Maximally Reliable Exponential Prediction Equations for Data-Rate-Limited Tracking Servomechanisms

Certain instruments attempt to determine the value of a variable by measuring the difference between it and a prediction of it at regular intervals of time. Examples of these instruments include echo-ranging radars and sonars. These measurements enter a computer which immediately substitutes the measurements into equations which predict the next value of the variable, thereby closing the loop illustrated in Fig. 1. This prediction must be supplied to the instrument because it is assumed that the instrument can measure sufficiently accurately only if it knows approximately where to look for the next value of the variable. Conversely, large errors in this prediction are assumed to blind or otherwise confuse the instrument. More precisely, it is assumed that positive limits L and l! on the prediction error E are given, where E is defined as the difference between the prediction £ of the variable and its true value x. It is assumed that if E stays within the interval --L ^ E ^ L, the instrument almost never grossly mismeasures the variable. However, even when E stays within this interval, it is assumed that the instrument slightly mis-