A Finite Depth Motion Filter is a stateless sensor fusion, error estimation and smoothing algorithm that can replace a Kalman Filter in situations in which a stateful design is not desired. By analogy to signal processing, a Kalman filter is an infinite response filter, where the infinite time history is captured in the state vector and state covariances. A Finite Depth Motion Filter is the finite impulse response equivalent. While the primary motivation in our application was to avoid stateful logic, we found other advantages to the finite solution, particularly robustness to missing data and interruptions in the data stream.