Adaptive Kernel Learning Kalman Filtering With Application to Model-Free Maneuvering Target Tracking

Kernel method is a non-parametric linearization method for system modeling, which uses nonlinear projection from input data space to high-dimensional Hilbert feature space and employs kernel function for hiding the projection operator in a linear learner to replace inner product calculation in Hilbert space and to avoid the curse of dimensionality. Kernel method is data-driven and learnable to nonlinear model. For independency to a priori model, it provides a novel way of state estimation for nonlinear dynamic systems with model uncertainties. In this paper, an adaptive kernel learning Kalman filtering method is proposed and applied into the problem of maneuvering target tracking. Without use of a priori system model, the method performs Kalman filtering in a reproducing kernel Hilbert space (RKHS) by estimating conditional embedding operator (CEO) as system state transfer function from training data. For the stochastic uncertainty in system model, the maximum correntropy criterion (MCC) is introduced to obtain kernel parameter optimization and balance of estimation performance, while a sliding window is designed for online updating estimation of state transfer function to get adaptability to unknown system dynamics. Such the construction for kernel Kalman filtering (KKF) is helpful to extend application from time-series signal processing to state estimation of uncertain dynamical systems. Simulation scenarios include average sunspot prediction, hovering target tracking and hypersonic maneuvering target tracking, corresponding to verification in low-dynamic, periodic-dynamic and high-dynamic systems. Numerical results have illustrated that the proposed adaptive KKF can realize model-free tracking for target that has nonlinear dynamical motion, shown adaptability to non-cooperative target maneuver and better precision and convergence speed than typical model-based algorithms.