Analytical Investigation of Time Correction in Asynchronous Alpha-Beta Tracking Filters with Application to en Route Altitude Tracking

摘要

In the analysis of the alpha-beta tracking filter, it is normally assumed that the tracking filter and data source operate in synchronism at a constant data rate. An analytical solution is obtained for the case in which the tracking filter and data source operate asynchronously, thus violating the standard assumptions. In order to compensate for the asynchronous operation of the filter, the technique of time correction is used to adjust the measured data point via the estimated velocity in order to approximate the synchronous operation of the filter and the data source. A specific example is given in which the influence of time correction on the performance of the altitude tracker is evaluated in terms of the filter performance for extended time-interval position prediction as is used in Conflict Alert. It is shown that errors in the predicted positions, on the order of a few thousand feet, can be introduced if the time-correction process is not incorporated into the altitude tracking algorithm. In addition, it is shown that the magnitude of the errors increases significantly as the altitude change rate increases, while for an altitude tracker with time correction the position prediction performance is essentially constant for all altitude change rates of practical significance. The computational resources required for the implementation of the time-correction process are inconsequential as compared to the total requirements of the tracking functions. (Author)