SIXTH
ANNUAL 
The Subspace

Daniel R. Fuhrmann Department of Electrical Engineering Campus Box 1127 Washington University St. Louis, MO 63130 tel: (314) 9356163 email: danf@saturn.wustl.edu Abstract matrix is proposed. Unlike previous algorithms for subspace tracking, our method is based explicitly on a dynamic model for the timevarying subspace. The subspace S(t), as a function of time, is considered as a trajectory in a Grassmann manifold, and is given a coordinate representation via the projection matrix P(t). A general dynamic model for trajectories in the space of projection matrices (of fixed size N and rank K) is given by the differential equation
Our goal is to observe a sequence of data vectors x(0), x(T), x(2T), ... where x(t) lies in or near the range space of P(t), and using our dynamic model, estimate the trajectory P(t) along with the constant or slowly time varying matrix A. Specifically, one iteration of our algorithm, applied for each new data vector x, is as follows:

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