A nonlinear filtering problem is investigated, and the discrete representation theorem is used to synthesize the optimal filter. An optimal filtering algorithm is described, and hybrid techniques are employed to effect several methods of implementing the algorithm on a hybrid computer. These implementations are then compared (via Monte Carlo analysis) on the bases of speed and accuracy. It is c...

In this paper, the filtering problem is revisited in the basic Gaussian homogeneous linear system driven by fractional Brownian motions. We exhibit a simple approximate filter which is asymptotically optimal in the sense that, when the observation time tends to infinity, the variance of the corresponding filtering error converges to the same limit as for the exact optimal filter.

Independent analyses using Fisher information, optimal filtering, and information theory show that matched filtering images with hypothetical patterns in the logarithmic domain provides an optimal method for pattern recognition in the presence of signal-dependent noise arising from complex Gaussian fluctuations in the received fields. This provides a mathematical justification for the use of lo...