Improving GNSS Attitude Determination
Using Inertial and Magnetic Field Sensors
Determination of horizontal attitude poses a general problem for navigation applications, especially those using small aerial platforms and requiring low-cost solutions. A team of German engineers are exploring a method that combines accelerometers, gyroscopes, and a magnetic field sensor with a GNSS compass to provide a multi-sensor attitude system for portable, small-sized launcher applications. Constraints applied within an extended LAMBDA method result in a shortened time to first fix and increased reliability of the ambiguity resolution. Other promising results include bridging GNSS dropouts as well as enhanced integrity monitoring.
This article describes an integration of a single-frequency GNSS, two-antenna heading system with low-cost inertial and magnetic field sensors in order to improve the availability and reliability of pure GNSS attitude determination. This method calculates a redundant attitude solution in an error-state Kalman filter using different sensor setups. As a result, the process of carrier phase ambiguity resolution accelerates.
Our approach exploits the known baseline length and an estimation of the inertial yaw and pitch angles are exploited in an extension of the LAMBDA method for a significant reduction in the ambiguity search. This not only reduces the time to first fix (TTFF) but also increases the reliability of the fixed ambiguities. With regard to small-sized and portable launcher applications, we emphasize a leveled system structure and short baseline lengths of up to 20 centimeters.
Measurement results demonstrate that our system enables single-epoch ambiguity resolution. The existence of the precise GNSS heading information facilitates an online calibration of magnetic field sensors. In turn, a calibrated magnetic field sensor enables the recovering of heading information during GNSS outages without any loss of accuracy.
The Challenge of Attitude Determination
A GNSS compass, however, provides attitude information unafflicted by any systematic offset errors. With an array of at least three antennas, the entire orientation of the antenna structure can be determined. The necessary accuracy, even for short antenna baselines in the sub-meter range, is gained by carrier phase processing. However, this entails additional complexity due to the required resolution of carrier phase ambiguities.
A widespread technique to identify carrier phase ambiguities is the LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) method described in the article by P. Teunissen listed in the Additional Resources section near the end of this article.). Using a floating estimation of the ambiguities and the corresponding variance matrix, we can solve the integer least-squares problem in a very efficient way, achieving dual-frequency data resolution within a few observation epochs. However, real-time ambiguity resolution based on data from low-cost, single-frequency GNSS receivers is not readily possible.
Employing relative positioning, however, introduces new opportunities because additional information can be provided. A reduction of the ambiguity search space is accomplished by accounting for the known baseline length (For details, see the articles by P. Clark et alia and R. Mönikes et alia 2005 listed in Additional Resources). As a result, real-time resolution of double-differenced ambiguities from single-frequency data is possible.
For a further acceleration of the ambiguity identification process, an extension of the LAMBDA algorithm has been proposed (Mönikes et alia 2007) to enable a seamless integration of yaw and pitch angle constraints in the LAMBDA method, which in turn yields an additional shortening of the time to first fix.
In this article, we describe our combination of a single-frequency GNSS compass with low-cost inertial and magnetic field sensors to test this approach. With regard to launcher applications where leveled system alignment can be assured, we use a two-antenna system with a fixed baseline length of 20 centimeters. Hence, the GNSS attitude solution only consists of heading (yaw angle) and elevation (pitch angle) information.
Using inertial sensor data, redundant attitude estimation is carried out in an error-state Kalman filter which can be exploited as yaw and pitch angle constraints in the Extended LAMBDA method proposed by Mönikes et alia. Besides the reduction in the time to first fix, another benefit accrues from the creation of a redundant attitude solution. Where a pure GNSS attitude system would fail during signal outages, the redundant inertial attitude could bridge short periods of time and therefore form a more reliable attitude determination system.
In the next section, we briefly introduce the algorithmic basis of our system, namely the Extended LAMBDA method. Thereafter, we present the inertial attitude filter with its system and measurement models. Subsequent discussion illustrates the fusion of both independent attitude determination systems is illustrated. After presenting test results, we will describe possible system refinements, including aspects of integrity monitoring and an online calibration of the magnetic field sensor.
Extended LAMBDA Method
For a fixed system structure the baseline length can be assumed as known. Furthermore, some GNSS compass applications allow for restrictions concerning potential attitude angles. For example, expected pitch angles for ships or trains are small. The Extended LAMBDA method enables one to account for constraints with the aim of a further reduction in the ambiguity search space. In other words, we only investigate those combinations of ambiguities leading to a base vector consistent with the constraints.
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Yaw and Pitch Angle Constraints. The formulation of an equation for attitude angle constraints is based on the orthogonal projection of the normalized base vector.
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Inertial Attitude Filtering
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Inertial Sensor Setup
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Time to First Fix. In the first static test, a baseline length of 20 centimeters was used and the construction was approximately horizontally aligned. During a measurement campaign of 15 minutes, inertial data, and GNSS raw data were logged. During this initial time period, the GNSS compass was not rotated. We used offline processing to investigate the time to first fix (TTFF). In order to gain statistically sustainable results, a new filter was started with every GNSS epoch (one hertz) and the corresponding TTFF, recorded.
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Accuracy. Besides the capability of ambiguity fixing, the most important quality indicator for our system is the achievable heading accuracy. The major advantage of a GNSS heading system compared to an inertial system is that we should expect no offset. Hence, the accuracy of GNSS heading information can be assessed by static measurements. In principle, the accuracy decreases with smaller baseline lengths as errors in the estimated base vector yield larger attitude errors.
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As can be seen from the plot in Figure 6, GNSS provides a much more reliable yaw angle solution. Hence, it is reasonable to replace the magnetic field measurement aiding for horizontal attitude with the GNSS yaw angle solution whenever available. Consequently, the magnetic field sensor is only required during GNSS outages.
Online Calibration of the Magnetic Field Sensor. In order to calibrate the magnetic field sensor, reference heading information is necessary. Thus, accomplishing an online calibration of the magnetic field sensor is possible as long as GNSS heading information is available. A way to do this is by modeling errors as bias and scale factors and computing them in an estimation process.
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Integrity Monitoring. Due to the stochastic nature of measurement errors, incorrect fixes can never be completely excluded. On the basis of residual integrity monitoring, the detection of errors is only possible after several minutes when the direction to satellites has measurably changed. Additionally, false alarm should be avoided as no reliable GNSS solution is provided during the period of ambiguity fixing.
This article demonstrates that the time to first fix is greatly reduced by using the Extended LAMBDA method and constraints based on redundant attitude information. This enables a more sensitive integrity monitoring, because an immediate ambiguity fix is guaranteed.
Our method also provides new measurements for monitoring, namely, the given baseline length and the redundant attitude information. Therefore, in addition to the residual cycle slip detection for carrier phase measurements, a verification of the GNSS attitude solution based on fixed ambiguities is carried out. If the estimated baseline length differs more than 10 percent from the given baseline length, the current fix is rejected. The same applies for large deviations of GNSS attitude from inertial attitude.
The reduction of the ambiguity search space caused by exploiting attitude constraints not only results in shortening the time to first fix but also increases the reliability of the ambiguity resolution. Furthermore, the availability of a redundant attitude solution enables bridging GNSS dropouts and enhanced integrity monitoring.
In order to improve the pure inertial attitude quality, an online calibration of the magnetic field sensor was implemented. The measurement results show that even for the short baseline length of 20 centimeters the maximum error of yaw angles is less than two degrees with a standard deviation of less than one degree.
For the complete story, including figures, graphs, and images, please download the PDF of the article, above.
ManufacturersThe GNSS compass hardware shown in Figure 2 consists of two Magellan AC12 GNSS receivers (subsequently a product of Ashtech, Inc., which was acquired by Trimble, Sunnyvale, California, USA) and two single-frequency ANN-MS-1-00 patch antennas from u-blox, Thalwil, Switzerland. Our inertial attitude system is solely comprised of low-cost micro-electro-mechanical (MEMS) components, namely ADIS 16255 gyroscopes from Analog Devices, Inc., Norwood, Massachusetts USA, SCA 3000 D01 accelerometers from Murata Electronics Oy (formerly VTI Technologies Oy, Vantaa, Finland), and an HMC 5843 three-axis magnetic field sensor from Honeywell, Inc., Plymouth, Minnesota, USA.
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