  We propose an iterative method for joint state and parameter estimation using
measurements on a time interval [0,T] for systems that are backward output
stabilizable. Since this time interval is fixed, errors in initial state may
have a big impact on the parameter estimate. We propose to use the back and
forth nudging (BFN) method for estimating the system's initial state and a
Gauss--Newton step between BFN iterations for estimating the system parameters.
Taking advantage of results on the optimality of the BFN method, we show that
for systems with skew-adjoint generators, the initial state and parameter
estimate minimizing an output error cost functional is an attractive fixed
point for the proposed method. We treat both linear source estimation and
bilinear parameter estimation problems.
