System Identification for Unmanned Marine Vehicles using Interval Analysis S K Das, V Kumar and D Pal Robotics & Automation CSIR-CMERI Durgapur, West Bengal INDIA, PIN-713209 Email: subhrakanti.das82@gmail.com K Banerjee and C Mazumdar Deptt of EIE & CSE University of Jadavpur Kolkata, West Bengal INDIA PIN-700032 Abstract—The aim in the present paper remains to describe a system identification method for unmanned marine vehicles using interval analysis in order to come up with estimation of parameter intervals instead of real values, such that the actual dynamics of the system shall remain confined within guaranteed bounds. The bounds are propagated through the system equations using such interval based parameters. The proposed method exploits guaranteed error bounds for the state variables as observed by different sensors. Unlike conventional Kalman estimators the adopted method rules out the requirement for determining co- variance matrices and approximated Jacobians. Interval based variables are used in constructing interval matrices. Principle of Least Squares is used in solving the system equation involving such non-punctual (interval) matrices. In this context a sophisti- cated interval matrix inversion technique is employed within the least squares framework in finally determining the parameter intervals. I. I NTRODUCTION Unmanned Marine Vehicles are systems capable of autonomous maneuvering and navigation targeted towards oceanography or respective sea operations. A thorough un- derstanding of the system’s dynamic behavior as governed by the various modalities of the system along with several uncer- tainties, is thus essential for successful control and guidance of the vehicle. This is often realized by open loop system identification, in order that the model parameters are fitted against data collected from actual operations of the vehicle under sophisticated configurations as for instance fixed thrust or motion profiles etc. The parameters are initialized with values known from some initial analysis or design. However, the accuracy of parameter identification is largely defined by the observations as collected during experiments with the ve- hicle, mainly accelerations, linear and angular velocities. The uncertainties associated with such data in the form of sensor noise as well as external disturbances, may significantly affect the parameters evaluated through identification. Conventional estimators like Kalman filters have been employed in order to estimate the parameters using system model equations, thereby taking into consideration the measurement noise associated with sensors. In the same line of thought the aim in the present paper remains to describe a sensor fusion approach using interval analysis in order to come up with parameter intervals instead of real values, such that the actual dynamics of the system shall remain confined within guaranteed bounds propagated through the system equations using such interval based parameters. The proposed method exploits guaranteed error bounds for the state variables as observed by different sensors. Unlike conventional Kalman estimators the adopted method rules out the requirement for determining co-variance matrices and approximated Jacobians. Interval based variables are used in constructing interval matrices. Principle of Least Squares is used in solving the system equation involving such non-punctual (interval) matrices. In this context a sophisticated interval matrix inversion technique is employed within the least squares framework in finally determining the parameter inter- vals. Conventional approaches are proved to be inapplicable for the present case. Hansen’s interval hull technique for finding out an inverted interval matrix is used as the basis for the proposed approach. The organization of the paper is as follows- section II summa- rizes a priori art in the field of system identifications carried out for unmanned marine vehicles. Conventional estimators like Kalman filters are discussed in this regard. Section III describes the problem associated with identifying model parameters. The general dynamics of such systems are formulated and a Least Square solution framework is established. Subse- quently, section IV presents the methodology adopted towards identifying parameter intervals. A discussion regarding the problems encountered with available methods due to Krawczyk or Nirmala and Ganesan, is presented at the outset. Following the inconsistencies, a partitioned hull approach towards finding interval matrix inverse is described. Finally, experimental setup is detailed and field results are obtained. Parameter intervals are estimated using a data set collected during a single trial. Overestimated intervals are constricted heuristically. The con- stricted intervals are verified with another data set. Results are summarized accordingly. II. PRIORI ART A multi-layered connectionist neural network (N-N) model is adopted in the work of Hassan et al [1]. Two phase N-N has been designed with the first layer identifying single degrees of freedom parameters, and the subsequent identifying couped parameters. However, the work ignores typical stochastic errors associated with sensors from which data are collected during the trials. As a result, training of the neural network remains subject to stochastic disturbances associated with correspond- ing measurements. Jay et al in his thesis work [2], adopted a least squares fit to side slip and turn rate data using maximum likelihood of batch processing, in order to estimate steering equation parameters. The identification process requires some controller 978-1-4799-3646-5/14/$31.00 ©2014 IEEE