Speaker
Description
Understanding biological oscillators often requires reconstructing internal states from measurement time series. This becomes difficult when dynamics contain slow–fast manifolds that produce strongly nonlinear trajectories. Under such conditions, common state estimation methods face fundamental limitations. In particular, the Kalman–Bucy filter assumes system dynamics can be locally approximated by a single Gaussian distribution, which fails in strongly nonlinear regimes. Particle filtering can capture such dynamics but often incurs high computational cost due to Monte Carlo sampling. To address these limitations, we introduce an asymmetric particle Gaussian mixture filter (AP-GMF) for nonlinear oscillatory systems. The posterior distribution is represented by Gaussian particles whose structure adapts dynamically. Particles are split based on local nonlinearity and combined using the Kullback–Leibler divergence, enabling efficient approximation. Compared with the asymmetric particle population density method, AP-GMF achieves comparable or higher accuracy with fewer particles. We evaluate AP-GMF on the van der Pol oscillator, a general nonlinear oscillator, across multiple parameter regimes. The method consistently outperforms existing filters, including the level-set Kalman filter and the continuous–discrete cubature Kalman filter. We also provide a parallel implementation enabling accurate state estimation at practical computational cost.
