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Chirp radar:selection of α-β filter gain by minimizing maximum root-mean-square error

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
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


In this paper, the features of algorithm that is designed to track the maneuvering objects are studied. These maneuvering objects are detected by a chirp radar. Usage of linear frequency modulated signals results in so-called range-Doppler coupling, which yields a displacement of measured position from a true range of moving objects. Besides that, an α-β filter develops a lag error in its estimates while tracking maneuvering objects. The variance of estimate does not accurately represent actual error. Therefore, an optimal filter parameters α and β, at which the track accuracy is improved, are derived. The track accuracy is governed as total variance which equals to the sum of the position estimate variance and position lag error. Also, the calculation procedure of lag errors is described.
The minimization of the total variance provides a procedure of calculating optimal filter parameters α and β for deterministic tracking index ρ and normalized range-Doppler coupling coefficient kT. Thus, the optimal α-β relationship minimizes the total variance, so it improves tracking of maneuvering objects.
Besides that, for negative normalized range-Doppler coupling coefficient kT, there are such filter parameters at which lag error equals to zero. In that case, for any deterministic tracking index ρ, the total variance depends on the estimate variance only. Moreover, these filter parameters meet a criteria of minimum of the total variance.

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