Thermal Calibration of Low Cost MEMS Sensors ... - Semantic Scholar

Thermal Calibration of Low Cost MEMS Sensors for Land Vehicle Navigation System P. Aggarwal, Z. Syed, N. El-Sheimy Department of Geomatics Engineering, The University of Calgary, Canada Abstract— For vehicle navigation, Global Positioning System (GPS) provides long term accurate positions, but only when direct lines of sight to four or more satellites exist. Inertial Navigation Systems (INS), on the other hand, are self contained sensors that can provide short term accurate navigation information. The integration of the two systems can effectively provide continuous navigation data even during GPS signal outages. Traditional inertial systems were heavy, bulky and costly. In the past two decades, the use and development of light weight, compact and cost effective Micro-Electro-Mechanical Systems (MEMS) based inertial sensors has made the civilian integrated vehicle navigation systems more affordable. However, these sensors still have to make their way in the field due to their significant error sources such as turn-on biases or scale factors variations. Moreover, the performance characteristics of these sensors are highly dependent on the environmental conditions such as temperature variations. Hence there is a need for the development of accurate, reliable and efficient thermal models to reduce the effect of these errors that can degrade the system performance. I.

INTRODUCTION

Navigation, by definition, provides the best possible estimate of the moving object in terms of its position, velocity and attitude [1] by measurement systems such as Inertial Navigation Systems (INS) and Global Positioning System (GPS). The current market of positioning and navigation systems is clearly dominated by the Global Positioning System (GPS) as one of the major components for providing absolute positioning information. GPS provides accurate long term position and velocity information at relatively low frequency data rate, when GPS receiver has direct lines of sight to four or more satellites. However GPS signal outages may occur due to obstruction in the pathway of the signal. On the other hand, MEMS-based INS provides accurate navigation data over short time intervals at much higher rates, typically 100Hz. But it suffers from performance degradation over long periods of time due to the combined effects of errors like noises, biases, drifts and scale factor instabilities [2]. These errors can be corrected using frequent updates from external sources like GPS, which forms the basis of integrated INS/GPS systems. When GPS and INS are integrated together, an accurate, drift free and high resolution navigation system can be achieved for most outdoor situations. The integrated system can effectively deal with small GPS signal outages. Inertial sensor errors can be divided into two parts: random and deterministic or systematic [3]. In order to

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integrate MEMS inertial sensors with GPS, and to provide a continuous and reliable navigation solution, the characteristics of different error sources and the understanding of the stochastic variation of these errors are of significant importance [4]. The random errors include bias-drifts or scale factor drifts, and the rate at which these errors change with time. These random errors have to be modeled stochastically. The deterministic error sources include the bias and the scale factor errors which can be removed by specific calibration procedures in a laboratory environment. However, for low cost sensors such as MEMS, these errors are quite large and their repeatability is typically poor because of the environmental dependence, especially temperature, which makes frequent calibration a necessity [5]. More explicitly, the actual values of the bias and the scale factor vary from those obtained through calibration process due to the difference between the operational and calibration temperatures [6]. If the thermal variations for both accelerometer and gyroscope biases and scale factors are not properly modeled and compensated, the position accuracy will be degraded since these errors get accumulated with time. Hence there is a need for developing accurate, reliable and efficient thermal models. In this paper, we aim at establishing a thermal model for low cost MEMS inertial sensors that will be used for integrated vehicle navigation applications. Also the effect of varying temperature on the MEMS inertial sensor errors is examined in detail. Consequently, local and global thermal models are developed to compensate for the effects of bias and scale factor errors due to temperature variations. In section III, the field test results obtained by using the Soak, Ramp thermal models along with the values obtained from the usual sixposition static method are presented. The last section will conclude the study of this paper. II. METHODOLOGY The process of characterizing the stochastic variation at different temperatures is one of the most important steps in developing a reliable low cost integrated navigation system. The actual values of the bias and the scale factor vary from those obtained through calibration process (six-position method) due to the difference between the operational and calibration temperatures [6, 7]. Unless an accurate temperature-dependent stochastic model is developed, the mechanization parameters will have larger errors and could potentially degrade system performance. In this section the basic theory for designing thermal model is explained.

A. Methods of Thermal Testing The purpose of thermal testing is to determine the variation of the basic sensor parameters when operated under different temperatures. Two main approaches for thermal testing, Thermal Soak method and Thermal Ramp method [1], are being used to investigate thermal effect of sensors. A.1.Thermal Soak Method In thermal Soak Method, the IMU is enclosed in a thermal chamber and given ample of time (around one hour) to stabilize its temperature at set temperature points. Once temperature of the IMU and the thermal chamber is stabilized, the system starts to record the data. A.2. Thermal Ramp Method In this method, the temperature of the thermal chamber is continuously linearly increased or decreased for a certain period of time. A simple linear interpolation method is being used to establish the thermal ramp model. More advanced interpolation methods like Cubic Spline Interpolation and Piecewise Cubic Hermite Interpolation are not used because their results were similar to the linear interpolation. In the linear interpolation method if two parameters po and p1 are known at temperatures to and t1, then an intermediate value is given by (1)

p (t ) =

t − t0 t1 − t p0 + p1 t1 − t0 t1 − t0

(1)

Fig. 1. MEMS IMU using sensors from ADI

C. Thermal Turntable Unit In the test setup, a turntable and a thermal chamber are assembled together to form a Thermal-Turntable Unit as shown in Fig. 2.

Fig. 2. Thermal turntable setup

where, t is the required temperature point and p(t) is the calculated value at that point. In this study, both the Soak and the Ramp method are used to investigate thermal effect of sensors and a comparison is shown between the two models. B. Low cost MEMS IMU Unit Thermal tests were conducted on the custom built MEMS unit called ADI MEMS IMU Sensor Triad (ADI). This unit was designed by the MMSS research group at the University of Calgary and was built as a very low-cost alternative using MEMS inertial sensor chips, as shown in Fig. 1. The IMU used surface micromachined MEMS gyroscopes (ADXRS150) and accelerometers (ADXL105) manufactured by Analog Devices, Inc. Hence, the name ADI sensor triad was given to the IMU. This ADI unit has temperature sensors fabricated for the three single axis gyroscopes and accelerometer X.

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The rotating axle of the turntable is extended into the thermal chamber through a narrow round opening in the chamber’s side wall. The ADI MEMS is placed in the chamber and is fixed on the extended tabletop of the turntable. This placement of the IMU allows it to be freely rotated under controlled temperature. The data were collected in the Inertial Lab at the University of Calgary. The IMU signals were sampled at 100 Hz at different temperatures and saved on a laptop via a 16-Bit A/D card (DAQCard-6036E) from National Instrument for post processing. III. RESULTS A. Thermal Soak Calibration Results As mentioned before, in this method the temperature is stabilized before recording data. The variation of the bias and scale factor of the ADI sensor triad with temperature is evaluated at temperatures ranging from -25 oC to +70 oC. The measured biases for accelerometers and gyroscopes at different temperatures measured by the temperature sensors of the respective sensors are shown in Fig. 3 and 4 respectively, while the scale factor variation is shown in Fig 5. The measured biases and scale factors are provided after removing the constant bias and scale factor estimated from the conventional 6-position static test.

over the entire temperature range (Fig. 4). Hence there is a need for designing an accurate thermal calibration model for low cost MEMS sensors to accurately compensate for these bias and scale factor drifts with temperatures. Scale factor variation shown in Fig. 5 is significantly less, compared to the bias variation. For gyro Y the (maximum) scale factor variation is 0.07 %. Tables 1 and 2 give the obtained biases for gyroscopes and accelerometers respectively after the constant bias compensation using the 6-position static calibration results. It is also obvious that the biases and scale factors are not changing linearly with temperature. TABLE I GYROSCOPE BIASES VARIATION WITH TEMPERATURE

Temp (oC) -21.6 -16.7 -11.7 -6.6 -1.5 3.6 8.5 13.4 18.2 23.3 28 32.7 37.4 42.5 52.1 57.1 61.9 67.2 71.9

Fig. 3. Variation of accelerometer biases with temperature from accelerometer’s temperature sensor

GyroX (rad/s) -0.281 -0.296 -0.311 -0.294 -0.312 -0.245 -0.105 0.050 -0.228 -0.121 0.171 0.059 0.001 -0.107 -0.234 -0.271 -0.343 -0.209 -0.262

Temp (oC) -20.5 -15.5 -10.6 -5.5 -0.5 4.5 9.4 14.3 19 24.1 28.8 33.5 38.2 43.2 52.8 57.6 62.4 67.6 72.2

Fig. 4. Variation of gyroscope biases with temperature from the gyro temperature sensor

GyroY (rad/s) -1.077 -1.112 -1.136 -1.042 -0.839 -0.532 -0.251 0.041 -0.204 -0.207 0.345 0.558 0.734 0.944 1.356 1.514 1.990 1.820 2.018

Temp (oC) -20.1 -15.4 -10.6 -5.6 -0.6 4.4 9.2 14 18.5 23.5 28.2 32.7 37.2 42.2 51.6 56.4 61 66.2 70.6

GyroZ (rad/s) -3.353 -2.746 -2.006 -1.898 -1.477 -1.238 -1.188 -1.029 0.389 0.308 -0.428 -0.243 0.054 0.387 1.138 1.456 1.644 0.594 0.317

TABLE II ACCELEROMETER BIASES VARIATION WITH TEMPERATURE

Temp (oC) -32 -26.5 -21 -15.4 -9.7 -5.2 0 4.9 11.3 16.9 21.9 26.6 31.3 36.7 46.5 51.5 56 61.2 65.4

Fig. 5. Variation of scale factor with temperature from the respective sensor’s temperature sensor

As observed from Fig. 3 and 4, the biases of accelerometers and gyroscopes vary significantly with temperature. For accelerometers, the bias drift can be as high as 1 m/s2 (Fig. 3) while for gyroscopes, the drift in biases can reach 5 deg/sec

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Acc X (m/s2) 0.339 0.287 0.220 0.170 0.131 -0.005 -0.049 -0.114 0.150 0.094 0.038 -0.025 -0.099 -0.164 -0.319 -0.374 -0.477 -0.544 -0.600

Acc Y (m/s2) 0.345 0.290 0.235 0.192 0.154 0.025 -0.022 -0.113 0.041 0.029 0.004 -0.005 -0.015 -0.036 -0.084 -0.106 -0.143 -0.158 -0.184

Acc Z (m/s2) -0.522 -0.460 -0.385 -0.314 -0.250 -0.117 -0.054 0.044 -0.088 -0.047 -0.008 0.0168 -0.029 0.057 0.088 0.089 0.111 0.053 0.137

B. Thermal Ramp Calibration Results In Ramp method, a controlled continuous increase of temperature profile is executed without any time for

temperature stabilization. The temperature of the thermal chamber is varied from 0 oC to 30 oC in steps of 0.2 V. The measured biases for accelerometers and gyroscopes at different temperatures after removing the 6-position static calibrated biases are shown in Fig. 6 and 7 respectively.

Fig. 8. Trajectory with simulated GPS outages

The quality of the position estimation is often evaluated by simulating a set of short-term GPS signal outages and checking the position drifts during these GPS signal outages where the INS has to work as a stand-alone navigation system. In Fig. 8, four 30-second GPS signal outages are introduced (blue color). The IMU position errors during these GPS signal outages were obtained by comparing the ADI IMU standalone navigation solution to the reference trajectory solution. The reference solution is acquired from the smoothed integration estimation of the CIMU/DGPS data processed by Applanix Corporation POSPac™ software.

Fig. 6. Variation of accelerometer biases with temperature

D. Comparison between Drifts in 6-position, Ramp and Soak Method Calibrated Field Test Data The results for 6-position static test calibration are shown in Fig. 9 while that for soak and ramp thermally calibrated data are shown in Fig. 10 and 11.

Fig. 7. Variations of gyroscope biases with temperature recorded from the gyroscope’s temperature sensors

Comparing Figs. 3-7, we can see that the bias variation pattern for either accelerometers or gyroscopes is significantly different when evaluated with two different thermal methods. One reason for the difference is the inability of the MEMS sensors to respond to quick temperature changes. C. Field Test Description Thermal models for the calibration of MEMS sensors were evaluated using kinematic data collected in December 2005 by MMSS group using ADI sensor triad, a navigation grade IMU and GPS receivers. The ADI MEMS Sensor was installed in the cargo area of the test van on a rigid platform. The OEM4 GPS receiver and a navigation grade IMU (CIMU from Honeywell) were installed on the vehicle roof. This test was performed around the University of Calgary campus and consisted of typical kinematic motions.

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Fig. 9. Six-position static test calibration

IV. CONCLUSION MEMS IMU accelerometer and gyroscope can vary as large as 0.94 m / s 2 and 5 deg/sec respectively, over the temperature range from -25 oC to 70 oC. If these thermal variations are not corrected or compensated, they will lead to huge position errors because low cost units like ADI use temperature sensors to optimize repeatability rather than accuracy. Moreover the low cost MEMS IMU units such as ADI need considerable time for its temperature to stabilize at the desired set temperature point (1-2 hours). In case Thermal Ramp method is used to obtain corresponding bias and scale factor values at each temperature point, the values obtained won’t be accurate as the sensor needs considerably long period (1-2 hours) to stabilize at the recorded temperature. Hence Thermal Ramp method obtained biases and Scale Factors are quite different from the Thermal Soak Method and they are also inaccurate. The field test results showed an improvement of 17 % that can be achieved using the proposed Soak thermal compensation model as compared to the results obtained by using 6-position static model.

Fig. 10. Soak thermally calibrated

ACKNOWLEDGMENT This study was supported in part by research fund from the Natural Science and Engineering Research Council of Canada (NSERC) and Geomatics for Informed Decisions (GEOIDE), Network Centers of Excellence (NCE) to Dr. Naser ElSheimy. Dr. Eun-Hwan Shin is acknowledged as a co-author of the AINSTM toolbox used in this paper. The authors would like to thank K. Chiang, C. Goodall, S. Nassar, W. El-Hamid of the MMSS group at University of Calgary who helped during field tests. REFERENCES Fig. 11. Ramp thermally calibrated

[1]

We can see position errors obtained by using Soak thermal compensation method are smaller than those obtained by using 6-position method. However the position errors obtained by using the Ramp Thermal compensation model are larger than those corresponding to the 6-position method. The major reason is that the low cost MEMS IMU units such as ADI need considerable time for its temperature to stabilize at the desired set temperature point. Usually the temperature stabilization process takes 1-2 hours. Therefore the Ramp Thermal model is not really effective in compensating the biases and scale factors in practical field operation. The values at four outages are listed in Table III.

[2]

[3] [4]

[5]

[6]

TABLE III DRIFT ERRORS FOR ADI DATA FOR THREE METHODS

Max Drift (M) MEAN

6-position Static 66.116 17.790 66.142 15.125 41.294

Soak Calibration 33.986 12.380 67.283 23.275 34.231

Ramp Calibration 190.106 104.676 151.593 56.181 125.640

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