Abstract

Maximum a posteriori (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, although a priori information 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 upon a priori knowledge. This second term reduces to a measure of trajectory smoothness in the special case of a Gauss–Markov a priori frequency model. Lastly, a MAP detection scheme is suggested for cases in which the presence of such signals is an issue.

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