Application of Calibration and Decalibration to Kalman Filters

Abstract

The method of calibration and decalibration of nonlinear, dynamic systems in more-nonlinear coordinates has previously been shown to recover the improved performance with less-nonlinear coordinates in simulation and control problems (where the nonlinearity index is used to quantify the degree of nonlinearity of a given set of coordinates). In this thesis, that method is applied to another application – that of state estimation using Kalman filtering. A Kalman filter can be formulated in both continuous and discrete time using more-nonlinear (i.e. less favorable) coordinates but calibrated using less-nonlinear (i.e. more favorable) coordinates. It is found in simulations that the techniques of calibrating and decalibrating in the less favorable coordinates recover the performance that would have been achieved using a filter formulated using the more favorable coordinates. For illustrative examples, a calibrated Kalman-Bucy filter is applied to a rectilinear oscillator while a calibrated conventional Kalman filter is applied to the problem of relative orbit determination in Cartesian Hill frame coordinates, using either spherical coordinate differences or orbit element differences as the less nonlinear coordinate set. These examples demonstrate that calibration and decalibration can improve filter performance, so long as alternative coordinates exist which are known to enjoy lower error when the given dynamic system is linearized in those coordinates.