An information domain algorithm for estimating poorly observable initial condition statistics

References 1 and 2 present an algorithm for finding maximum likelihood estimates of the initial condition statistics of a dynamic linear state-space model using outputs from a collection of Kalman smoother runs on non-identically distributed test data. This DL (Data Likelihood) algorithm requires that all components of the initial condition state vector be observable on each test in the collection. The algorithm presented here, the information DL algorithm, does not require complete observability on each test. This is achieved by using different sufficient statistics to formulate the algorithm in the information, rather than the covariance domain. The resulting algorithm maintains the simplicity of the standard DL algorithm. In this paper we formulate information DL and give numerical examples of the algorithm performance. We also analyze theoretical properties of the algorithm and its relation to the standard DL algorithm.