Parameter identification of ship motion model based on multi-innovation methods

  • Shuo Xie
  • Xiumin Chu
  • Chenguang LiuEmail author
  • Jialun Liu
  • Junmin Mou
Original article


In consideration of the defects of traditional least squares and extended Kalman filtering methods that are used for parameter identification of ship response model, i.e., low precision and converge rate, multi-innovation least squares and improved multi-innovation extended Kalman filtering are proposed in this paper, respectively. Specifically, a forgetting factor is introduced to reduce the cumulative impact of past interference in multi-innovation extended Kalman filtering, and relevant bounded convergence of the improved method has been analyzed theoretically. Based on \(10^\circ /10^\circ \), \(20^\circ /20^\circ \) and \(30^\circ /30^\circ \) zig-zag tests on a real experiment platform and simulations with KVLCC2 ship model, comparisons on identification precision and convergence rate between the proposed multi-innovation identification methods and traditional methods are conducted. Meanwhile, comparisons between the multi-innovation least squares and the improved multi-innovation extended Kalman filtering are also carried out. The simulation and actual experiment results indicate that both the identification accuracy and convergence rate of the proposed improved multi-innovation extend Kalman filtering method are higher than those of the traditional identification methods and the multi-innovation least squares method.


Ship response model Parameter identification Multi-innovation method Nomoto model Forgetting factor 



Least squares


Recursive least squares


Multi-innovation least squares


Extended Kalman filtering


Multi-innovation extended Kalman filtering


Root mean squares error


Correlation coefficients


Multi-innovation length

\(\psi \)

Heading angle


Heading rate

\(\delta \)

Actual rudder angle

\(\delta _E\)

Rudder angle order


Output vector of RLS

\(\varvec{\varphi }\)

Information vector of RLS

\(\varvec{\theta }\)

Parameter vector of RLS


Innovation of RLS


Multi-innovation vector of MI-LS

\(\varvec{\phi }\)

Extended information vector of MI-LS


Extended state of EKF


Measurement state of EKF


transition function of EKF


transition matrix of EKF


Measurement matrix of EKF


State noise of EKF


State noise variance of EKF


Measurement noise of EKF


Measurement noise variance of EKF


State gain vector of EKF at moment k


State gain matrix of MI-EKF under multi-innovation length p at time k


Multi-innovation with length p of MI-EKF at time k



The work presented in this paper was funded by Natural Science Foundation of Hubei Province Project (no. 2015CFA111), the Project of Ministry of Transport, PRC (no. 2015326548030), the China Postdoctoral Science Foundation (no. 2018M632923) and financially supported by the Double First-rate Project of WUT(Wuhan university of Technology).


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Copyright information

© The Japan Society of Naval Architects and Ocean Engineers (JASNAOE) 2019

Authors and Affiliations

  1. 1.National State Key Laboratory of Information Engineering in Surveying, Mapping and Remote SensingWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Wuhan University of TechnologyWuhanPeople’s Republic of China

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