M.A. Murzova – Post-graduate Student, Moscow Institute of Physics and Technology (State University); 

Engineer, PJSC «Radiofizika» (Moscow)

E-mail: mariya.trofimenko@phystech.edu

V.E. Farber – Dr.Sc.(Eng.), Professor, Head of Department, PJSC «Radiofizika» (Moscow);  Professor, Moscow Institute of Physics and Technology (State University)

E-mail: vladeffar@mail.ru

The use of LFM waveforms results in that the range measurements of moving objects are biased due to the range-Doppler coupling in the signal. Thus, in developing tracking filter it is necessary to take into account the range-Doppler coupling.

In this paper, the features of a tracking filter using linear frequency modulated (LFM) waveforms are studied. An interrelation of firstorder polynomial filters (two-state Kalman filter, diffusion filter, α-β filter) estimating true and biased range of moving objects is analyzed. The diffusion filter is defined as a two-state Kalman filter with introduction of additional term into correlation matrix of extrapolation errors. The additional term is a diagonal matrix having diffusion coefficients as the matrix elements. The expressions of diffusion coefficients are derived. The tracking accuracies of diffusion filter in steady state are the same as tracking accuracies of fixed memory least squares filter (or growing-memory filter at n = N). The gains of α-β filter at which tracking accuracies of this filter in steady state are the same as tracking accuracies of fixed memory least squares filter are derived. Also a performance comparison of first-order polynomial filters estimating true and biased range of moving objects is studied. An initial state estimate and error covariance matrix are derived from two measurements with the LFM waveform. The increase of difference between two range-Doppler coupling coefficients corresponding with these measurements improves the initial variance of range rate estimation. Besides that at the negative range-Doppler coupling coefficient the variance of extrapolated range of filter estimating true range is better than the variance of extrapolated range of filter estimating biased range.

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