First-order Markov process representation of binary radar data sequences

Study of radar detection-trial data sequences has indicated the existence of interscan correlation. The theory of simple or first-order Markov chains is here applied to characterize the statistics of such sequences of correlated binary data consisting of detections (l\´s) and nondetections (0\´s) of a tracked target upon successive radar scans. Both stationary discrete and non-stationary continuous parameter processes are considered, for which relations are derived between four transition probabilities. and the absolute detection probability, , and the so-called blip-scan ratio. The discrete parameter, first-order Markov chain theory, presented first, is extended to the case wherein the blip-scan ratio may be expressed as a function of time. It is possible to employ the resulting nonstationary, continuous parameter solution to simulate radar data for aircraft flights of arbitrary patterns. Certain restrictions upon the admissible class of blip-scan functions are presented. In the case of the continuous parameter first-order process, the scan-to-scan correlation coefficient is shown to be restricted to positive values. An application is made to an automatic initiation problem.