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.

Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering

Abstract: Kalman ¯lters are often used to estimate the state variablesof a dynamic system. However, in the application of Kalman¯lters some known signal information is often either ignored ordealt with heuristically. For instance, state variable constraints(which may be based on physical considerations) are often ne-glected because they do not ¯t easily into the structure of theKalman ¯lter. This paper develops an analytic method of in-corporating state variable inequality constraints in the Kalman¯lter. The resultant ¯lter is a combination of a standard Kalman¯lter and a quadratic programming problem. The incorporationof state variable constraints increases the computational e®ort ofthe ¯lter but signi¯cantly improves its estimation accuracy. Theimprovement is proven theoretically and shown via simulationresults obtained from application to a turbofan engine model.This model contains 16 state variables, 12 measurements, and 8component health parameters. It is shown that the new algo-rithms provide improved performance in this example over un-constrained Kalman ¯ltering.INTRODUCTION

Unscented Kalman filtering for nonlinear structural dynamics

Abstract: Joint estimation of unknown model parameters and unobserved state components for stochastic, nonlinear dynamic systems is customarily pursued via the extended Kalman filter (EKF). However, in the presence of severe nonlinearities in the equations governing system evolution, the EKF can become unstable and accuracy of the estimates gets poor. To improve the results, in this paper we account for recent developments in the field of statistical linearization and propose an unscented Kalman filtering procedure. In the case of softening single degree-of-freedom structural systems, we show that the performance of the unscented Kalman filter (UKF), in terms of state tracking and model calibration, is significantly superior to that of the EKF.

Decoupled Kalman filters for phased array radar tracking

Abstract: Kalman filters have been used in numerous phased array radars to track satellites, reentry vehicles, and missiles. This paper considers the design of these filters to reduce computational requirements, ill-conditioning, and the effects of nonlinearities. Several special coordinate systems used to represent the Kalman filter error covariance matrix are described. These covariance coordinates facilitate the approximate decoupling required for practical filter design. A tutorial discussion and analysis of ill-conditioning in Kalman filters is used to motivate these design considerations. This analysis also explains several well-known phenomena reported in the literature. In addition, a discussion of nonlinearities and methods to mitigate their ill effects is included.

Simplification of the Kalman filter for meteorological data assimilation

Abstract: The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

A New Approximate Solution of the Optimal Nonlinear Filter for Data Assimilation in Meteorology and Oceanography

Abstract: This paper introduces a new approximate solution of the optimal nonlinear filter suitable for nonlinear oceanic and atmospheric data assimilation problems. The method is based on a local linearization in a low-rank kernel representation of the state's probability density function. In the resulting low-rank kernel particle Kalman (LRKPK) filter, the standard (weight type) particle filter correction is complemented by a Kalman-type correction for each particle using the covariance matrix of the kernel mixture. The LRKPK filter's solution is then obtained as the weighted average of several low-rank square root Kalman filters operating in parallel. The Kalman-type correction reduces the risk of ensemble degeneracy, which enables the filter to efficiently operate with fewer particles than the particle filter. Combined with the low-rank approximation, it allows the implementation of the LRKPK filter with high-dimensional oceanic and atmospheric systems. The new filter is described and its relevance demonstrated through applications with the simple Lorenz model and a realistic configuration of the Princeton Ocean Model (POM) in the Mediterranean Sea.