Topic
Invariant extended Kalman filter
About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.
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TL;DR: This brief addresses the stochastic stability problem of the extended Kalman filter by means of analyzing the prediction error covariance matrix (PECM) and the estimation error performance of the estimator.
Abstract: In order to tackle the intermittent observations, this brief addresses the stochastic stability problem of the extended Kalman filter by means of analyzing the prediction error covariance matrix (PECM) and the estimation error performance of the estimator. With the transmitted measurement output of the filter modeled as a Bernoulli process, the existence of a crucial arrival rate is proved such that the PECM is mean bounded when the arrival rate exceeds a threshold value. Moreover, offline sufficient conditions for the stochastic stability of the estimation error are also derived. A numerical example is given to demonstrate the feasibility of the proposed method.
48 citations
TL;DR: A new systematic and efficient way to approximate a non-Gaussian and measurement-dependent function by a weighted sum of Gaussian density functions is developed and a way to alleviate the growing memory problem inherited in the Gaussian sum filter is suggested.
48 citations
TL;DR: A closed-form state estimator for some polynomial nonlinear systems is derived by exploiting full Taylor series expansion to compute mean and covariance of any random variable distribution that has been transformed through aPolynomial function.
Abstract: A closed-form state estimator for some polynomial nonlinear systems is derived in this paper. Exploiting full Taylor series expansion we first give exact matrix expressions to compute mean and covariance of any random variable distribution that has been transformed through a polynomial function. An original discrete-time Kalman filtering implementation relying on this exact polynomial transformation is proposed. The important problem of chaotic synchronization of Chebyshev maps is then considered to illustrate the significance of these results. Mean square error between synchronized signals and consistency criteria are chosen as performance measures under various signal-to-noise ratios. Comparisons to the popular extended Kalman filter and to the recent unscented Kalman filter are also conducted to show the pertinence of our filtering formulation
48 citations
11 Dec 1991
TL;DR: In this article, the optimal solution of a two-stage estimation problem in the presence of random bias is provided, under an algebraic constraint, where the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage (a bias-free filter) and the second stage(a bias filter).
Abstract: The authors provide the optimal solution of a two-stage estimation problem in the presence of random bias. Under an algebraic constraint, the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage (a bias-free filter) and the second stage (a bias filter). The results presented provide a basis for assessing the suboptimality of a two-stage estimator when used for a specific system. By treating the bias vector as a target acceleration, the two-state Kalman estimator can be used for tracking maneuvering targets. >
48 citations
TL;DR: The lag shifted whiteness test (LSWT) as mentioned in this paper extends the use of the Kalman filter as a damage detector to situations where variability in the loading makes a standard Whiteness test ineffective.
48 citations