The Near Constant Acceleration Gaussian Process Kernel for Tracking

Time series prediction is traditionally the domain of the state-based Kalman filter and very general Kalman filter process models, such as the near constant acceleration model (NCAM), have been developed to successfully track moving targets. However, the standard Kalman filter uses Markov process models and, consequently, it is difficult to track processes which include a complex periodic component. Gaussian processes are a generalisation of the Kalman filter and are able to model periodic behaviour efficiently and succinctly. However, no equivalent Gaussian process model for near constant acceleration has been formulated. We develop an equivalent Gaussian process kernel for NCAM to be used for time-series prediction.