I.J. Image, Graphics and Signal Processing, 2015, 7, 24-32 Published Online June 2015 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijigsp.2015.07.04 Copyright © 2015 MECS I.J. Image, Graphics and Signal Processing, 2015, 7, 24-32 Stochastic Characterization of a MEMs based Inertial Navigation Sensor using Interval Methods Subhra Kanti Das 1 , Dibyendu Pal 1 , Virendra Kumar 1 , S. Nandy 1 1 Robotics & Automation, CSIR-CMERI, India, PIN-713209 E-mail: subhrakanti.das82@gmail.com Kumardeb Banerjee 2 , Chandan Mazumdar 2 2 Jadavpur University, Kokata, PIN-700032 Abstract—The aim here remains to introduce effectiveness of interval methods in analyzing dynamic uncertainties for marine navigational sensors. The present work has been carried out with an integrated sensor suite consisting of a low cost MEMs inertial sensor, GPS receiver of moderate accuracy, Doppler velocity profiler and a magnetic fluxgate compass. Error bounds for all the sensors have been translated into guaranteed intervals. GPS based position intervals are fed into a forward- backward propagation method in order to estimate interval valued inertial data. Dynamic noise margins are finally computed from comparisons between the estimated and measured inertial quantities It has been found that the intervals as estimated by proposed approach are supersets of 95% confidence levels of dynamic errors of accelerations. This indicates a significant drift of dynamic error in accelerations which may not be clearly defined using stationary error bounds. On the other side bounds of non-stationary error for rate gyroscope are found to be in consistence with the intervals as predicted using stationary noise coefficients. The guaranteed intervals estimated by the proposed forward backward contractor, are close to 95% confidence levels of stationary errors computed over the sampling period. Index Terms—Stochastic, dynamic, error, MEMs, inertial, interval, methods, INS, GPS. I. INTRODUCTION Process dynamics in conventional approach towards multi-sensor data fusion, are only known with some degree of certainty. The basic approach to handling this inconvenience has traditionally been to appeal to a probabilistic description of this uncertainty, via the inclusion of a process and a measurement noise, and apply a statistically optimal filter such as the Kalman Filter. This approach carries with it the necessity to introduce experimentally some distribution law describing the process and measurement noise. An alternative approach to treating processes with uncertain data is to apply the notions and methods of interval analysis. The idea of using interval arithmetic to describe the uncertainty in the system model was proposed in the late 90’s (Chen et al, 1997). This type of uncertainty can easily arise in practice. For example, when modelling from first principles, the values of certain physical parameters may not be known exactly, but known to lie within certain bounded limits with absolute certainty. Or when using system identification techniques to model a dynamic system, several models that differ only in the values of the matrix coefficients may be obtained under slightly different conditions, and these may all be contained in an interval. Coming to sensor fusion, stochastic estimators are instrumental only in realizing covariance for overall estimation error. This is however significantly affected by the measurement error margin, which in the conventional approach remains unchanged throughout the entire estimation cycle. Interestingly the stationary measurement error margins fed into the estimation block initially are liable to evolve over time, due to unprecedented drifts encountered by the sensors. It is in this context that work is carried out in incorporating an interval based sensor fusion algorithm for an integrated navigational sensor suite. The algorithm is capable of determining dynamic error margins for a low cost MEMs based inertial navigation sensor on the one hand. At the other side the algorithm is shown to effectively reduce the error bounds for an integrated GPS, compass and Doppler velocity profiler meant for autonomous navigation of unmanned marine vehicles. As regards navigation measure for autonomous marine vehicles, use of commercially available low cost MEMs inertial navigation sensors has grown into a recent trend. Although their suitability for short range operations is very obvious due to their high levels of drift, the cost effectiveness gives way for integration of other navigation aids. Extensive work has been put into studies of errors commonly associated with such systems. Various calibration and stochastic modelling methods have been proposed in this regard. However most of the proposed methods aim only at the stationary characteristic of such errors, with little attention towards dynamic drifts. The two distinct types of error sources to be considered for MEMs inertial sensors are deterministic and stochastic. Fig. 1 illustrates a categorization of typical