sampling. First, in order to obtain particles drawn from the constrained important density function, we construct and solve a general optimization function theoretically fusing equality constraints and the importance density function. Furthermore, to reduce the computation time caused by the number of particles, the constrained Kullback‐Leiler distance sampling method is given to online adapt the number of particles needed for state estimation. A simulation study in the context of road‐confined vehicle tracking demonstrates that the proposed filter outperforms the typical constrained ones for equality constrained dynamic systems. [ABSTRACT FROM AUTHOR]