Alpha beta filter

About: Alpha beta filter is a research topic. Over the lifetime, 5653 publications have been published within this topic receiving 128415 citations.

Nondivergent simultaneous map building and localization using Covariance Intersection

Abstract: The Covariance Intersection (CI) framework represents a generalization of the Kalman filter that permitsfiltering and estimation to be performed in the presence of unmodeled correlations. As described in previous papers, unmodeled correlations arise in virtually all real-world problems; but in many applications the correlations are so significant that they cannot be "swept under the rug" simply by injecting extra stabilizing noise withina traditional Kalman filter. In this paper we briefly describe some of the properties of the CI algorithm anddemonstrate their relevance to the notoriously difficult problem of simultaneous map building and localization for autonomous vehicles.Keywords: Autonomous vehicles, data fusion, filtering, Covariance Intersection, Kalman filter, map building, matrixinequalities, nonlinear filtering. 1 INTRODUCTION The Kalman filter has been one of the most important and widely used engineering tools since its development in the early 1960s. The Kalman filter represents information about estimated or measured quantities in termsof a mean and covariance. Its importance is that it provides a mathematically rigorous method for combiningmultiple estimates that are assumed to be independent in the probabilistic sense. In other words, if the errors(or noise) associated with two estimates are due to unrelated processes, then the Kalman filter can combine thetwo estimates so that the resulting "filtered" estimate has error less than or equal to that of either of the twoprior estimates. A more general formulation of the Kalman filter can combine estimates with a known degreeof correlation, which is defined by the cross covariance between the two estimates, but it cannot be applied ifsuch information is not known. In practice most estimates are not independent and cross covariances cannot bedetermined.

A comparison of error subspace Kalman filters

Abstract: Three advanced filter algorithms based on the Kalman filter are reviewed and presented in a unified notation. They are the well-known ensemble Kalman filter (EnKF), the singular evolutive extended Kalman (SEEK) filter, and the less common singular evolutive interpolated Kalman (SEIK) filter. For comparison, the mathematical formulations of the filters are reviewed in relation to the extended Kalman filter as error subspace Kalman filters. The algorithms are presented in their original form and possible variations are discussed. A comparison of the algorithms shows their theoretical capabilities for efficient data assimilation with large-scale non-linear systems. In particular, problems of the analysis equations are apparent in the original EnKF algorithm due to the Monte Carlo sampling of ensembles. Theoretically, the SEIK filter appears to be a numerically very efficient algorithm with high potential for use with non-linear models. The superiority of the SEIK filter is demonstrated on the basis of identical twin experiments using a shallow-water model with non-linear evolution. Identical initial conditions for all three filters allow for a consistent comparison of the data assimilation results. These show how choices of particular state ensembles and assimilation schemes lead to significant variations of the filter performance. This is related to different qualities of the predicted error subspaces, as is demonstrated in an examination of the predicted state covariance matrices.

A Fresh Look at the Kalman Filter

Abstract: In this paper, we discuss the Kalman filter for state estimation in noisy linear discrete-time dynamical systems. We give an overview of its history, its mathematical and statistical formulations, and its use in applications. We describe a novel derivation of the Kalman filter using Newton's method for root finding. This approach is quite general as it can also be used to derive a number of variations of the Kalman filter, including recursive estimators for both prediction and smoothing, estimators with fading memory, and the extended Kalman filter for nonlinear systems.

Adaptive two‐stage Kalman filter in the presence of unknown random bias

Abstract: The well-known conventional Kalman filter gives the optimal solution but requires an accurate system model and exact stochastic information. In a number of practical situations, the system model has unknown bias and the Kalman filter with unknown bias may be degraded or even diverged. The two-stage Kalman filter (TKF) to consider this problem has been receiving considerable attention for a long time. Until now, the optimal TKF for system with a constant bias or a random bias has been proposed by several researchers. In case of a random bias, the optimal TKF assumes that the information of a random bias is known. But the information of a random bias is unknown or incorrect in general. To solve this problem, this paper proposes two adaptive filters, such as an adaptive fading Kalman filter (AFKF) and an adaptive two-stage Kalman filter (ATKF). Firstly, the AFKF is designed by using the forgetting factor obtained from the innovation information and the stability of the AFKF is analysed. Secondly, the ATKF to estimate unknown random bias is designed by using the AFKF and the performance of the ATKF is verified by simulation. Copyright © 2006 John Wiley & Sons, Ltd.

Extended Kalman Filter

Abstract: of the Kalman Filter that is suited to work with systems whose model contains non-linear behavior. The algorithm linearizes the non-linear model at the current estimated point in an iterative manner as a process evolves. Although EKF can be used in a very wide range of applications, the Radar Tracker example was chosen to demonstrate Altera’s unique solution. Typically EKF requires significant computational efforts due to multiple matrix operations, including matrix inversion. This design demonstrates the possibility of offloading a CPU by executing a portion of the algorithm in FPGA fabric.