Xsens MTi Series Guide

MTi and MTx User Manual
and Technical Documentation
Document MT0100P
Revision E, December 2nd 2005
Xsens Technologies B.V.
Capitool 50 phone [phone]
P.O. Box 545 fax [phone]
7500 AM Enschede e-mail [email protected]
The Netherlands internet www.xsens.com

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Revisions
Revision Date By Changes
A June 1 2005 PS First version.
B June 3 2005 PS Minor editorial changes, def. RGS in Euler on
section 2.3.3 corrected.
C August 8 2005 SS Added pin definitions for MTi RS-422 version.
Added wire color definitions for USB-CA#.
Added specification of SyncIn, SyncOut and
Analog In.
Added explanations on sensor fusion algorithm
settings
D September 8 2005 SS Added specification & pinout of MTi analog
outputs version
E December 2 2005 RG Added pin definitions for MTx RS-485 standalone
version
Added pin definitions for MTx Xbus version
Corrected product code ODU connector
© 2005, Xsens Technologies B.V. All rights reserved. Information in this document is subject
to change without notice. Xsens is a registered trademark of Xsens Technologies B.V. MTi
and MTx are trademarks of Xsens Technologies B.V.

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MT0100P.Eiii
Table of Contents
1INTRODUCTION 1
1.1 PRODUCT DESCRIPTION 1
1.1.1 MTi – miniature gyro-enhanced Attitude and Heading Reference Sensor 1
1.1.2 MTx – miniature inertial 3DOF Orientation Tracker 1
1.2 OVERVIEW MTI AND MTX DEVELOPMENT KIT 2
1.2.1 Contents 2
1.3 TYPICAL USER SCENARIOS 3
1.3.1 Getting Started with the MT Software 3
1.3.2 Interface through COM-object API 3
1.3.3 Direct low-level communication with MTi or MTx 3
1.4 SENSOR FUSION 4
2OUTPUT SPECIFICATION 5
2.1 CO-ORDINATE SYSTEMS 5
2.1.1 Calibrated Sensor readings 5
2.1.2 Orientation co-ordinate system 6
2.2 ORIENTATION PERFORMANCE SPECIFICATION 7
2.2.1 Sensor fusion algorithm settings 7
2.3 ORIENTATION OUTPUT MODES 8
2.3.1 Quaternion orientation output mode 9
2.3.2 Euler angles orientation output mode 10
2.3.3 Rotation Matrix orientation output mode 10
2.4 CALIBRATED DATA PERFORMANCE SPECIFICATION 12
2.5 CALIBRATED DATA OUTPUT MODE 13
2.5.1 Physical sensor model 13
2.5.2 Calibrated inertial and magnetic data output mode 14
2.5.3 Un-calibrated raw output mode 14
2.6 RESET OF OUTPUT OR REFERENCE CO-ORDINATE SYSTEMS 16
2.6.1 Output with respect to non-default coordinate frames 16
2.6.2 Heading reset 16
2.6.3 Global reset 16
2.6.4 Object reset 17
2.6.5 Alignment reset 18
2.7 TIMESTAMP OUTPUT 18
2.8 ANALOG OUTPUTS 18
2.8.1 Conversion to Euler angles 18
2.8.2 Accuracy 18
2.8.3 Accurate measurement of analog outputs 19
3BASIC COMMUNICATION 21
3.1 INTRODUCTION 21
3.2 STATES 21
3.3 MESSAGES 22
3.3.1 Message structure 22
3.3.2 Message usage 23
3.3.3 Common messages 24
3.4 COMMUNICATION TIMING 28
3.4.1 Orientation output mode timing 28
3.4.2 Calibrated data output mode timing 29
3.5 INTERNAL CLOCK ACCURACY 29
3.6 DEFAULT SERIAL CONNECTION SETTINGS 29
3.6.1 General definitions for binary data 30

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4PHYSICAL SPECIFICATIONS 31
4.1 PHYSICAL SENSOR OVERVIEW 31
4.2 PHYSICAL PROPERTIES OVERVIEW 31
4.3 POWER SUPPLY 31
4.4 PHYSICAL INTERFACE SPECIFICATIONS 32
4.4.1 USB-serial data and power cables overview 32
4.4.2 Pin and wire color definitions MTi-28A##G## (MTi RS-232, standard version) 33
4.4.3 Pin and wire color definitions MTi-68A##G## (MTi RS-422) 34
4.4.4 Pin and wire color definitions MTi-28A##G##D (MTi RS-232, analog outputs) 35
4.4.5 Pin and wire color definitions MTx-28A##G## (MTx RS-232, standard version) 36
4.4.6 Pin and wire color definitions MTx-48A##G## (MTx RS-485 standalone) 37
4.4.7 Pin and wire color definitions MTx-49A##G## (MTx Xbus) 38
4.4.8 Additional interface specification 38
4.5 HOUSING MECHANICAL SPECIFICATIONS 40
4.5.1 Dimensions MTi 41
4.5.2 Dimensions MTx 42
5OPERATING GUIDELINES 43
5.1 NORMAL OPERATING PROCEDURE 43
5.2 PLACEMENT CONSIDERATIONS 43
5.2.1 Transient accelerations 43
5.2.2 Vibrations 44
5.2.3 Magnetic materials and magnets 44
6IMPORTANT NOTICES 46
6.1 ENVIRONMENTAL OPERATING CONDITIONS 46
6.2 ABSOLUTE MAXIMUM RATINGS 46
6.3 MAINTENANCE 47
6.4 WARRANTY AND LIABILITY 47
6.5 CUSTOMER SUPPORT 48

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1 Introduction
The MTi and MTx are both complete miniature inertial measurement units with integrated 3D
magnetometers (3D compass), with an embedded processor capable of calculating roll, pitch
and yaw in real time, as well as outputting calibrated 3D linear acceleration, rate of turn
(gyro) and (earth) magnetic field data.
The major difference between the MTi and the MTx is in the casing shape and weight,
connector and general ruggedness. The MTi further supports various advanced IO options
such as RS-422 and analog output (DAC).
This documentation describes the use, basic communication interfaces and specifications of
both the MTi and the MTx. Where they differ it is clearly indicated.
1.1 Product Description
1.1.1 MTi – miniature gyro-enhanced Attitude and Heading Reference Sensor
The MTi is a miniature, gyro-enhanced Attitude and Heading Reference System (AHRS). Its
internal low-power signal processor provides drift-free 3D orientation as well as calibrated 3D
acceleration, 3D rate of turn (rate gyro) and 3D earth-magnetic field data. The MTi is an
excellent measurement unit for stabilization and control of cameras, robots, vehicles and other
equipment.
Fields of use
•robotics
•aerospace
•autonomous vehicles
•marine industry
•bore industry
1.1.2 MTx – miniature inertial 3DOF
Orientation Tracker
The MTx is a small and accurate 3DOF inertial Orientation Tracker. It provides drift-free 3D
orientation as well as kinematic data: 3D acceleration, 3D rate of turn (rate gyro) and 3D
earth-magnetic field. The MTx is an excellent measurement unit for orientation measurement
of human body segments.
Example fields of use
•biomechanics
•exercise and sports
•virtual reality
•animation
•motion capture

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1.2 Overview MTi and MTx Development Kit
Photos of the MTi (left) and MTx (right) Development Kit
1.2.1 Contents
•MTi or MTx miniature inertial measurement unit
•Device individual calibration certificate
•Quick Setup Sheet
•USB-serial data and power cable, 5 meters (CA-USB2/ CA-USB2x/ CA-USB6)
•MTi and MTx User Manual and Technical Documentation [MT0100P]1
•MTi and MTx Low-level Communication Documentation [MT0101P]
•MT Software Development Kit
oMT Software (PC Windows 2000/XP)
oLow-level communication class (C++ source code)
oMotionTracker object, COM object API (Windows)
oExample source code (C/C++, MATLAB, LabVIEW, VisualBasic)
oMagnetic Field Mapper add-on (PC Windows 2000/XP)
oMT SDK documentation [MT0200P]
oMT Software documentation [MT0201P]
oMT Magnetic Field Mapper Documentation [MT0202P]
•A letter with your individual software license code.
NOTE: the most recent version of the software, source code and documentation can always
be downloaded on the support section of www.xsens.com.
1this document

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1.3 Typical User Scenarios
This section is intended to help you find the right documentation for the way you want to use
your MTi or MTx.
1.3.1 Getting Started with the MT Software
The easiest way to get started with your MTi or MTx is to use the MT Software. This easy
to use software with familiar Windows user interface lets you view 3D orientation in real-
time, log ASCII data files, change and view various device settings and properties. It is an
easy way to get to know and to demonstrate the capabilities of the MTi and MTx miniature
inertial measurement units.
ÆPlease refer to the MT Software User Manual for more information on this topic!
1.3.2 Interface through COM-object API
If you want to develop a software application that uses the MTi or MTx you can consider
using the COM-object API (MTObj.DLL) which provides easy to use function calls to obtain
data from the sensor or to change settings. The COM-object takes care of the hardware
communication interfacing and it is an easy way to get (soft) real-time performance. Both
polling and events based methods are supported.
ÆPlease refer to the MT Software Development Kit Documentation for more
information on this topic!
NOTE: This provides backwards compatibility of your software developed for the MT9-B
1.3.3 Direct low-level communication with MTi or MTx
Direct interfacing with the MTi or MTx (RS-232/422) is the natural choice if you are looking
for full-control, maximum flexibility and/or have hard real-time performance requirements.
The MTi/MTx’s low power embedded DSP does all the calculations/calibration, you just
retrieve the data from the COM-port using the MTi/MTx binary communication protocol
using with streaming (free-running) mode or polling (request) mode. Even this part is made
easy for you by the inclusion of the source code (C++) of the “Xbus” communication class in
the MT SDK. Example C/C++ application code should get you quickly started on your
development platform of choice.
Applies to: Windows PC platform
Applies to: Windows PC platform
Applies to: Any (RT)OS or processor platform!

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ÆPlease refer to the MTi and MTx Low-level communication protocol
documentation and the MT Software Development Kit Documentation for more
information on this topic!
1.4 Sensor fusion
The MTi / MTx’s low power-DSP runs a proprietary sensor fusion algorithm developed in-
house by Xsens, tailor-made to the MTi and MTx, that can accurately calculate absolute
orientation in three-dimensional space from miniature rate of turn sensors (gyroscopes),
accelerometers and magnetometers in real-time.
The design of the algorithm can be explained as a sensor fusion algorithm where the
measurement of gravity (accelerometers) and magnetic north (magnetometers) compensate for
otherwise unlimited increasing (drift) errors from the integration of rate of turn data. This type
of drift compensation is often called attitude and heading referenced and such a system is
often called an Attitude and Heading Reference System (AHRS).
Sensor Fusion
Algorithm
3D driftless
orientation
3D
gyroscopes
3D
accelero-
meters
3D
magneto-
meter

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2 Output Specification
In this chapter the various output modes of the MTi and MTx are described. The two major
modes, Orientation output and Calibrated data output, are discussed separately. However,
please note that the two output modes can easily be combined, so that you get a combined
data packet of orientation data and inertial calibrated data together, with the same time stamp.
2.1 Co-ordinate systems
2.1.1 Calibrated Sensor readings
All calibrated sensor readings (accelerations, rate of turn, earth magnetic field) are in the right
handed Cartesian co-ordinate system as defined in figure 1. This co-ordinate system is body-
fixed to the device and is defined as the sensor co-ordinate system (S). The 3D orientation
output is discussed below in section 2.2.
Figure 1 MTi and MTx with sensor-fixed co-ordinate system overlaid (S).
The co-ordinate system is aligned to the external housing of the MTi and MTx.
The aluminum base plate of the MTi is carefully aligned with the output coordinate system
during the individual factory calibration. The alignment of the bottom plane and sides of the
aluminum base-plate with respect to (w.r.t.) the sensor-fixed output coordinate system (S) is
within 0.1 deg.
High accuracy alignment between the (plastic) housing and the sensor-fixed output coordinate
system (S) is not possible for the MTx for obvious reasons. The actual alignment between the
Sco-ordinate system and the bottom part of the plastic housing is guaranteed to <3°.
The non-orthogonality between the axes of the body-fixed co-ordinate system, S, is <0.1°.
This also means that the output of 3D linear acceleration, 3D rate of turn (gyro) and 3D
magnetic field data all will have orthogonal XYZ readings within <0.1°as defined in figure 1.

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2.1.2 Orientation co-ordinate system
The MTi and MTx calculates the orientation between the sensor-fixed co-ordinate system, S,
and a earth-fixed reference co-ordinate system, G. By default the local earth-fixed reference
co-ordinate system used is defined as a right handed Cartesian co-ordinate system with:
•X positive when pointing to the local magnetic North.
•Y according to right handed co-ordinates (West).
•Z positive when pointing up.
The 3D orientation output (independent of output mode, see chapter 3) is defined as the
orientation between the body-fixed co-ordinate system, S, and the earth-fixed co-ordinate
system, G, using the earth-fixed co-ordinate system, G, as the reference co-ordinate system.
Example:
Please refer to section 2.6 for further details on output co-ordinate systems and different
options to redefine the output co-ordinate systems.
True North vs Magnetic North
As defined above the output coordinate system of the MTi / MTx is with respect to local
Magnetic North. The deviation between Magnetic North and True North (known as the
magnetic declination) varies depending on your location on earth and can be roughly obtained
from various models of the earths magnetic field as a function of latitude and longitude. The
MTi / MTx can accept a setting of the declination value. This is done by setting the “heading”
in the MT Software, SDK or by direct communication with the sensor. The output will then
be offset by the declination and thus referenced to “local” true north.
Local magnetic
north
Local
vertical
z
x
y MTi/MTx co-
ordinate
system (S)
Fixed co-ordinate
system (G)
X
Z
Y
All co-ordinate systems are right handed.

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2.2 Orientation performance specification
Typical performance characteristics of MTi and MTx orientation output.
Dynamic Range: all angles in 3D
Angular Resolution: 0.05°RMS (2)
Static Accuracy (roll/pitch): <0.5°
Static Accuracy (heading)(3):<1.0°
Dynamic Accuracy: 2°RMS (4)
Update Rate: user settable, max 120 Hz (5)
2.2.1 Sensor fusion algorithm settings
The MTi and MTx has been designed to operate with the highest possible accuracy under a
wide range of operating conditions. Under some circumstances however the performance may
benefit from some of the advanced settings available in the Sensor Fusion Algorithm. Mainly
when transient accelerations are expected it may be attractive to the advanced user, to tweak
or explore the influence of some advanced settings of the algorithm.
NOTE: Normal operation does not require the user to change these settings.
Weighting factor
Indicates how much the sensor data from the magnetometer should be weighted relative to the
accelerometer data. A number of 1 indicates the magnetometer data is considered equal to the
accelerometer data and this should be the default value. A number of 0.0 will completely
disregard any data from the magnetometers, otherwise valid range is <0.1 ; 10].
Filter Gain
The gain is the most important tweaking option. Very roughly the gain equals the “cross-
over” frequency of the sensor fusion algorithm in Hertz. For example, a value of 1 for the
gain means, more or less, that frequency components of the calculated orientation vector
exceeding 1 Hz will be determined by the rate of turn sensors and components below 1 Hz
will be determined by the accelerometers and magnetometers. The actual implementation is of
course more sophisticated but this serves as an example for understanding.
Valid values are larger than 0.01 and lower than 50, i.e. <0.01 .. 50], some values may lead to
unstable operation of the algorithm under certain conditions. The recommended default
value of the gain is 1.
Adapt to Magnetic Disturbances
Large amounts of ferrous material (iron, nickel and cobalt but not e.g. aluminum and most
stainless steels) will disturb the homogenous earth magnetic field used as a reference by the
21σstandard deviation of zero-mean angular random walk
3in homogenous magnetic environment
4may depend on type of motion
5inertial data max update rate is 512 Hz

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MT6. The sensitivity of the system to such disturbance can be significantly reduced by an
advanced sensor fusion algorithm setting called AMD (Adapt to Magnetic Disturbances). The
default or “normal” operating mode should however be with this option turned OFF as drift
around the vertical (yaw/heading) will occur over time.
2.3 Orientation output modes
The orientation as calculated by the MTi or MTx is the orientation of the sensor-fixed co-
ordinate system (S) with respect to a Cartesian earth-fixed co-ordinate system (G). The output
orientation can be presented in different parameterizations:
•Unit Quaternions (also known as Euler parameters)
•Euler angles7, roll, pitch, yaw (XYZ Earth fixed type, also known as Cardan or
aerospace sequence)
•Rotation Matrix (directional cosine matrix)
A positive rotation is always “right-handed”, i.e. defined according to the right hand rule
(corkscrew rule). This means a positive rotation is defined as clockwise in the direction of the
axis of rotation.
NOTE: This section is intended to give detailed information on the definition of the various
orientation output modes of the MTi and MTx. The output sequence of the elements in the
vectors and matrices defined here holds for all interface options (RS-232/422, API, GUI). For
more detailed information about the respective interfaces please refer to their specific
documentation;
RS-232/422 ÆMTi and MTx Low-level Communication Documentation
API ÆMT Software Development Kit Documentation
GUI ÆMT Software
6Any disturbance in the magnetic field due to the object the MT is attached to can be compensated for, please
refer to the “Magnetic Field Mapping” software plug-in.
7Please note that due to the definition of Euler angles there is a mathematical singularity 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.

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2.3.1 Quaternion orientation output mode
A unit quaternion vector can be interpreted to represents a rotation about a unit vector n
through an angle α.
A unit quaternion itself has unit magnitude, and can be written in the following vector format;
Quaternions are an efficient, non-singular description of 3D orientation and a quaternion is
unique up to sign:
An alternative representation of a quaternion is as a vector with a complex part, the real
component is the first one, q0.
The inverse (qSG) is defined by the complex conjugate (†) of qGS. The complex conjugate is
easily calculated;
As defined here qGS rotates a vector in the sensor co-ordinate system (S) to the global
reference co-ordinate system (G).
Hence, qSG rotates a vector in the global reference co-ordinate system (G) to the sensor co-
ordinate system (S), where qSG is the complex conjugate of qGS.
q= ¡ q
kqk=1
q
GS
= (cos(
®
2
); nsin(
®
2
))
q
GS
=(q
0
;q
1
;q
2
;q
3
)
x
G
=q
GS
x
S
q
y
GS
=q
GS
x
S
q
SG
q
y
GS
=(q
0
;¡q
1
;¡ q
2
;¡q
3
)=q
SG
The output definition in quaternion output mode is:
q0 q1 q2 q3 TS
MTData
MID 50 (0x32)
All data elements in DATA field are FLOATS (4 bytes)
TS= time stamp (optional)

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2.3.2 Euler angles orientation output mode
The definition used for 'Euler-angles' here is equivalent to 'roll, pitch, yaw/heading' (also
known as Cardan). The Euler-angles are of XYZ Earth fixed type (subsequent rotation around
global X, Y and Z axis, also known as aerospace sequence).
•φ= roll8= rotation around XG, defined from [-180°…180°]
•θ= pitch9= rotation around YG, defined from [-90°…90°]
•ψ= yaw10 = rotation around ZG, defined from [-180°…180°]
NOTE: Due to the definition of Euler angles there is a mathematical singularity when the
sensor-fixed X-axis is pointing up or down in the earth-fixed reference frame (i.e. pitch
approaches ±90°). This singularity is in no way present in the quaternion or rotation matrix
output mode.
The Euler-angles can be interpreted in terms of the components of the rotation matrix, RGS, or
in terms of the unit quaternion, qGS;
Here, the arctangent (tan-1) is the four quadrant inverse tangent function.
NOTE: that the output is in degrees and not radians.
2.3.3 Rotation Matrix orientation output mode
The rotation matrix (also known as Direction Cosine Matrix, DCM) is a well-known,
redundant and complete representation of orientation. The rotation matrix can be interpreted
as the unit-vector components of the sensor coordinate system S expressed in G. For RGS the
unit vectors of Sare found in the columns of the matrix, so col 1 is XSexpressed in Getc. A
8“roll” is also known as: “bank”
9“pitch” is also known as: “elevation” or “tilt”
10 “yaw” is also known as: “heading”, “pan” or “azimuth”
Á
GS
=tan
¡1
µ
R
32
R
33
¶
=tan
¡1
µ
2q
2
q
3
+2q
0
q
1
2q
2
0
+2q
2
3
¡1
¶
µ
GS
=¡ sin
¡1
(R
31
)=¡ sin
¡1
(2q
1
q
3
¡2q
0
q
2
)
Ã
GS
=tan
¡1
µR
21
R
11
¶=tan
¡1
µ2q
1
q
2
+2q
0
q
3
2q
2
0
+2q
2
1
¡1
¶
The output definition in Euler-angle output mode is:
roll pitch yaw TS
MTData
MID 50 (0x32)
All data elements in DATA field are FLOATS (4 bytes)
TS= time stamp (optional)

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rotation matrix norm is always equal to one (1) and a rotation RGS followed by the inverse
rotation RSG naturally yields the identity matrix I3.
The rotation matrix, RGS, can be interpreted in terms of quaternions;
or in terms of Euler-angles;
As defined here RGS, rotates a vector in the sensor co-ordinate system (S) to the global
reference system (G):
It follows naturally that, RSG rotates a vector in the global reference co-ordinate system (G) to
the sensor co-ordinate system (S).
For the rotation matrix (DCM) output mode it is defined that:
Here, also the row-order/col-order is defined.
R
GS
=R
Z
Ã
R
Y
µ
R
X
Á
=
2
4cosà ¡ sinà 0
sinà cosà 0
001
3
5
2
4cosµ 0 sinµ
010
¡sinµ0cosµ
3
5
2
410 0
0cosÁ¡sinÁ
0sinÁ cosÁ
3
5
=
2
4cosµcosà sin Ásinµcosà ¡ cosÁsin à cosÁsinµcosà + sinÁsin Ã
cosµsin à sin Ásin µsin à + cosÁcosà cosÁsin µsin à ¡ sin ÁcosÃ
¡ sinµ sinÁcosµ cosÁcosµ
3
5
R
GS
=
2
4adg
beh
cf i
3
5=
2
4R
11
R
12
R
13
R
21
R
22
R
23
R
31
R
32
R
33
3
5
x
G
=R
GS
x
S
=(R
SG
)
T
x
S
R
GS
R
S
G
=I
3
kRk=1
R
SG
=
2
4abc
def
ghi
3
5
R
GS
=
2
4q
2
0
+q
2
1
¡q
2
2
¡q
2
3
2q
1
q
2
¡2q
0
q
3
2q
0
q
2
+2q
1
q
3
2q
0
q
3
+2q
1
q
2
q
2
0
¡q
2
1
+q
2
2
¡q
2
3
2q
2
q
3
¡2q
0
q
1
2q
1
q
3
¡2q
0
q
2
2q
2
q
3
+2q
0
q
1
q
2
0
¡q
2
1
¡q
2
2
+q
2
3
3
5
=
2
42q
2
0
+2q
2
1
¡12q
1
q
2
¡2q
0
q
3
2q
1
q
3
+2q
0
q
2
2q
1
q
2
+2q
0
q
3
2q
2
0
+2q
2
2
¡12q
2
q
3
¡2q
0
q
1
2q
1
q
3
¡2q
0
q
2
2q
2
q
3
+2q
0
q
1
2q
2
0
+2q
2
3
¡1
3
5

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2.4 Calibrated data performance specification
rate of
turn acceleration magnetic field temperature
Unit [deg/s] [m/s2] [mGauss] [°C]
Dimensions 3 axes 3 axes 3 axes -
Full Scale (units) +/- 300* +/- 17 +/- 750 -55…+125
Linearity (% of FS) 0.1 0.2 1 <1
Bias stability (units 1σ)11 5 0.02 0.5 -
Scale factor
stability (% 1σ)11 - 0.05 0.5 -
Noise density (units √Hz) 0.05 0.001 0.4 0.0625
12
Alignment
error(13) (deg) 0.1 0.1 0.1 -
Bandwidth (Hz) 40 30 10 -
These specifications are valid for an MTi with standard configuration.
*) The standard configuration of the MTx is with a rate gyro with a range of 1200 deg/s.
The following custom configurations are available, standard configuration highlighted in
bold:
Accelerometer Rate gyro
Full scale ± 17 m/s2 (1.7 g) ±1200 deg/s (MTx default)
± 100 m/s2(10 g) ± 900 deg/s
± 300 deg/s (MTi default)
± 150 deg/s
Specifications of custom units may vary.
11 temperature compensated, deviation over operating temperature range (1σ)
12 minimal resolution of digital readout, absolute accuracy is ±0.5 °C
13 after compensation for non-orthogonality (calibration)
The output definition in rotation matrix (DCM) output mode is:
a b c d e f g h i TS
MTData
MID 50 (0x32)
All data elements in DATA field are FLOATS (4 bytes)
TS= time stamp (optional)

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2.5 Calibrated data output mode
NOTE: This section is intended to give detailed information on the definition of the calibrated
inertial data output modes of the MTi and MTx. The output sequence of the elements of the
vectors defined here holds for all interface levels (RS-232/422, API, GUI). For more detailed
information about the respective interfaces please refer to their specific documentation;
RS-232/422 ÆMTi and MTx Low-level communication Documentation
API ÆMT Software Development Kit Documentation
GUI ÆMT Software
2.5.1 Physical sensor model
This section explains the basics of the individual calibration parameters of each MTi and
MTx. This explains the values found on the MT Test and Calibration Certificate that
comes with each MTi and MTx.
The physical sensors inside the MTi and MTx (accelerometers, gyroscopes and
magnetometers) 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 relation:
(
)
1
TT
−
=−sK ub
The model really used is more complicated and is continuously being developed further. From
factory calibration each MTi / MTx has been assigned a unique gain matrix, KTand the bias
vector, bTThis calibration data is used to relate the sampled digital voltages, u, (unsigned
integers from the 16 bit ADC’s) 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 direction of the sensitive axes with respect to the ribs of the
sensor-fixed coordinate system (S) housing. E.g. the first accelerometer misalignment 1
r
describes the sensitive direction of the accelerometer on channel one. The three sensitive
directions are used to form the misalignment matrix:
With Orepresenting higher order models and temperature modelling, etc.
Each MTi and MTx is also modeled for temperature dependence of both gain and bias for all
sensors and other effects. This modeling is not represented in the simple model in the above
equations, but is implemented in the firmware.
KT=
2
4G100
0G
20
00G
3
3
5
2
4a1;x a1;y a1;z
a2;x a2;y a2;z
a3;x a3;y a3;z
3
5+O
G=
2
4G
1
00
0G
2
0
00G
3
3
5
A=
2
4a1;x a1;y a1;z
a2;x a2;y a2;z
a3;x a3;y a3;z
3
5

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The basic parameters in the above model of your individual MTi or MTx can be found on the
MT Test and Calibration Certificate.
2.5.2 Calibrated inertial and magnetic data output mode
Output of calibrated 3D linear acceleration, 3D rate of turn (gyro) and 3D magnetic field data
is in sensor-fixed coordinate system (S).
The units of the calibrated data output are as follows:
Vector Unit
Acceleration m/s2
Angular velocity
(rate of turn) rad/s
Magnetic field
a.u. (arbitrary units)
normalized to earth field
strength
The calibrated data is “unprocessed”, i.e. only the physical calibration model is applied to the
16-bit values retrieved from the AD-converters. There is no additional filtering, or other
temporal processing applied to the data. The bandwidths of the signals are as stated in the
datasheet and section 2.4.
NOTE: The linear 3D accelerometers measure all accelerations, including the acceleration
due to gravity. This is inherent to all accelerometers. Therefore, if you wish to use the 3D
linear accelerations output by the MTi / MTx to estimate the “free” acceleration (i.e. 2nd
derivative of position) gravity must first be subtracted.
2.5.3 Un-calibrated raw output mode
In un-calibrated raw output format the “raw” readings from the 16-bit AD-converters in the
MTi / MTx are outputted. This means the physical calibration model described in the previous
section is not applied. This gives you open access to the basic level of the sensor unit, but in
most cases this level of use is not recommended. However, if your main purpose is for
logging and post-processing, it may be advantageous as it is always possible to go back to the
“source” of the signal. In this mode the device temperature is also outputted (housing ambient
only).
The output definition in calibrated data output mode is:
accX accY accZ gyrX gyrY gyrZ magX magY magZ TS
MTData
MID 50 (0x32)
All data elements in DATA field are FLOATS (4 bytes)
TS= time stamp (optional)

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NOTE: The data fields are 2 bytes (16 bits) as opposed to the 3 byte floats for the other
output modes.
Temperature output format
The 2 byte temperature data field in the un-calibrated raw output mode of the MTi / MTx can
be interpreted as a 16 bits, 2-complement number. However, please note that the resolution of
the temperature sensor is not actually 16-bit but 12-bit.
For example you can interpret the 2-byte temperature as follows:
00.00hex = 0.0 °C
00.80hex = +0.5 °C
FF.80hex = -0.5 °C
19.10hex = +25.0625°C
E6.F0hex = -25.0625 °C
The temperature-field is a 16-bit two-complement number of which the last byte represents
the value behind the comma. To calculate the temperature value use the formula
T = (– 216 + x) / 256 if x ≥215
or T = x / 256 if x < 215, where x is the 16-bit value of the Temp field.
For example, the value 59120 (0xE6F0) corresponds with a temperature of -25.0625 °C.
The output definition in un-calibrated raw output mode is:
acc1 acc2 acc3 gyr1 gyr2 gyr3 mag1 mag2 mag3 TS
MTData
MID 50 (0x32)
temp
Each data element in DATA field is 2 bytes (16 bit) unsigned integers!
See below for reading the temperature data
TS= time stamp (optional)

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2.6 Reset of output or reference co-ordinate systems
2.6.1 Output with respect to non-default coordinate frames
In some situations it may occur that the sensor axes are not exactly aligned with the axes of
the object of which the orientation has to be recorded. It may be desired to output the
orientation and/or calibrated inertial data in an object-fixed frame, as opposed to an sensor-
fixed frame. Four features have been added to the software to facilitate in obtaining the output
in the desired coordinate frames.
1. A heading reset that redefines the X-axis of the global coordinate frame while
maintaining the Z-axis along the vertical. After the heading reset the orientation will
be expressed with respect to the new global (earth fixed) reference frame.
2. A global reset that permits the user to use the MTI / MTx to define all the axes of the
global coordinate frame (including Z-axis, up/down).
3. An object reset that defines how the sensor it oriented with respect to the coordinate
axes to which it is attached. After the object reset, both the orientation and the
calibrated sensor data are expressed with respect to the axes of the object.
4. A combined object/heading reset, referred to as alignment.
NOTE: For all co-ordinate system reset functions it is important to remember that the housing
of the MTx can not be considered an accurate reference. Placement and subsequent aligning
must be done very carefully otherwise (alignment) errors may be induced.
2.6.2 Heading reset
Often it is important that the global Z-axis remains along the vertical (defined by local gravity
vector), but the global X-axis has to be in a particular direction. In this case a heading reset
may be used, this is also known as “bore sighting”. When performing a heading reset, the new
global reference frame is chosen such that the global X-axis points in the direction of the
sensor while keeping the global Z-axis vertical (along gravity, pointing upwards). In other
words: The new global frame has the Z axis along gravity, pointing upwards, the X-axis in the
plane spanned by the vertical and the sensor X-axis, perpendicular to the global Z-axis and the
Y-axis such that a right handed coordinate system is formed.
NOTE: After a heading reset, the yaw may not be exactly zero, this occurs especially when
the X-axis is close to the vertical. This is caused by the definition of the yaw when using
Euler angles, which becomes unstable when the pitch approaches ± 90 deg.
2.6.3 Global reset
When performing a full “global” reset, the MTi / MTx axes (S) is used to define the axes of
the new global coordinate frame (G). When pressing the reset button or sending the reset
command, Shas to be orientated in such a way that the sensor axes all point in exactly the
same direction as the axes of the global coordinate frame. After this the orientation output will
be with respect to the newly defined global axes.