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.

Reduced-order estimation Part 1. Filtering

Abstract: This paper presents a method for designing an ‘optimum’ unbiased reduced-order filter. For the proposed approach to work, the order of the filter must be greater than a certain minimum determined by the number of independent observations of the system available. The filler is much like a Luenberger observer for the state to be estimated, but with parameters optimized with respect to the noises in the system. A reduced-order innovation process is proposed that has properties similar to those of the full-order innovation process when the reduced filter is optimized. The approach offers the possibility of significant reduction in real-time computational requirements compared with the full-order filter, though at the cost of some loss of performance. The algorithm for the reduced-order filter is simple to implement— quite similar to that of the Kalman filter. An example is presented to compare the performance of the proposed method with the full-order Kalman filter.

The Kalman filter: A robust estimator for some classes of linear quadratic problems

Abstract: In this paper, theoretical justification is established for the common practice of applying the Kalman filter estimator to three classes of linear quadratic problems where the model statistics are not completely known, and hence specification of the filter gains is not optimum. The Kalman filter is shown to be a minimax estimator for one class of problems and to satisfy a saddlepoint condition in the other two classes of problems. Equations for the worst case covariance matrices are given which allow the specifications of the minimax Kalman filter gains and the worst case distributions for the respective classes of problems. Both time-varying and time-invariant systems are treated.

Experimental validation of the Kalman-type filters for online and real-time state and input estimation:

Abstract: In this study, a novel dual implementation of the Kalman filter proposed by Eftekhar Azam et al. (2014, 2015) is experimentally validated for simultaneous estimation of the states and input of structural systems. By means of numerical simulations, it has been shown that the proposed method outperforms existing techniques in terms of robustness and accuracy for the estimated displacement and velocity time histories. Herein, dynamic response measurements, in the form of displacement and acceleration time histories from a small-scale laboratory building structure excited at the base by a shake table, are considered for evaluating the performance of the proposed Dual Kalman filter and in order to compare this with available alternatives, such as the augmented Kalman filter (Lourens et al., 2012b) and the Gillijn De Moore filter (GDF) (2007b). The suggested Bayesian approach requires the availability of a physical model of the system in addition to output-only measurements from limited degrees of freedom. Two ...

A Kalman filter approach to catch-at-length analysis

Abstract: A state-space representation of a length-structured population under commercial harvest is described and a Kalman filter is used to develop the conditional likelihood equation needed for estimating the underlying system parameters. The state of the system is characterized using conventional fisheries theory with commercial harvest representing the observations taken on the population. The conditional likelihood framework embedded in the Kalman filter facilitates the incorporation of both system stochasticity as well as observation error in the development of the overall likelihood equation. Within this framework a maximum likelihood approach is used to estimate population parameters while taking into account both sources of error.