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.

Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem

Abstract: This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian problem, (ii) the ensemble Kalman-Bucy filter (EnKBF) which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems, and (iii) the feedback particle filter (FPF) which represents an extension of the EnKBF and furthermore provides for an consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement the update step (to account for conditioning due to the observations) in the filter. In contrast to the commonly used sequential Monte Carlo methods, the EnKBF and FPF avoid the resampling of the particles in the importance sampling update step. Moreover, the feedback control structure provides for error correction potentially leading to smaller simulation variance and improved stability properties. The paper also discusses the issue of non-uniqueness of the filter update formula and formulates a novel approximation algorithm based on ideas from optimal transport and coupling of measures. Performance of this and other algorithms is illustrated for a numerical example.

A sub-optimal algorithm for automatic map building

Abstract: This paper examines the problem of automatically constructing a map of an unknown environment from a vehicle whose location is also unknown. The application of the Kalman filter to this problem is briefly described and the practical limitation of the filter in this context is discussed. A suboptimal algorithm, the relative filter, is introduced that avoids many of the computational and practical problems of the direct Kalman filter approach to this problem. The performance of the full Kalman filter and the relative filter is compared in a real map building scenario.

A sequential Monte Carlo filter for joint linear/nonlinear state estimation with application to DS-CDMA

Abstract: A sequential Monte Carlo filter is considered which combines previously developed sequential importance sampling (SIS) techniques for conditional linear Gaussian models with measurement linearization for construction of approximate simulation densities. The resulting sequential Monte Carlo Kalman filter (SMC-KF) consists of a bank of conventional Kalman filters individually tuned to sampled trajectories of the nonlinear state variables. Sampling is according to a Gaussian distribution, with mean and covariance determined by extended Kalman filter-type equations. The SMC-KF is then applied to joint delay and multipath channel estimation in direct-sequence code-division multiple access (DS-CDMA). A combined analytical/simulation technique is employed to compare performance of the SMC-KF and a previously derived extended Kalman filter (EKF)-based DS-CDMA channel estimator.

Storm surge prediction using Kalman filtering

Abstract: In this study the theory of Kalman filtering has been employed to develop a new method for predicting water-levels along the Dutch coast. The combination of the standard Kalman filter with a non-linear tidal model of the entire North Sea is, from a computational point of view, not (yet) feasible. Therefore, in this investigation two different approaches have been developed. The first is based on the approximation of the tidal movement in the Dutch coastal area by a one-dimensional model. The two-dimensional effects due to the wind and the Coriolis force are taken into account by introducing some additional, empirical equations. The finite difference scheme and the system noise processes, introduced to describe the uncertainty associated with the model, are chosen such that numerical difficulties are avoided. Water-levels and velocities as well as the uncertain parameters in the model are estimated on-line by the Kalman filter. Since the model is continuously being adapted to the changing conditions, even this simple conceptual model gives satisfactory predictions. However, the time interval over which accurate predictions can be produced is limited because the one-dimensional approximation is only realistic for a smal1 part of the southern North Sea. To increase the prediction interval the second Kalman filter approach that is developed in this investigation is based on a two-dimensional model of the entire North Sea. The extension of the one-dimensional filter to two space dimensions does not give rise to conceptual problems but, as noted before, impose an unacceptably greater computational burden. In order to reduce this burden, the Kalman filter is approximated by a time-invariant one. In this case the time-consuming filter equations do not have to be computed over again as new measurements become available, but need only be solved once. Furthermore, by defining the system noise processes on a coarse grid and by employing a Chandrasekhar-type filter algorithm; a computationally attractive implementation of the filter is obtained. It is shown that the algorithm can be vectorized efficiently and that using a CDC CYBER 205 vector processor it is possible to combine the steady-state filter approach with very large models. Numerical difficulties can be avoided by carefully choosing the finite difference scheme, the boundary treatment and most important, the system noise processes. The filter has been tested extensively using simulated data as well as field data. The results show excellent filter performance, especially if we take into account that the number of measurements available (as yet) has been very limited. With respect to the results of the deterministic model without using tbe water-levels measurements available, the improvement obtained by filtering these measurements is substantial.