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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 6547312, 8 pages
Research Article

Heave Motion Measurement by Adaptive Filter Based on Longuet-Higgins Wave Model

School of Instrumentation Science & Opto-Electronics Engineering, Beihang University (BUAA), 37 XueYuan Road, Haidian District, Beijing 100191, China

Correspondence should be addressed to Jiazhen Lu; moc.361@aaubzjl

Received 13 September 2016; Accepted 7 February 2017; Published 28 February 2017

Academic Editor: Alberto Borboni

Copyright © 2017 Jiazhen Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A method is proposed to obtain heave motion information based on the Longuet-Higgins wave model. The Longuet-Higgins wave model which is closer to the sea wave is introduced. Based on it, random process of the noise is analyzed and the highpass filter is designed to reduce errors. Then it is the key point in this article that an adaptive algorithm is put forward because of the complexity of the waves. The algorithm adjusts the cutoff frequency to reduce the amplitude attenuation of the filter by analyzing the wave. For the same reason the comprehensive parameter of the phase compensation can be also obtained by the algorithm. Simulation measurement results show that under the rough sea situation the maximum value of absolute error is 0.4942 m according to the normal method, the method is 0.1170 m, and the average error ratio of the rough sea test reduces to 3.89% from 12.54%, which demonstrates that the adaptive filter is more effective in measuring heave movement. A variety of simulation cases show that the adaptive filter can also improve the precision of the heave motion under different sea situations.