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.

Estimation precision comparison of Cubature Kalman filter and Unscented Kalman filter

Abstract: In order to select the appropriate filtering method from the UKF and CKF for the different dimensions nonlinear systems estimation,the two filters are analyzed and compared through the Taylor expansion of function and the numerical stability.Due to the different dimension,the captured high-order item degree of function Taylor expansion and the numerical stability are different to appear different filter precisions,so that the filter choice ways of different dimension are acquired.Simulation results show the correctness of with the theoretical analysis.

Online natural gradient as a Kalman filter

Abstract: We cast Amari’s natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural gradient descent on the log-likelihood of the observations. In the i.i.d. case, this relation is a consequence of the “information filter” phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant interpretations for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.

An algorithm based on two-step Kalman filter for intelligent structural damage detection

Abstract: Summary In the traditional extended Kalman filter approach, unknown structural parameters are included in the extended state vector. Then, the sizes of the extended state vector and the corresponding state equation are quite large, and the state equation is highly nonlinear with respect to the extended state vector. This may cause identification divergent for a large number of unknown parameters. Also, such strategy requires large computational effort and storage capacities, which is not appropriate for intelligent structural damage detection implemented by smart sensors with microprocessors. In this paper, an algorithm based on a two-step Kalman filter approach is proposed to remove the aforementioned drawbacks of the traditional extended Kalman filter. In the first step, recursive estimation of structural state vector is derived by Kalman filter with assumed structural parameters. In the second step, structural parameters and the updated structural state vector are estimated by the Kalman filter and the recursive estimation in the first step. Thus, the number of estimated variables in each step is reduced, which reduces the computational effort and storage requirements. This superiority is important for intelligent structural damage detection implemented by smart sensor in wireless sensor network. The proposed algorithm is first validated by numerical simulations results of structural damage detection of the phase-I 3-D ASCE benchmark building for structural health monitoring, a 30-story shear building with minor damage, and an experimental test of damage detection of a lab multistory frame model. Then, it is applied to structural damage detection of a lab multistory model-employed smart sensors embedded with the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

Generalised Kalman filter tracking with multiplicative measurement noise in a wireless sensor network

Abstract: A new generalised Kalman filtering algorithm using a multiplicative measurement noise model is developed for tracking moving targets in a wireless sensor network. This multiplicative error model facilitates more accurate characterisation of the distance dependence measurement errors of range-estimating sensors. Two new formulations of extended Kalman filter (EKF) and unscented Kalman filter (UKF), called generalised EKF (GEKF) and generalised UKF (GUKF) are derived. Comparing with conventional EKF and UKF formulations, it is shown that GEKF and GUKF can achieve smaller tracking error than traditional EKF and UKF. Simulation results are also reported that demonstrated the superior performance of GEKF and GUKF over existing methods.