Tampere University of Technology, Finland ... Jarmo Takala received his M.Sc. and Dr.Tech. degrees .... (Maybeck 1982) might be the best solution for this.
Barometer-Aided Road Grade Estimation Jussi Parviainen, Jani Hautamäki, Jussi Collin and Jarmo Takala Tampere University of Technology, Finland
BIOGRAPHY Jussi Parviainen received his M.Sc. degree in May 2007 from Tampere University of Technology (TUT), Finland, majoring signal processing. He is currently Ph.D. student in TUT and his research interests are related to navigation and positioning by integrating sensors with satellite positioning systems. Jani Hautamäki is an undergraduate research assistant working in the Department of Computer Systems, TUT. He is majoring in computer science. Jussi Collin is a Senior Research Scientist at TUT. He received his Dr. Tech. degree from TUT in 2006. The topic of his dissertation was “Investigations of SelfContained Sensors for Personal Navigation”. His current research topic is sensor-aided navigation systems. Jarmo Takala received his M.Sc. and Dr.Tech. degrees from TUT in 1987 and 1999, respectively. Currently he is Professor at TUT/Department of Computer Systems. His research interests include digital signal processing systems. ABSTRACT In this paper, we propose a reduced inertial system, where the road grade is estimated with the aid of an accurate MEMS barometer and, therefore, aid the measurements of the accelerometers in the navigation unit. In the system, only one gyro, one accelerometer, and a barometer are used to augment the navigation during GPS outages. Several field tests with a passenger car on steep hills have been carried out to find the limitations of the reduced INS, and to see the effect of barometer in navigation. The results show that a barometer can identify the change of the road grade but there is notable error accumulation due to positive feedback in the speed estimation loop. 1.
INTRODUCTION
In an accurate land vehicle navigation, it is crucial to have uninterrupted navigation solution. The solution must be available also during satellite navigation outages, which may occur, e.g., in urban canyons and
tunnels. An inertial navigation system (INS), including three accelerometers and three gyros can be used to propagate the position estimate during the outages. As gyros are the most expensive components of an INS, recently reduced inertial systems with only one gyro have been proposed, e.g., Sun et al. (2008) , Davidson et al. (2008), Iqbal et al. (2008), and completely gyro free approach in Collin et al. (2002). The underlying assumption is that changes in pitch and roll are limited when the unit is installed in a road vehicle. However, in this case, any change in the road grade induces errors to the position solution as the gravity correction cannot be projected to the tilted navigation frame. The recent studies of road grade estimation are carried out especially using heavy duty vehicles, e.g., Bae et al. (2001), McIntyre et al. (2009), and Jansson et al. (2006). Dean et al. (2008) presents a method for estimating the location of the vehicle using road grade map and pitch sensor. There are also recent studies on collecting mapping databases with the aid of a barometer (Casino, 2005). In this paper, we propose a reduced inertial system, where the road grade is estimated with the aid of an accurate barometer. This road grade is used to aid the measurements of the accelerometer. We describe an experimental navigation system consisting of accurate differential GPS (DGPS), one horizontal gyro, three accelerometers, and an accurate Micro Electro Mechanical System (MEMS) barometer. This system has been used in field tests in a normal passenger car on steep hills. The field test results have been analysed to find out the limitations of the reduced INS and to see the effect of barometer aiding in the navigation. A 20 Hz DGPS navigation solution was used as a reference and the error in longitudinal distance as a function of outage time was used as the accuracy measure. The main novelty in this paper is to use the barometer based estimate for the road grade and to correct the accelerometer reading and carry out the longitudinal inertial navigation solution. Only the longitudinal velocity and position are estimated in order to avoid errors caused by gyroscope heading estimation. The paper is organized as follows. First, barometric altimeters are introduced. Then the procedure to correct accelerometer readings by using barometric altimeters is introduced. Subsequently, the measurement setup
and experimental results are presented. Finally, conclusions are drawn. 1.
BAROMETRIC ALTIMETER
As it is commonly known, there is a direct link between air pressure and altitude. A popularly used term is pressure altitude. However, barometric altimeters do not produce absolute height information without the knowledge of local sea level pressure. The normal air pressure on the sea level is approximately 101300 Pa but it varies locally depending on the weather. If the weather conditions are stable, near the Earth’s surface a difference of 100 Pa in pressure equals approximately 8 meters in altitude difference (FMI, 2009); as the altitude increases, the pressure decreases. Altitude can be modelled more accurately by using the International Standard Atmosphere (ISA) (Manual of ICAO Standard Atmosphere, 1964) and (U.S. Standard Atmosphere, 1976). The equation for altitude h is 1
,
(1)
where is the pressure measured at altitude , is the gas constant, is the temperature lapse rate, is and are acceleration due to gravity, and temperature and pressure, respectively, at the sea level. If the altitude is known and the sea level pressure is to be solved, the equation can be written as . 1
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Figure 1 Road grade angle and accelerometer axis
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BAROMETER-AIDED VELOCITY ESTIMATION
The road grade information is needed to distinguish the acceleration of the vehicle from gravity based acceleration. Acceleration as measured by accelerometer can be modeled as sin
(3)
where is true acceleration, is road grade angle, is the accelerometer bias, and is small non-modeled error. As the model shows the gravity component cannot be distinguished from the bias if the road grade angle is not known. If we estimate the road grade and the bias, the longitudinal velocity (accelerometer is mounted in the direction of longitudinal axis) can be estimated as sin
(4)
and distance travelled in the longitudinal direction is (2)
This is useful especially if there are no reference barometers available but an external aiding system, e.g., GPS, exists. When good GPS signals are available, we can solve the altitude component and estimate the current local pressure by using (2). However, we need to remember that there are many disturbances which are affecting the pressure reading inside the vehicle. This is demonstrated in our previous study, Parviainen et al. (2008). 2.
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ROAD GRADE
The term road grade means the pitch angle of the vehicle caused by the road tilt as illustrated in Fig. 1. In order to estimate a road grade, we use the speed of the vehicle and vertical velocity. In our approach, we use a barometer to approximate the vertical velocity. One accelerometer is used to produce the speed solution with the sensing axis coarsely aligned parallel to the longitudinal axis of vehicle. Thus, we assume that the device is mounted in the cradle and is not moved during the navigation.
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(5)
To estimate the road grade, the following simple equation can be used: sin
(6)
where is the vertical velocity measured by barometer and is longitudinal velocity. Road grade angles are . We can clearly not large, so it is assumed that see that the road grade estimation in (6) is valid only when the vehicle is moving. Also, as measurement noise is always present, it is feasible to set a velocity threshold that decides when (6) is practical, e.g., > 1 m/s. As one can see from (4) and (6), there is a positive feedback for the errors in the speed estimation loop. Thus, GPS fixes are needed to reset the error accumulation. This means that the system can operate only during short GPS outages, e.g., outages are less than a minute, and low noise velocity measurements are needed. Therefore, before using the pressure data, it is reasonable to try to remove the out-of-band noise from it. As the road grade changes very slowly, a low pass filter with sharp cut-off would be attractive. With
such filter, phase delay can cause problems in the following processing steps. Optimally tuned non-causal zero-phase filter, for example fixed-lag smoother (Maybeck 1982) might be the best solution for this filtering problem. However, as the results show, prefiltering is not a crucial step in the processing.
Accelerometer triad SCA3000–D01 by VTI Technologies was used but, in this study, we used the information from only one accelerometer, which was mounted in the direction longitudinal axis of a vehicle during measurements. The sampling frequency of this sensor was approximately 100 Hz.
Before the velocity and distance estimation can be used as described in (4) - (6), the accelerometer bias must be estimated. This estimation must be done while GPS signals are available. E.g., extended Kalman filter (EKF) can be used to approximate the accelerometer bias.
Dual frequency differential GPS receiver DL-4+ by NovAtel was used to get an accurate reference for our road grade measurements. Accuracy of this receiver is approximately 10 cm in the differential GPS mode, which makes it suitable for a reference position. During vehicle tests the antenna was mounted on the roof of the vehicle in order to get good GPS satellite signals.
The principal method to compute the road grade angle estimate during GPS outage is depicted in Fig. 2. Dashed blocks contain initial road grade, accelerometer bias, and initial velocity, which are obtained while GPS signals are available. It is also possible use accelerometer based zero velocity detection, e.g., method in Davidson et al. (2009) can be used to remove the error accumulation when the vehicle is stationary during a GPS outage. 4.
INSTRUMENTATION
The experimental reduced INS system used in field tests contained barometer, accelerometer, and DGPS receiver. The pressure measurements were carried out using SCP1000 MEMS barometers from VTI Technologies. In our tests, the barometer sampling frequency was approximately 1 Hz. The pressure sensor is small, diameter and height are 6.1 mm and 1.7 mm, respectively, thus, it can be easily integrated into a mobile device.
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EXPERIMENTAL RESULTS
The field tests were carried out in order to evaluate our system. In the tests, we drove intentionally steep hills to evaluate the barometer-aided inertial navigation system. Accelerometer triad was mounted inside the measurement vehicle in a fixed position. As described in earlier chapters the DGPS device was used as a reference system. Figure 3 presents the original and the moving average filtered with span 7 output of the pressure sensor converted to altitude in a test drive. The mean sea level pressure is calculated by using (2) where the GPS altitude is used in the time t0. The DGPS reference altitude is also drawn in the Figure and we can see that the pressure altitude follows very well with the DGPS solution. The local mean sea level pressure did not change remarkably during this test ride.
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Figure 2 The block diagram of the velocity estimation during GPS outage
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Figure 3 Original and moving average filtered with span 7 outputs of MEMS pressure sensor converted to altitude. Reference solution is DGPS altitude.
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Figure 4 Original and the moving average method with span 7 outputs of MEMS pressure sensor converted to altitude and DGPS reference altitude. The zoom of Figure 3.
Figure 4 is the zoom of Fig. 3 where the filtering method can be distinguished from original. Usually, the hardest place for the causal filter is the point where the slope of the pressure data changes. However, if a small lag in the processing is approved, the moving average filter with span of seven samples can be used, which smoothes the barometer data successfully in Fig. 3. Figure 5 shows the road grade angles in degrees where the accelerometer and the barometer are used with the method described in (4) - (6). The reference road grade is calculated using vertical and horizontal velocity measured by DGPS, where good satellite signals were available. The figure demonstrates that with this test the shape of curves matches very well.
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Figure 6 In the upper plot is presented accelerometer based velocity measurement with and without barometer aiding and reference velocity measured by DGPS receiver. In the lower plot is presented the profile of the road (i.e. altitude of the vehicle measured by DPGS).
difference from the minimum to the maximum point is almost 40 meters.
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In Figures 6 and 7 in the upper plot is demonstrated the velocities calculated in steep hills. Figures show that the velocity solution curve, where the barometer correction is not used, differs clearly from the DGPS reference velocity. However, the barometer corrected solution is much closer to the DGPS reference solution. The lower plots of the Figures 5 and 6 demonstrate the altitude profile of the road. In both situations altitude
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Figure 5 Examples of road grade angles.
Figure 7 In the upper plot is presented accelerometer based velocity measurement with and without barometer aiding and reference velocity measured by DGPS receiver. In the lower plot is presented the profile of the road (i.e. altitude of the vehicle measured by DPGS).
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Figure 8 The error of travelled distance calculated from the hillside in the data presented in Figure 6.
Figures 8 and 9 show the error of travelled longitudinal distance of the beginning of tests presented in Figures 6 and 7, respectively. The results vary very much depending on tests. E.g., in Fig. 8, we can see that there is almost no error at all in during the first 20 seconds but, in some cases, error may grow in some first seconds to many tens of meters. However, without barometer aiding, reduced INS navigation is not possible when driving in the hillside, as velocity estimation shows in the Figures 6 and 7. Similarly like in previous figures, Fig. 10 presents the error of travelled distance. There the green curve presents the solution where no filtering was used in the barometer data. In the blue curve, smooth filtering (moving average with span of 7) to the barometer was applied and the red dashed curve is uncorrected barometer solution. We can see that smooth filtering improves the solution but there is no radical change. 6.
This paper presented that a MEMS barometer can assist an inertial measurement unit which has only one gyro and one horizontal accelerometer. The experimental results show that this indeed improves the 600
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system in the hillside area. The barometer helps in estimating the road grade which is needed to remove the gravity component sensed by the accelerometer. During our vehicle tests the ventilation was kept almost constant and a window was closed. As is discussed in (Parviainen et. al 2008) disturbances of this kind can induce jumps in the barometric and ruin the altitude and road grade solution temporally. This kind of errors must be taken into account when implementing navigation systems where a barometer is present. Our system uses only one accelerometer and, therefore, needs to be aligned parallel to the longitudinal axis of vehicle. However, as nowadays low-cost 3-D accelerometers are available, we could exploit these to calibrate the measurements; during the calibration system will find the attitude in which it is aligned. In addition, we can use gyro to obtain full 2-D navigation solution. These are left to the future work. REFERENCES
Bae, H. S., Ruy, J., and Gerdes, J. (2001). Road grade and vehicle parameter estimation for longitudinal control using GPS. In Proceedings of the 4th IEEE Conference on Intelligent Transportation Systems, San Francisco, CA. Casino, R. (2005). Method and system for obtaining road grade data. United States Patent 6847887
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Figure 10 The error of travelled distance calculated from the hillside in the data. In the figure is presented original and smoothed barometer data.
7.
CONCLUSION
Collin, J., Lachapelle, G. and Käppi, J. (2002). MEMS-IMU for Personal Positioning in a Vehicle - A Gyro-Free Approach. In Proceedings of Institute of Navigation, ION/GPS 2002
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Figure 9 The error of travelled distance calculated from the hillside in the data presented in Figure 7.
Davidson, P., Hautamäki, J., Collin, J., and Takala, J. (2009). Improved Vehicle Positioning in Urban Environment through Integration of GPS and LowCost Inertial Sensors. In Proceedings of European Navigation Conference (ENC-GNSS 2009)
Davidson, P., Hautamäki, J. and Collin, J. (2008). Using Low-Cost MEMS 3D Accelerometers and One Gyro to Assist GPS Based Car Navigation System. In Proceedings of 15th Saint Petersburg International Conference on Integrated Navigation Systems Dean, A. J., Martini, R. D. and Brennan, S.N. (2008). Terrain-based road vehicle localization using particle filters. In Proceedings of American Control Conference. Sun, D., Petovello, M. and Cannon, E. GPS/Reduced IMU with a Local Terrain Predictor in Land Vehicle Navigation. International Journal of Navigation and Observation, Vol. 2008, 15 pages FMI, (2009), Finnish Meteorological [referred 12.10.2009], http://www.fmi.fi/
Institute,
Iqbal, U., Okou, A.F. and Noureldin, A. (2008). An integrated reduced inertial sensor system — RISS / GPS for land vehicle. In Proceedings of Position, Location and Navigation Symposium, (IEEE/ION PLANS 2008) Jansson, H., Kozica, E., Sahlholm, P. and Johansson K. H. (2006). Improved road grade estimation using sensor fusion. Reglermöte, Stockholm, Sweden.
Kalman. R. E. (1960). A new approach to linear filtering and prediction problems. Transactions of the ASME Journal of Basic Engineering. pages 35–45. Manual of ICAO Standard Atmosphere, (1964), International Civil Aviation Organization Doc. 7488/2, ICAO, Montreal, Canada. Maybeck, P. S. (1982). Stochastic Models, Estimation and Control Volume 2. Academic Press. McIntyre, M. L., Ghotikar, T. J., Vahidi, A., Xubin S. and Dawson, D.M. (2009). A Two-Stage LyapunovBased Estimator for Estimation of Vehicle Mass and Road Grade. IEEE Transactions on Vehicular Technology, Vol. 58, No. 7, pages 3177 – 3185. Parviainen, J., Kantola, J. and Collin, J. (2008). Differential Barometry in Personal Navigation. In Proceedings of Position, Location and Navigation Symposium, (IEEE/ION PLANS 2008) U.S. Standard Atmosphere, (1976), U.S. Government Printing Office, Washington, D.C.
