## UV identification techniques and results 41 Leastsquares identification method

The least-squares method is a classical identification method which is suitable for determining parameters of complex models, Ljung (1999). The authors have used this method to determine the coupled mathematical model. The main disadvantage of this method is that the observed vehicle has to be persistently excited in all directions for which the model is to be determined. Having this in mind, the VideoRay ROV was driven in a so-called "S-maneuver" in which the vehicle is moving forward-backward and rotating left to right at the same time. This way all couplings in the model are identified.

Based on the coupled model presented and derived in Section 2.4, equations (8), (9) and (10) can be set for surge, yaw and sway motion, respectively, where a1 = nJn,, a2 = _1w., an = R, = B-, , fi, = , v, = and y, =

6 ¡z-Nj- "-1 m-X,-.' m-X,-.' ri m-X,-. ' ' 1 m-Y,-, ' i m-Y,-, r = a1r + a2N + a3uv u = ß1u + ß2X + ß3rv

The identified parameters P3 and y3 should be inverse and reciprocal. The identification results show that both parameters are close to 1 so it can be approximated that p3 = —y2 = 1, i.e. added mass terms in surge and sway direction are equal. As a consequence of this a3 = 0, i.e. yaw motion is not coupled to other two motions. Finally the identified model of the VideoRay ROV can be shown in a matrix form using (11). Details can be found in Miskovic et al. (2007a). The validation results, which also give comparison between the coupled and uncoupled identified model, are shown in Fig. 9.

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