Doppler Stretch and Delay Statistical Performance Comparison for Wideband and Narrowband Signal Model

Abstract

Narrowband approximation of Doppler effect by a frequency shift is inappropriate for some problems of radiolocation, hydro acoustics or passive location. In this case it is necessary to use Doppler stretch (time-scaling) as a signal parameter. Statistical performance of joint Doppler stretch and delay for arbitrary spectral width signal without narrowband approximations is derived in this paper.Narrowband and wideband parameters relations are investigated for triangle impulse with linear spectral modulation. Besides, Fisher Information Matrices (FIM) differences are analyzed. In the narrowband limit consideration of results in well-known FIM of Doppler shift and delay estimation are proposed. Another feature of wideband FIM is reference time dependence on time delay variance. Transition from Doppler stretch to Doppler frequency shift considering narrowband limitations results in translation invariant FIM.The article shows that reference time variance of delay estimation is related to estimated parameter modification and velocity influence on delay. Also, estimation variances in narrowband signal model differ from wideband parameter variances by magnitude of spectrum width to central frequency ratio.