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.

Coherent signals, such as a time varying voltage appearing on a radio antenna, are fundamentally different than non-coherent signals, such as the power magnitude of an individual pixel in a CCD camera. This discussion explores the details of the differences between coherent and non-coherent signals and demonstrates a generalized detector for coherent signals based on Hermetian quadratic forms. Hermetian quadratic forms appear frequently in coherent signal detection and classification processes. This includes power detection and many adaptive processing applications. We show how to generalize this concept to Neural Nets and other Machine Learning systems, and provide examples of the benefits of doing so.