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.

Stabilizing the fast Kalman algorithms

Abstract: The fast Kalman algorithms are stabilized by introducing a quantity that measures the accumulation of the roundoff errors. This quantity is used to correct the variables of the algorithm at every time step. The correction is defined as the solution of a specific minimization problem. The resulting algorithm still has the nice complexity properties of the original algorithm (linear in the number of parameters to be estimated), but it has a much more stable behavior. >

An Adaptive Two-Dimensional Kalman Tracking Filter

Abstract: A continuously adaptive two-dimensional Kalman tracking filter for a low data rate track-while-scan (TWS) operation is introduced which enhances the tracking of maneuvering targets. The track residuals in each coordinate, which are a measure of track quality, are sensed, normalized to unity variance, and then filtered in a single-pole filter. The magnitude Z of the output of this single-pole filter, when it exceeds a threshold Z1 is used to vary the maneuver noise spectral density q in the Kalman filter model in a continuous manner. This has the effect of increasing the tracking filter gains and containing the bias developed by the tracker due to the maneuvering target. The probability of maintaining track, with reasonably sized target gates, is thus increased, The operational characteristic of q versus Z assures that the tracker gains do not change unless there is high confidence that a maneuver is in progress.

A Discrete-Time Robust Extended Kalman Filter for Uncertain Systems With Sum Quadratic Constraints

Abstract: This technical note outlines the formulation of a novel discrete-time robust extended Kalman filter for uncertain systems with uncertainties described in terms of sum quadratic constraints. The robust filter is an approximate set-valued state estimator which is robust in the sense that it can handle modeling uncertainties in addition to exogenous noise. Riccati and filter difference equations are obtained as an approximate solution to a reverse-time optimal control problem defining the set-valued state estimator. In order to obtain a solution to the set-valued state estimation problem, the discrete-time system dynamics are modeled backwards in time.

Extended Kalman filter for extended object tracking

Abstract: In this work, we present a novel method for tracking an elliptical shape approximation of an extended object based on a varying number of spatially distributed measurements. For this purpose, an explicit nonlinear measurement equation is formulated that relates the kinematic and shape parameters to a measurement by means of a multiplicative noise term. Based on the measurement equation, we derive an extended Kalman filter (EKF) for a closed-form recursive measurement update. The performance of the proposed method is demonstrated with simulations.