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Kalman filter with range-Doppler coupling compensation: choice of diffusion coefficients

DOI 10.18127/j00338486-201910(15)-06

Keywords:

M.A. Murzova – Post-graduate Student, Moscow Institute of Physics and Technology (State University); Engineer, PJSC «Radiofizika» (Moscow)
E-mail: mariya.trofimenko@phystech.edu


In this paper, features of a tracking filter using linear frequency modulated (LFM) waveforms are studied. 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, the range-Doppler coupling error is taken into account in developing tracking filter.
An influence of diffusion process (or process noise) parameters on the tracking accuracies of diffusion filter is studied. The diffusion filter is defined as a two-state Kalman filter with introduction of additional term into covariance matrix of extrapolation errors. Besides that, an observation matrix includes a range-Doppler coupling coefficient. The additional term is determined by transition and covariance matrices of diffusion process. The expressions for transition and covariance matrices are derived from the equivalence of tracking accuracies of the diffusion filter in steady state and a fixed memory least squares filter. Also, the estimate covariance matrix of the diffusion filter coincides with an estimate covariance matrix of a diffusion filter whose an observation matrix doesn’t include the range-Doppler coupling coefficient and a filtered state estimate is corrected by a range-Doppler coupling error estimate after every filtering step.
Two different models of diffusion process satisfying described above requirements are provided. The model of diffusion process is determined by transition and covariance matrices. Besides that, study results give opportunity to choose the diffusion process parameters, so that to provide specified tracking accuracies of the diffusion filter.

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May 29, 2020

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