Showing papers on "Alpha beta filter published in 1967"

Divergence in the Kalman Filter

Abstract: Under certain conditions, the orbit estimated by a Kalman filter has errors that are much greater than predicted by theory. This phenomenon is called divergence, and renders the operation of the Kalman filter unsatisfactory. This paper investigates the control of divergence in a Kalman filter used for autonomous navigation in a low earth orbit. The system studied utilizes stellar-referenced angle sightings to a sequence of known terrestrial landmarks. A Kalman filter is used to compute differential corrections to spacecraft position, spacecraft velocity, and landmark location. A variety of filter modifications for the control of divergence was investigated. These included the Schmidt-Pines analytical modification and an "empirical" modification based upon Pines' machine noise treatment. Several simplified approximations to the theoretically optimum analytical modifications were also investigated. The principal numerical results are presented in graphs of the magnitude of the error in estimated position and velocity vs time for sixteen orbits. These graphs compare actual position and velocity errors with the theoretical estimates furnished by the trace of the position and velocity covariance matrices. Numerical results indicate that a properly modified filter achieves a steady-state operating level.

A square root formulation of the Kalman- Schmidt filter.

Abstract: Kalman filter alternate form extended to include multiple simultaneous correlated measurements, testing with ballistic model and using square root formulation for trajectory determination

Application of the extended kalman filter to ballistic trajectory estimation.

Abstract: : In this report an extended Kalman filter for ballistic trajectory estimation is presented The filter equations are basically the same as those in the previous Final Report on this contract The several modifications are explained in detail, and values for all filter parameters are given The filter was tested against simulated radar data for a number of different cases; performance was excellent in all cases For comparison purposes a second-order exponentially weighted polynomial filter was used on the same data; the performance was significantly worse than for the extended Kalman filter The extended Kalman filter was also run at slower data rates and with multiple interruptions of data with only a slight degradation in performance A precomputed approximation to the weighting matrix was calculated on the basis of several runs; this approximation performed nearly as well as the fully implemented filter Use of this approximation reduced computational requirements by an order of magnitude (Author)