Performance Evaluation of INS Based MEMES Inertial Measurement Unit

Transcription

1 Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (215) ISSN EISSN Performance Evaluation of Based MEMES Inertial Measurement Unit Othman Maklouf 1, Salah Abdulhadi 2 Mahmoud Benhamid 3 and Hanin Shibl 4 Abstract Inertial navigation system () is a self-contained navigation system which provides position and velocity information through direct measurements from an inertial measurement unit (IMU). The advantage of is its independence from external electromagnetic signals, and its ability to operate in all environments. This allows an to provide a continuous navigation solution, with excellent short term accuracy. However, the suffers from timedependent error growth which causes a drift in the solution, thus compromising the long term accuracy of the system. The accuracy of the is highly depends upon the grade of the IMU used, typical IMU's are very expensive sensor, however, with a low cost version comes low performance. In this paper, we will investigate the design and implementation of 2-D navigation algorithm using MEMES IMU. First, the inertial sensors and the errors subjected to their measurement are discussed. Then importance of sensors calibration as well as the alignment of the strapdown inertial navigation system is illustrated. The mechanization equations in the navigation frame are explained. simulation is carried out The limitations of the inertial navigation systems are investigated in order to understand why sometimes is integrated with other navigation aids and not just operating in stand-alone mode. Finally, In order to perform numerical simulations, A MATLAB batch of M-file script and SIMULINK was used to model and simulate navigation algorithm. The paper also provides experimental results. The relative effectiveness of the navigation algorithm is highlighted. A field test on a four-wheel drive car is carried out. T Keywords Inertial Navigation; IMU; Strapdown I. INTRODUCTION HE basic principle of an is based on the integration of accelerations observed by the accelerometers on board the moving platform. The system accomplishes this task through appropriate processing of the data obtained from the specific force and angular velocity measurements. Thus, an appropriately initialized inertial navigation system is capable of continuous determination of vehicle position, velocity and attitude without the use of the external information [1]. A major advantage of using inertial units is that given the acceleration and angular rotation rate data in three dimensions, Othman Maklouf is with the Aeronautical Engineering Department, Faculty of Engineering. Tripoli University. LIBYA. Salah Abdulhadi is with the Electronic Engineering Department, Engineering Academy Tajoura. LIBYA. Mahmoud Benhamid is with the Computer Engineering Department, Engineering Academy Tajoura. LIBYA. Hanin Shibl is with the Electronic Engineering Department, LIBYA. the velocity and position of the vehicle can be evaluated in any navigation frame. For land vehicles, a further advantage is that unlike wheel encoders, an inertial unit is not affected by wheel slip. However, the errors caused by bias, scale factors and nonlinearity in the sensor readings cause an accumulation in navigation errors with time and furthermore inaccurate readings are caused by the misalignment of the unit's axes with respect to the local navigation frame. This misalignment blurs the distinction between the acceleration measured by the vehicles motion and that due to gravity, thus causing inaccurate velocity and position evaluation. Since an inertial unit is a dead reckoning sensor, any error in a previous evaluation will be carried onto the next evaluation, thus as time progresses the navigation solution drifts [2]. Rotational motion of the body with respect to the inertial reference frame may be sensed using gyroscopic sensors and used to determine the orientation of the accelerometers at all times. Given this information, it is possible to transform the accelerations into the computation frame before the integration process takes place. At each time-step of the system's clock, the navigation computer time integrates this quantity to get the body's velocity vector. The velocity vector is then time integrated, yielding the position vector. Hence, inertial navigation is the process whereby the measurements provided by gyroscopes and accelerometers are used to determine the position of the vehicle in which they are installed. By combining the two sets of measurements, it is possible to define the translational motion of the vehicle within the inertial reference frame and to calculate its position within that frame [3]. II. COORDINATE FRAMES Three coordinate frames are important for this work. These include the ECEF (Earth-Centered Earth-Fixed) frame (e frame), the body frame (b frame) and the local level frame (LLF). The three frames are shown in Fig. 1. The origin of the ECEF frame is the center of the Earth s mass. The X-axis is located in the equatorial plane and points towards the mean Meridian of Greenwich. The Y axis is also located in the equatorial plane and is 9 degrees east of the mean Meridian of Greenwich. The Z-axis parallels the Earth s mean spin axis. LLF is a local geodetic frame serves as local reference directions for representing vehicle attitude and velocity for operation on or near the surface of the Earth; for this reason, it is often referred to as navigation frame (n-frame). A common 53

2 Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (215) ISSN EISSN orientation for LLF coordinates is the North-East-Up (NEU) system. The origin of the LLF frame is coincides with sensor frame. The Z-axis is orthogonal to the reference ellipsoid pointing up[2]. As seen from Fig. 2 the two accelerometers are fixed in X and Y directions, these directions represent the body coordinates. The measured acceleration will be transformed to the navigation frame (ENU) using the following transformation matrix[4]. a E cos an sin sin a x cos ay (1) n l b R b a a (2) Where : are the accelerations in the (East and North directions) navigation frame. : is azimuth angle. : is the acceleration in the body frame defined by the accelerometers. : is the rotation matrix which rotates to the navigation frame. Fig.1 Coordinates frames [6] III. TWO DIMENSIONAL REPRESENTATION OF For a vehicle moving in 2D space, it is necessary to monitor both the translational motion in two directions and the change in the direction of vehicle (i.e. rotational motion). Two accelerometers are required to detect the acceleration in two directions. One gyroscope is required to detect the direction of the vehicle (rotational motion) in a direction perpendicular to the plane of motion[6]. Strap down systems mathematically transform the output of the accelerometers attached to the body into the navigation coordinate system before performing the mathematical integration. These systems use the output of the gyroscope attached to the body to continuously update the transformation necessary to convert from body coordinate to navigation. The derivation of the transformation matrix is explained as follow. Fig. 2 Two Dimensional vector representation of transformation matrix. [5] IV. GENERAL CHARACTERISTICS OF INERTIAL SENSORS An usually contains three accelerometers, placed perpendicularly to one another, each of which is capable of detecting acceleration in a single direction. The most important characteristics describing the performance of each inertial is given hereafter. A. Bias A sensor bias is always defined by two components: A deterministic component called bias offset which refers to the offset of the measurement provided by the sensor from the true input; and a stochastic component called bias drift which refers to the rate at which the error in an inertial sensor accumulates with time. The bias offset is deterministic and can be quantified by calibration while the bias drift is random in nature and should be treated as a stochastic process [1]. B. Scale factor The scale factor is the relationship between the output signal and the true physical quantity being measured and it is usually expressed in parts per million (ppm). The scale factor is deterministic in nature and can be quantified or determined through lab calibration. The variation of the scale factor with the variation of the exerted acceleration/angular rate or temperature represents the scale factor stability and is usually called the non-linear part of the scale factor error [1]. C. Output stability The output stability of a sensor defines the run-to-run or switch-on-to-switch-on variation of the gyrodrift/accelerometer-bias as well as in-run variation of gyrodrift/accelerometer-bias. The run-to-run stability can be evaluated from the scatter in the mean output for each run for a number of runs given that the sensor is turned off then on again between each two successive runs. The in-run stability of a sensor is deduced from the average scatter of the measured drift in the output about the mean value during a single run [1]. 54

3 Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (215) ISSN EISSN D. Thermal sensitivity Thermal sensitivity refers to the range of variation of the sensor performance characteristics, particularly bias and scale factor errors, with a change in temperature. A bias or scale factor correlation with temperature variation can be defined graphically or numerically (using a mathematical expression) through intensive lab thermal testing. Such correlations can be stored on a computer for online use to provide compensation for temperature variation, provided a thermal sensor is supplied with the sensor [1]. V. EFFECT OF INERTIAL SENSOR ERRORS ON NAVIGATION PARAMETERS An uncompensated accelerometer bias error (usually expressed in terms of m/sec2) will introduces a linear error in velocity and a quadratic error in the position. This is given in fig. 3 [5]. Fig.4 ADIS16334 IMU VII. 2-D SIMULATION OF To understand the mechanization of the strap down in (2-D model), an algorithm is carried out under MATLAB/SIMULINK environment. The block diagram of this algorithm is shown in fig. 5. In this computational algorithm the raw measurement data from the IMU is transformed from the body frame to the navigation frame using the transformation matrix, this transformation matrix is simply a direction cosine matrix given in (1), after this transformation is done a double integration are performed to calculate the position, velocity, and attitude in the navigation frame. Fig. 3 Effect Of un compensated accelerometer bias on position determination [5] In the other case an uncompensated gyro bias (usually expressed in terms of deg/h or rad/sec) will introduces a quadratic error in velocity and a cubic error in position [5]. The computation process is more complicated as it sounds because any errors in the accelerometer or gyroscope measurements will lead to errors in the determined position, velocity and attitude. Gyroscope errors will result in errors in the transformation matrix between body and navigation frame, while accelerometer errors will result in errors in the integrated velocity and position. The integration will result in errors proportional to the integration time, t and its square, t² for velocity and position respectively. VI. HARDWARE This section provides the necessary details on the hardware and sensors implemented in this work. Fig. 4 shows ADIS16334 Low Profile Six Degree of Freedom Inertial Sensor from analog device. It is a low-profile, highperformance IMU. This IMU uses a serial peripheral interface for data communications. This interface enables direct connection with a large variety of embedded processor products. Fig. 5 Block diagram of algorithm using Simulink under MATLAB VIII. SIMULATION RESULTS In order to validate the functionality of the proposal navigation algorithm a car like robot model is used [7], this model is implemented using Simulink with MATLAB code see fig. 6. For testing the algorithm the following steps are carried out: Generation of the reference trajectory. Carry out the simulation in error free case (no sensor error). Accelerometer bias, gyro bias, and initial tilt error were taken as a case study and their effects on the derived trajectory are illustrated. A. trajectory In order to evaluate the algorithm, a reference trajectory was generated. A Simulink code under MATLAB environment is used to generate this reference trajectory. The suggested reference trajectory has been adopted in all 55

4 Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (215) ISSN EISSN simulation results for analysis and comparison studies. Fig. 7 shows the reference trajectory in the local level frame. The Errors Accelerometer Bias(μg) Gyro Bias(Deg./hr) Initial Misallignment(Dg) TABLE I THE VALUES OF THE ERRORS Minimum The Values Intermediate Maximum Fig. 6 Block diagram of algorithm validation using car like robot model under Simulink with MATLAB 1-1 Real A. Accelerometer's bias effect In order to study the effect of the accelerometer bias on the derived trajectory, three values have been adopted. The adopted values are.5μg,.5μg and.5μg which represented the low, medium and high error respectively. First,.5μg is set into the program. Figure 8 shows the reference and the derived trajectories. Obviously there is a difference between the two trajectories. Secondly.5μg and.5μg is set to the program respectively. It is clear that from Figs. 9 and 1, the difference between the two trajectories is increased as the accelerometer bias increased. This is due to the improper measurement of the accelerometer which in turn, results in improper computation in velocity and position y(m) Accelerometer Bias (x,y) =.5 compared with Real x(m) -4-5 Fig. 7 and derived trajectories with.5μg accelerometer bias IX. ERROR ANALYSIS The reference trajectory created earlier is applied as an input for the proposed algorithm. Simulation runs have been conducted to discuss the effect of various types of errors that may degrade the performance of navigation system. First an simulation is demonstrated without sensor errors. The derived trajectory matches up quite closely with the reference generated one as shown in Fig.7. Second, when sensor s errors are included, In this work the effects of the various errors (accelerometer bias,, gyro bias, initial tilt) have been studied. Table 3.1 gives the values of the mentioned errors adopted in the simulation. The accelerometer bias, gyro bias, initial tilt error have been chosen as case study for the effect of the errors on the derived trajectory Fig.8 and derived trajectories with.5μg accelerometer bias Accelerometer Bias (x,y) = Fig.9 reference and derived trajectories with.5μg accelerometer bias 56

5 Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (215) ISSN EISSN As one would expect, the difference between the two trajectories as well as the error in both horizontal and vertical positions will increase. This is clear in Figs 11and 12 where the values are list on these figures. 3.5 x increased. This is illustrated in Figs 14 and 15. Clearly when the gyro bias is increased to.1 rad/hr the deviation between the two trajectories as well as the error in the horizontal and vertical position are increased. In this case the derived trajectory couldn't match up the reference trajectory due to the large drift of gyro bias. This is illustrated in Figs 16 and 17, where the values are listed in these figures Accelerometer Bias (x,y) =.5-1 Gyroscope Bias (x,y) = north ((m) x 1 4 Fig.1 reference and derived trajectories with.5μg accelerometer bias Fig.13 and derived trajectories with.1 rad/h gyro bias 2 1 Gyroscope Bias (x,y) = Fig.11 Error in horizontal position due to accelerometer bias Fig. 14 and derived trajectories.1 rad/h gyro bias Gyroscope Bias (x,y) =.1 Fig. 12 Error in vertical position due to accelerometer bias B. Gyro's bias effect The same scenario is adopted. Three values of gyro bias have been selected. These values are.1 rad/hr,.1rad/hrand.1 rad/hr which represented the low, medium and high respectively. Fig. 13 shows the difference between the reference and the derived trajectories when a.1 rad/hr gyro drift is set. Due to this drift which in turn results in improper projection of the accelerometer measurement into the reference frame, a deviation between the two trajectories has been occurred. This deviation is increased as the bias Fig. 15. and derived trajectories with.1 rad/h gyro bias 57

6 Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (215) ISSN EISSN Initial Tilt Alignment = (3deg) Fig.16 Error in horizontal position due to gyro bias Fig.18 reference and derived trajectories with 3 deg tilt error Initial Tilit Aligment = (45deg) -2 C. Initial tilt error Fig.17 Error in vertical position due to gyro bias Also three values 3 deg,45 deg and 6 deg as initial tilt error are set to the program. Figs 18, 19 and 2 show the difference between the two trajectories with tilt error equal to 3 deg, 45 deg, and 6 deg respectively. Obviously, the derived trajectory is deviated too much from the reference trajectory. This is also shown in Figs 21 and 22 as error in the horizontal and vertical position. The reason is that, since the horizontal plane is unleveled, the east and north accelerometer will read a component of the gravity from the beginning instead of reading zero component if the horizontal plane is leveled. Then these components will results in error which accumulated with time. Clearly, the computed horizontal and vertical position will behave in similar manner. Increasing this tilt error the results get worst Fig. 19 reference and derived trajectories with 45 deg tilt error Initial Tilit Alignment = (6deg) Fig. 2 reference and derived trajectories with 6 deg tilt error 58

7 Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (215) ISSN EISSN consists of the two readings from the accelerometers and the one rate gyro, these readings are shown in fig 24. Closly looking in the IMU output data reveals that, these data are highly corrupted with noise which is the main feathres of MEMES IMU, this will result in a very high drift in stand alone systems..5 Fig.21 error in horizontal position due to tilt error m/sec 2 m/sec 2 rad/sec Time x Time x Time x 1 4 Fig.24 The recorded data from ADIS16334 IMU The recorded data from the IMU is set in to the SIMULINK with MATLAB block diagram shown in fig. 25, this block diagram contains the navigation algorithm discussed previous section. The out put of this block diagram will express the real trajectory of the moving land vehicle. Fig. 26 shows the car trajectory estimated by the algorithm. Fig. 22 Error in vertical position due to tilt error X. EXPERIMENTAL WORK The experiments are conducted using a car with the IMU mount on it fig.23. A laptop is the host computer is connected to IMU and the data are recorded. Fig. 25 The SIMULINK block diagram used for analyzing the recorded data x 14 Estimated Land Vehicle Trajectory using 1 North (m) Fig. 23. experimental setup The data was then taken and analyzed in MATLAB using the developed model. The recorded data from the IMU is East (m) Fig. 26 trajectory estimated of the of the moving land vehicle. 59

8 Int'l Journal of Computing, Communications & Instrumentation Engg. (IJCCIE) Vol. 2, Issue 1 (215) ISSN EISSN XI. CONCLUSION In this work, the limitations of the inertial navigation systems are investigated in order to understand why sometimes is integrated with other navigation aids and not just operating in stand-alone mode. Accelerometer bias, gyro bias and initial tilt error are taken as a case study and their effects on the derived trajectory are studied. The deviation of the derived trajectory from the reference one is due to the values of these errors. Errors analysis shows that the initial tilt error has significant effect on the derived trajectory so the accurate alignment is necessary to minimize this effect. The low cost IMU used in this work is not capable of running by itself and providing accurate positioning information. The system therefore sees to drift with time. In order to minimize these errors, external measurements at regular time intervals must be utilized. Different types of update measurements can be used in order to update the position, the velocity or the attitude. GPS is one of the main position update methods. Other methods could be velocity update from a wheel speed sensor or attitude update from a compass. REFERENCES [1] Titterton D.H. and Weston, J.L. Strapdown inertial navigation technology; Peter Peregrinus Ltd., London, UK, [2] MohanderS.Grewal, Lawrance R. Weill, Angus P. Anderws Global positioning system inertial navigation system and integration Copyright 2nd Edition 27, A John Wiley &Sons, Inc [3] A. D. King, B.Sc., F.R.I.N., Inertial Navigation Forty Years of Evolution Marconi Electronic Systems Ltd. GEC REVIEW, VOL. 13, NO. 3, [4] El-Sheimy. Inertial techniques and /DGPS Integration. ENGO 623- Lecture Notes, the University of Calgary, Department of Geomatics Engineering, Calgary (24) [5] El-Sheimy, N., The Potential of Partial IMUs for Land Vehicle Navigation., Geomatics department, University of Calgary (28) [6] Eric N Moret., Dynamic Modeling and Control of a Car-Like Robot M.Sc. Thesis, Virginia Polytechnic Institute and State University, (23). 6