Comparison of markov and least-squares missile position and velocity estimates
HAUL R. HUNZIKER · AIAA Journal · 1964
^N increase of precision in missile position and velocity estimates can be obtained by using smoothing and rate filters that consider the serial (time) correlation of the errors in the measurements of a radio tracking system. We will consider the estimation of the position and velocity vector of a vehicle that is observed by a radio tracker that provides three coordinates as functions of the time. The following considerations generally apply to the case of a radio tracking system measuring range, azimuth, and elevation or range and two direction cosines or range and two range differences. However, our numerical example corresponds to the AZUSA Mark II continuous wave (CW) radar, for which there is available trajectory and error structure data. First we will proceed to compare minimum variance (Markov) smoothing and first-derivative filters with least-squares filters. In order to make a simple comparison, we will apply the continuous theory of Zadeh and Ragazzini rather than the digital filters that can be constructed by algebraic means in the sampled-data case. Under very general conditions, Swerling has shown that this optimum linear estimate based on continuous observation during a finite time T is the limit of optimum linear estimates based on sampled data as the sample spacing tends to zero. Since the sample spacing of AZUSA Mark II is -£§ sec, we will assume that these continuous estimates are sufficiently close to the discrete estimates for the sampled-data case. Thus we will be concerned with the calculation of the ratio