A novel [z log(z)]-based closed form approach to parameter estimation of k-distributed clutter plus noise for radar detection

Abstract

In this paper, we present a novel [z log(z)]-based approach to the evaluation of estimators of the K-distributed clutter plus thermal noise parameters. In doing this, we start by deriving expressions of log-based moments of the received data, i.e., means of [log(z)] and [z log(z)], which are related to the parameters of the K plus noise distribution, the digamma, and the hypergeometric functions. Then, by accommodating a single pulse and noncoherent integration of N pulses, respectively, we first determine the new estimators in terms of log-based moments and first-and second-order moments. As the computation of these nonlinear estimates requires the use of numerical routines, we resort to the inverse of the harmonic mean of the received data to get equivalent but more interesting estimates in which expressions are independent of the confluent hypergeometric functions. Monte Carlo simulations show that the proposed estimators are more efficient than existing methods for various clutter plus noise situations.

Analysis of polarimetric bistatic sea clutter using the NetRAD radar system

“…The formula is reported in equation (3). Another approach is based on the estimates of the mean of the data and of the mean of the logarithm of the data, as discussed in chapter 13 of [15] and in [29][30][31], and reported in equation (4) where N is the number of non-coherently integrated pulses.…”

“…The estimator based on the mean of the logarithm of the data in equation (4) has been extended to take into account the effect of thermal noise, either proposing suitable numerical methods to obtain a value of the shape parameter [31], or developing a closed-form of the estimator when more than a single pulse are non-coherently integrated together [29]. Moment matching approach has been also used, for instance estimating the second, fourth, and sixth moment as in [23], or exploiting the knowledge of the noise power PN as in equation (6), where the first and second moment of the intensity of the clutter plus noise data are used, as reported in chapter 5 and 13 of [15] and in [22,31].…”

K-clutter plus noise parameter estimation using fractional positive and negative moments

“…A good analysis of the effect of additive noise on some estimation methods is well presented and discussed in [2]. This estimation problem has been discussed and some interesting estimation procedures with different degrees of accuracies are proposed in the literature [3][4][5][6][7][8][9][10]. In this context, Watts et al [3][4][5] presented a method based on the first three integer intensity moments.…”

“…Then, by accommodating lower fractional-order moments and moments of order one and two, the shape parameter estimator is derived and its effectiveness is assessed via computer simulations. Moreover, by extending the method of Blacknell and Tough [7] to the estimation of the K plus noise distribution parameters, Sahed et al [10] derived closed form expressions of the [z(log(z))] estimator. This estimator is given in terms of a confluent hypergeometric function for which numerical methods can be used to solve the resulting shape parameter equation.…”

“…To further improve the estimation accuracy of the results obtained in [3,9,10], we start by providing the expressions of positive-and negative-order moments for N integrated pulses. Then, a side-by-side multiplication of both moments' expressions happens to get rid of the explicit noise power parameter.…”