A new kernel-based approach for spectral estimation

Zorzi, Mattia

doi:10.23919/ecc51009.2020.9143975

Cited by 5 publications

(2 citation statements)

References 29 publications

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“…Regarding the smoothness, SS is the one inducing more smoothness on the impulse response. It is worth noting that many other extensions can be obtained, see for instance Chen & Ljung (2015a); Dinuzzo (2015); Zorzi & Chiuso (2018); Chen & Ljung (2015b); Zorzi (2020). All these kernels depend on few hyperparameters that are learnt from the data by minimizing the so called negative log-marginal likelihood.…”

Section: Introductionmentioning

confidence: 99%

A second-order generalization of TC and DC kernels

Zorzi¹

2021

Preprint

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Kernel-based methods have been successfully introduced in system identification to estimate the impulse response of a linear system. Adopting the Bayesian viewpoint, the impulse response is modeled as a zero mean Gaussian process whose covariance function (kernel) is estimated from the data. The most popular kernels used in system identification are the tuned-correlated (TC), the diagonal-correlated (DC) and the stable spline (SS) kernel. TC and DC kernel admits a closed form factorization of the inverse and determinant which is inherently related to the fact that the they solve a band extension problem, respectively, while maximizing the entropy. The SS kernel induces more smoothness than TC and DC on the estimated impulse response, however, the aforementioned properties do not hold in this case. In this paper we propose a second-order extension of the TC and DC kernel which induces more smoothness than TC and DC, respectively, on the impulse response. Moreover, these generalizations admit a closed form factorization of the inverse and determinant and represent the maximum entropy solution of a band extension problem, respectively. Interestingly, these new kernels belong to the family of the so called exponentially convex local stationary kernels: such a property allows to immediately analyze the frequency properties induced on the estimated impulse response by these kernels. Finally, numerical results show that the second-order TC kernel exhibits a performance similar to the one of the SS kernel. Thus, the former can represent an alternative to the latter in order to estimate the kernel hyperparameters in an efficient way.

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Section: Introductionmentioning

confidence: 99%

A second-order generalization of TC and DC kernels

Zorzi¹

2021

Preprint

Self Cite

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“…The covariance extension problem has been formerly studied to design high resolution spectral estimators for stationary stochastic processes, [1], [15], [22], [30] including the approximate moments matching case [4], [13]. Within this framework, an important aspect is that it is possible to take as objective function a pseudo-distance (or divergence) between the spectral density to be estimated and a given spectral density, called prior.…”

Section: Introductionmentioning

confidence: 99%