A Regularized Variable Projection Algorithm for Separable Nonlinear Least Squares Problems

DOI10.1109/TAC.2018.2838045zbMath1482.93717OpenAlexW2804206910MaRDI QIDQ4629809

Han-Xiong Li, C. L. Philip Chen, Guang-yong Chen, Min Gan

Publication date: 28 March 2019

Published in: IEEE Transactions on Automatic Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/tac.2018.2838045

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Least squares and related methods for stochastic control systems (93E24)

Related Items (50)

Adaptive regularised kernel-based identification method for large-scale systems with unknown order ⋮ Numerical approximation of partial differential equations by a variable projection method with artificial neural networks ⋮ Lopsided shift-splitting preconditioner for saddle point problems with three-by-three structure ⋮ Parameter estimation for a class of radial basis function-based nonlinear time-series models with moving average noises ⋮ Efficient parameters estimation method for the separable nonlinear least squares problem ⋮ A novel reduced-order algorithm for rational models based on Arnoldi process and Krylov subspace ⋮ Weight least squares algorithm for rational models with outliers ⋮ Separable multi-innovation Newton iterative modeling algorithm for multi-frequency signals based on the sliding measurement window ⋮ Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator ⋮ Accelerated identification algorithms for rational models based on the vector transformation ⋮ Filtering‐based multi‐innovation recursive identification methods for input nonlinear systems with piecewise‐linear nonlinearity based on the optimization criterion ⋮ Two‐stage recursive identification algorithms for a class of nonlinear time series models with colored noise ⋮ Maximum likelihood extended gradient‐based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable‐gain nonlinearity ⋮ Maximum likelihood least squares‐based iterative methods for output‐error bilinear‐parameter models with colored noises ⋮ Parameter identification of a nonlinear radial basis function‐based state‐dependent autoregressive network with autoregressive noise via the filtering technique and the multiinnovation theory ⋮ Auxiliary model multiinnovation stochastic gradient parameter estimation methods for nonlinear sandwich systems ⋮ Three‐stage multi‐innovation parameter estimation for an exponential autoregressive time‐series model with moving average noise by using the data filtering technique ⋮ Iterative parameter identification algorithms for the generalized time‐varying system with a measurable disturbance vector ⋮ Augmented flexible least squares algorithm for time‐varying parameter systems ⋮ Auxiliary model‐based iterative parameter estimation for a nonlinear output‐error system with saturation and dead‐zone nonlinearity ⋮ An efficient recursive identification algorithm for multilinear systems based on tensor decomposition ⋮ Least squares parameter estimation and multi-innovation least squares methods for linear fitting problems from noisy data ⋮ Variable projection methods for separable nonlinear inverse problems with general-form Tikhonov regularization ⋮ Fitting the exponential autoregressive model through recursive search ⋮ Auxiliary variable-based identification algorithms for uncertain-input models ⋮ Improved gradient descent algorithms for time-delay rational state-space systems: intelligent search method and momentum method ⋮ Highly‐computational hierarchical iterative identification methods for multiple‐input multiple‐output systems by using the auxiliary models ⋮ Multi-innovation stochastic gradient parameter and state estimation algorithm for dual-rate state-space systems with \(d\)-step time delay ⋮ Two-stage gradient-based iterative algorithm for bilinear stochastic systems over the moving data window ⋮ The innovation algorithms for multivariable state‐space models ⋮ Gradient-based iterative identification method for multivariate equation-error autoregressive moving average systems using the decomposition technique ⋮ A generalized minimal residual based iterative back propagation algorithm for polynomial nonlinear models ⋮ Hierarchical least squares identification for feedback nonlinear equation-error systems ⋮ Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation ⋮ The filtering based auxiliary model generalized extended stochastic gradient identification for a multivariate output-error system with autoregressive moving average noise using the multi-innovation theory ⋮ Highly computationally efficient state filter based on the delta operator ⋮ On some parameter estimation algorithms for the nonlinear exponential autoregressive model ⋮ Maximum likelihood gradient identification for multivariate equation‐error moving average systems using the multi‐innovation theory ⋮ State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors ⋮ The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle ⋮ Method of moments for 3D single particleab initiomodeling with non-uniform distribution of viewing angles ⋮ Combined estimation of the parameters and states for a multivariable state‐space system in presence of colored noise ⋮ Separable multi‐innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems ⋮ Stochastic average gradient algorithm for multirate FIR models with varying time delays using self‐organizing maps ⋮ Maximum likelihood-based recursive least-squares estimation for multivariable systems using the data filtering technique ⋮ Maximum likelihood iterative identification approaches for multivariable equation-error moving average systems ⋮ Hierarchical parameter and state estimation for bilinear systems ⋮ Data filtering-based parameter and state estimation algorithms for state-space systems disturbed by coloured noises ⋮ Parameter estimation for a special class of nonlinear systems by using the over-parameterisation method and the linear filter ⋮ Parameter estimation for an exponential autoregressive time series model by the Newton search and multi-innovation theory

This page was built for publication: A Regularized Variable Projection Algorithm for Separable Nonlinear Least Squares Problems