Adaptive Kernel Kalman Filter Multi-Sensor Fusion

The adaptive kernel Kalman filter (AKKF) is an effective Bayesian inference method for non-linear system estimation/tracking. With the AKKF, the posterior distributions of hidden states are embedded into a kernel feature space and approximated by the feature mappings of particles with associated kernel weights. The kernel weighted mean vector and associated covariance matrix are predicted and updated according to the kernel Kalman rule (KKR). In this paper, the AKKF is extended for the use in multi-sensor bearing–only tracking (BOT) systems. First, the centralized fusion based AKKF is formulated as a baseline for the AKKF application in multi-sensor BOT systems. Then, considering the computational capacities, transmitted power and forward link bandwidth constraints, the semi-centralized fusion based AKKF is proposed. In this extended AKKF scheme, the prediction and update steps are executed at the fusion center (FC) and sensors separately. The prior and posterior kernel weight vectors and matrices are exchanged between the FC and sensors. Simulation results are presented to assess the performance of the proposed extended AKKFs compared with fusion based particle filter (PF) and Gaussian particle filter (GPF) for a multi-sensor BOT problem.