Bayesian forecasting and dynamic models (2nd ed.)
Bayesian forecasting and dynamic models (2nd ed.)
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
From moments of sum to moments of product
Journal of Multivariate Analysis
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Sparse Spectrum Gaussian Process Regression
The Journal of Machine Learning Research
IEEE Transactions on Signal Processing
A tutorial on particle filters for online nonlinear/non-GaussianBayesian tracking
IEEE Transactions on Signal Processing
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A novel Gaussian state estimator named Chebyshev polynomial Kalman filter is proposed that exploits the exact and closed-form calculation of posterior moments for polynomial nonlinearities. An arbitrary nonlinear system is at first approximated via a Chebyshev polynomial series. By exploiting special properties of the Chebyshev polynomials, exact expressions for mean and variance are then provided in computationally efficient vector-matrix notation for prediction and measurement update. Approximation and state estimation are performed in a black-box fashion without the need of manual operation or manual inspection. The superior performance of the Chebyshev polynomial Kalman filter compared to state-of-the-art Gaussian estimators is demonstrated by means of numerical simulations and a real-world application.