The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

This paper proposed a method to identify nonlinear systems via the fuzzy weighted least squares support machine (FW-LSSVM). At first, we describe the proposed modeling approach in detail and suggest a fast learning scheme for its training. Because the training sample data of independent variable and dependent variable has a certain error, and we obtain the sample which has a certain fuzziness f...

We present a software package for structured total least-squares approximation problems. The allowed structures in the data matrix are block-Toeplitz, block-Hankel, unstructured, and exact. Combination of blocks with these structures can be specified. The computational complexity of the algorithms is O(m), where m is the sample size. We show simulation examples with different approximation prob...

Least-Squares Support Vector Machines (LS-SVM’s), originating from Stochastic Learning theory, represent a promising approach to identify nonlinear systems via nonparametric estimation of nonlinearities in a computationally and stochastically attractive way. However, application of LS-SVM’s in the identification context is formulated as a linear regression aiming at the minimization of the l2 l...

A new algorithm, multiple concurrent recursive least squares (MCRLS) is developed for parameter estimation in a system having a set of governing equations describing its behavior that cannot be manipulated into a form allowing (direct) linear regression of the unknown parameters. In this algorithm, the single nonlinear problem is segmented into two or more separate linear problems, thereby enab...

Volterra lters have been applied to many nonlinear system identiication problems. However, obtaining good lter estimates from short and/or noisy data records is a diicult task. We propose a penalized least squares estimation algorithm and derive appropriate penalizing functionals for Volterra lters. An example demonstrates that penalized least squares estimation can provide much more accurate l...

Parameter estimation schemes based on least squares identification and detection ideas are proposed for ease of computation, reduced numerical difficulties, and bias reduction in the presence of colored noise correlated with the states of the signal generating system. The algorithms are simpler because in the edculations, the state vector is at one point replaced by a quantized version. This te...