In this project, we consider the problem of tracking in complex nonlinear dynamical systems. While the Kalman filter is known to be the mean-squared error optimal tracker under linear dynamics and linear measurements, more sophisticated models and algorithms are required for complex dynamics. Here, we consider switching systems where the dynamical properties vary (“switch modes”) over time. For example, the dynamics of a vehicle may switch as it transitions from interstate to urban conditions, human speech dynamics switch as speakers change and stock market dynamics switch with discrete news events. In this work, we use mode-dependent neural networks to capture different nonlinear dynamics in a given system, and we developed a new algorithm, dubbed the Switching Neural Network Tracker (SNNT), to track modes and states over time. The proposed Bayesian system includes Markovian dynamics to model mode transitions and employes the Unscented Transform to mitigate computational complexity while estimating posterior probabilities. Examples using a synthetic robot motion data and measured honeybee dance data demonstrate accurate mode identification and a dramatic reduction in state estimation error relative to non-switching systems.
Video copyright: https://www.cc.gatech.edu/~borg/ijcv_psslds/