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This paper is inspired by a recent contribution by Rao and Garnier about identification of continuous time models. They show examples where methods that directly estimate continuous time models, based on smoothed differentiated input-output data outperform methods that are based on discrete time model estimation. The reasons for that situation are investigated in this contribution. It turns out that...
In this contribution we discuss some variance properties of a two-step ARX estimation scheme. An expression for the co-variance of the final low order model is calculated and it is discussed how one should minimize this covariance. The implication of the results is that identification of the dynamics of a system could very easily be performed with standard linear least squares (two times), even if...
This contribution aims to enrich the recently introduced kernel-based regularization method for linear system identification. Instead of a single kernel, we use multiple kernels, which can be instances of any existing kernels for the impulse response estimation of linear systems. We also introduce a new class of kernels constructed based on output error (OE) model estimates. In this way, a more flexible...
In this companion paper, the choice of kernels for estimating the impulse response of linear stable systems is considered from a classical, “frequentist”, point of view. The kernel determines the regularization matrix in a regularized least squares estimate of an FIR model. The quality is assessed from a mean square error (MSE) perspective, and measures and algorithms for optimizing the MSE are discussed...
The identification of multiple affine subspaces from a set of data is of interest in fields such as system identification, data compression, image processing and signal processing and in the literature referred to as subspace clustering. If the origin of each sample would be known, the problem would be trivially solved by applying principal component analysis to samples originated from the same subspace...
In all adaptation problems it is essential to estimate the system's (or signal's) characteristics as quickly as possible. There are several design variables that effect this ability. Forgetting factors in recursive algorithms, band-pass filtering to select interesting frequency ranges, and similar, are of major importance for this problem. Also the model order will affect the speed of adaptation since...
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