This paper discusses parameter estimation and detection in laplace distributed noise. The received signal is modeled as r($DOT@) $EQ As($DOT@,$theta@) $PLU n($DOT@), where A is an unknown amplitude, $theta is the parameter vector to be estimated and n($DOT@) is independent laplace distributed noise. The simultaneous maximum likelihood estimator of (A,$theta@) is derived. The derived estimator is based on a combination of a weighted median filter$LB@1$RB and a generalized form of the ordinary matched filter$LB@2$RB@. Examples of performance for four different detectors are given for a case of binary detection, when the amplitude A or the signal shape s($DOT@,$theta@) 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.