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.

Power system harmonic analysis using the Kalman filter

Abstract: This paper explores the practical application of the Kalman filter to the analysis of harmonic levels in power systems. The merits and limitations of different possible implementations are investigated and the effect of fundamental frequency variation is examined. The tuning of the Kalman filter for desired dynamic response is discussed and an adaptive tuning algorithm derived for the improved convergence of nonlinear models. The effectiveness of the resulting schemes are tested under a variety of typical power system operating conditions.

UDU/T/ covariance factorization for Kalman filtering

Abstract: There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

Extended Kalman filter under maximum correntropy criterion

Abstract: As a nonlinear extension of Kalman filter, the extended Kalman filter (EKF) is also based on the minimum mean square error (MMSE) criterion. In general, the EKF performs well in Gaussian noises. But its performance may deteriorate substantially when the system is disturbed by heavy-tailed impulsive noises. In order to improve the robustness of EKF against impulsive noises, a new filter for nonlinear systems is proposed in this paper, namely the maximum correntropy extended Kalman filter (MCEKF), which adopts the maximum correntropy criterion (MCC) as the optimization criterion instead of using the MMSE. In MCEKF, the state mean and covariance matrix propagation equation are used to obtain a prior estimation of the state and covariance matrix, and then a fixed-point algorithm is used to update the posterior estimates. The robustness of the new filter is confirmed by simulation results.

Particle degeneracy: root cause and solution

Abstract: We have solved the well known and important problem of particle degeneracy for particle filters. Our filter is roughly seven orders of magnitude faster than standard particle filters for the same estimation accuracy. The new filter is four orders of magnitude faster per particle, and it requires roughly three orders of magnitude fewer particles to achieve the same accuracy as a standard particle filter. Typically we beat the EKF or UKF accuracy by approximately two orders of magnitude for difficult nonlinear problems.

Characterization of Kalman filter residuals in the presence of mismodeling

Abstract: The mean and covariance of a Kalman filter residual are computed for specific cases in which the Kalman filter model differs from a linear model that accurately represents the true system (the truth model) Multiple model adaptive estimation (MMAE) uses a bank of Kalman filters, each with a different internal model, and a hypothesis testing algorithm that uses the residuals from this bank of Kalman filters to estimate the true system model At most, only one Kalman filter model will exactly match the truth model and will produce a residual whose mean and standard deviation have already been analyzed All of the other filters use internal models that mismodel the true system We compute the effects of a mismodeled input matrix, output matrix, and state transition matrix on these residuals The computed mean and covariance are compared with simulation results of flight control failures that correspond to mismodeled input matrices and output matrices