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Comparison of the algorithms of nonlinear filtering of radio signals in receivers of GNSS


V.S. Efimenko, D.N. Voronchikhin

Algorithms that are used in tracking systems are the weakest link in modern radio devices and define their whole anti jam capability. In this article authors demonstrate the comparison of different algorithms of the optimal filtering: the Strаtonoviсh's filter, the optimal trajectory filter (OTF), the extended Kalman filter (EKF), the unscented Kalman filter (UKF), the particle filter. Using of this algorithms allows to provide benefits in tasks of primary signal processing. Implementation of the algorithms of filtering is connected with different numerical approximations used to calculate extrapolated distribution. The Stratonovich's filter requires calculation of great amount of multidimensional integrals in the whole state-space grid pattern. The OTF differs from Strаtonoviсh's filter by searching of the maximal likelihood estimation of the whole trajectory instead of point estimation at certain time point. The EFK uses Gaussian approximation of a posteriori density function. The UKF carries out application of true nonlinear function to the approximated distribution contained into a set of sigma points. The particle filter is based on using Monte Carlo with sequential importance sampling for the estimation of а posteriori density. The characteristics of all observed filters are compared for the chosen second order dynamic model. We were guided by receiving conditions typical for radio navigation system in which issues of anti jam capability is especially important on account of the extremely low power of the signal. In this article the comparison of filters realization labor intensiveness is carried out by the operating time.

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