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.

An improved real-time adaptive Kalman filter with recursive noise covariance updating rules

Abstract: Kalman filter (KF) is used extensively for state estimation. Among its requirements are the process and observation noise covariances which are unknown or partially known in real life applications. Biased initializations of the covariances result in performance degradation of KF or divergence. Therefore, an extensive research is carried on to improve its performance however, relying on a moving window, heavy computations, and the availability of the exact model are the fundamental problems in most of the proposed techniques. In this paper, we are using the idea of the recursive estimation of KF to propose two recursive updating rules for the process and observation covariances respectively designed based on the covariance matching principles. Each rule is a tuned scaled version of the previous covariance in addition to a tuned correction term derived based on the most recent available data. The proposed adaptive Kalman filter AKF avoided the aforementioned problems and proved itself to have an improved performance over the conventional KF. The results show that the AKF estimates are more accurate, have less noise and more stable against biased covariance initializations.

Unscented Kalman filter with nonlinear dynamic process modeling for GPS navigation

Abstract: This paper preliminarily investigates the application of unscented Kalman filter (UKF) approach with nonlinear dynamic process modeling for Global positioning system (GPS) navigation processing. Many estimation problems, including the GPS navigation, are actually nonlinear. Although it has been common that additional fictitious process noise can be added to the system model, however, the more suitable cure for non convergence caused by unmodeled states is to correct the model. For the nonlinear estimation problem, alternatives for the classical model-based extended Kalman filter (EKF) can be employed. The UKF is a nonlinear distribution approximation method, which uses a finite number of sigma points to propagate the probability of state distribution through the nonlinear dynamics of system. The UKF exhibits superior performance when compared with EKF since the series approximations in the EKF algorithm can lead to poor representations of the nonlinear functions and probability distributions of interest. GPS navigation processing using the proposed approach will be conducted to validate the effectiveness of the proposed strategy. The performance of the UKF with nonlinear dynamic process model will be assessed and compared to those of conventional EKF.

Applicable filtering framework for online multiclass freeway network estimation

Abstract: Real-time traffic flow estimation is important for online traffic control and management. The traffic state estimator optimally matches traffic measurements from detectors with traffic flow predictions from a dynamic traffic model under a certain control strategy. The current and widely used estimator is based on the Extended Kalman Filter algorithm (EKF). Basically, EKF is developed from the recursive Bayesian estimation technique for Gaussian random distribution of the state. This approximation may result in large errors in the estimation and even lead to divergence of the filter in highly non-linear dynamic system such as heterogeneous traffic flow operations. The aims of this paper are therefore twofold. On the one hand, we present a generalized stochastic macroscopic traffic model for multiclass freeway networks. The model is developed in the form that can be applied by filtering methods. On the other hand, we implement an accurate probabilistic framework to the real-time multiclass freeway network estimation. The framework uses a variation of Kalman Filter, namely Unscented Kalman Filter, and a different filter that is based on a sequential Monte Carlo method, namely Unscented Particle Filter. We investigate the performance of the proposed framework with respect to accuracy and computational effort using real-life data collected in a freeway network in England. We expect that the developed tool is useful for traffic operators and planners in controlling large-scale multiclass freeway networks.

State estimation under bit-rate constraints

Abstract: This paper considers the problem of estimating the state of a dynamic system from measurements obtained via a digital link with finite data rate R. The structures of the optimal coder and estimator for Markovian systems are derived. In particular, it is shown that the optimal coder for a Gauss-Markov system consists of a Kalman filter, followed by a stage which encodes the current Kalman estimate according to the symbols previously transmitted. A new suboptimal coder-estimator for linear systems is then constructed. Provided that a certain inequality linking the data rate to the dynamical parameters is satisfied, and under very mild assumptions on the noise distributions, this coder-estimator yields an expected absolute estimation error of the same order as in the classical situation with no data rate constraint. Hence if the classical estimation error approaches zero, then the rate-constrained error goes to zero at exactly the same speed.