Topic
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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the steady-state or asymptotic behavior of the Kalman filter is analyzed in terms of the phase portrait of a universal nonlinear dynamical system.
Abstract: The main purpose of this paper is to address a fundamental open problem in linear filtering and estimation, namely, what is the steady-state or asymptotic behavior of the Kalman filter, or the Kalman gain, when the observed stationary stochastic process is not generated by a finite-dimensional stochastic system, or when it is generated by a stochastic system having higher-dimensional unmodeled dynamics. For example, some time ago Kalman pointed out that the usual positivity conditions assumed in the classical situation are not in fact necessary for the Kalman filter to converge. Using a "fast filtering" algorithm, which incorporates the statistics of the observation process as initial conditions for a dynamical system, this question is analyzed in terms of the phase portrait of a "universal" nonlinear dynamical system. This point of view has additional advantages as well, since it enables one to use the theory of dynamical systems to study the sensitivity of the Kalman filter to (small) changes in initial conditions; e.g., to changes in the statistics of the underlying process. This is especially important since these statistics are often either approximated or estimated. In this paper, for a scalar observation process, necessary and sufficient conditions for the Kalman filter to converge are derived using methods from stochastic systems and from nonlinear dynamics---especially the use of stable, unstable, and center manifolds. It is also shown that, in nonconvergent cases, there exist periodic points of every period $p$, $p\ge 3$ that are arbitrarily close to initial conditions having unbounded orbits, rigorously demonstrating that the Kalman filter can also be "sensitive to initial conditions."
35 citations
TL;DR: In this article, three recursive Bayesian filters are implemented: an extended Kalman filter (EKF), an unscented Kalman Filter (UKF), and a particle filter (PF).
35 citations
01 Jan 2003
TL;DR: In this paper, it is pointed out that powerful signal processing techniques such as gradient methods, Kalman filtering, and the particle filter can be used and combined in factor graphs, and that these techniques can be applied to factor graphs.
Abstract: The paper is a collection of remarks, some rather plain, on various issues with factor graphs. In particular, it is pointed out that powerful signal processing techniques such as gradient methods, Kalman filtering, and the particle filter can be used and combined in factor graphs.
35 citations
TL;DR: The decomposition of a linear process model into a cascade of simpler subsystems and the use of a Kalman filter to individually estimate the states of these subsystems is proposed and the performance achieved by the cascaded observers is comparable and in certain cases even better than the performance of the centralized observer.
35 citations
TL;DR: A new approach is presented for the estimation of the noise covariances associated with the linear discrete Kalman filter.
Abstract: A new approach is presented for the estimation of the noise covariances associated with the linear discrete Kalman filter
35 citations