A recursive subspace identification algorithm for autonomous underwater vehicles (AUVs) is proposed in this paper. Due to the advantages at handling nonlinearities and couplings, the AUV model investigated here is for the first time constructed as a Hammerstein model with nonlinear feedback in the linear part. To better take the environment and sensor noises into consideration, the identification problem is concerned as an errors-in-variables (EIV) one which means that the identification procedure is under general noise assumption. In order to make the algorithm recursively, propagator method (PM) based subspace approach is extended into EIV framework to form the recursive identification method called PM-EIV algorithm. With several identification experiments carried out by the AUV simulation platform, the proposed algorithm demonstrates its effectiveness and feasibility. 1. Introduction In recent years, autonomous underwater vehicles (AUVs) have attracted increasing attentions due to their remarkable features such as high agility, excellent convenience and low cost in applications of underwater explorations and developments. However, contradictions lay between more and more complicated missions for AUV and the control and navigation systems that are not accurate enough. System identification methods have provided an alternative way other than traditional expensive instruments dependent approaches to improve the abilities of autonomous systems in various aspects [1–5]. As a result, a variety of researches have been put forward to identify the ordinary differential model of AUVs for model based control and navigation. Rentschler and coworkers [1] have demonstrated an iterative procedure to revise the model and controller of Odyssey III AUV to obtain better flight performances. Nonlinear observers based identification algorithm with sliding mode observer and EKF is also proposed for designation of nonlinear controller in [2]. For a more robust navigation system in case of sensor fault, Hegrenaes and Hallingstad [3] have used least squares algorithm to estimate both sea current disturbances and model parameters of the HUGIN 4500 AUV. However, due to the complexity of AUV system, many nonlinearities and coupled terms exist in ordinary differential equations that make the identification of whole pack of hydrodynamic coefficients quite complicated and time consuming. As a consequence, AUV differential model usually need to be simplified through eliminations of nonlinear and coupled terms before identification process. For example, in the research of Tiano et
References
[1]
M. E. Rentschler, F. S. Hover, and C. Chryssostomidis, “System identification of open-loop maneuvers leads to improved AUV flight performance,” IEEE Journal of Oceanic Engineering, vol. 31, no. 1, pp. 200–208, 2006.
[2]
J. Kim, K. Kim, H. S. Choi, W. Seong, and K.-Y. Lee, “Estimation of hydrodynamic coefficients for an AUV using nonlinear observers,” IEEE Journal of Oceanic Engineering, vol. 27, no. 4, pp. 830–840, 2002.
[3]
？. Hegrenaes and O. Hallingstad, “Model-aided INS with sea current estimation for robust underwater navigation,” IEEE Journal of Oceanic Engineering, vol. 36, no. 2, pp. 316–337, 2011.
[4]
R. Qi, L. Zhu, and B. Jiang, “Fault tolerant reconfigurable control for MIMO systems using online fuzzy idenfication,” International Journal of Innovative Computing, Information and Control, vol. 10, no. 10, pp. 3915–3928, 2013.
[5]
S. A. Hisseini, S. A. Hadei, M. B. Menhaj, et al., “Fast euclidean direction search algorithm in adaptive noise cancellation and system identification,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 1, pp. 191–206, 2013.
[6]
A. Tiano, R. Sutton, A. Lozowicki, and W. Naeem, “Observer Kalman filter identification of an autonomous underwater vehicle,” Control Engineering Practice, vol. 15, no. 6, pp. 727–739, 2007.
[7]
Z. Cai and E.-W. Bai, “Making parametric Hammerstein system identification a linear problem,” Automatica, vol. 47, no. 8, pp. 1806–1812, 2011.
[8]
X.-M. Chen and H.-F. Chen, “Recursive identification for MIMO Hammerstein systems,” IEEE Transactions on Automatic Control, vol. 56, no. 4, pp. 895–902, 2011.
[9]
J. P. No？l, S. Marchesiello, and G. Kerschen, “Subspace-based identification of a nonlinear spacecraft in the time and frequency domains.,” Mechanical Systems and Signal Processing, vol. 43, no. 1-2, pp. 217–236, 2013.
[10]
S. J. Qin, “An overview of subspace identification,” Computers & Chemical Engineering, vol. 30, no. 10–12, pp. 1502–1513, 2006.
[11]
W. Lin, S. J. Qin, and L. Ljung, “On consistency of closed-loop subspace identification with innovation estimation,” in Proceedings of the 43rd IEEE Conference on Decision and Control (CDC '04), vol. 2, pp. 2195–2200, Nassau, Bahamas, December 2004.
[12]
M. Lovera, T. Gustafsson, and M. Verhaegen, “Recursive subspace identification of linear and non-linear Wiener state-space models,” Automatica, vol. 36, no. 11, pp. 1639–1650, 2000.
[13]
C. T. Chou and M. Verhaegen, “Subspace algorithms for the identification of multivariable dynamic errors-in-variables models,” Automatica, vol. 33, no. 10, pp. 1857–1869, 1997.
[14]
Z. Yan, D. Wu, J. Zhou, and W. Zhang, “Recursive identification of autonomous underwater vehicle for emergency navigation,” in Proceedings of the Oceans, pp. 1–6, IEEE, Hampton Roads, Va, USA, 2012.
[15]
A. Alenany and H. Shang, “Recursive subspace identification with prior information using the constrained least squares approach,” Computers & Chemical Engineering, vol. 54, pp. 174–180, 2013.
[16]
A. Akhenak, Deviella, L. Bako, et al., “Online fault diagnosis using recursive subspace identification: application to a dam-gallery open channel system,” Control Engineering Practice, vol. 21, no. 6, pp. 791–806, 2013.
[17]
B. Yang, “Projection approximation subspace tracking,” IEEE Transactions on Signal Processing, vol. 43, no. 1, pp. 95–107, 1995.
[18]
T. Gustafsson, “Instrumental variable subspace tracking using projection approximation,” IEEE Transactions on Signal Processing, vol. 46, no. 3, pp. 669–681, 1998.
[19]
H. Oku and H. Kimura, “Recursive 4SID algorithms using gradient type subspace tracking,” Automatica, vol. 38, no. 6, pp. 1035–1043, 2002.
[20]
G. Mercère, L. Bako, and S. Lec？uche, “Propagator-based methods for recursive subspace model identification,” Signal Processing, vol. 88, no. 3, pp. 468–491, 2008.
[21]
T. I. Fossen, Guidance and Control of Ocean Vehicles, John Wiley & Sons, New York, NY, USA, 1994.
[22]
D. Luo and A. Leonessa, “Identification of MIMO Hammerstein systems with non-linear feedback,” IMA Journal of Mathematical Control and Information, vol. 25, no. 3, pp. 367–392, 2008.
[23]
L. Ljung, System Identification: Theory for Users, Prentice Hall, Upper Saddle River, NJ, USA, 1987.
[24]
M. Verhaegen and P. Dewilde, “Subspace model identification—part 1. The output-error state-space model identification class of algorithms,” International Journal of Control, vol. 56, no. 5, pp. 1187–1210, 1992.
