Maximum entropy stochastic realization and robust filtering via convex optimization

We consider the problem of maximum entropy stochastic realization given partial, uncertain covariance data of an observed time series. The covariance uncertainties are described by upper and lower bounds on the covariance sequence and the associated power spectral density. Such a problem does not have an analytic solution in general; however, it can be formulated as a nonlinear convex optimization problem which can be solved globally and very efficiently by recently developed interior-point methods. Maximum entropy realization can be applied in robust filtering in the context of designing the linear estimation filter that minimizes the worst-case mean square error given uncertain covariances. We give an example of robust Kalman filter design to illustrate the ideas