Linear-Quadratic Estimation of a Parameter
Pascal Bondon · 2005
The problem of estimating the amplitude of a signal appears in many aspects of signal processing such as, for example, amplitude modulation in communication theory. When the probability distribution of the noise is unknown, the calculation of the maximun likelihood estimator is impossible. In this case, a linear estimator which is unbiased with minimum variance is usually implemented because it is simple to calculate and only requires the knowledge of the covariance matrix of the noise. In this paper, we investigate the direct generalization of the linear estimation which is the linear-quadratic estimation. The explicit expressions of the unbiased estirnaforand of its minimum variance are given in terms of the moments of the noise up to the fourth-order. This method is quite general, and the diminution of the estimation variance with regard to the linear estimation is shown to he proportional to the square of the third-order moment of the noise.