System Overview

• Test and Calibration
• Physical sensor model
• Coordinate systems
  • Calibrated inertial data and magnetic field data
  • Orientation increment and Velocity increment (dq and dv)
  • Orientation data
  • Velocity data
  • Position data
  • Calibrated ∆q and ∆v outputs
  • Calibrated inertial and magnetic data outputs
  • High-rate (HR) inertial data outputs
  • Free acceleration
• Xsens Sensor Fusion Algorithms
  • Internal Sensor Bias Estimation
  • Roll and Pitch estimation
  • Heading/yaw estimation
  • Velocity and Position estimation
    • Transient accelerations
    • Loss of GNSS
  • Initialization
  • Filter Profile options
  • Additional settings, options and features
• Series interface options
• Timing and synchronization

Test and Calibration

A correct calibration of the sensor components inside the industrial motion tracker is essential for an accurate output. The quality and importance of the calibration are of highest priority. Each Xsens’ industrial motion tracker is calibrated and tested by subjecting each device to a wide range of motions and temperatures.

The individual calibration parameters are used to convert the sensor component readout (digitized voltages) to physical quantities as accurately as possible, compensating for a wide range of deterministic errors. Additionally, the calibration values are used in Xsens sensor fusion algorithms, as discussed later in this document.

Each industrial motion tracker contains individual test and calibration data in its eMTS (electronic Motion Tracker Settings). It is digitally signed by a Test Person and states the calibration values determined during the calibration of the industrial motion tracker at Xsens’ calibration facilities. The values can be seen by connecting the industrial motion tracker to MT Manager and navigating to Device Settings → Modelling Parameters.

Next to the calibration values shown in MT Manager, each device is calibrated according to more complicated models to ensure accuracy (e.g. non-linear temperature effect, cross coupling between acceleration and angular rate[1]).

Physical sensor model

This section explains the basics of the individual calibration parameters of each industrial motion tracker .

The physical sensors inside the industrial motion tracker (accelerometers, gyroscopes and magnetometers)[6] are all calibrated according to a physical model of the response of the sensors to various physical quantities, e.g. temperature. The basic model is linear and according to the following relationship:

(s=K_T^{-1}(u-b_T))

During factory calibration, a unique gain matrix, K_T and the bias vector, b_T, are assigned to each industrial motion tracker. This calibration data is used to relate the sampled digital voltages, u, from the sensors to the respective physical quantity, s.

The gain matrix is split into a misalignment matrix, A, and a gain matrix, G. The misalignment specifies the directions of the sensitive axes with respect to the ribs of the sensor-fixed coordinate system (S_xyz) housing. E.g. the first accelerometer misalignment matrix element a_1,x describes the sensitive direction of the accelerometer on channel one. The three sensitive directions are used to form the misalignment matrix:

With O representing higher order models, temperature modelling, g-sensitivity corrections, etc.

Each individual industrial motion tracker is modeled for temperature dependence of both gain and bias for all sensors and other effects. This modeling is not represented by the simple model in the above equations but is implemented in the firmware with the temperature coefficient being determined individually for each device during the calibration process. The basic indicative parameters in the above model of your individual industrial motion tracker can be found in MT Manager (Device Settings dialog).

Coordinate systems

Data from the industrial motion tracker is represented in various coordinate systems, which are explained below.

Calibrated inertial data and magnetic field data

The default sensor-fixed frame (S_xyz) is a right-handed Cartesian coordinate system that is fixed to the device. When the sensor is rigidly attached to another object or vehicle but not aligned, it may be convenient to rotate the sensor coordinate system S_xyz to an object coordinate system (O_xyz).

Refer to BASE: MTi reference co-ordinate systems for more information on the available orientation resets.

S_xyz or O_xyz are the coordinate frames used to express the rate of turn, acceleration and magnetic field outputs. The encased version of the industrial motion tracker shows S_xyz on the sticker. Figure Default coordinate system of MTi 1-series and Figure Default coordinate system of MTi 600-series, Xsens Avior series and Xsens Sirius series depict the sensor coordinate system on the MTi 1series, MTi 600-series, Xsens Avior series and Xsens Sirius series . Later in this document, small x, y and z are the axes labels for S_xyz and O_xyz. Capital X, Y and Z stand for the local-earth fixed coordinate system (L_XYZ).

The housing and PCB of the MTi 600-series, Xsens Avior series and Xsens Sirius series are carefully aligned with the output coordinate system during the individual factory calibration. The non-orthogonality between the axes of S_xyz is <0.05°. This also means that the output of 3D linear acceleration, 3D rate of turn and 3D magnetic field data all will have orthogonal xyz readings within <0.05°.

Some of the commonly used data outputs and their reference coordinate systems are listed in the table below.

Orientation increment and Velocity increment (dq and dv)

The Strap Down Integration (SDI) output of the industrial motion tracker contains orientation increments (dq) and velocity increments (dv). These values represent the orientation change and velocity change during a certain interval based on the output rate. The output rate is selectable up to 100 Hz or 400 Hz depending on the product. The dq and dv values are always represented in the same coordinate system as calibrated inertial data and magnetic field data, which can be S_xyz or O_xyz.

Orientation data

By default, the local earth-fixed reference coordinate system L_XYZ is defined as a right-handed Cartesian coordinate system with[2]:

• X positive to the East (E).
• Y positive to the North (N). 
• Z positive when pointing up (U).

This coordinate system is known as ENU (East-North-Up) and is the standard in inertial navigation for aviation and geodetic applications. See the figure below for a visualization. Note that it is possible to change L_XYZ into a different convention, like NWU (North-West-Up) or NED (North-East-Down), by changing an alignment matrix or applying an orientation reset. Refer to BASE: MTi reference co-ordinate systems for more information on the available orientation resets.

Visualization of the local earth-fixed coordinate system (L_XYZ) and Position representation systems WGS84 (φ, λ) and ECEF (X_ecef, Y_ecef, Z_ecef)

The 3D orientation output is defined as the orientation between the body-fixed coordinate system, S_xyz or O_xyz, and the local earth-fixed co-ordinate system, L_XYZ.

Orientation output modes

The output orientation can be presented in different equivalent representations:

• Unit Quaternions;
• Euler angles[3]: roll, pitch, yaw (XYZ Earth fixed type) are output following the aerospace sequence (Z-Y’-X”);
• Rotation Matrix (directional cosine matrix).

A positive rotation is always “right-handed”, i.e. defined according to the right-hand rule (corkscrew rule), see Figure Right hand rule. This means a positive rotation is defined as clockwise in the direction of the axis of rotation.

Right hand rule

Refer to BASE by Xsens to find more information on how quaternions, Euler angles and the rotation matrix relate to each other.

Interpretation of yaw as heading

With the default ENU L_XYZ coordinate system, the industrial motion tracker's yaw output is defined as the angle between East (X) and the horizontal projection of the sensor roll axis (x), positive about the local vertical axis (Z) following the right-hand rule [4]. The table below shows the different yaw values corresponding to the different local coordinate systems that are available for the industrial motion tracker.

When using the ENU convention (default), the yaw output is 0º when the vehicle (x-axis of the industrial motion tracker) is pointing East (X axis of L_XYZ). When it is required that the yaw output is 0º when the x-axis of the industrial motion tracker is pointing north, it is recommended to select NWU or NED as the local coordinate system. In article Changing or resetting the MTi reference co-ordinate systems the various alignment resets are described.

When using the GNSS/INS products in an automotive application, as best practice, pay proper attention to mounting of the industrial motion tracker on the automotive platform/vehicle. It is recommended to always mount the device with the x-axis pointing to the front of the vehicle irrespective of the local coordinate frame used for the output data.

True North vs. Magnetic North

As defined above, the output coordinate system of the industrial motion tracker is with respect to local Magnetic North. The deviation between Magnetic North and True North (known as the magnetic declination) varies depending on the location on earth and can be roughly obtained from the latest World Magnetic Model[5] of the earth’s magnetic field as a function of latitude and longitude. The industrial motion tracker accepts a setting of the declination value. This is done by setting the position in the MT Manager, SDK or by low-level communication. The yaw/heading will then be corrected for the declination calculated internally and thus referenced to “local” True North. The GNSS/INS products automatically set the current position when a GNSS-position fix is available. Therefore, the user does not have to insert it.

Velocity data

Velocity data, calculated by the sensor fusion algorithm, is provided in the same coordinate system as the orientation data (L_XYZ), and thus adopts orientation resets as well (if any is applied). The velocity output is available in all GNSS/INS products (MTi-G-710, MTi-7, MTi-8, MTi-670(G) and MTi-680(G)).

Note that the velocity data coming directly from the PVT (Position Velocity Time) data retrieved from any GNSS receiver provided with any Xsens development kit is represented in the NED reference frame. Different GNSS receivers may represent the velocity in different coordinate frames.

Position data

Position data, calculated by the sensor fusion algorithm, is represented in Latitude, Longitude and Altitude as in the WGS84 datum. The position output is available in all GNSS/INS products (MTi-G-710, MTi-7, MTi-8, MTi-670(G) and MTi-680(G)).

It is possible to retrieve position data calculated by the sensor fusion algorithm in Earth Centered – Earth Fixed (ECEF) format. See figure Visualization of the local earth-fixed coordinate system and Position representation systems WGS84 for a visualization and the MT Low Level Communication Protocol Documentation for more information.

Calibrated ∆q and ∆v outputs

The calibrated ∆q (delta_q) and ∆v (delta_v) outputs are the coning and sculling compensated strapdown integrated data in the sensor-fixed coordinate system (S_xyz) or (O_xyz). Note that the value of the output depends on the output frequency, as the values are integrated over the sample time. Delta_q can also be noted as dq, delta_angle, del_q or OriInc. Delta_v can also be noted as dv, delta_velocity, del_v or VelInc.

It is possible to multiply consecutive delta_q values to find the total orientation change over a specific period. Note that this data is not drift free, it still contains the sensor bias, as it has not been processed by the sensor fusion algorithm. Use the orientation output for drift free orientation.

Calibrated inertial and magnetic data outputs

Output of calibrated 3D linear acceleration, 3D rate of turn and 3D magnetic field data is in the sensor-fixed coordinate system (S_xyz) or (O_xyz). The units of the calibrated data output are as shown in the table Output specifications inertial and magnetometer data outputs.

High-rate (HR) inertial data outputs

High-rate calibrated 3D acceleration (accelerometer) and 3D rate of turn (gyroscope) are outputted in the sensor-fixed coordinate system (S_xyz) or (O_xyz). The units of the calibrated data output are as shown in the table Output specifications high rate calibrated inertial data outputs. HR calibrated data is available at a higher rate than regular calibrated inertial data outputs. It is outputted as a separate data packet next to the other data outputs. The maximum output rate, degree of signal processing, and calibration applied depends on the device type.

Refer to MT Low Level Communication Protocol Documentation for more details.

Free acceleration

Free acceleration (Data ID 0x4030) is the acceleration in the local frame (L_XYZ) from which the local gravity is deducted. The output is in m/s².

Xsens Sensor Fusion Algorithms

The orientation and position output of the VRU/AHT, AHRS and GNSS/INS are computed by Xsens’ proprietary sensor fusion algorithm. It uses signals from the rate gyroscopes, accelerometers, magnetometers and optionally a GNSS receiver and barometer to compute a statistical optimal 3D orientation and position estimates of high accuracy without drift for both static and dynamic movements.

The design of a typical algorithm can be summarized as a sensor fusion algorithm where the measurement of gravity (by the 3D accelerometers) and Earth's magnetic north (by the 3D magnetometers) compensate for otherwise slowly, but unlimited, increasing (drift) errors from the integration of rate of turn data (angular velocity from the rate gyroscope). This type of drift compensation is often called attitude and heading referencing and such a system is referred to as an Attitude and Heading Reference System (AHRS).

In products where a GNSS receiver is available, GNSS data is continuously used to aid the estimation of the device’s roll, pitch and heading next to position and velocity. An additional benefit is that short term GNSS outages can be coped with, through dead-reckoning, ensuring continuous data output. Such a system is referred to as GNSS/INS.

Internal Sensor Bias Estimation

The Xsens algorithm continuously estimates the gyroscope bias. For the rate of turn around the x-axis and the y-axis (roll and pitch axes), the gyroscope bias is estimated using gravity (accelerometers). In a homogenous magnetic field and with filter profiles using the magnetometer, the gyroscope bias around the z-axis will also successfully be estimated.

In some situations, the heading cannot be referenced to the Earth's magnetic field. This is the case when the magnetic field is not used (for example for VRU/AHT devices) or when the magnetic field is distorted. There are several ways to mitigate the drift in yaw (rotation around the z-axis):

1. When the industrial motion tracker has sufficient movement in roll and pitch (>30 degrees for more than 10 seconds), the gyroscope bias will be estimated for the z-gyroscope. When rotating the device back to roll and pitch around 0 degrees, the yaw will be more stable than before the roll/pitch movements.
2. The yaw drift can also be stabilized by using Active Heading Stabilization (AHS). Refer to section Additional setting options and features of this document for more details.
3. It is also possible to estimate the gyroscope bias using the manual gyro bias estimation feature when the device does not rotate (also called No Rotation Update). More information about the Manual Gyro Bias Estimation feature can be found on BASE. For the MTi-680(G), an automated (non-user-initiated) version is available: the Continuous Zero Rotation Update (CZRU).

Roll and Pitch estimation

The Xsens sensor fusion algorithm stabilizes the inclination (i.e. roll and pitch combined) using the accelerometer signals. An accelerometer measures the specific force that is composed of the gravitational acceleration plus the linear acceleration due to the movement of the object with respect to its surroundings. The algorithm uses the assumption that on average the acceleration due to the movement is zero. Using this assumption, the direction of the gravity can be observed and used to stabilize the attitude. The orientation of the industrial motion tracker in the gravity field is accounted for such that centripetal accelerations or asymmetrical movements cannot cause a degraded orientation estimate performance. The key here is the amount of time over which the acceleration must be averaged for the assumption to hold. During this time, the gyroscopes must be able to track the orientation to a high degree of accuracy. In practice, this limits the amount of time over which the assumption holds true.

However, for some applications, this assumption does not hold. For example, an accelerating automobile may generate significant permanent accelerations for time periods lasting longer than the maximum duration the sensor’s rate gyroscopes can reliably keep track of the orientation. This may degrade the accuracy of the orientation estimates because the application does not match the assumptions made in the algorithm. Note, however, that as soon as the movement again matches the assumptions made, the algorithm will recover and stabilize. The recovery to optimal accuracy can take some time.

NOTE: To be able to accurately measure orientations as well as position in applications which can encounter long-term accelerations, we offer solutions that use aiding data from a GNSS receiver: the GNSS/INS products.

Heading/yaw estimation

By default, yaw is referenced by using the local (earth) magnetic field (e.g. in the AHRS product versions). In other words, the measured magnetic field is used as a compass. If the local Earth magnetic field is temporarily disturbed, the algorithm will track this disturbance instead of incorrectly assuming there is no disturbance. However, in the case of structural magnetic disturbance (>10 to 30 seconds, depending on the filter profile settings) the computed heading will slowly converge to a solution using the 'new' local magnetic north. Note that the magnetic field has no direct effect on the inclination estimate.

The filter profile ‘Fixed Mag Ref’ will assume a magnetic reference upon startup and keep that reference regardless of new magnetic environments (available on MTi 600-series, Xsens Avior series and Xsens Sirius series, see MTi 600-series Datasheet, Xsens Avior series Datasheet and Xsens Sirius series Datasheet).

In the special case the industrial motion tracker is rigidly strapped to an object containing ferromagnetic materials, structural magnetic disturbances will be present. In that case, Xsens offers an easy-to-use solution to recalibrate the magnetometers based on those structural magnetic disturbances (refer to chapter Magnetic materials and magnets of this document).

Next to the solutions described in the article Estimating Yaw in magnetically disturbed environments to mitigate effects of magnetic disturbances, the sensor fusion algorithm in a GNSS/INS device makes use of data from the GNSS receiver. This means that the GNSS/INS device has an increased resistance towards magnetic disturbances. It is for example possible to estimate the heading based on comparison between accelerometer data and the GNSS acceleration. For GNSS/INS devices, the magnetometer data is only actively used in the GeneralMag filter profile, the other filter profiles are completely independent of the magnetic field.

Velocity and Position estimation

Transient accelerations

The GNSS/INS algorithm adds robustness to its orientation and position estimates by combining measurements and estimates from the inertial sensors and GNSS receiver in order to compensate for transient accelerations. It results in improved estimates of roll, pitch, yaw, position and velocity.

Loss of GNSS

When the GNSS/INS device has limited/mediocre GNSS reception or even no GNSS reception at all, the sensor fusion algorithm seamlessly adjusts the filter settings in such a way that the highest possible accuracy is maintained. The GNSS/INS industrial motion tracker will continue to output position, velocity and orientation estimates, although the accuracy is likely to degrade over time as the filters will have to rely on dead-reckoning. The GNSS status will be monitored continuously such that the filter can take GNSS data into account again when available and sufficiently trustworthy. In case the loss of GNSS lasts longer than a specific period (depending on product type, e.g. 45 seconds), the device will enter a state in which it stops outputting position and velocity estimates, and no longer uses velocity estimates in its sensor fusion algorithms until GNSS reception is re-established.

Initialization

The Xsens sensor fusion algorithms not only estimate orientation, but also keep track of variables such as sensor biases or properties of the local magnetic field. For this reason, the orientation output may need some time to stabilize once the industrial motion tracker is put into measurement mode. Time to obtain optimal stable output depends on a number of factors. An important factor determining stabilizing time is determined by the time to correct for small errors in the bias of the gyroscopes. The bias of the gyroscope may slowly change due to different effects such as temperature change or exposure to impact.

For the MTi-670(G)/680(G), it is highly recommended to set the initial heading (Yaw) of the device after power-up. Refer to the MTi 600-series Datasheet or the SetInitialHeading command in the MT Low-Level Communication Protocol Document for more information.

Filter Profile options

As described above, the algorithm uses assumptions about the acceleration and the magnetic field to obtain orientation. Because the characteristics of the acceleration or magnetic field differ for different applications, the Xsens algorithm makes use of filter profiles to be able to use the correct assumptions given the application. This way, it can be optimized for different types of movement. For optimal performance in a given application, the correct filter profile must be set by the user. Each product offers different filter profile options. Refer to the specific documentation to know more about the filter profiles[7].

Additional settings, options and features

The table below summarizes the additional options offered to adapt and optimize the algorithm to cover more scenarios and possible corner cases.

Series interface options

The industrial motion tracker series product lines are able to communicate and output data via many different interfaces. The table below provides a convenient overview for the MTi 1-series, MTi 600-series, Xsens Avior series and Xsens Sirius series. Details on the interfaces for each product are available in the respective datasheets or hardware integration manuals.

Timing and synchronization

The industrial motion tracker products support multiple features for synchronizing data with external devices and timing. Please refer to the respective datasheets or manuals for more information.

[1] Also known as “g-sensitivity”.

[2] The default reference coordinate system L_XYZ only applies to the industrial motion tracker in Normal (Xbus) or CAN output mode. Refer to the Low Level Communication Protocol Documentation for detailed orientation output specifications when using the ASCII (NMEA) output mode.

[3] Please note that, due to the definition of Euler angles, there is a mathematical singularity (gimbal lock) when the sensor-fixed x-axis is pointing up or down in the earth-fixed reference frame (i.e. pitch approaches ±90°). In practice, this means roll and pitch is not defined as such when pitch is close to ±90 deg. This singularity is in no way present in the quaternion or rotation matrix output mode.

[4] IEEE Std 1559^TM-2009: IEEE Standard for Inertial Systems Terminology

[5] Xsens releases a firmware update when a new WMM version is available

[6] The barometer and GNSS receiver do not require additional calibration.

[7] Datasheet for the MTi 1-series, MTi 600-series, Xsens Avior series and Xsens Sirius series. MTi User Manual for the other Xsens MTi products