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.

Forecasting, Structural Time Series Models and the Kalman Filter

Abstract: List of figures Acknowledgement Preface Notation and conventions List of abbreviations 1. Introduction 2. Univariate time series models 3. State space models and the Kalman filter 4. Estimation, prediction and smoothing for univariate structural time series models 5. Testing and model selection 6. Extensions of the univariate model 7. Explanatory variables 8. Multivariate models 9. Continuous time Appendices Selected answers to exercises References Author index Subject index.

A new method for the nonlinear transformation of means and covariances in filters and estimators

Abstract: This paper describes a new approach for generalizing the Kalman filter to nonlinear systems. A set of samples are used to parametrize the mean and covariance of a (not necessarily Gaussian) probability distribution. The method yields a filter that is more accurate than an extended Kalman filter (EKF) and easier to implement than an EKF or a Gauss second-order filter. Its effectiveness is demonstrated using an example.

An Introduction to the Kalman Filter

Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

introduction to random signals and applied kalman filtering

Abstract: Probability and Random Variables Mathematical Description of Random Signals Response of Linear Systems to Random Inputs Wiener Filtering The Discrete Kalman Filter Applications and Additional Topics on Discrete Kalman Filtering The Continuous Kalman Filter Discrete Smoothing and Prediction Linearization and Additional Topics on Applied Kalman Filtering The Global Positioning System: A Case Study.

Analysis Scheme in the Ensemble Kalman Filter

Abstract: This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low. This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.