Linearized Reduced Order Filtering

When a nonlinear dynamical or observational model is used to describe a system, the Kalman filter cannot be used to estimate the state without some approximation being made. If the approximation used is linearization of the equations about the state estimate, the resulting modification of the Kalman filter is often called an extended Kalman filter. In this paper we obtain a similar result, where the filter is constrained to be of reduced order to avoid excessive computational complexity.