If you intend to use an inertial measurement system...  
... which technical data you should analyze and compare before making your decision  
by Dr.-Ing. Edgar v. Hinüber, CEO iMAR Navigation GmbH  
Keywords: inertial navigation system, inertial measurement system, inertial measurement unit, attitude heading reference sys-  
tem, inertial sensor, gyroscope, accelerometer, angular random walk, bias, drift, free inertial, unaided inertial navigation, GNSS  
denied, aided navigation, INS, IMU, IMS, AHRS  
Preface  
Indeed, it is often very challenging for both inexperienced and advanced  
users of inertial technology to make the right decision in an environment  
of complex marketing information about which of the various inertial  
measurement systems, inertial navigation systems, attitude and heading  
reference systems, inertial measurement units, or at least inertial sen-  
sors on the market best and most economically meets their require-  
ments.  
With this article, we aim to help the reader better understand the physics  
behind inertial navigation or inertial measurement systems and sensors,  
and to evaluate the information. We also aim to enable you to better val-  
idate the datasheets provided by suppliers, identify inconsistencies that  
are unfortunately often present, and find your best technical and eco-  
nomic solution. Only in this way can you be sure that the product you select truly meets your requirements.  
Tatsächlich ist es oft sehr schwierig, sowohl für unerfahrene als auch für fortgeschrittene Benut-  
zer von Trägheitstechnologie, im Umfeld vielschichtiger Marketing-Informationen die richtige Ent-  
scheidung zu treffen, welches der verschiedenen Trägheitsmesssysteme, Trägheitsnavigations-  
systeme, Lage-Kurs-Referenzsysteme, Trägheitsmessgeräte oder zumindest Trägheitssensoren  
auf dem Markt am besten und wirtschaftlichsten ihren Anforderungen entspricht.  
Mit diesem Artikel helfen wir dem Leser, die Physik hinter der Trägheitsnavigation oder den Träg-  
heitsmesssystemen und Sensoren besser zu verstehen und die Informationen zu bewerten. Wir  
versuchen auch, Sie besser in die Lage zu versetzen, die Datenblätter der Anbieter selbst zu  
validieren, leider oft vorhandene Inkonsistenzen zu identifizieren und Ihre beste technische und  
wirtschaftliche Lösung zu finden. Nur so können Sie sicher sein, dass das von Ihnen ausgewählte  
Produkt tatsächlich Ihren Anforderungen genügt.  
Introduction into Inertial Measurement Technology:  
Inertial navigation and guidance systems were initially developed for rocket guidance and control. Today,  
their applications span a wide range of fields, from horizontal directional drilling deep underground to  
spacecraft navigation. In fact, inertial technology has become an integral part of everyday life. For exam-  
ple, every modern car is equipped with at least one gyroscope and two accelerometers for the Electronic  
Stability Program (ESP) or airbag control, ensuring safe travel even in challenging conditions. Likewise,  
every smartphone incorporates accelerometers, gyroscopes, a GNSS receiver, and a magnetometer.  
A typical Inertial Navigation System (INS) relies on gyroscopes (angular rate sensors) and accelerome-  
ters as its primary sensors. Gyroscopes are used to determine the vehicle's orientation, compensating  
for gravitational effects on the accelerometer data. This process involves solving a complex set of differ-  
ential equations in real-time to convert the sensor measurements into estimates of velocity, position,  
attitude, and heading, based on a known initial position in latitude and longitude.  
Modern Inertial Navigation Systems (INS) commonly utilize 'strap-down' technology, where all inertial  
sensors (gyroscopes and accelerometers) are rigidly mounted to the vehicle. In earlier designs, 'gimbal'  
technology was used, with gyroscopes mechanically stabilizing accelerometers in space. In strap-down  
systems, stabilization is achieved through mathematical calculations, subjecting all inertial sensors to the  
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vehicle's full dynamic range. Despite the absence of mechanical gimbals, strap-down systems are signif-  
icantly more robust operationally than gimbaled systems, although they demand higher sensor range,  
scale factor accuracy, and sensor durability.  
All unaided inertial navigation systems experience drift over time, as small measurement errors accumu-  
late, resulting in progressively larger errors in velocity and, especially, position due to double integration  
over time. The methods for compensating and correcting this drift, particularly in real-time applications,  
differ substantially across market solutions. Only suppliers who excel in providing unaided inertial navi-  
gation with the highest performance — especially under challenging environmental conditions, often re-  
garded as the 'king class of inertial measurement technology' — are capable of delivering compelling  
solutions for aided navigation scenarios as well.  
Control theory, particularly Kalman filter-based techniques, provides a framework for integrating comple-  
mentary data from various sensors, a process known as sensor data fusion. Common supplementary  
sensors used to support INS-based systems include satellite navigation systems like GPS, GALILEO,  
BeiDou and GLONASS (GNSS), as well as odometers, air data sensors, magnetometers, radio position-  
ing systems, and more. Additionally, specific techniques such as Zero Velocity Update (ZUPT) and Posi-  
tion Update (PUPT) can enhance accuracy for particular applications. (Link)  
The significant risks of other signal processing methods, such as AI-based approaches, which are  
often greatly underestimated by inexperienced users, are discussed in a dedicated chapter of this paper,  
particularly regarding their use not only in safety-critical or reference measurement applications.  
Trägheitsnavigations- und -führungssysteme wurden ursprünglich zur Steuerung von Raketen  
entwickelt. Heutzutage werden sie in vielen Anwendungen eingesetzt, von der horizontalen Rich-  
tungsbohrtechnik tief unter der Erdoberfläche bis zur Navigation von Raumfahrzeugen. Heutzu-  
tage kommt jeder täglich mit Trägheitstechnologie in Kontakt: Zum Beispiel enthält jedes mo-  
derne Auto mindestens ein Gyroskop und zwei Beschleunigungssensoren für das ESP (elektro-  
nisches Stabilitätsprogramm) oder für die Airbag-Steuerung, um das Reisen auch in schwierigen  
Umgebungen so sicher wie möglich zu machen. Auch jedes Smartphone enthält heute Beschleu-  
nigungssensoren, Gyroskope sowie einen GNSS-Empfänger und ein Magnetometer.  
Ein typisches Trägheitsnavigationssystem (INS, inertial  
navigation system) verwendet als Sensoren Gyroskope  
(Drehratensensoren) und Beschleunigungssensoren.  
Die Gyroskope werden dabei verwendet, um die Orien-  
tierung des Fahrzeugs zu bestimmen und insbesondere  
auch, um die Messdaten der Beschleunigungssensoren  
in Bezug auf die Schwerkraft zu kompensieren. Das be-  
deutet, eine große Menge an Differentialgleichungen in  
Echtzeit zu lösen, um diese Messwerte in Schätzungen  
von Geschwindigkeiten, Position, Lage und Kurs umzu-  
wandeln, ausgehend von einer bekannten Anfangsposi-  
tion in Breiten- und Längengrad.  
Die heutige Implementierung von Trägheitsnavigations-  
systemen (INS) erfolgt in der sogenannten "strap-down"-Technologie, bei der alle Trägheits-  
sensoren (Gyroskope und Beschleunigungssensoren) steif am Fahrzeug montiert sind. In der  
Vergangenheit wurden die Systeme in der sogenannten "gimbal"-Technologie entworfen, bei der  
die Gyroskope verwendet wurden, um die Beschleunigungssensoren mechanisch im Raum zu  
stabilisieren. In strap-down-Systemen erfolgt die Stabilisierung mathematisch, und daher sind  
alle Trägheitssensoren den vollen Fahrzeugdynamiken ausgesetzt. Aufgrund fehlender mecha-  
nischer Gimbals sind die strap-down-Systeme im Betrieb viel robuster als die gimballed Systeme,  
aber die Anforderungen an den Messbereich, die Skalenfaktorgenauigkeit und die Robustheit der  
Sensoren sind entsprechend höher.  
Alle ungestützten Trägheitsnavigationssysteme leiden aufgrund der erforderlichen mathemati-  
schen Integration von Drehraten und Beschleunigungen zur Bestimmung der Lagewinkel und  
Position unter einer zeitabhängigen Drift, weil kleine Fehler in den Messungen zu progressiv grö-  
ßeren Fehlern in Geschwindigkeit und insbesondere Position aufgrund der doppelten Integration  
über der Zeit führen. In der Kompensation und Korrektur dieser Drift insbesondere in  
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Echtzeitanwendungen unterscheiden sich die am Markt angebotenen Lösungen ganz erheblich.  
Nur wer als Systemlieferant die ungestützte Trägheitsnavigation (free inertial navigation, unaided  
navigation) als „Königsklasse der Inertialmesstechnik“ in schwierigen Umgebungsbedingungen  
führend beherrscht und anbieten kann, der kann auch für gestützte Navigationslösungen (aided  
navigation) überzeugende Lösungen liefern.  
Regelungstechnik im Allgemeinen und insbesondere Kalman-Filter basierte Verfahren bieten den  
Rahmen für die Kombination von Informationen aus verschiedenen komplementären Sensoren  
– die sogenannte Sensordatenfusion. Die hierfür am häufigsten ergänzenden Sensoren, die zur  
Stützung INS-basierter Systeme verwendet werden, sind Satellitennavigationssysteme wie GPS,  
GALILEO, GLONASS, …(GNSS), Odometer, Luftdatensensoren, Magnetometer, Funkortungs-  
systeme usw. Des weiteren erlauben besondere Methoden wie ZUPT, PUPT (Zero Velocity Up-  
date, Position Update) usw. anwendungsspezifische Genauigkeitsverbesserungen. (Link)  
Die signifikanten und von unerfahrenen Anwendern zumeist deutlich unterschätzen Risiken  
anderer Signalverarbeitungsmethoden wie KI basierter Verfahren für den Einsatz nicht nur in  
sicherheitsrelevanten oder Referenzmesstechnik-Anwendungen werden in einem eigenen Kapi-  
tel in dieser Abhandlung erörtert.  
The right INS for your Application:  
It is a big difference to operate an inertial measurement  
system in static lab conditions or low dynamic environment or in the "real-world".  
Check the performance of the IMS (IMS = inertial measurement system) for the envi-  
ronment you want to operate the system in. Link  
•
Will it be used on an aircraft (transportation aircraft, helicopter, drone or  
fighter?),  
•
•
•
or on a rail vehicle (surface or underground?),  
or on a passenger car or a truck or a tank,  
or on a naval ship, a ferry or a speed boat or on an underwater surveying  
vehicle,  
•
•
or inside of a missile or a torpedo,  
or will it be used e.g. in a drilling application or in pipeline surveying or for  
machinery guidance,  
•
or will it be used e.g. to acquire the field of gravity with high accuracy?  
To support your needs as best as possible, you can send us the Inquiry Form  
from our web site, filled with your application related information:  
https://www.imar-navigation.de/downloads/faq/enquiry_imar.docx or  
https://www.imar-navigation.de/downloads/faq/enquiry_imar.pdf  
Compare the conditions of operation given in the data sheet of the system intended  
to be used: Is the condition well defined and will it meet your application requirements?  
•
•
Will GNSS be available in your application in the way as it is assumed inside  
the data sheets of the systems you are investigating?  
Do you require operation also in GNSS denied environment, e.g. under jam-  
ming or spoofing impacts? Is the solution, described in the datasheet, able  
to handle operation in such GNSS denied environment?  
•
•
What is the behavior of the system under coning motion, under vibration and  
under temperature gradients?  
What operation mode is required for your application and is the advertised  
solution able to comply? See the next chapters of this paper regarding free  
inertial navigation, pure inertial navigation, aided navigation, surveying,  
ZUPT and PUPT aiding, ...)  
•
Do you need accurate, reliable and available results of the system during  
your data sensitive or safety critical missions or anywhere, where you have  
to rely on the data output? Then any AI based solution might not be the right  
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choice even if it might be slightly cheaper in purchasing. Cost should be  
compared in case of a failed mission due to an unpredicted AI decision.  
Sensor Technology Selection and Sensor Data Fusion:  
Each inertial sensor  
technology has its specific advantages and drawbacks which have to be considered  
regarding the foreseen application and desired accuracy. Some sensor technologies  
come e.g. with a very high stability of sensor performance (e.g. ring laser gyros) while  
others are for instance optimized for very light weight or low cost, but being affected  
by possible accuracy aging effects (like MEMS based sensors).  
Inertial Sensors: Take into consideration that MEMS based gyros (working on Cori-  
olis law using vibratory excitation) as well as spinning dynamical tuned gyros (DTG)  
show a so-called g-dependent drift, i.e. they produce a drift (angular rate offset) de-  
pendent on linear and quad-  
ratic acceleration and environ-  
mental vibration impacts. High  
performance ring laser gyros  
(RLG = ring laser gyros) and  
hemispherical resonator gyro-  
scopes (HRG) as well as mid  
performance fiber optical gy-  
ros (FOG) do not show such  
GNSS  
pos & vel & stddev  
& raw data  
Output  
pos, vel, attitude, hea-  
ding, rates, accels, std-  
devs, time, status, BIT,  
raw data etc.  
ODO/VMS  
pulses / CAN  
Ext Aid  
Accel / Rate  
6 axes raw data  
temperatures  
pos / vel / mag / air /  
DVL / LiDAR…, stddev,  
time stamp  
g-dependent  
drift,  
while  
higher performance fiber optical gyros (FOG) also show performance degradation due  
to physical reasons, caused by vibration impacts and temperature gradients.  
Sensor Data Fusion: The signal processing on system level (“sensor data fusion”)  
has to take care for all sensor errors. Therefore, the iMAR sensor data fusion is able  
e.g. not only to estimate the common inertial sensor offsets, but also estimates and  
compensates the scale factor drifts, misalignments and other effects in real-time  
(more than 40 states are estimated, compared to the classical and most common  
implementations of competitors with only 15 states). (Link)  
With over 30 years of experience in sensor data fusion and integration, iMAR  
incorporates all state-of-the-art gyro technologies and performance classes in its sys-  
tems, ranging from MEMS to FOG, RLG, and HRG, depending on the application  
requirements. The company utilizes a robust real-time sensor data fusion process with  
more than 40 states to estimate and compensate for most residual errors and even  
the aging effects of inertial sensors. Link  
Additional complementary sensors can also be integrated into the sensor data fusion  
process, such as GNSS (single and dual antenna), wheel sensor data (odometer,  
VMS), DVL (Doppler Velocity Log), EM-Log, magnetometer data (magnetic heading  
— though caution is advised with these sensors, as they are highly sensitive to envi-  
ronmental influences that cannot be compensated for if they change during the mis-  
sion), air data sensors, and more.Link  
The physics underlying the mathematics of inertial navigation is, among other things,  
described by Newton's axioms. While the fundamental mathematical framework and  
solutions to navigation equations have been well known for many decades, the real  
challenge lies in implementing these solutions in a robust, efficient, highly reliable,  
and readily available manner. Achieving this requires a vast amount of experiential  
knowledge, which the iMAR team has accumulated over more than 30 years across  
hundreds of different applications.  
In the absence of such expertise, less experienced providers of PNT solutions may  
find it tempting to turn to so-called artificial intelligence (AI) methods, as these can  
quickly demonstrate promising results in a well-trained environment. AI techniques  
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are well-established in fields like image, speech, and video processing, particularly  
where the physical modeling of phenomena remains challenging for engineers and  
scientists. However, because the learning processes of AI agents are only sporadi-  
cally verifiable, there is a consensus among experienced users and experts that AI-  
based systems should not be employed in mission-critical or safety-relevant applica-  
tions. The real behavior of these systems cannot be entirely predicted, posing a sig-  
nificant risk to the mission.  
At iMAR, we firmly believe that only physics has to determine the behavior of our  
measurement systems. Our deterministic real-time results arise from the intelligent  
signal processing conducted by our experienced engineers and scientists, not from  
opaque AI. Our customers choose our systems because they value the exceptional  
reliability, availability, and accuracy of our solutions, even in critical missions during  
daily operations. We achieve this through our mathematically and physically pre-  
cise algorithms — and intentionally not through AI (artificial intelligence) interpreted  
so-called “measurement results”.  
AI methods are utilized in our work only in areas where they can contribute, such as  
object detection or classification, and do not have any safety-critical implications.  
Die Physik, der die Mathematik der Inertialnavigation folgt, wird u.a. durch die  
Newton’schen Axiome beschrieben. Während die grundsätzliche mathematische  
Beschreibung und Lösung der Navigationsgleichungen seit vielen Jahrzehnten  
allgemein bekannt ist, liegt die besondere Herausforderung darin, die Lösung  
robust, effizient, hochgradig zuverlässig und verfügbar zu realisieren. Hierzu be-  
darf es eines enormen Erfahrungswissens, welches sich das iMAR-Team in über  
30 Jahren in hunderten verschiedener Anwendungen erarbeitet hat und täglich  
weltweit demonstriert.  
Kann man auf ein solches Wissen nicht aufsetzen, erscheint es für einen Anbi-  
eter von PNT-Lösungen auf den erste Blick sehr attraktiv, auf Metoden der sog.  
künstlichen Intelligenz (KI) zu ersetzen, denn hiermit kann er im trainierten  
Umfeld recht schnell passable Lösungen vorzeigen. KI-Verfahren sind bestens  
in Bereichen der Bild-, Sprach- und Videomanipulation etabliert und insb. dort,  
wo eine physikalische Beschreibung von Sachverhalten den Anwendern heute  
noch schwer fällt. Da der Lernprozess solcher KI-Agenten jedoch nur sporadisch  
prüfbar ist, ist es in erfahrenen Anwenderkreisen Konsenz, dass auf KI-  
Methoden basierte Systeme nicht in Daten- oder sicherheitsrelevanten Anwen-  
dungen zum Einsatz kommen, da das reale Verhalten derartiger Systeme nicht  
hinreichend voraussagbar ist, womit ein enormes Sicherheitsrisiko gegeben sein  
kann.  
Deshalb gilt bei iMAR: Nur die Physik bestimmt das Verhalten unserer Mess-  
systeme. Unsere deterministischen Echtzeitergebnisse entstehen durch die in-  
telligente Signalverareitung unserer projekterfahrenen Ingenieure und Wissen-  
schaftler, und nicht durch intransparente KI. Unsere Kunden verwenden un-  
sere Systeme, denn sie schätzen die außerordentliche Zuverlässigkeit, Ver-  
fügbarkeit und Genauigkeit unserer Lösungen auch in kritischen Missionen im  
täglichen Einsatz. Dies erreichen wir durch unsere mathematisch-physikalisch  
präzisen Algorithmen - und ganz bewusst nicht durch AI (artificial inteligence)  
interpretierte sogenanten "Messergebnissen".  
AI-Methoden kommen bei uns nur dort zum Einsatz, wo diese z.B. bei Ob-  
jekterkennung oder Klassifizierung einen Beitrag liefern können abr keinen  
sicherheitsrelevanten Einfluss haben.  
Gyro Bias:  
If the inertial system operates unaided (without odometer/velocity or GNSS or mag-  
netometer aiding or similar), the gyro bias indicates the increase of the angular error  
over time (in deg/h or deg/s). If the system is aided with speed information (e.g.  
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odometer / wheel sensor or Doppler log), the roll and pitch gyro drift can be compen-  
sated in the measurement system by sensor data fusion and the gyro drift mainly  
affects the heading accuracy over time. If the system consists of low drift gyros, also  
the true heading can be estimated using gravity and earth rate information (so-called  
north-seeking or gyro compassing).  
If the system is aided with position information (e.g. GPS or GALILEO or GLONASS  
or LiDAR etc.), also the heading drift can be corrected and true heading can be ob-  
tained (even with medium grade performance gyros), if the applied motion dynamics  
is sufficient, i.e. if the heading state is observable in the Kalman filter1. But of course  
the smaller the gyro drift the better all possible angular corrections and the longer the  
allowed time where the aiding information may be not present (e.g. GPS in urban  
canyons)!  
If the system is operated in free inertial navigation mode, the gyro bias is responsible  
for the position and velocity error over time (so-called Schuler oscillation).  
Gyro Scale Factor Error:  
This is an indication of the angular error which occurs during ro-  
tation. E.g. with 300 ppm scale factor error (=0.03%) the angular error is in the area  
of 0.1 degree after a one revolution turn. With a ring laser gyro or hemispherical res-  
onator gyro system with < 10 ppm scale factor error the angular error is less than 1  
arcsec (0.0003 deg) if the rotation angle is 30 deg.  
Misalignment:  
A misalignment between the gyro axes (or accelerometer axes) causes a cross-  
coupling between the measurement axes. A misalignment of 0.1 mrad inside of the  
system (e.g. residual calibration mismatch) leads to a roll error of 0.036 degree during  
a one revolution turn around the yaw axis (if the system is unaided). The smaller the  
required misalignment, the higher the requirements to sensor performance and cali-  
bration equipment (e.g. iMAR's multi-axes turn-tables).  
Accelerometer Offset:  
An  
offset in an accel-  
erometer intro-  
duces an error  
during alignment,  
specifically in the  
determination of  
the initial roll and  
pitch angles, as it  
directly affects the  
accuracy of meas-  
uring gravity (ap-  
proximately 9.81  
m/s²). For in-  
stance, an offset  
of 0.1 mg results  
in an angular error  
of about 0.006 de-  
grees in either  
pitch or roll (0.1  
mg = g × sin(0.006  
deg)). These sen-  
sor offsets can be  
estimated during  
operation through  
15 °/h/sqrt(Hz) resp. 0.25 °/sqrt(hr)  
0.8 °/hr  
Allan Variance of a gyro  
1
Observability means, that the sensor data fusion has enough information available to estimate certain states like gyro bias or  
heading. Example: If an aircraft flies always straight forward at constant speed, it is impossible to estimate vertical gyro bias or  
heading using a single antenna GNSS aiding, because due to the mentioned motion no significant acceleration or angular rate  
will be measured.  
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the system’s integrated Kalman filter data fusion, utilizing GPS, DGPS, RTK data, or  
the Zero Velocity Update Procedure (ZUPT), provided there is sufficient motion dy-  
namics.  
Bandwidth:  
In general, the dynamic performance of an inertial measurement system (IMS) im-  
proves with higher internal sampling rate and bandwidth of the inertial sensors. Proper  
internal data synchronization (time stamping) is also essential for accurate signal pro-  
cessing, especially when the IMS operates in challenging dynamic environments. A  
high-precision internal time reference and hardware-based time stamping for all data  
are crucial for ensuring reliable performance in an INS. Furthermore, low latency in  
data output is mandatory for utilizing an INS in trajectory or attitude control applica-  
tions, such as those involving autonomous vehicles.  
Gyro Random Walk:  
This value, expressed in deg/sqrt(hr), represents the noise of the gyro  
used. A larger value indicates more noise in the measured angular rates and angles.  
Some manufacturers also specify this as noise density in deg/h/sqrt(Hz). Both values  
are equivalent for white noise gyro output; dividing the second value by 60 converts it  
to deg/sqrt(hr). An angular random walk (ARW) of 0.003 deg/sqrt(hr) suggests that  
the angular error (uncertainty) due to random walk is approximately 0.001 deg after 6  
minutes (unaided) or 0.0004 deg after 1 minute (all values reported as one sigma).  
The angular random walk is crucial for the accuracy of north-seeking, as halving the  
random walk reduces the time required for north-seeking by a factor of four, provided  
the gyro’s resolution is sufficiently high.  
The accompanying plot of the Allan Variance for a mid-performance gyro graphically  
illustrates the square-root ARW of a MEMS gyro (to obtain the ARW in [deg/sqrt(hr)],  
take the value at 1 second and divide it by sixty). At 1 second, the square-root of the  
Allan Variance is 15 deg/hr. This yields an Angular Random Walk (ARW) of 15/60  
deg/sqrt(hr) = 0.25 deg/sqrt(hr) = 0.0042 deg/s/sqrt(Hz) = 15 deg/hr/sqrt(Hz) (assum-  
ing white gyro noise). The bias stability, indicated by the minimum point of the graph,  
is 0.8 deg/hr at a correlation time of 3,000 seconds. Overall, this demonstrates that  
we are utilizing a relatively high-quality MEMS gyro.  
Position error of an unaided, free inertial INS:  
We must distinguish between short-term  
accuracy and long-term accuracy in an inertial navigation system (INS). Additionally,  
it's important to differentiate between arbitrary moving objects, such as aircraft, ships,  
or spacecraft, and land-based vehicles that travel on roads — applications character-  
ized by specific motion constraints.  
Long-time accuracy of an arbitrary moving, unaided, free inertial  
INS:  
Definition: An arbitrary moving unaided free inertial INS operates in a mode devoid  
of any external aids, meaning there is no GNSS, magnetometer, air data, Doppler log,  
LiDAR, RF positioning, or ZUPT. In this mode, the INS can move without limitations,  
provided it remains within the measurement range of the inertial sensors.  
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In this context, the system experiences a position error known as Schuler oscillation.  
This position error, typically measured in nautical miles per hour (nm/hr), reflects the  
global position error of the free inertial INS due to residual accelerometer and gyro  
errors. The oscillation occurs with a period of approximately 84 minutes, as well as  
with a 24-hour cycle. The amplitude of the oscillation is influenced by the accelerom-  
eter offset, while the average position drift, or 'shift,' is affected by gyro drift. This is a  
simplified model for explanatory purposes; further details can be derived from the in-  
ertial differential equations.  
The figure shows such long time behavior of a free inertial navigation (example: data  
obtained from iNAT-RQT over more than 3 days): Link  
This Schuler Oscillation plot displays position error in meters and time in hours. For  
example, the free inertial INS shows a position error of 3 km after 70 hours (equivalent  
to 0.02 nm/hr)  
As illustrated in the plot, it is crucial to clarify how the value of 'free inertial drift' is  
derived. Due to the 24-hour oscillation, you can observe that the position error after  
11 hours is identical to that after 70 hours. The conditions of data acquisition also play  
a significant role: this plot was generated following only 10 minutes of initial alignment.  
Why do some vendors claim much lower free inertial drifts?  
If the INS is aided prior to drift determination (for instance, by operating it with signifi-  
cant motion dynamics and external aids like GNSS), and if the system is aided by an  
EM-log (example: naval vessels, submarines), it is possible to achieve drift values  
below 1 nm per 100 hours, or even over 360 hours. However, it is essential to note  
that this scenario does not represent 'pure inertial, unaided' operation, as the INS  
requires adequate position aiding for a substantial duration (e.g., 12 hours) and at  
least periodical velocity aiding to provide such results. Many datasheets, however, do  
not adequately explain this requirement, nor do they mention that these systems need  
to be temperature-controlled and require significant time for power-up.  
Short-time accuracy of an arbitrary moved unaided INS (free iner-  
tial navigation):  
Definition: A free inertial operating INS functions in a mode devoid of any external  
aidings, meaning no GNSS, magnetometer, air data, Doppler log, LiDAR, RF posi-  
tioning, or other assistance. Short-term operation refers to a duration that is signifi-  
cantly shorter than the Schuler period of 84 minutes (as previously mentioned).  
In this operational mode, the values (expressed in meters or meters per second) are  
relevant for measurements lasting less than approximately 20 to 40 minutes, as  
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Schuler oscillation is not significant for short-term measurements. An accelerometer  
offset results in a position error that increases quadratically over time.  
delta_s = 0.5 x delta_a x T²  
[m]  
(a)  
with delta_a = accelerometer offset [m/s²] and T = measuring time [s].  
Example for a medium accurate system:  
delta_a = 1 mg 0.01 m/s², T = 100 sec ➔ delta_s = 50 m  
The gyro drift delta_omega affects the position error corresponding to the equation  
delta_s = g/6 x delta_omega x T³ [m] (b)  
with delta_omega in [rad/s] and g = 9.81 m/s² .  
An attitude (roll/pitch) error of e.g. delta_attitude affects the position error due to a  
wrong compensation of the gravity on the horizontal IMS axes:  
delta_s = 0.5 x g x sin (delta_attitude) x T²  
[m]  
(c)  
Example, how you can validate manufacturer’s statements  
(with data from a vendor’s datasheet): IXSEA LANDINS  
If a provider promotes an inertial measurement system (IMS) with a roll/pitch accuracy  
of 0.005 degrees and claims a horizontal position error of 0.7 m (and a vertical position  
error of only 0.5 m) after 300 seconds in free inertial navigation mode—without odom-  
eter aiding, without ZUPT, and without internal vibration isolators—you can easily ver-  
ify and calculate two key factors using the simple thumb rule equations provided  
above:  
•
Position error due to 0.005 deg roll or pitch error after 300 sec (free inertial):  
0.5 x 9.81 m/s² x sin(0.005°) x (300 sec)² = 38 m (from equation (c))  
•
What must be the accelerometer accuracy to achieve 0.7 m after  
300 sec (free inertial)?  
0.7 m / (0.5 x (300 sec)²) = 1.5 µg (!!) absolute accuracy over 300 sec  
(from equ. (a))  
The simple calculations reveal a discrepancy in the reported performance data; either  
the position error must be significantly worse, or the attitude error must be much  
smaller to achieve the advertised specifications. For context, an absolute accuracy of  
1.5 µg in accelerometer bias approaches gravimeter accuracy, yet such reliability is  
typically not available in industrial or military land navigation systems. It's important to  
note that gravity itself changes by approximately 0.3 µg for every meter of elevation!  
Position error of an unaided, pure inertial INS on road vehicles  
(taking only into account motion specific constraints):  
Long-time accuracy of an pure inertial INS without ZUPT aiding:  
Definition: The INS is operated on a land vehicle driving on a road or off-road. The  
vehicle has no capability to fly or to swim – this we call “motion constraints”. The  
vehicle has sufficient grip on the surface. No external aiding is available, i.e. no  
GNSS, no wheel sensor (odometer), no magnetometer, no LiDAR, no RF position-  
ing etc. Over long duration and distance no ZUPT or PUPT shall be required.  
Unaided Road and Outdoor Navigation:  
Condition: No GNSS, no odometer, no RF aiding, no magnetometer aiding - but  
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using advanced iMR proprietary algorithms which take generalized motion specific  
constraints of the vehicle into account.  
Even without odometer and without GNSS or any other external aiding sources, in  
road based applications a very high position accuracy can be achieved. The opera-  
tional sensor mode we call “pure inertial”. We are using iMAR proprietary algorithms  
regarding specific motion constraints based on our more than 30 years knowledge  
and experience on the motion behavior of road vehicles (cars and trucks). With this  
experience, which covers both, light weight vehicles as well as heavy trucks, we can  
keep the unaided position accuracy within a few meters during performing a  
100 km trip within a duration of e.g. 1 hour (typically 0.03 % CEP50 of distance  
travelled in horizontal accuracy and 0.02 % DT PE50 in vertical accuracy), and  
this without any ZUPT or PUPT and any odometer aiding2. These proprietary al-  
gorithms are applicable in both, in real-time as well as in post-processing.  
This allows fully autonomous navigation or at least to survive extremely long GNSS  
outages (“GNSS denied environment”) in real-time with a very high accuracy, if we  
compare the “pure inertial” result to “free inertial” results. Link. Our specific algorithms  
using such knowledge are the result of advanced algorithm design with decades of  
experience in all areas of inertial navigation and localization.  
It can be seen from the above plots, that the odometer aiding (VMS) will not improve  
the position performance for the above mentioned conditions significantly. This may  
safe cost of installation at the integrator. The motion of the vehicle should, as usual,  
contain sufficient motion dynamics and changes in heading to achieve this perfor-  
mance.  
2
Have in mind, that datasheet of conventional high performance INS for military applications, provided by compet-  
itors, annunce values of about 0.11 % horizontal and 0.1 % vertical, but with (!) odometer (VMS – vehicle motion  
sensor, wheel sensor) aiding, while the iMAR solution provides the above given accuracy also without any VMS  
(and without GNSS).  
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A benefit of the VMS is an advanced motion / standstill detection, which is fully sup-  
ported by the iMAR agorithms too. Due to the used motion constraints we list this  
method under “pure inertial, with constraints”.  
position deviation – 100 km DT, without odometer, without GNSS (dashed  
lines)  
position deviation – 100 km, with odometer aiding, without GNSS (dashed  
If a vendor claims a much better position accuracy in real-world (!) environment, it is  
advised that the user performes extensive tests to validate such promised data in his  
application. Lab conditions are often far away from real world conditions – and e.g.  
defining a “closed loop” test track and only comparing the test results at the end of the  
mission does not reflect the truth. iMAR has specially designed a verification method  
to qualify the performance of INS systems in GNSS denied environment. It has been  
published in 2024-10-23 at the international IEEE conference DGON ISA 2024 (link).  
Long-time accuracy of an pure inertial INS with ZUPT aiding:  
Definition: A free inertial operating INS with periodical ZUPT aiding means, that the  
INS is in free inertial operation mode (no external aiding, i.e. no GNSS, no magne-  
tometer, no air data, no Doppler log, no LiDAR, no RF positioning, …..) and the INS  
can be operated at zero velocity condition (ZUPT) periodically, i.e. all 10 minutes. This  
operational mode can be applied to land based vehicles (driving on the road) but not  
to aircrafts or ships.  
To improve the long-time performance of position determination without aiding (no  
GNSS, no odometer!), the system can be set to zero-velocity all x minutes (ZUPT,  
zero velocity update). During this stand-still period, which may take 10 seconds all 10  
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minutes (example), the internal Kalman filter is able to estimate the internal residuals  
of the gyros and accelerometers and can improve the position performance dramati-  
cally (e.g. position error over 70 km distance with iNAT-RQT has been shown to be  
approx. 5 meters as an example).  
Position error of an unaided, pure inertial INS for Pedestrian Navigation in GNSS  
denied environment:  
Definition: The INS is operated on the foot of a pedestrian. The pedestrian is allowed  
to move arbitrarily – walking, running, crawling, climbing ladders etc. No aiding (no  
RF / WiFi, no magnetometer, no GNSS) is required.  
With specific hardware, algorithms and constraints about a walking person it is possi-  
ble to determine the position of a walking person in real-time without any external  
aiding information within an accuracy of better than 1 % distance walked, nearly what-  
ever the motion is (walking, running, jumping, crawling, ….).  
The Plot shows the walk of a firefighter within a builduing: Distance 338 m, final posi-  
tion error 0.5 m  
The specific constraint allow that the position error will increase in good approximation  
only with the walked distance. And the INS which is used weighs only a few grams.  
Ask iMAR Sales engineers for details about iTHESEUS, the best of class autonomous  
pedestrian localization system (Link).  
Position error of an aided INS under arbitrary motion: When the INS is aided, it's im-  
portant to distinguish between position aiding (e.g., via GNSS) and velocity aiding  
(e.g., through an odometer, wheel sensor, VMS, EM-log or GNSS Doppler velocity).  
Position aiding:  
The INS provides high accuracy during short time periods while it shows significant  
position drift over long-time measurements. GNSS e.g. provides position information  
with high noise and low data rate, but the position error does not increase over meas-  
uring time. We talk about complementary performance features of INS and GNSS.  
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Therefore, using the Kalman filter for sensor data fusion, the short-term accurate INS  
can be coupled with a long time accurate (complementary) position / velocity localiza-  
tion system (e.g. GNSS). iMAR’s Kalman filter has typically not to be adapted to spe-  
cific applications, but iMAR’s architecture allows this, if required (e.g. to add additional  
states for additional sensors, constraints, parametrization of covariances, stability  
analysis etc.). In such applications of INS/GNSS coupling, while the inertial sensors  
provide an excellent short term position and velocity accuracy with unmatched high  
neighborhood accuracy, the total accuracy of the global position can never be better  
than the global position error of the position aiding system (e.g. GNSS). E.g. if GNSS  
shows a constant position error over a longer duration, also the INS/GNSS solution  
will follow those position error. Of course, short term deviations of the GNSS accuracy  
(e.g. short term spoofing) or slippage of the odometer are detected and isolated by  
iMAR’s sensor data fusion algorithms. Using dissimilar sources of aiding (GNSS,  
ZUPT, odometer) the total position error are further minimized.  
Typical performance of an INS/GNSS coupled system with RTK (real time kinematic)  
GNSS perforace is about 1…2 centimeters. Strong differences in the performance of  
different systems of known manufacturers can be seen in the case of signal degrada-  
tion of GNSS like multi-path and during GNSS outages in urban canyons or similar  
environment. The datasheet of the providers sometimes provide so-called perfor-  
mance tables, which give some standard deviations of position and velocity errors ,  
but they are usually not comparable because the test methods are often quite differ-  
ent. E.g. if a test drive contains 20 % urban canyon and 80 % highway, the obtained  
position standard deviation may look nice despite there might be strong position out-  
liers over a short (but significant) duration (Link). iMAR uses highest performance  
INS/GNSS/ODO reference systems as well as its proprietary mult-pass post-pro-  
cessing to validate the performance of real-time solutions against a most accurate  
ground truth. The following figure shows such analysis.  
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Velocity aiding / Dead Reckoning:  
If velocity is provided for aiding (e.g. from a wheel sensor / odometer or from Doppler  
velocity log) instead of position, the position error of the Kalman filter based sensor  
data fusion will grow mainly with the scale factor error of the velocity aiding sensor. If  
GNSS aiding is present for a certain time before it will be interrupted (e.g. before the  
vehicle enters a longer tunnel), the GNSS data will be used together with the IMS and  
the odometer data to estimate the scale factor of the odometer precisely and auto-  
matically, together with some other installation parameters like mounting misalign-  
ment errors. This also allows to determine the position of the vehicle during very long  
outages of the GNSS signal with high precision. As an example, using an iNAT-  
M300/SLN (MEMS based IMS) with wheel sensor, GNSS aiding and integrated sen-  
sor data fusion, the position error after 10 km GNSS outage had been demonstrated  
to be typically about 8 m (i.e. < 0.1 %).  
Alignment:  
Every inertial measurement system requires an initial position and orientation for op-  
timal operation. The initial position can be obtained through user input (such as way-  
point or landmark input from a map), GNSS, or other sources. The initial orientation  
can be determined using various methods, with implementations varying significantly  
depending on the performance of the core inertial sensors. Typically, the alignment  
process consists of three stages of signal processing: leveling (either dynamic or  
static), coarse alignment, and fine alignment. We distinguish between static alignment  
(when the system is at a standstill) and dynamic alignment (during motion):  
•
Statc Alignment: The INS is at standstill  
o
Determination of roll and pitch: Roll and pitch can be obtained by us-  
ing the integrated accelerometers inside the field of gravity, if their  
performance is good enough. If a vendor claims a day-to-day accu-  
racy of the integrated acceerometers of 1 mg and at the same time a  
roll and pitch accuracy after static alignment of 0.02° (0.5 mrad),  
check the validity (thumb rule: static roll/pitch accuracy [°] cannot be  
better than accel_bias [mg] x 180/PI.  
o
Determination of yaw (true heading) is possible via four different  
methods:  
▪
Gyro Compassing: If the day-to-day bias3 of the gyros (also  
called gyro drift) is good enough. Thumb rule: If the gyro bias  
is 0.015 deg (day-to-day), the very best achievable value of  
true heading (no motion, static alignment) is 1 mrad, sec Lat  
i.e. 0.057° sec Lat (i.e. atan2(0.015 °/h / 15.05 °/h).  
▪
▪
by Stored Heading, i.e. if the haeding had been stored at  
last power down and if the vehicle has not moved between  
power-on and last power down. A myriad of procedures are  
used, not all of them are satisfying in real-world applications.  
by using dual-antenna GNSS: Here GNSS is used to deter-  
mine the heading from a local RTK solution between two  
GNSS antennas. See chapter True Heading for details.  
•
Dynamic Alignment: The INS is in motion  
▪
under dynamic conditions the determination of roll and pitch  
is more complex and requires additional information like  
GNSS or VMS / odometer / Doppler Log etc. or periodical  
ZUPTs.  
▪
The classical dynamic alignment requires sufficient motion  
excitation and availability of some position or velocity aiding.  
Using the integrated sensor data fusion attitude, heading and  
all other initial data are determined. This procedure also  
3 Do not confuse „bias drift“ (day-to-day) with „bias instability“ (sometimes also named „bias stability“). Typically the  
bias instability is about 10…100 times smaller than the bias drift, but it is not relevant for gyro compassing, be-  
cause during gyro compassing the earth rate hase to be measured independent on the motion of the vehicle.  
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works wel lfor systems, which are not capable to perform a  
gyro compassing or which do not contain a dual-antenna  
GNSS receiver, i.e. all systems with a gyro bias of about >  
0.1 deg/hr. Dynamic alignment is also suitable to improve the  
performance of higher performance inertial systems.  
Once the static or dynamic alignment has been finished, the inertial system enters the  
navigational mode.  
True Heading:  
The “true heading” performance of an INS is always an important parameter.  
There are several methods to obtain “true heading” – but do not mix them with “Course  
over Ground”!  
a) If the INS contains high performance gyroscopes like ring laser or fiber optical  
gyros or hemispherical resonator gyros (drift < 0.1 deg/hr), it can perform an  
autonomous gyro compassing, i.e. it measures the earth rotation rate, deter-  
mines the levelling by measuring the gravity vector and calculates from these data  
the true north (heading) beside of roll, pitch and other values. See chapter Align-  
ment for some thumb rules.  
b) If the INS does not contain such high performance gyroscopes, it can obtain the  
true heading only from a combination of a position aiding (e.g. GNSS) and the  
inertial sensors, assuming sufficient motion dynamics will be present.  
c) Using only GNSS (without inertial sensors), a so-called “track over ground” can  
be determined, which is obtained from the GNSS velocity in East and North di-  
rection, i.e. atan2(veast/vnorth). Of course, this information shows only the direction  
of the motion of the GNSS antenna over ground, but it says nothing about the true  
heading of the vehicle (i.e. the direction of the vehicle’s “nose”)! Hence with a  
single GNSS antenna and without additional inertial sensors and without sufficient  
motion dynamics it is not (!) possible to determine the true heading.  
d) Using a dual antenna GNSS system (like iNAT-M300/SLN-DA) as stand-alone  
solution, true heading can be determined as long as both antennas can observe  
the same (!) GNSS satellites. As a thumb rule have in mind, that a dual-antenna  
system is limited by physics to an accuracy of about 0.17° heading accuracy per  
1 meter antenna baseline, which corresponds to 3 mm position accuracy at 1 m  
baseline (i.e. atan2(0.003 m / 1 m). So, if a vendor specifies a pure dual-antenna  
absolute accuracy (not standard deviation!) of 0.006° at 1 meter baseline4, check  
the validity. GNSS outages can be bridged by the gyros – i.e. the better the gyro  
performance, the longer the duration of acceptable GNSS outages. Link  
Conclusion:  
If the IMS contains inertial sensors with drift > 0.1 deg/hr and only a single antenna  
GNSS receiver (standard setup) [see case b)], it is feasible to determine true heading,  
but this requires two constraints (subject of physical laws):  
a) The vehicle has to be under motion, and  
b) The vehicle has to perform sufficient changes in heading to provide enough ob-  
servability to the Kalman filter based data fusion to be able to estimate true head-  
ing with sufficient accuracy  
An IMS without gyro compassing capability and without dual-antenna GNSS aiding is  
not able to determine true heading of its carrying vehicle, if the vehicle is moving only  
on a straight line without changes of direction (this feature is called as “lack of observ-  
ability”). As soon as a change of heading occurs, the observability is given and the  
system can provide the desired information. It is very important to take this into  
4
found on the web site, on the datasheet and inside the reference Manual of an Australian vendor of „advanced  
navigation“ systems for defence and industrial applications [01/2024]  
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account when selecting the right IMS/GNSS solution for the foreseen application  
(therefore it had been explained in this document extensively). Link  
Caution:  
Some vendors promise impossible performance: One of them e.g. claims to achieve  
a true heading (pure inertial, i.e. without GNSS or other aidings) of 0.1 deg sec lat,  
but in the same datasheet he also confirms a gyro bias day-to-day drift of 0.05 deg/hr  
(remember: the “bias instability” parameter is not relevant for free inertial gyro com-  
passing!). A quick calculation regarding earth rate shows, that the best you can  
achieve by physics with 0.05 deg/hr is a true heading of  
Δψ = atan (0.05 deg/hr / 15.04 deg/hr) = 0.19 deg sec lat (and not 0.1 deg)  
We typically do not publish datasheet from other vendors, but we decided todo so in  
this case, because we have many questions from customers regarding this issue:  
From Datasheet downloaded in 2024-10-25 from the vendor’s web site (BOREAS  
D70):  
Time Stamping / Synchronization / Latency / Jitter:  
Especially when an inertial  
measurement system (IMS) is used for control tasks or surveying applications, precise  
time stamping of inertial data, odometer data, and all other aiding information (such  
as GNSS and machine vision) is essential. For this reason, iMAR’s measurement  
systems, equipped with the proprietary iNAT architecture, offer high-performance time  
stamping capabilities.  
For example, if a target is moving at 100 m/s, a timing error of just 1 millisecond would  
result in a position error of 10 cm. Given that RTK aiding can achieve about 1 cm  
accuracy, it's clear why a synchronization accuracy of at least 25 µs is essential, along  
with high internal clock performance. Additionally, inertial navigation systems (INS)  
designed for advanced applications can provide NTP data for time synchronization.  
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In some cases, integrating a semiconductor-based atomic clock may be beneficial for  
prolonged operation in GNSS-denied environments.  
When utilizing an inertial navigation system (INS) for control tasks, such as autono-  
mous vehicle guidance or platform stabilization, minimal latency and jitter in both the  
acquired data and output are essential. The architecture of iMAR’s systems—such as  
iNAT, iPRENA, iCOMBANA, iSULONA, iTraceRT-MVT, and iATTHEMO—ensures  
best-in-market performance in this regard. (Link)  
EMI / EMC Protection:  
Inertial measurement systems for military or aviation use come with high  
EMI/EMC protection levels.  
The systems manufactured by iMAR are specifically designed for markets with de-  
manding EMI/EMC requirements, including surveying, vehicle testing, aerial laser  
scanning, pipeline inspection, vehicle and camera stabilization, drilling, and aircraft  
guidance and control. Given the wide range of applications and the need for high  
reliability, iMAR systems are protected  
and qualified according to stringent stand-  
ards such as MIL-STD 461, MIL-STD 704,  
and DO-160, in addition to environmental  
qualifications per MIL-STD 810 or DO-  
160. These measures help prevent unexpected electromagnetic interference and re-  
lated performance degradation. Due to our high qualification standards, approximately  
50% of all iMAR systems originally designed for the industrial market are also utilized  
in advanced military applications. Here is a link to our EMI/EMC lab, Spezial-EMV  
GmbH, located in St. Ingbert, Germany. This facility offers EMI/EMC qualification and  
certification services for customers worldwide. Spezial-EMV GmbH is a wholly-owned  
subsidiary of iMAR Navigation and is situated on the iMAR Campus in St. Ingbert,  
Germany.  
Ensure that the protection level of the system you intend to use meets these require-  
ments as well. In particular, inertial measurement systems offered by competitors for  
commercial or surveying applications often lack adequate EMI/EMC protection. This  
deficiency can result in operational problems in real-world environments.  
MTBF:  
The reliability of an Inertial Navigation System (INS) is crucial for critical applications.  
Typically, high-performance inertial sensor assemblies exhibit a calculated mean time  
between failure (MTBF) of approximately 100,000 hours. Field experience data may  
indicate even higher values; however, caution should be exercised when comparing  
these figures. The MTBF derived from field data often does not account for the full  
range of environmental factors considered in model-based calculations.  
So be cautious if you read a value of e.g. “500’000 hrs MTBF” of a full INS.  
•
In which environment was the MTBF calculated? Refer to the categories in  
MIL-STD 810H or DO-160G for details and a better understanding.  
Is this data solely based on field conditions, which may not fully account for  
the complete range of environmental impacts, such as vibration and temper-  
ature?  
•
•
Keep in mind that the calculated MTBF for high-performance electronics,  
even with advanced EMI/EMC and over-voltage protection and integrated  
GNSS engine, along with MIL connectors (excluding inertial sensors), is typ-  
ically by far less than 200’000 hours.  
Open Interfaces: Open interfaces are essential for users to achieve maximum flexibility when uti-  
lizing the system. These interfaces include user interfaces as well as connections to  
external sensors, such as optional GNSS engines, odometers, depth/altitude sensors,  
visual odometry, and DVL, among others. Additionally, the system architecture should  
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support custom-specific interfaces as needed. For more details, please refer to  
iMAR’s proprietary but published iXCOM protocol. Link  
GUI / Wizard: Users who are new to operating an inertial measurement system may require assis-  
tance to implement it effectively. Typically, a graphical user interface (GUI) is provided  
to facilitate the configuration of the IMS on the vehicle.  
In addition to configuration support, the GUI should allow for real-time visualization of  
acquired data as well as playback mode. An installation wizard is also beneficial for  
helping operators survey the lever arms between the GNSS antenna, odometer, cam-  
era, and the inertial measurement unit. Finally, the GUI should include maintenance  
features to enable quick system analysis in the field.  
As an example you can see the recommended features of such GUI here: iXCOM-  
CMD  
Surveying Applications, Post-Processing: For surveying applications, results may be  
needed both in real-time and during post-processing. For real-time use, the aforemen-  
tioned solutions are available, including INS/GNSS-RTK options, with optional support  
from LiDAR and other aids. Link  
For post-processing, various solutions are available on the market, each differing sig-  
nificantly in their methods and algorithms. Post-processing enables forward and back-  
ward calculations to correct for most modeled sensor errors. Keep in mind that, due  
to the nature of post-processing, the position and velocity errors at the start and end  
of the measurement period will appear to be zero. Link  
Gravimetry:  
Airborne gravimetry or gradiometry involves measuring gravity disturbances from a  
moving aircraft. This requires highly specialized algorithms and ultra-precise inertial  
sensors, with results obtained through post-processing. The physical challenge lies in  
achieving a gravity measurement accuracy of 1 µg (1 mGal) aboard an aircraft or ship  
experiencing motion dynamics of up to 1 g. iMAR has  
been offering the world's leading system for airborne  
gravimetry for several years. Link  
Customized Solutions: Many applications demand customized  
solutions involving inertial sensor systems. With over  
30 years of expertise, iMAR is equipped to deliver tai-  
lored solutions, from prototypes to production batches  
of several thousand units. Feel free to contact our Tech-  
nical Sales team for a detailed analysis of your require-  
ments — our skilled engineers and scientists will par-  
ticipate in the meeting to provide the best technical and  
commercial solution for your application.  
Many other factors also significantly influence the performance of an inertial measurement system. If you  
have any additional questions, please feel free to contact us for further information.  
Easy-to-Use Interfaces: iMAR's inertial measurement solutions feature user-friendly communica-  
tion and data interfaces, refined over more than 30 years of experience across a wide  
range of applications, including commercial, industrial, automotive, and military sec-  
tors. Supported interfaces include Ethernet/TCP/IP/UDP, EtherCAT, UART  
RS422/RS232, CAN, NMEA183, ARINC429, HDLC, SDLC, NTP, and more, as well  
as custom hardware and software interfaces.  
To further support integrators and users, iMAR also provides ROS 2 nodes, Python  
scripts, an SDK for C++, and a Wireshark dissector.  
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Customer Support:  
Specifying and purchasing an inertial measurement system is one thing  
— integrating it and configuring it optimally for use is a technically demanding task for  
many users. That’s why our team at iMAR Navigation provides comprehensive sup-  
port, from system selection to integration, available in both German and English, and  
if needed, anywhere in the world.  
With over 30 years of extensive experience across nearly all ap-  
plications of inertial measurement technology, our support team  
is always ready to assist you!  
Ein Inertialmesssystem zu spezifizieren und zu kaufen  
ist die eine Sache - es zu integrieren und für den Einsatz  
optimal zu konfigurieren ist für viele Anwender eine tech-  
nisch anspruchsvolle Aufgabe. Daher bieten wir, iMAR  
Navigation, Ihnen eine Rundum-Unterstützung von der Auswahl bis zur Inte-  
gration Ihres Messsystems an, in deutscher und englischer Sprache und  
gerne an jedem Ort der Erde.  
Mit über 30 Jahren umfassender Erfahrung in nahezu allen Anwendungen der  
inertialen Messtechnik steht Ihnen unser Support-Team jederzeit gerne zur  
Verfügung!  
Feel free to reach out to our support and sales engineers with any further questions!  
sales@imar-navigation.de  
Additional information can be found on our download site at www.imar-navigation.de  
iMAR Navigation GmbH  
Solutions for Inertial Navigation & Control  
Im Reihersbruch 3  
66386 St. Ingbert / Germany  
Leading  
Inertial Measurement Solutions Made in Germany  
Phone:  
Fax:  
+49-6894-9657-0  
(switchboard)  
+49-6894-9657-636 (sales team)  
+49-6894-9657-15 (support team)  
+49-6894-9657-22  
sales@imar-navigation.de  
https://www.imar-navigation.de  
https://www.youtube.com/@iMAR-Navigation/playlists  
iMAR  
10/2024 rev. 2.51 DocNo.: DOC181020012 technical modifications reserved w/o notice  
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