Nonparametric Method for Joint Estimation of Broadband Signal Delay and Its Doppler Factor under Influence of Multiplicative Interference

The paper presents a nonparametric method for joint estimation of the delay time and Doppler factor of a pseudo-randomly phase-shift keying signal under a priori uncertainty about the probability distribution law of the white multiplicative interference in its observation. When estimating the signal parameters, the Doppler deformation of the envelope and shift of the carrier frequency are considered. The problem of estimating the signal delay time at a known Doppler factor is studied separately. The parameter estimation problem is investigated, assuming that the noise component is a process with independent and identically distributed random quantities (white noise).

The proposed method minimizes the goal function that uses observing BDS statistics. The delay time and the Doppler factor are determined by calculating the minimum value of the goal function of the mismatch between the observed signal and its model under conditions of joint variation of parameters. Properties of joint nonparametric estimates of the signal delay time and the Doppler factor obtained for different parameters of the BDS statistics have been investigated. There are presented dependences of mathematical expectations and mean square errors of joint estimates of the delay and Doppler factor of the received signal for several probability density distributions at different parameters of the multiplicative interference scale, including those with heavy tails. Using statistical simulation, it has been shown that the proposed method makes it possible to obtain acceptable estimates of signal parameters under a priori uncertainty about the distribution of multiplicative interference.