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In this paper we describe a maximum a posteriori likelihood (MAPL) state and parameter estimator for a scalar discrete-time system with multiplicative noise. We develop a MAPL function and show that its maximization leads to parameter estimation equations which are coupled together with a nonlinear two-point boundary-value problem (b. v. p.) from which we obtain state estimates. We present an iterative procedure for obtaining MAPL estimates which decouples the state and parameter estimates. Simulation results, which illustrate convergence properties of the iterative procedure, are included.