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.
Papers published on a yearly basis
Papers
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TL;DR: Through flight tests, it is shown that the PIKF has an obvious accuracy advantage over the IEKF and unscented Kalman filter (UKF) in velocity.
Abstract: This paper deals with the problem of state estimation for the integration of an inertial navigation system (INS) and Global Positioning System (GPS). For a nonlinear system that has the model error and white Gaussian noise, a predictive filter (PF) is used to estimate the model error, and based on this, a modified iterated extended Kalman filter (IEKF) is proposed and is called predictive iterated Kalman filter (PIKF). The basic idea of the PIKF is to compensate the state estimate by the estimated model error. An INS/GPS integration system is implemented using the PIKF and applied to synthetic aperture radar (SAR) motion compensation. Through flight tests, it is shown that the PIKF has an obvious accuracy advantage over the IEKF and unscented Kalman filter (UKF) in velocity.
121 citations
TL;DR: This paper applies an efficient embedded Runge-Kutta pair possessing superior stability and many other attractive features to improve performance of the complex computational procedure consisting of the extended Kalman filter and the underlying adaptive ODE solver.
Abstract: This paper addresses an accurate and effective implementation of the continuous-discrete extended Kalman filtering method. The technique under discussion is grounded in numerical solution of the moment differential equations to predict the state mean of the stochastic dynamical system and the corresponding error covariance matrix. Here, we apply an efficient embedded Runge-Kutta pair possessing superior stability and many other attractive features, including automatic global error control, in order to improve performance of the complex computational procedure consisting of the extended Kalman filter and the underlying adaptive ODE solver. Thus, we introduce a new continuous-discrete adaptive extended Kalman filter and show its advantage over the standard variant on two test examples. In practice, this technique allows for much longer sampling intervals without any loss of accuracy, and that improves the applied potential of the extended Kalman filtering method, significantly.
121 citations
15 Sep 1996
TL;DR: In this article, a new nonlinear filter referred to as the state-dependent Riccati equation filter (SDthis article) is presented, which is derived by constructing the dual of a little known nonlinear regulator control design technique which involves the solution of a state-dependent RICE (SDRE) and which has been appropriately called the SDRE control method.
Abstract: A new nonlinear filter referred to as the state-dependent Riccati equation filter (SDREF) is presented. The SDREF is derived by constructing the dual of a little known nonlinear regulator control design technique which involves the solution of a state-dependent Riccati equation (SDRE) and which has been appropriately called the SDRE control method. The resulting SDREF has the same structure as the continuous steady-state linear Kalman filter. In contrast to the linearized Kalman filter (LKF) and the extended Kalman filter (EKF) which are based on linearization, the SDREF is based on a parameterization that brings the nonlinear system to a linear structure having state-dependent coefficients (SDC). In a deterministic setting, before stochastic uncertainties are introduced, the SDC parameterization fully captures the nonlinearities of the system, It was shown in Cloutier et al. (1996) that, in the multivariable case, the SDC parameterization is not unique and that the SDC parameterization itself can be parameterized. This latter parameterization creates extra degrees of freedom that are not available in traditional filtering methods. These additional degrees of freedom can be used to either enhance filter performance, avoid singularities, or avoid loss of observability. The main intent of this paper is to introduce the new nonlinear filter and to illustrate the behaviorial differences and similarities between the new filter, the LKF, and the EKF using a simple pendulum problem.
121 citations
Journal Article•
TL;DR: Based on the orthogonality principle, a strong tracking filter-a suboptimal multiple fading extended Kalman filter (SMFEKF) is proposed in this article, which improves the sub-optimal fading Extended Kalman Filter (SFEF).
120 citations
TL;DR: This paper deals with convergence analysis of the extended Kalman filters for sensorless motion control systems with induction motor with results theoretically achieved and validated by means of experimental tests carried out on an IM prototype.
Abstract: This paper deals with convergence analysis of the extended Kalman filters (EKFs) for sensorless motion control systems with induction motor (IM). An EKF is tuned according to a six-order discrete-time model of the IM, affected by system and measurement noises, obtained by applying a first-order Euler discretization to a six-order continuous-time model. Some properties of the discrete-time model have been explored. Among these properties, the observability property is relevant, which leads to conditions that can be directly linked with the working conditions of the machine. Starting from these properties, the convergence of the stochastic state estimation process, in mean square sense, has been shown. The convergence is also explored with reference to the difference between the samples of the state of the continuous-time model and that estimated by the EKF. The results theoretically achieved have been also validated by means of experimental tests carried out on an IM prototype.
120 citations