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The GNSS lever arm (antenna offset) and its role in the GNSS/INS sensor fusion algorithm

Introduction

With the release of the MTi-680G GNSS/INS (with integrated RTK GNSS receiver), Xsens has also introduced a new configuration parameter called the GNSS lever arm. The GNSS lever arm is an essential parameter in order to achieve reliable cm-level position, velocity and orientation data. This article provides a more in-depth analysis of the GNSS lever arm, in addition to the information provided in the Datasheets.

 

What is a GNSS lever arm and what role does it have in the GNSS/INS sensor fusion algorithm?

The GNSS lever arm setting accounts for the displacement between your MTi (where all inertial data are measured) and the location of the GNSS receiver’s antenna. Providing this information to the MTi will allow the sensor fusion core to compensate for the difference in dynamics between these two measurement locations. The following image visualizes these differences in dynamics:

lever_arm_clean.png

As can be seen in the image, the MTi is positioned at the center of rotation of the system, e.g. a car, robot or drone. The GNSS antenna is mounted onto the same vehicle at a distance from the MTi that is significantly larger than the measurement accuracy of the GNSS receiver. As the vehicle rotates, the MTi remains at the same global location and only experiences a rotation. In contrast, the GNSS antenna experiences a linear displacement in addition to the rotation.

There are two primary reasons for providing the MTi with this lever arm information:

  1. Knowing this exact offset allows the sensor fusion core of the MTi to transform the GNSS receiver data such that it matches the dynamics of the inertial measurement data. An incorrect lever arm setting can result in an undefined state estimation, and in turn this can lead to a decreased performance of the sensor fusion algorithm, such as wrong estimations of position, velocity and orientation. Taking the image above as an example, it can for instance create situations in which the MTi “thinks” that the vehicle is moving based on GNSS data, whereas it is actually only rotating around its axes.
  2. The lever arm will be subtracted from the position output data that is generated by the MTi. The position data will therefore indicate the location of the MTi, instead of the location of the GNSS antenna.

 

What is the relationship between the positioning accuracy of the GNSS receiver and the GNSS lever arm?

The short answer to this question is that the GNSS lever arm becomes more important as the accuracy of the GNSS measurements increases. Consider again the image that was used to visualize the GNSS lever arm in the previous paragraph. The displacement between the three measurements (the "path") is clearly determined by the GNSS receiver because it has sufficient measurement accuracy. Now consider the same experiment, but using a GNSS receiver with a measurement accuracy of only 1 meter (instead of 1 centimeter). The three consecutive measurements are not accurate enough to determine the path of the GNSS antenna. Based on the three measurements and the limited measurement accuracy we cannot even say with certainty that the antenna has moved at all. In this situation, the GNSS lever arm does not play a significant role and it is ignored by the MTi.

The importance of the GNSS lever arm does not only depend on the accuracy of the GNSS measurements; the length of the GNSS lever arm also has an influence. Consider a large maritime vessel, with an MTi-G-710 mounted at the center of its hull, and the antenna mounted on top of a mast, 10 meters above the MTi. If the vessel experiences strong Roll and Pitch dynamics, then the mast-mounted antenna will experience linear displacements that are observable even with lower-precision GNSS receivers. In this case, providing GNSS lever arm information to the filter can improve the performance of the MTi.

Currently, the MTi-680G is the only product in the MTi portfolio that supports this the lever arm setting because of its internal GNSS receiver with RTK support. The sensor fusion cores of the MTi-7, MTi-670 and MTi-G-710 assume that the GNSS antenna is positioned at roughly the same location as the MTi itself.

 

How do I measure and store the GNSS lever arm?

The GNSS lever arm is a parameter that needs to be measured and stored by the user after installation of the MTi. It is stored in the MTi’s memory as a vector of X-Y-Z coordinates, relative to the origin* of the sensor frame of the MTi. The unit is meters, but if possible the lever arm should be determined with centimeter-level accuracy.

N.B.: The default value for the GNSS lever arm is [0, 0, 0] (m). This means that by default, the MTi assumes that the MTi and its GNSS antenna are located at the same place!

Below image shows an example of how the GNSS lever arm is measured for an MTi and its GNSS antenna, after they have been integrated into a car. The X-Y-Z coordinates should be measured according to the sensor coordinate frame, which has been printed on the side label of the MTi. Careful attention needs to be paid to the sign of the coordinates: i.e. if the antenna is mounted to the right of the MTi, then the Y coordinate should be a negative value.

The final GNSS lever arm vector for this vehicle is [1.00, 0.50, 0.80] (m).

Lever_arm_car.png

The GNSS lever arm can be set and stored using the Device Settings window in MT Manager, or by using the setGnssLeverArm low-level communication command.

*The exact location of the origin of the MTi can be found in the product’s Datasheet.

 

warning.png Violation of the GNSS lever arm

The GNSS lever arm is considered to be a static offset, meaning that the sensor fusion core of the MTi assumes that the relative distances (with respect to the sensor frame of the MTi) do not change over time. Violating the configured lever arm parameters, or providing the MTi with incorrect lever arm parameters, can cause degradation of the position, velocity and orientation data outputs of the MTi.

Violation of the GNSS lever arm can occur to some extent when the MTi and its GNSS antenna are mounted onto a vehicle or object that is flexible (non-rigid). Violation also often occurs during desk tests: For instance when, for testing purposes, an MTi is connected to a PC and the GNSS antenna is left near a window in order to achieve a GNSS fix. If then the MTi itself is moved or rotated, the GNSS lever arm will be violated immediately.  

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