Maximumaposteriori(MAP) techniques are applied to the problem of estimating the unknown parameters of a frequency modulated narrow‐band signal in additive white Gaussian noise. Signals are assumed to have unknown amplitude, initial phase, and frequency versus time history, althoughaprioriinformation concerning the frequency trajectory may be available. In addition, it is assumed that the signal frequency trajectory can be adequately modeled by a continuous piecewise linear function of time. It is shown that the MAP estimator maximizes a linear combination of (1) coherent match of signal induced outputs to received observations, and (2) a term dependent only uponaprioriknowledge. This second term reduces to a measure of trajectory smoothness in the special case of a Gauss–Markovapriorifrequency model. Lastly, a MAP detection scheme is suggested for cases in which the presence of such signals is an issue.