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.

A kalman filter based background updating algorithm robust to sharp illumination changes

Abstract: A novel algorithm, based on Kalman filtering is presented for updating the background image within video sequences. Unlike existing implementations of the Kalman filter for this task, our algorithm is able to deal with both gradual and sudden global illumination changes. The basic idea is to measure global illumination change and to use it as an external control of the filter. This allows the system to better fit the assumptions about the process to be modeled. Moreover, we propose methods to estimate measurement noise variance and to deal with the problem of saturated pixels, to improve the accuracy and robustness of the algorithm. The algorithm has been successfully tested in a traffic surveillance task by comparing it to a background updating algorithm, based on Kalman filtering, taken from literature.

A Unification of Ensemble Square Root Kalman Filters

Abstract: In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular ‘‘evolutive’’ interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.

Study of the General Kalman Filter for Echo Cancellation

Abstract: The Kalman filter is a very interesting signal processing tool, which is widely used in many practical applications. In this paper, we study the Kalman filter in the context of echo cancellation. The contribution of this work is threefold. First, we derive a different form of the Kalman filter by considering, at each iteration, a block of time samples instead of one time sample as it is the case in the conventional approach. Second, we show how this general Kalman filter (GKF) is connected with some of the most popular adaptive filters for echo cancellation, i.e., the normalized least-mean-square (NLMS) algorithm, the affine projection algorithm (APA) and its proportionate version (PAPA). Third, a simplified Kalman filter is developed in order to reduce the computational load of the GKF; this algorithm behaves like a variable step-size adaptive filter. Simulation results indicate the good performance of the proposed algorithms, which can be attractive choices for echo cancellation.

Robust Kalman filter for descriptor systems

Abstract: This note is concerned with the problem of state estimation for descriptor systems subject to uncertainties. A Kalman type recursive algorithm is derived. Numerical examples are included to demonstrate the performance of the proposed robust filter