Enlarging the Region of Convergence of Kalman Filters Employing Range Measurements
William S. Widnall · AIAA Journal · 1973
Advances in nonlinear filter theory have produced the Gaussian second-order filter. This extension of the Kalman filter compensates for measurement nonlinearity by appropriate bias compensation and a priori measurement variance increase. This paper develops the Gaussian second-order measurement equations appropriate for the nonlinear elongation of measured range. The required additions to a linearized Kalman filter are not complex. The performance improvement obtainable is demonstrated in a spacecraft rendezvous navigation simulation. Divergence of the standard linearized filter occurs if the initial error exceeds 1 km. Divergence in the second-order filter does not occur unless the initial error exceeds 10 km.