Functional Bayesian Filter
We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). Applying kernel method and the representer theorem to perform linear quadratic estimation in a functional space, we derive a Bayesian recursive state estimator for a general nonlinear dynamical system in the original input space. Unlike existing nonlinear extensions of Kalman filter where the system dynamics are assumed known, the state-space representation for the Functional Bayesian Filter (FBF) is completely learned from measurement data in the form of an infinite impulse response (IIR) filter or recurrent network in the RKHS, with universal approximation property. Using positive definite kernel function satisfying Mercer's conditions to compute and evolve information quantities, the FBF exploits both the statistical and time-domain information about the signal, extracts higher-order moments, and preserves the properties of covariances without the ill effects due to conventional arithmetic operations. This novel kernel adaptive filtering algorithm is applied to recurrent network training, chaotic time-series estimation and cooperative filtering using Gaussian and non-Gaussian noises, and inverse kinematics modeling. Simulation results show FBF outperforms existing Kalman-based algorithms.
Code (0)
등록된 구현이 없습니다.
Tasks
State EstimationTime SeriesTime Series AnalysisSimilar Papers 제목 키워드 기반
Kernel Operator-Theoretic Bayesian Filter for Nonlinear Dynamical Systems
Motivated by the surge of interest in Koopman operator theory, we propose a machine-learning alternative based on a functional Bayesian perspective for operator-theoretic modeling of unknown, data-driven, nonlinear dynam…
Explainable Gated Bayesian Recurrent Neural Network for Non-Markov State Estimation
The optimality of Bayesian filtering relies on the completeness of prior models, while deep learning holds a distinct advantage in learning models from offline data. Nevertheless, the current fusion of these two methodol…
Computational EfficiencyState EstimationTrack Initialization and Re-Identification for~3D Multi-View Multi-Object Tracking
We propose a 3D multi-object tracking (MOT) solution using only 2D detections from monocular cameras, which automatically initiates/terminates tracks as well as resolves track appearance-reappearance and occlusions. More…
3D Multi-Object TrackingMulti-Object TrackingObjectObject Tracking+1Functional Bayesian Neural Networks for Model Uncertainty Quantification
In this paper, we extend the Bayesian neural network to functional Bayesian neural network with functional Monte Carlo methods that use the samples of functionals instead of samples of networks' parameters for inference …
Uncertainty QuantificationBI-EqNO: Generalized Approximate Bayesian Inference with an Equivariant Neural Operator Framework
Bayesian inference offers a robust framework for updating prior beliefs based on new data using Bayes' theorem, but exact inference is often computationally infeasible, necessitating approximate methods. Though widely us…
Bayesian InferenceGaussian Processes