A nonlinear approach to estimate the amplitude of a signal

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 maximum likelihood estimator is impossible. Generally a linear estimator without bias and with minimum variance is used because it is simple to calculate and only requires the knowledge of the covariance matrix of the noise. The amplitude is estimated here with a polynomial of the observations. The coefficients of the polynomial are determined such that the estimator is unbiased with minimum variance regardless of the amplitude. This method is quite general since it only requires the knowledge of some higher-order moments of the noise