The purpose of this paper is to derive optimum estimators for the estimation of signal parameters when the signal is emersed in an additive, not necessarily Gaussian noise field. Also, expressions for evaluating their performance are derived and, for the nonrandom signal case, the results compared with the familiar Cramer–Rao equation which provides a lower bound for the variance of an unbiased estimate. A new lower bound is derived for the variance of an unbiased estimate of the signal power for the case where the signal is a zero mean, random process and again the performance of the estimator, which is optimum for this type of signal, is compared with this new bound. In general it is found that the performance of the optimum estimator when operated in a non‐Gaussian noise field is superior to that which can be obtained when the noise is Gaussian.