A New Technique for Increasing the Flexibility of Recursive Least Squares Data Smoothing

During the past few .years, a need has arisen for data smoothing techniques which can be applied, in real time, to radar observations of bodies traveling along highly predictable trajectories. The observations are usually processed in digital computers, so that much effort has been expended in devising techniques suited to the advantages and limitations of computers. This paper is concerned with one such technique, recursive least squares smoothing, whose theoretical foundation was established several years ago.1 It is our purpose to show how this technique can be made considerably more flexible so as to encompass a wide variety of practical situations while maintaining its suitability for computer use. By the term "recursive," we mean that a smoothed coordinate is determined from a previously computed average of past data (one number) and a new observation. Thus the storage requirements are independent of the number of observations and arc actually quite modest. We will also use the term "optimum smoothing," which is to be interpreted in the least squares sense, i.e., the weighting of data inversely proportional to S21