COMPUTATION OF EXTENDED ROBUST KALMAN FILTER FOR REAL-TIMEATTITUDE AND POSITION ESTIMATION                                                                                                                                   Group Members:                                   Muhammad Siddique Farooq               204384                                               GhulamMustafa                                                204178 Instructor:                                             Muhammad Shezad Younia Abstract:            This paperexplains the implementation of extended robust Kalman filter. This demonstratesa method of real time computation of the filter on parallel computing devices.The solution of the filter expressed as a set of simultaneous linear equationswhich can be evaluated using givens rotation.

The paper also represents ERKF inthe development of attitude and position reference system for cargo transportvehicle. This paper concludes by analyzing the performance of the ERKF andverifying the validity of the givens rotation method. Kalman Filter:Inside the huge tool compartment of scientific tools thatcan be utilized for stochastic estimation from noisy sensor estimations, astandout amongst the most surely understood and frequently utilized tools iswhat is known as the Kalman filter. The Kalman filter is named after Rudolph E.Kalman, who in 1960 published his well known paper depicting a recursive answerfor the discrete-data linear filtering problem.The Kalman filter is basically an arrangement of equationsthat implement an optimal estimator that reduces the estimated error atmaximum.

The Kalman filter has been the subject of broad research and application,especially in the area of navigation. This is likely due in extensive part toadvances in digital computing that made the utilization of the filter in realtime practical problems, yet additionally to the relative simplicity and robustnature of the filter itself. Seldom do the conditions essential for optimalityreally exist, but then the filter obviously functions admirably in spite ofsituations, for some applications despite this circumstance.The Kalmanfilter is to estimate the state of a discrete-time controlled process which is governed by the linearstochastic difference equation                     With measurement  whichis                             The random variables wk and Vk represent the process andmeasurement noise respectively. Extended Kalman Filter (EKF):A Kalman filter that linearizes itself about the meanand covariance is said to be asExtended Kalman Filter or EKF. Calculations, in this specificpaper were made using provided rotations. While talking about vehicle statedetermination the system was composed of inertial measurement units and GPS.

IMU was using uncertain results of rates of accelerometers and gyros. The dynamic equations for attitude model are given by and  areroll, pitch and yaw respectively. Transformationmatrix between angular velocities is  Recursive algorithm used in the paper is shown in below.   Experimental Results:IMU and GPS were used tofind position (lat, long, alt) and attitude (roll, pitch, heading) of avehicle. Micro electro mechanical system based sensors were used.

The IMU updatefrequency was 400Hz having a built-in algorithm to compute linear and angularvelocities and orientations by sensors. It used gyros, accelerometers andmagnetometers. Velocities (angular and linear) were measured about the vehicleframe of reference and orientation was observed in terms of Euler angles. TheGPS provided the values of yaw, roll, pitch, lat, long and alt. Its frequencewas 10Hz which was far less than that of IMU which was 400Hz.

 Attitude Estimation:As we can see in thefigures below, variations in roll and pitch are considerably acceptable whilethat in heading are higher which was exactly as expected for ground vehicle.                                                 Roll                        Pitch                 Heading or yaw Moreover it was observedthat GPS measurements were more reliable and certain in this specific case thanthose of inertial measurement unit which were have more uncertainty. Further,because of extended robust Kalman filter the estimations of heading were robustto uncertainties in the IMU measurements. Position Estimation:Estimation of position wasfitted with GPS readings.

Further, when due to unavailability of GPS, inertialnavigation systems were measured, it used the frequency of 400Hz instead of10Hz, used in the case of GPS. The extended robust Kalman filter wasimplemented by the approach of inversion of conventional matrix as well as thatof proposed given rotation. The respective singular values (max and min) of theposition system matrix were also discussed.Position:         Latitude                                  Longitude               Altitude Conclusion:In this paper attitude andyaw reference system was discussed and presented which was based on inertialmeasurement unit and GPS data using extended robust Kalman filter. Theestimation of heading, given by the filter was according to the accurate GPSmeasurements. The estimations of position were made at higher frequencies dueto the use of INS based on the prediction of attitude of the body. And thefilter made it sure that the predictions were robust to uncertainties in bothmodels. Moreover a method of computing the extended Kalman filter in real timewas presented and cross verified which was based on QR decomposition.

Furtherit was discussed that this method had increased computational effectivenessover conventional approach.  References: 1-      Bijker, J. and Steyn, W. (2008).Kalman filter configurations for a low-cost loosely integrated inertialnavigation system on an airship, Control EngineeringPractice 16(12): 1509-1518 2-      Golub, G.

H. and Loan, C. F. V.(1996). Matrix Computations, The Johns Hopkins University Press.

 3-      Robust Recursive Kalman Filtering for Attitude Estimation by RobertoS. Inoue ? Marco H. Terra (September2, 2011) 4-      A Robust Extended Kalman Filter forDiscrete-time Systems with UncertainDynamics, Measurements and Correlated Noise Rodrigo Fontes Souto, StudentMember, IEEE, Joa˜o Yoshiyuki Ishihara, Member, IEEE, Geovany Arau´jo Borges, Member, IEEE (June 10-12, 2009 5-      Nonlinear Dynamic System Identification Based on FuzzyKalman Filter Dan´ ubia Soares Pires and Ginalber Luiz de Oliveira Serra FederalInstitute of Education, Science and Technology Department of Electroelectronics Laboratoryof Computational Intelligence Applied to Technology S˜ao Luis – MA, Brazil 6-     A NewApproach to Linear Filteringand Prediction Problems by R.E. Kalman Research Institute for Advanced Study,2 Baltimore,Md.

(1960)

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