Maximum likelihood estimation of geodesic subspace trajectories using approximate methods and stochastic optimization

Signal subspace methods are widely used in array processing and other applications. Traditionally, these methods require that the subspace is stationary (i.e., fixed) over the time window being analyzed. For many applications, the subspace is significantly time-varying because of, for example, the dynamics of the array and/or target motion. Recently, a geometric-based model of subspace trajectories based on geodesics on the Grassmann manifold has been developed for these nonstationary cases. Some approximate methods for the maximum likelihood estimation of geodesic subspace trajectories are presented as part of a global stochastic optimization approach. These methods are demonstrated on real USA Army battlefield acoustic sensor data with some promising preliminary results.