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: These algorithms were validated by testing them on a well-known target tracking computer experiment and resulting in two new estimation strategies, called the EK-SVSF and the UK- SVSF, respectively.
Abstract: The extended Kalman filter (EKF) and the unscented Kalman filter (UKF) are among the most popular estimation methods. The smooth variable structure filter (SVSF) is a relatively new sliding mode estimator. In an effort to use the accuracy of the EKF and the UKF and the robustness of the SVSF, the filters have been combined, resulting in two new estimation strategies, called the EK-SVSF and the UK-SVSF, respectively. The algorithms were validated by testing them on a well-known target tracking computer experiment.
87 citations
01 Jun 1997
TL;DR: A modular and flexible approach to adaptive Kalman filtering using the framework of a mixture-of-experts regulated by a gating network, which compares very favorably with the classical Magill filter bank, in terms of: estimation accuracy; quicker response to changing environments; and numerical stability and computational demands.
Abstract: This paper proposes a modular and flexible approach to adaptive Kalman filtering using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters such as process and measurement noise. The gating network performs on-line adaptation of the weights given to individual filter estimates based on performance. This scheme compares very favorably with the classical Magill filter bank, which is based on a Bayesian technique, in terms of: estimation accuracy; quicker response to changing environments; and numerical stability and computational demands. The proposed filter bank is further enhanced by periodically using a search algorithm in a feedback loop. Two search algorithms are considered. The first algorithm uses a recursive quadratic programming approach which extremizes a modified maximum likelihood function to update the parameters of the best performing filter in the bank. This particular approach to parameter adaptation allows a real-time implementation. The second algorithm uses a genetic algorithm to search for the parameter vector and is suited for post-processed data type applications. The workings and power of the overall filter bank and the suggested adaptation schemes are illustrated by a number of examples.
86 citations
23 Apr 2012
TL;DR: In this paper, the authors proposed the use of the Unscented Kalman Filter (UKF) as the integration algorithm for the inertial measurements, which improves the mean and covariance propagation needed for the Kalman filter.
Abstract: The Extended Kalman Filter (EKF) has been the state of the art in Pedestrian Dead-Reckoning for foot-mounted Inertial Measurements Units. However due to the non-linearity in the propagation of the orientation the EKF is not the optimal Bayesian filter. We propose the usage of the Unscented Kalman Filter (UKF) as the integration algorithm for the inertial measurements. The UKF improves the mean and covariance propagation needed for the Kalman filter. Although the UKF provides a better estimate of the orientation, with Zero velocity UPdaTes (ZUPT) measurements, the yaw and the bias in the gyroscope associated with it becomes unobserved and might generate errors in the positioning. We studied the changes in the magnetic field during the stance phase and their relationship with the turn rates to propose three measurements using the magnetometer signal that will be called Magnetic Angular Rate Updates (MARUs). The first measurement uses the change in the angle of the magnetic field in the horizontal plane to measure the change in the yaw and provides a simple measurement for the UKF implementation. The second measurement relates the change in the magnetic field vector to the turn rate and provides information on the bias of the gyroscope for an UKF. The last measurement uses a first order approximation to generate a linear relationship with the gyroscope bias and therefore it can be used in an EKF. Finally we proposed a metric for the reliability of the stance as a way to use the pre and post stance information but adjusting the covariance of the measurements gradually from swing to stance. These methods were tested on real and simulated signals and they have shown improvements over the original PDR algorithms.
86 citations
TL;DR: Data assimilation in a two-dimensional hydrodynamic model for bays, estuaries and coastal areas is considered and the use of coloured model noise provides a numerically more efficient algorithm as well as a better performance of the filter.
Abstract: Data assimilation in a two-dimensional hydrodynamic model for bays, estuaries and coastal areas is considered. Two different methods based on the Kalman filter scheme are presented. These include (1) an extended Kalman filter in which the error covariance matrix is approximated by a matrix of reduced rank using a square root factorisation (RRSQRT KF), and (2) an ensemble Kalman filter (EnKF) based on a Monte Carlo simulation approach for propagation of errors. The filtering problem is formulated by utilising a general description of the model noise process related to errors in the model forcing, i.e. open boundary conditions and meteorological forcing. The performance of the two Kalman filters is evaluated using a twin experiment based on a hypothetical bay region. For both filters, the error covariance approximation sufficiently resolves the error propagation in the model at a computational load that is significantly smaller than required by the full Kalman filter algorithm. Furthermore, the Kalman filters are shown to be very robust with respect to defining the errors. Even in the case of a severely biased model error, the filters are able to efficiently correct the model. In general, the use of coloured model noise provides a numerically more efficient algorithm as well as a better performance of the filter. The error covariance approximation in the RRSQRT KF is shown to be more efficient than the error representation in the EnKF. For strongly non-linear dynamics, however, the EnKF is preferable. Copyright © 1999 John Wiley & Sons, Ltd.
86 citations
09 Oct 2006
TL;DR: The main conclusions from the simulations are that the performance of the extended Kalman filter and the unscented Kalmanfilter is comparable, joint filtering performs significantly better than dual filtering, and a larger number of detectors results in better state estimation, but has no significant influence on the parameter estimation error.
Abstract: We present a comparison for several filter configurations for freeway traffic state estimation. Since the environmental conditions on a freeway may change over time (e.g., changing weather conditions), parameter estimation is also considered. We compare the performance of the extended Kalman filter and the unscented Kalman filter for state estimation, parameter estimation, joint estimation and dual estimation. Furthermore, the performance is evaluated for different detector configurations. The main conclusions from the simulations are that (1) the performance of the extended Kalman filter and the unscented Kalman filter is comparable, (2) joint filtering performs significantly better than dual filtering, and (3) a larger number of detectors results in better state estimation, but has no significant influence on the parameter estimation error
86 citations