Method for learning switching linear dynamic system models from data

摘要

From a set of possible switching states and responsive to a sequence of measurements, a corresponding sequence of switching states is determined for a system having a plurality of dynamic models, associates each model with a switching state such that a model is selected when its associated switching state is true. A state transition record is determined, based on the measurement sequence. The sequence of switching states is determined by backtracking through the state transition record. Alternatively, the switching state model is decoupled from the dynamic system model. The decoupled switching state model is transformed into a hidden Markov model (HMM) switching state model, while the decoupled dynamic system model is transformed into a time-varying dynamic system model. A solution to the dynamic system model is estimated using a Kalman filter. Next, variational parameters of the HMM switching state model are determined based on the estimated-solution, where the variational parameters measure an agreement of each model from the plurality of dynamic models with the solution. A sequence of switching states for the HMM switching state model is then determined based on the variational parameters of the HMM switching state model. finally, variational parameters of the dynamic system model are determined based on the determined sequence of switching states, such that the variational parameters are proportional to a combination of model parameters form the plurality of dynamic models weighted by the probability of the switching states.