Showing papers on "Invariant extended Kalman filter published in 1968"

An analysis of the divergence problem in the Kalman filter

Abstract: The effect of modeling errors in a linear discrete stochastic system upon the Kalman filter state estimates is investigated. Errors in both plant dynamics and noise covariances are permitted. The errors are characterized in such a manner that a linear recursion relation for the actual estimation error covariances can be derived. Conditions which guarantee that the covariance matrix remains bounded are described in terms of the asymptotic stability of the homogeneous part of the covariance equation and the boundedness of the forcing terms in the inhomogeneous equation.

Degradation of linear filter performance due to modeling error

Abstract: Differential equations for determining the dynamic and steady-state effects of a particular class of disturbances on the error in the estimate of the state vector of a stochastic linear dynamic system are obtained. For the problem of evaluating near optimal filter performance, the technique permits the performance degradation due to the deletion of certain state vector components in the design of a Kalman filter to be obtained.

Optimum differentiation using Kalman filter theory

Abstract: Consideration is given to the construction of an optimum differentiator to give the minimum-variance unbiased estimate of the first derivatives of random signals corrupted by white noise It is assumed that the signals are differentiable and are the outputs of a known linear finite-dimensional (possibly time-varying) system excited by white noise Extension of the results to consider higher-order differentiation is straightforward

An approximation of the Kalman filter equations

Abstract: This correspondence presents the results of the application of the matrix inversion lemma to the Kalman filter equation. This operation eliminates the inversion process in the Kalman filter and enables one to sequentially compute the optimum estimate of the state without the use of the inversion process.

Real-time implementation of the kalman filter for trajectory estimation

Abstract: : The study addressed itself to the problem of real-time implementation of the Kalman filter for estimating ballistic trajectories. The Kalman filter is an extremely effective algorithm for estimation of ballistic trajectories, although the computational requirements of ballistic trajectories, although the computational requirements of the fully implemented Kalman filter are quite severe. In this report, several approaches that may be used to modify the Kalman filtering algorithm in order to reduce the computational requirements are described. The most promising approach of those considered is the piecewise- recursive Kalman filter. As shown by the numerical results obtained from extensive computer simulations, the piecewise-recursive Kalman filter can process measurements of a single target at a computational speed (on the Univac 1108) that is about 20 to 25 times faster than real time for the endoatmospheric cases and about 500 times faster than real time for the exoatmospheric cases, and yet obtain estimation accuracy approaching that of the fully implemented Kalman filter. This increased filter capability is invaluable for the real-time estimation of multiple targets.

Derivation of a suboptimal linear filter

Abstract: A linear filter using sample extrapolation and averaging is derived and tested. Extensions to include correlated observation noise and incomplete measurement are discussed. The filter is easily implemented for low-order linear plants but is inferior to the Kalman filter for all but the simplest cases.

Sensitivity of the Kalman Filter with Respect to Parameter Variations

Abstract: : Techniques are given for sensitivity analysis of the Kalman filter with respect to simultaneous variations in measurement noise, plant noise, dynamic model, sampling period, and filter gain These analytical techniques will greatly aid the design and evaluation of Kalman filters and other types of filters Two basic assumptions were used: There are nominal quantities about which variations may be taken, and The estimation-error covariances are the filter performance measures

Stochastic peak tracking and the Kalman filter

Abstract: The peak tracking problem can be reduced to a Kalman falter problem [1] with the additional variable of the excursion amplitude c , which is then obtained by maximizing the expected peak. In the special case where the parameters do not change, the method yields two tracking procedures depending on the criterion used: 1) Tracking for a limited time and then settling for the parameter value so determined. It is shown that the expected error is proportional to t-1, where t is the tracking time [2]. 2) A procedure which agrees with the Kiefer-Wolfowitz stochastic approximation method [3]. It is shown further that the expected total reduction in peak value (due to error and hunting loss) is proportional to t^{-1/2}.