A.N. Bystrov, V.I. Djigan

The paper considers the influence of the sampling period and the effects of amplitude quantization of the input signal on the properties of a tracking range finder, which is a part of radar system. Digital range finder is a nonlinear discrete-time tracking system, which behavior depends on the parameters of processed signals conversion to the digital form. The main contribution to nonlinear properties of such system makes the discrimination characteristics of the digital time discriminator, which is a part of f range finder. Analysis shows that the discrimination characteristics of the digital time discriminator can be considered as result of amplitude quantization of linearized discrimination characteristics, depending on the quantization of the input signal. Analysis of the characteristics of the considered range finder in the case of the linearized tracking system was conducted and mathematical expressions for the equivalent bandwidth of tracking system were obtained. These expressions allow to calculate the weights of a digital low-pass filter which is a part of a range finder. The weights minimize the total error of range measurement in steady state. The influence of quantization effects of discrimination characteristics on the parameters of range finder and on tracking accuracy has been examined for three procedures of calculating of the resultant characteristics: with a rounding, with truncation of an additional code and with truncation of forward and reverse codes. This analysis has been conducted with the use of the method of statistical linearization, which is based on the replacement of the nonlinear element (the discrimination characteristics) with the statistically equivalent linear element. As the result of the analysis the coefficients of statistical linearization of determined and centered random component of the input signal of time discriminator have been calculated at an arbitrary ratio of noise and instrumental errors. The cases of noise errors, small or large in comparison with the instrumental errors of tracking range finder have been considered in detail. The accuracy of the digital tracking system in a steady regime for various forms of discrimination characteristics has been examined. These results show that the rounding method is preferable since in this case the non-linearity influences to a lesser degree, than at other methods of calculation of the discrimination characteristics. The analysis has shown that at small noise the instrumental error makes a basic contribution to a random component of the distance measuring error, and determined component can be non zero even with the stationary target. At a certain threshold value of the input noise the linearization of discrimination characteristics occurs, thus it possible not to consider the effects of quantization. The software model of the tracking range finder was used to verify the results of the analysis. The conclusions and mathematical relationships given in the work are confirmed by the results of the simulation of the tracking range finder.