Estimation of Motion Intensity of Extended Objects Using Generalized Weibull Distribution

Abstract—The estimation of the scale parameter of the generalized Weibull probability density function by the criterion of the conditional risk minimum is considered and analyzed. Optimal estimates of the envelope intensity of the signals reflected from extended objects are obtained, provided that the intervals in the motion of these objects are independent random variables. These estimates are compared with the best unbiased estimate for various loss functions. It is shown that the convergence of the risk of the best unbiased estimate to the risk of the optimal estimate for the loss function, equal to the error module, is faster than the quadratic loss function. It is noted that the optimal estimates for the invariant and power loss functions coincide. The lower and upper $\varepsilon$-confidence boundaries are obtained and the conditions under which the obtained estimates correspond to the estimation of the Weibull distribution parameter are determined.