I.F. Kupryashkin, V.P. Likhachev, A.B. Shelest

The problem of an estimation of a kind of function of phase modulation (FPM) signals with demanded accuracy arises as at the analysis of passage of radio signals with linear frequency modulation through space with dispersive properties, and at processing the radiohologram of the purpose formed at inverse SAR, that directly defines the quality of the formed radar-tracking. FPM of an impulse with rectangular bending around it is set in the form of the polynom of N-th degree containing factors, described by a vector of non-energetic parameters , making sense of an initial phase, frequency, speed of change of frequencies, etc. It is necessary, that estimation of a vector is carried out on a maximum likelhood method on a background of white noise. Thus expression for covariation matrix of errors of estimations of elements of a vector is written down with Fisher's information matrix. In the algebraic form expressions for complex function of uncertainty of a signal on vector parameter and diagonal elements of Fisher's matrix are received. The received result is generalized on a case of a joint estimation of elements of a vector . By the reference of a matrix the covariation matrix of errors of estimations of factors of decomposition FPM in series is defined. The often arising in practice of a radio engineering monitoring problem of potential accuracy of a joint estimation of bearing frequency and speed of change of frequency of the linear frequency modulated pulse with rectangular bending around and unknown an initial phase on a background of white noise is considered. Also it is shown, that in case of formation of the radar-tracking image of the maneuvering air purpose by a method of inverse SAR presence in FPM to nonlinearity of 3-rd order leads to deterioration of accuracy of an estimation of bearing frequency (its dispersion will increase in 6,25 times).