Gaussian second-order filter for proportional navigation of exoatmospheric interceptors with angles-only measurements
Hari B. Hablani · Guidance, Navigation, and Control Conference and Exhibit · 1998
The objective of the paper is to develop a suitable filter for proportional navigation of exoatmospheric interceptors with angles-only measurements. The paper first probes into the errors caused by the use of spherical coordinates for propagating a state estimate vector and error covariance matrix. The propagation of a spherical state vector using three approximate transition matrices is shown to introduce errors of different levels, compared with the propagation of cartesian coordinates using a simple and exact transition matrix. Employing cartesian coordinates then, an extended Kalman filter is first attempted to estimate the azimuth and elevation rates from the angle measurements. Because this filter retains only the instantaneous linear relationship between the estimated angles and range, the filter does not yield satisfactory angular rate estimates. Consequently, the paper next develops a Gaussian second-order filter which retains, in the updates across measurements, the linear and quadratic relationships between estimated line-of-sight angles and range. This filter is shown to produce highly accurate angular rate estimates, resulting in desired small miss distances over a wide span of estimation errors in the initial range.