On the trade-off between model expansion, model shrinking, and parameter estimation accuracy in least-squares data analysis

2005 ◽  
Vol 79 (8) ◽  
pp. 460-466 ◽  
Author(s):  
C. Kotsakis
Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 356 ◽  
Author(s):  
Xiao Zhang ◽  
Feng Ding ◽  
Ling Xu ◽  
Ahmed Alsaedi ◽  
Tasawar Hayat

This paper is concerned with the joint state and parameter estimation methods for a bilinear system in the state space form, which is disturbed by additive noise. In order to overcome the difficulty that the model contains the product term of the system input and states, we make use of the hierarchical identification principle to present new methods for estimating the system parameters and states interactively. The unknown states are first estimated via a bilinear state estimator on the basis of the Kalman filtering algorithm. Then, a state estimator-based recursive generalized least squares (RGLS) algorithm is formulated according to the least squares principle. To improve the parameter estimation accuracy, we introduce the data filtering technique to derive a data filtering-based two-stage RGLS algorithm. The simulation example indicates the efficiency of the proposed algorithms.


Author(s):  
Galina Vasil’evna Troshina ◽  
Alexander Aleksandrovich Voevoda

It was suggested to use the system model working in real time for an iterative method of the parameter estimation. It gives the chance to select a suitable input signal, and also to carry out the setup of the object parameters. The object modeling for a case when the system isn't affected by the measurement noises, and also for a case when an object is under the gaussian noise was executed in the MatLab environment. The superposition of two meanders with different periods and single amplitude is used as an input signal. The model represents the three-layer structure in the MatLab environment. On the most upper layer there are units corresponding to the simulation of an input signal, directly the object, the unit of the noise simulation and the unit for the parameter estimation. The second and the third layers correspond to the simulation of the iterative method of the least squares. The diagrams of the input and the output signals in the absence of noise and in the presence of noise are shown. The results of parameter estimation of a static object are given. According to the results of modeling, the algorithm works well even in the presence of significant measurement noise. To verify the correctness of the work of an algorithm the auxiliary computations have been performed and the diagrams of the gain behavior amount which is used in the parameter estimation procedure have been constructed. The entry conditions which are necessary for the work of an iterative method of the least squares are specified. The understanding of this algorithm functioning principles is a basis for its subsequent use for the parameter estimation of the multi-channel dynamic objects.


2021 ◽  
Vol 13 (4) ◽  
pp. 581 ◽  
Author(s):  
Yuanyuan Fu ◽  
Guijun Yang ◽  
Xiaoyu Song ◽  
Zhenhong Li ◽  
Xingang Xu ◽  
...  

Rapid and accurate crop aboveground biomass estimation is beneficial for high-throughput phenotyping and site-specific field management. This study explored the utility of high-definition digital images acquired by a low-flying unmanned aerial vehicle (UAV) and ground-based hyperspectral data for improved estimates of winter wheat biomass. To extract fine textures for characterizing the variations in winter wheat canopy structure during growing seasons, we proposed a multiscale texture extraction method (Multiscale_Gabor_GLCM) that took advantages of multiscale Gabor transformation and gray-level co-occurrency matrix (GLCM) analysis. Narrowband normalized difference vegetation indices (NDVIs) involving all possible two-band combinations and continuum removal of red-edge spectra (SpeCR) were also extracted for biomass estimation. Subsequently, non-parametric linear (i.e., partial least squares regression, PLSR) and nonlinear regression (i.e., least squares support vector machine, LSSVM) analyses were conducted using the extracted spectral features, multiscale textural features and combinations thereof. The visualization technique of LSSVM was utilized to select the multiscale textures that contributed most to the biomass estimation for the first time. Compared with the best-performing NDVI (1193, 1222 nm), the SpeCR yielded higher coefficient of determination (R2), lower root mean square error (RMSE), and lower mean absolute error (MAE) for winter wheat biomass estimation and significantly alleviated the saturation problem after biomass exceeded 800 g/m2. The predictive performance of the PLSR and LSSVM regression models based on SpeCR decreased with increasing bandwidths, especially at bandwidths larger than 11 nm. Both the PLSR and LSSVM regression models based on the multiscale textures produced higher accuracies than those based on the single-scale GLCM-based textures. According to the evaluation of variable importance, the texture metrics “Mean” from different scales were determined as the most influential to winter wheat biomass. Using just 10 multiscale textures largely improved predictive performance over using all textures and achieved an accuracy comparable with using SpeCR. The LSSVM regression model based on the combination of the selected multiscale textures, and SpeCR with a bandwidth of 9 nm produced the highest estimation accuracy with R2val = 0.87, RMSEval = 119.76 g/m2, and MAEval = 91.61 g/m2. However, the combination did not significantly improve the estimation accuracy, compared to the use of SpeCR or multiscale textures only. The accuracy of the biomass predicted by the LSSVM regression models was higher than the results of the PLSR models, which demonstrated LSSVM was a potential candidate to characterize winter wheat biomass during multiple growth stages. The study suggests that multiscale textures derived from high-definition UAV-based digital images are competitive with hyperspectral features in predicting winter wheat biomass.


2010 ◽  
Vol 118-120 ◽  
pp. 601-605
Author(s):  
Han Ming

Evaluation method of reliability parameter estimation needs to be improved effectively with the advance of science and technology. This paper develops a new method of parameter estimation, which is named E-Bayesian estimation method. In the case one hyper-parameter, the definition of E-Bayesian estimation of the failure probability is provided, moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation, and the property of E-Bayesian estimation of the failure probability are also provided. Finally, calculation on practical problems shows that the provided method is feasible and easy to perform.


2021 ◽  
pp. 107754632110191
Author(s):  
Fereidoun Amini ◽  
Elham Aghabarari

An online parameter estimation is important along with the adaptive control, that is, a time-dependent plant. This study uses both online identification and the simple adaptive control algorithm with velocity feedback. The recursive least squares method was used to identify the stiffness and damping parameters of the structure’s stories. Identification was carried out online without initial estimation and only by measuring the structural responses. The limited information regarding sensor measurements, parameter convergence, and the effects of the covariance matrix is examined. The integration of the applied online identification, the appropriate reference model selection in simple adaptive control, and adopting the proportional integral filter was used to limit the structural control response error. Some numerical examples are simulated to verify the ability of the proposed approach. Despite the limited information, the results show that the simultaneous use of online identification with the recursive least squares method and simple adaptive control algorithm improved the overall structural performance.


Automatica ◽  
1987 ◽  
Vol 23 (6) ◽  
pp. 707-718 ◽  
Author(s):  
S. Vajda ◽  
P. Valkó ◽  
K.R. Godfrey

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