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.

Recursive nonlinear filtering for angular data based on circular distributions

Abstract: Estimation of circular quantities is a widespread problem that occurs in many tracking and control applications. Commonly used approaches such as the Kalman filter, the extended Kalman filter (EKF), and the unscented Kalman filter (UKF) do not take periodicity explicitly into account, which can result in low estimation accuracy. We present a filtering algorithm for angular quantities in nonlinear systems that is based on circular statistics. The new filter switches between three different representations of probability distributions on the circle, the wrapped normal, the von Mises, and a Dirac mixture density. It can be seen as a systematic generalization of the UKF to circular statistics. We evaluate the proposed filter in simulations and show its superiority to conventional approaches.

The Kalman Filter

Abstract: The Kalman filter and its variants are some of the most popular tools in statistical signal processing and estimation theory. In this chapter, we introduce the Kalman filter, providing a succinct, yet rigorous derivation thereof, which is based on the orthogonality principle. We also introduce several important variants of the Kalman filter, namely various Kalman smoothers, a Kalman predictor, a nonlinear extension (the extended Kalman filter), and adaptation to cases of temporally correlated measurement noise.

Particle and Kalman filtering for state estimation and control of DC motors.

Abstract: State estimation is a major problem in industrial systems. To this end, Gaussian and nonparametric filters have been developed. In this paper the Kalman Filter, which assumes Gaussian measurement noise, is compared to the Particle Filter, which does not make any assumption on the measurement noise distribution. As a case study the estimation of the state vector of a DC motor is used. The reconstructed state vector is used in a feedback control loop to generate the control input of the DC motor. In simulation tests it was observed that for a large number of particles the Particle Filter could succeed in accurately estimating the motor's state vector, but at the same time it required higher computational effort.

Random-point-based filters: analysis and comparison in target tracking

Abstract: This paper compares state estimation techniques for nonlinear stochastic dynamic systems, which are important for target tracking. Recently, several methods for nonlinear state estimation have appeared utilizing various random-point-based approximations for global filters (e.g., particle filter and ensemble Kalman filter) and local filters (e.g., Monte-Carlo Kalman filter and stochastic integration filters). A special emphasis is placed on derivations, algorithms, and commonalities of these filters. All filters described are put into a common framework, and it is proved that within a single iteration, they provide asymptotically equivalent results. Additionally, some deterministic-point-based filters (e.g., unscented Kalman filter, cubature Kalman filter, and quadrature Kalman filter) are shown to be special cases of a random-point-based filter. The paper demonstrates and compares the filters in three examples, a random variable transformation, re-entry vehicle tracking, and bearings-only tracking. The results show that the stochastic integration filter provides better accuracy than the Monte-Carlo Kalman filter and the ensemble Kalman filter with lower computational costs.