least squares estimation
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Author(s):  
Sliver Ivan Del Carpio Ramirez ◽  
Jhon Rodrigo Ortiz Zacarias ◽  
Jalber Brayan Macuri Vazquez ◽  
Sario Angel Chamorro Quijano ◽  
Deyby Huamanchahua

2021 ◽  
pp. 1-10
Author(s):  
Jing Zhang ◽  
Yuhong Sheng ◽  
Xiaoli Wang

Parameter estimation of high-order uncertain differential equations is an inevitable problem in practice. In this paper, the equivalent equations of high-order uncertain differential equations are obtained by transformation, and the parameters of the first-order uncertain differential equation including Liu process are estimated. Based on the least squares estimation method, this paper proposes a means to minimize the residual sum of squares to obtain an estimate of the parameters in the drift term, and make the noise sum of squares equal to the residual sum of squares to obtain an estimate of the parameters in the diffusion term. In addition, some numerical examples are given to illustrate the proposed method. Finally, applications of the high-order uncertain spring vibration equations verify the viability of our method.


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