2020
Schürch, Manuel; Azzimonti, Dario; Benavoli, Alessio; Zaffalon, Marco
Recursive estimation for sparse Gaussian process regression Journal Article
In: Automatica, vol. 120, pp. 109-127, 2020, ISSN: 0005-1098.
Abstract | Links | BibTeX | Tags: Gaussian processes, Kalman filter, Non-parametric regression, Parameter estimation, Recursive estimation
@article{SCHURCH2020109127,
title = {Recursive estimation for sparse Gaussian process regression},
author = {Manuel Schürch and Dario Azzimonti and Alessio Benavoli and Marco Zaffalon},
url = {http://alessiobenavoli.com/wp-content/uploads/2020/07/2020automatica-gps-2.pdf},
doi = {https://doi.org/10.1016/j.automatica.2020.109127},
issn = {0005-1098},
year = {2020},
date = {2020-01-01},
journal = {Automatica},
volume = {120},
pages = {109-127},
abstract = {Gaussian Processes (GPs) are powerful kernelized methods for non-parametric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs to larger datasets, several sparse approximations based on so-called inducing points have been proposed in the literature. In this work we investigate the connection between a general class of sparse inducing point GP regression methods and Bayesian recursive estimation which enables Kalman Filter like updating for online learning. The majority of previous work has focused on the batch setting, in particular for learning the model parameters and the position of the inducing points, here instead we focus on training with mini-batches. By exploiting the Kalman filter formulation, we propose a novel approach that estimates such parameters by recursively propagating the analytical gradients of the posterior over mini-batches of the data. Compared to state of the art methods, our method keeps analytic updates for the mean and covariance of the posterior, thus reducing drastically the size of the optimization problem. We show that our method achieves faster convergence and superior performance compared to state of the art sequential Gaussian Process regression on synthetic GP as well as real-world data with up to a million of data samples.},
keywords = {Gaussian processes, Kalman filter, Non-parametric regression, Parameter estimation, Recursive estimation},
pubstate = {published},
tppubtype = {article}
}
Gaussian Processes (GPs) are powerful kernelized methods for non-parametric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs to larger datasets, several sparse approximations based on so-called inducing points have been proposed in the literature. In this work we investigate the connection between a general class of sparse inducing point GP regression methods and Bayesian recursive estimation which enables Kalman Filter like updating for online learning. The majority of previous work has focused on the batch setting, in particular for learning the model parameters and the position of the inducing points, here instead we focus on training with mini-batches. By exploiting the Kalman filter formulation, we propose a novel approach that estimates such parameters by recursively propagating the analytical gradients of the posterior over mini-batches of the data. Compared to state of the art methods, our method keeps analytic updates for the mean and covariance of the posterior, thus reducing drastically the size of the optimization problem. We show that our method achieves faster convergence and superior performance compared to state of the art sequential Gaussian Process regression on synthetic GP as well as real-world data with up to a million of data samples.
2019
Benavoli, A; Balleri, A; Farina, A
Joint Waveform and Guidance Control Optimization for Target Rendezvous Journal Article
In: IEEE Transactions on Signal Processing, vol. 67, no. 16, pp. 4357-4369, 2019, ISSN: 1053-587X.
Abstract | Links | BibTeX | Tags: Cognitive radar, Kalman filter, linear quadratic Gaussian control
@article{Benavoli2019d,
title = {Joint Waveform and Guidance Control Optimization for Target Rendezvous},
author = {A Benavoli and A Balleri and A Farina},
url = {http://alessiobenavoli.com/wp-content/uploads/2019/08/Joint_waveform_and_guidance_control.pdf},
doi = {10.1109/TSP.2019.2929951},
issn = {1053-587X},
year = {2019},
date = {2019-08-01},
journal = {IEEE Transactions on Signal Processing},
volume = {67},
number = {16},
pages = {4357-4369},
abstract = {The algorithm developed in this paper jointly selects the optimal transmitted waveform and the control input so that a radar sensor on a moving platform with linear dynamics can reach a target by minimizing a predefined cost. The cost proposed in this paper accounts for the energy of the transmitted radar signal, the energy of the platform control input, and the relative position error between the platform and the target, which is a function of the waveform design and control input. Similarly to the linear quadratic Gaussian control problem, we demonstrate that the optimal solution satisfies the separation principle between filtering and optimization and, therefore, the optimum can be found analytically. The performance of the proposed solution is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency modulated chirps. Results show the effectiveness of the proposed approach for optimal waveform design and optimal guidance control.},
keywords = {Cognitive radar, Kalman filter, linear quadratic Gaussian control},
pubstate = {published},
tppubtype = {article}
}
The algorithm developed in this paper jointly selects the optimal transmitted waveform and the control input so that a radar sensor on a moving platform with linear dynamics can reach a target by minimizing a predefined cost. The cost proposed in this paper accounts for the energy of the transmitted radar signal, the energy of the platform control input, and the relative position error between the platform and the target, which is a function of the waveform design and control input. Similarly to the linear quadratic Gaussian control problem, we demonstrate that the optimal solution satisfies the separation principle between filtering and optimization and, therefore, the optimum can be found analytically. The performance of the proposed solution is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency modulated chirps. Results show the effectiveness of the proposed approach for optimal waveform design and optimal guidance control.