Influence of the range Doppler coupling error on the characteristics of second-order filters

This paper mainly considers a growing-memory filter for tracking an object moving with constant acceleration and detected by chirp radar. Chirp radars employ linear frequency modulated (LFM) waveforms for object tracking which yields a displacement of measured position from a true range of moving objects. This effect may enable better track accuracy in range. The second order degree polynomial describes coordinates law for a constantly accelerating maneuvering object. The issues of lag errors, covariance matrix of the filtered state vectors, impulse responses and Kalman gains are discussed. For example, the growing-memory filter is most often used for initiating track. The growing-memory filter is derived in recursive and non-recursive form based on least-squares. It is shown that the growing-memory filter estimating a true object range (with the range-Doppler coupling coefficient) can be represented by the growing-memory filter estimating a biased object range (without the range-Doppler coupling coefficient) and compensating the estimated biased range by the estimated the range-Doppler coupling error. Expressions giving an interrelation between lag errors, covariance matrix of the filtered state vectors, impulse responses and Kalman gains of growing-memory filters estimating true and biased range of moving objects are derived.