A simultaneous maximum likelihood estimator based on a generalized matched filter

The paper discusses parameter estimation and detection in Laplace distributed noise. The received signal is modeled as r(·)=As(·,θ)+n(·), where A is an unknown amplitude, θ is the parameter vector to be estimated and n(·) is independent Laplace distributed noise. The simultaneous maximum likelihood estimator of (A,θ) is derived. The derived estimator is based on a combination of a weighted median filter [Astola and Nuevo, 1992] and a generalized form of the ordinary matched filter [Gustavsson and Borjesson, 1992]. Examples of performance for four different detectors are given for a case of binary detection, when the amplitude A or the signal shape s(·,θ) are varied. Simulations indicate that the performance of detectors based on the generalized matched filter is not particularly dependent on either the estimate of the amplitude A or the signal shape