Limits of Absolute Heading AccuracyUsing Inexpensive MEMS Sensors

Gregory Tomasch and Kris Winer

Tlera Corporation tleracorp@gmail.com

March 11, 2019

Abstract

We measure the absolute heading accuracy achievable using two popular MEMS motion sensor suites and avariety of readily-available calibration and sensor fusion solutions. We find that absolute heading error of 2degrees rms is routinely obtainable and that, in many cases, 1-degree rms error can be achieved. Examinationof the residual error shows it to be systematic and quasi-sinusoidal. We expect heading accuracy can beimproved further by addressing one or more sources of residual error including: correction of accelerometersensor non-orthogonality and misalignment between accelerometer and magnetometer sensor axes.

1. Introduction

Micro-electro-mechanical systems (MEMS)[1]technology has been used in sensors for atti-tude and orientation estimation ever since thefirst MEMS accelerometer was created[2] in1993. Today, MEMS orientation systems areavailable in a wide variety of sizes and costs,from large, sophisticated, and expensive in-tegrated units[3] used in planetary rovers byESA[4] to small, inexpensive sensors[5] usedin cell phones and quadcopters. The formersystems[6] offer absolute heading accuracy aslow as 1 degree root-mean-square (rms or 1sigma error), or even less with GPS augmen-tation, and are essential to well-publicizeddevelopments in autonomous vehicles androbotics[7]. Almost unknown is that similarperformance can be obtained using "cellphone"sensors like Invensense’s MPU9250[8] or STMicroelectronic’s LSM6DSM[9]+LIS2MDL[10]and inexpensive microcontrollers.

Most work on the subject of absoluteorientation estimation accuracy focuses oncharacterization[11] of individual sensorsor makes use of expensive computationalmethods[12] or sensor systems[4]. We havefound little[13] discussion of absolute head-ing accuracy using inexpensive MEMS sensors.

Most characterization methods rely on sophis-ticated optical methods to track actual orienta-tion (of vehicles) for comparison with the abso-lute orientation derived from inertial sensor fu-sion. Madgwick[13] used just such a method inhis original work on computationally-efficientsensor fusion algorithms in 2010. Characteriza-tions of large, expensive sensor systems typi-cally used in modern robotics are simply notrelevant to absolute orientation estimation viacell phone sensors and microcontrollers. Thereare commercial solutions[14] that use these lessexpensive technologies and quote 2 degree rmsheading accuracy. But how is this determined?Under what conditions? Perhaps proprietaryconsiderations keep this subject hidden fromview. In this paper, we probe the limits of ab-solute orientation accuracy using inexpensiveMEMS sensors and microcontrollers by demon-strating simple, straightforward methods thatanyone can use.

Improvements in MEMS sensor accuracy andthe advent of open-source, computationally-efficient sensor fusion algorithms[15] ala Madg-wick have made accurate absolute orientationestimation available at very low cost. Whilepitch and roll[16] can be estimated with anaccuracy of < 1 degree rms using just a three-

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axis accelerometer, a three-axis gyroscope, andstraightforward sensor fusion methods[17], ac-curate absolute heading estimation requires a 9degree-of-freedom (9 DoF) solution (accelerom-eter, gyroscope, and magnetometer) as well asmore sophisticated calibration and sensor fu-sion algorithms. We have found[18] that usingsimple offset bias calibration, open-source sen-sor fusion algorithms, and 9 DoF MEMS mo-tion sensors, typical absolute heading errorsof ~4 degree rms are routinely achievable ina relatively crude 90-degree-turning test. Thisaccuracy is fine for video[19] demonstrationsbut for real-world applications–like ergonomet-rics, head tracking, dead reckoning, and au-tonomous flight control–absolute heading ac-curacy needs to be ~1 degree rms or less.

Here we estimate the limits to absoluteheading accuracy achievable using inexpen-sive MEMs motion sensors with the followingimprovements in method:

Fusion algorithms- we use both open-source and proprietary fusion algo-rithms for comparison to PNI Corp’s"SpacePointTM" adaptive fusion algorithmembedded in the EM7180 motion co-processor;

Calibration- we use more sophisticatedmethods of accelerometer and magnetome-ter calibration for the off-board fusion al-gorithms and input sensor offset/scale cor-rections into the EM7180;

Test method- we calculate the EM7180and off-board orientation solutions simul-taneously and use an accurate 2D rotationstage to estimate absolute heading errors.

Despite the increased sophistication, thesecalibration and fusion methods are readilyavailable and straightforward to implement forthose whose applications require the best avail-able absolute orientation accuracy at very lowcost.

2. General Approach

EM Microelectronic’s EM7180[20] sensor fu-sion co-processor does an impressive job oftaking data from low-cost MEMS sensors withno additional calibration and converging toa stable and accurate absolute orientation so-lution. This is done by internally comparingthe gravitational and magnetic orientation so-lutions and adjusting the sensor signals accord-ing to a set of assumptions in the adaptationalgorithm. However, the EM7180 cannot per-fectly compensate for all sensor imperfectionsin all circumstances. Occasionally, for an indi-vidual set of sensors the EM7180 struggles toconverge to a stable solution and might alsosuffer from residual heading error. We havefound that estimating the accelerometer andmagnetometer sensor bias offsets and axis scaleerror corrections and inputting these into theEM7180 at startup can overcome this limitationin most cases.

However, the observation that there are prac-tical limits to the degree of sensor non-idealityan adaptive algorithm can fix raises severalquestions:

1. What practical heading accuracy level canthe user reasonably expect?

2. What are the relative contributions of sen-sor quality, sensor calibration and fusionalgorithm to heading estimate accuracy?

3. How "Good" does sensor calibration haveto be? Do more sophisticated calibrationmethods yield significantly better results?

4. For well-calibrated, high-quality sensors,how important is the actual fusion algo-rithm?

In order to start answering these questions,we have undertaken a simultaneous perfor-mance comparison between a baseline case andvarious options. The baseline case is using theEM7180 and its internal adaptive sensor cali-bration and proprietary fusion algorithms "as-is"; with no pre-calibration of the sensors. Thevarious absolute orientation solution optionsinclude one or more of the following:

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• Inputting accelerometer/magnetometeroffset bias and scale error corrections intothe EM7180 prior to algorithm startup;

• More sophisticated accelerometer andmagnetometer sensor calibration methodsfor use with alternative fusion algorithms;

• Our own proprietary fusion algorithm;• The open-source Madgwick 9 DoF fusion

filter.

To do this, we let the EM7180 calculate its ori-entation solution as usual and simultaneouslyoutput the raw sensor data stream. We appliedaccelerometer and magnetometer calibrationcorrections on the host MCU and processed thedata into parallel orientation solutions usingour own proprietary fusion algorithm or theopen-source Madgwick fusion algorithm. Notethat both methods were being applied to thesame sensor data at the same time, eliminatingall questions of trial-to-trial sensor variability.

3. Sensor Platforms

We consider Invensense’s MPU9250 (MPU6500accelerometer/gyroscope with embeddedAK8963C magnetometer) 9 DoF motion sensorand ST Microelectronic’s LSM6DSM combina-tion accelerometer/gyroscope coupled withST Microelectronic’s LIS2MDL magnetometer.Absolute orientation accuracy depends mostlyon the quality of the underlying sensor dataand how well the sensors are calibrated; noamount of sensor fusion sophistication canmake up for jittery data with large offsetbiases. These two sensor suites have proven tobe stable, low-jitter sensors capable of excellentheading accuracy as we will show. We pair thesensors with EM Microelectronic’s EM7180[21]motion co-processor. The EM7180 is an I2Cmaster to the slave sensors and managesconfiguration of and data reading from thesensors. The EM7180 provides scaled or rawsensor data and orientation quaternions to theMCU (Cortex M4F 80 MHz STM32L4) host.The EM7180 uses PNICorp’s "SpacePointTM"proprietary adaptive fusion algorithm and inmost cases provides absolute heading accuracyof 2 degrees rms or better with these sensors.

4. Sensor Calibration

Calibrating the gyroscopes is straightforward.We make use of the built-in calibration of theEM7180 which calculates the gyro offset biaseswhen the sensors are at rest. Even withoutthe use of the EM7180, calculating gyroscopeoffset bias this way, with the sensors flat (pcbnormal to gravity direction) and motionless isadequate. One could go further (we have not)by measuring and correcting the differences inaxial response.

The goal of accelerometer calibration is to re-move both the offset biases as well as the axialscaling differences. A popular simple methodfor estimating accelerometer offset biases is toplace the sensors flat and motionless and aver-age the accelerometer readings (accounting forgravity on the z axis). A better[23] althoughmore time consuming method that we use hereis to align each accelerometer axis (+/-x, +/- y,+/- z) with gravity, average readings to provideboth offset biases and axes scaling correction.

The goal of magnetometer calibration is alsoto remove both the offset biases as well as theaxial scaling differences. In this case, we needto rotate the magnetometer throughout 3-Spacesuch that we adequately sample the entire 3Dresponse surface. This will provide a cloud ofpoints[24] generally in the form of an ellipsoidwith two foci and not a sphere centered at thezero-field origin as we desire. A marginally ad-equate method for magnetometer calibrationis to center the ellipsoid on the origin (esti-mate simple offset biases) and scale the axialresponses. But a better[25] though more com-putationally intensive method we use here isto fit an ellipsoid to the cloud of points andcreate a 3x3 calibration matrix to spherize theresponse surface and center it on the origin.

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Figure 1: Production version of one of the two MPU9250 breakout boards[22] we used for these tests. MPU9250 is inthe center, EM7180 at lower left.

Figure 2: Prototype version of one of the two LSM6DSM+LIS2MDL breakout boards we used for these tests.LSM6DSM is in the center, LIS2MDL is top left, EM7180 at lower left.

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5. Heading Measurement

We purchased a used Zeiss rotation stage from a seller on E-Bay for the heading measurements.

Figure 3: Zeiss rotation stage used for the heading measurements. Sensor breakout is mounted via machine pin headersonto a STM32L476 development board, which fits into a slot machined into the acrylic cylinder for rigid andreproducible mounting.

The stage bezel is graduated in degrees and has a micrometer for turning and a stop for securepositioning. The rotation stage is capable of 0.1-degree accuracy.

We added an acrylic cylinder mounted onto the center of the stage with adhesive to serve as asensor platform. The purpose of the acrylic cylinder is to stand off the sensors from the metalin the rotation stage. Even though we do not believe the metal is ferromagnetic, we wanted tominimize any interaction. The acrylic makes it easy to check the level of the sensor platform andserves as a thermally stable platform for sensor board mounting.

The measurement procedure was to calibrate the sensors, level the stage on the table, mount thesensor board on top of an acrylic cylinder in the center of the rotation stage, place the stage ata known heading and record an average of 300 readings. Then rotate the stage 15 degrees andrepeat the measurement. The data was automatically downloaded into an excel spreadsheet where

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differences and standard deviations were calculated.

6. Measurement Results

Typical results for the MPU9250 and LSM6DSM+LIS2MDL using PNI Corp’s proprietary fusionalgorithms embedded in the EM7180 motion co-processor are shown in Figure 4. In this case weonly rely upon EM7180’s internal self-calibration capabilities; no bias offsets or scale correctionswere sent to the EM7180.

Figure 4: Absolute heading error as a function of true heading plotted for one MPU9250 and two LSM6DSM+LISMDLbreakout boards for the solutions using PNICorp’s proprietary sensor fusion algorithms but without sensoroffset and scale corrections applied. Blue is the MPU9250, gray and orange are the LSM6DSM+LIS2MDL.Depending upon the nature and degree of sensor imperfections, the residual heading error can vary dramati-cally

Simply relying on the EM7180 to internally compensate for all sensor non-ideality clearly hasits limits; many sensor sets yield good to excellent performance (1.0 – 3.0 degrees rms) whileoccasionally others give an abysmal outcome (12.5 degrees rms in this case). These results areconsistent with our early experience using the EM7180. In order to achieve better and morepredictable results, we set about developing better accelerometer and magnetometer calibrationtechniques. We use these to enhance the performance of the SpacePoint algorithm by pre-loadingthe EM7180 with bias offsets and scale corrections for the individual sensors. Figure 5 showsheading error results for the same three sensors characterized in the previous figure plus an

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additional Invensense USFS sensor set. Using the calibration enhancements, the results are bothvery good and dramatically more consistent.

Figure 5: Absolute heading error as a function of true heading plotted for two different breakout boards each for theMPU9250 and LSM6DSM+LISMDL solutions. Sensor fusion was done using PNICorp’s proprietaryalgorithm and calibration was enhanced by pre-loading the EM7180 with accelerometer/magnetometer biasoffsets and scale corrections. Blue and orange are MPU9250, gray and yellow are the LSM6DSM+LIS2MDL.The ST sensor boards are remarkably consistent with rms heading error approaching 1 degree. All data showsigns of remaining systematic error.

Table 1 shows the rms heading accuracy for the three sensors characterized in Figure 4 withand without enhanced sensor calibration.

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SensorRMS Heading Error

EnhancedSensor Cal (deg)

EM7180 InternalCal Only (deg)

Sentral_INV_USFS_1 2.2 12.5Sentral_ST_USFS_1 1.5 2.9Sentral_ST_USFS_2 0.8 1.0

Table 1: Comparison of PNICorp’s proprietary sensor fu-sion algorithm with and without accelerometerand magnetometer bias offset and scale correc-tions. Depending upon the particular sensor,the impact of the "Enhanced" sensor calibra-tions can range from minimal to profound.

In all three cases, the EM7180’s algorithmperformed better when accelerometer and mag-netometer sensor corrections were applied, ascompared to just relying on the EM7180’s abil-ity to self-calibrate. In the case of the problem-atic Invensense sensor (Sentral_INV_USFS_1)the impact of applying the enhanced calibra-tion techniques was quite profound; the rmsheading error improved from 12.5 to 2.2 de-grees.

We noticed that despite calibration enhance-ment the heading accuracy achievable witheach sensor breakout board still appears to bespecific to the board. This was especially truefor the MPU9250 solutions. If the MPU9250magnetometer offset biases were particularlylarge, then the resulting heading accuracywould suffer no matter how well we calibrated-out the offsets. This makes sense if the biasoffsets are due to large assembly strains andthe magnetometer is far from its normal oper-ating conditions. We noticed this less for theST sensors, perhaps because the separate phys-ical packages make such assembly strain lesslikely or less severe. So perhaps there is an ad-vantage in having a 9 DoF solution requiringtwo sensor packages despite the added costsin board area and alignment effort. Also, theLIS2MDL is not a Hall sensor, rather it usesanisotropic magnetoresistance[26] so is less af-fected by temperature changes and seems tooffer more stable performance compared tomany Hall sensors.

The rms heading accuracy in the four testsabove varies between 0.8 and 2.2 degrees rmswith these two particular ST sensors perform-

ing better overall in terms of both heading ac-curacy and performance consistency. In allcases there is a quasi-sinusoidal systematic er-ror component. This clearly indicates that our"sophisticated" sensor calibration techniquesare still not addressing all sources of system-atic error. Our future work will investigatean augmented version of the "Six position" ac-celerometer calibration technique to generatethe full 3x3 correction matrix for the accelerom-eter sensors. We also acknowledge that themagnetometer and accelerometer axes can berotated with respect to each other and that anyimpact from this eventuality is currently unad-dressed.

In Figure 6 we show the results of using ourown proprietary fusion filter using the samefour sensors used earlier. These results weregenerated on the host MCU at the same timeas the data presented in Figure 4. We usedthe raw sensor data stream from the EM7180and applied the enhanced calibration correc-tions on the host MCU. The algorithm gener-ates quaternions from fusing the accelerome-ter and gyroscope sensor data, compensatesthe magnetometer data for tilt and then com-putes heading. The filter is as computationally-efficient as the Madgwick or Mahony filters, soit can be easily performed on the host MCUbut provides heading estimation accuracy sim-ilar to the EM7180. Again, for this sampling ofsensors the ST solution performs most consis-tently with low rms heading error of 0.8 – 1.2degrees. Systematic sinusoidal error is also ob-served in the results, suggesting that the causesare not directly related to the fusion algorithm.We should also state that this algorithm mayhave better long-term predictability than theEM7180’s SpacePoint algorithm. The behav-ior of our algorithm is totally dependent uponthe quality of accelerometer and magnetometercalibration. It should be static in the absenceof sensor drift. If the algorithm delivers badresults, the sensors need to be recalibrated. Incontrast, if the EM7180 algorithm gives unan-ticipated results it is not clear what drifted; thesensors or the SpacePoint algorithm.

In Figures 7 we show results generated using

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Figure 6: Results of our proprietary filter using the same two different breakout boards each for the MPU9250 andLSM6DSM+LISMDL solutions. The one MPU9250 board with large magnetometer offset bias is still anoutlier.

the popular open-source 9 DoF Madgwick fu-sion filter. In this case we used a different set ofproduction USFS sensors because the originalprototype set was no longer available. We usedthe same simultaneous calculation method toevaluate the performance of the Madgwick 9DoF algorithm and compare directly to theEM7180’s SpacePoint algorithm results, shownin Figure 8 for reference. The rms heading er-ror for the EM7180-based results ranged from0.82 to 1.2 degrees while the Madgwick-basedheading error ranged from 0.76 to 3.0 degrees.So for one instance in four the Madgwick re-sult was as good as the SpacePoint result butin the other three trials the Madgwick resultwas significantly worse.

Table 2 shows a side-by-side comparison ofthe SpacePoint and simultaneous Madgwick fil-

ter results. Clearly, the SpacePoint algorithm’sperformance is superior.

SensorRMS Heading Error

SpacePointResult (deg)

Madgwick FilterResult (deg)

INV_PROD_1 1.2 1.5INV_PROD_2 0.8 0.8ST_PROD_1 1.2 3.0ST_PROD_2 0.9 1.9

Table 2: Comparison of PNICorp’s proprietary sensorfusion algorithm with the 9 DoF Madgwickfusion filter.

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Figure 7: Results of Madgwick 9DOF filter using two different production breakout boards each for the MPU9250 andLSM6DSM+LISMDL solutions. The heading error is generally poorer than either the EM7180 SpacePointalgorithm or our own proprietary fusion filter (Figures 6 and 8)

7. Conclusions

We have only examined a small sampling ofMPU9250 and LSM6DSM+LIS2MDL breakoutboards using these methods, and heading es-timation is limited to a 2D plane, but we canstill draw some conclusions from such limitedtesting.

Firstly, proprietary fusion methods suchas those embedded in the EM7180 motionco-processor or our own fusion method per-formed on the STM32L476 host are capableof ~1-degree rms heading accuracy with theright sensors and proper calibration. In termsof the right sensors, either the MPU9250 orLSM6DSM+LIS2MDL will do although we be-lieve the latter offer more consistency andhigher accuracy.

Secondly, if a performance-screened sensorboard shows very large magnetometer offsetbiases, we recommend discarding that boardfor uses where heading accuracy is critical.However, after applying our improved calibra-tion techniques, even our worst performingMPU9250 board with very large magnetome-ter offset biases showed a heading accuracy of2.2 degrees rms. This is perfectly adequate formany applications.

Thirdly, in terms of proper calibration, wehighly recommend the more complex methods.They will repay the increased effort in calibra-tion with heading accuracy (~1-degree rms vs.~2-degree rms, for example) that can be twicewhat could be achieved with the same sensorsand sensor fusion but easier (more lax) calibra-tion. Even if the user is relying on the EM7180

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Figure 8: Absolute heading error as a function of true heading plotted for two different production breakout boardseach for the MPU9250 and LSM6DSM+LISMDL solutions. Sensor fusion was done using PNICorp’sproprietary algorithm with enhanced calibration. Blue and orange are MPU9250, gray and yellow are theLSM6DSM+LIS2MDL. This data is shown here to provide context for the results presented in Figure 7.

and its adaptive algorithm, heading accuracyis both better and much more predictable ifaccelerometer and magnetometer sensor biasoffsets and scale corrections are input into theEM7180.

The results so far show that there is stillsystematic sinusoidal error in the heading esti-mation. We hope to understand and eliminatethis systematic bias and use this measurementmethodology to reach the limit where the sta-tistical sensor noise alone determines headingerror. In this case, we would expect to routinelybe able to achieve < 1-degree rms heading ac-curacy, at least with the ST sensor suite.

Our first suspicion regarding a possible rootcause for the residual sinusoidal error is incon-sistency between gravitational and magnetic

measurements. We believe this can be thoughtof as the general problem of tilt compensationerror in a tri-axial magnetic compass. For sucha device, it has been shown[27] that a tilt esti-mation error of 0.1 degree at a magnetic dipangle of 66 degrees (the magnetic dip anglein Northern California where these measure-ments were performed is ~60 degrees) resultsin sinusoidal heading error with an amplitudeof ~0.3 degrees. This being the case, if thegravity-based pitch and roll estimates are offor effectively misaligned to the magnetometeraxes by roughly 1 degree, it is easy to imaginea residual sinusoidal heading error of a severaldegrees in amplitude.

Immediate future work will focus on fur-ther improving accelerometer calibration data

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analysis to generate the full 3x3 correc-tion matrix[28] which will handle any non-orthogonality or cross-talk effects of the ac-celerometer sensors. We also plan to investi-gate the effects of residual rotations betweenthe accelerometer and magnetometer sensoraxes.

We further note that it would be desirable torepeat these measurements with a wider selec-tion of sensor breakout boards (the ST versionis currently in pilot production) as well as usean accurate 3D rotation stage to quantitativelymeasure the effects of pitch/roll (tilt) on head-ing accuracy.

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[2] Southwest Center for Microsystems Education (SCME), "History of microelectromechan-ical systems (MEMS)," [Presentation Slides], Retrieved Feb. 15, 2019 from http://scme-nm.org/files/History%20of%20MEMS_Presentation.pdf

[3] Analog Devices, "Tactical grade, ten degrees of freedom inertial sensor," ADIS16488ADatasheet, Rev. F.

[4] Hidalgo, Javier et al. "Improving planetary rover attitude estimation via MEMS sensorcharacterization," Sensors (Basel, Switzerland) vol. 12, no. 2, 2012

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[6] Memsic Inc., "GPS-Aided MEMS Inertial System," NAV440 Datasheet, Rev. A

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[11] G. Aslan and A. Saranli, "Characterization and calibration of MEMS inertial measurementunits," 2008 16th European Signal Processing Conference, Lausanne, 2008

[12] Kyal-ak, "IMU-TK: Inertial Measurement Unit ToolKit," GitHub repository,https://github.com/Kyle-ak/imu_tk, 2016

[13] Madgwick, S. O., "An efficient orientation filter for inertial and inertial/magnetic sensorarrays," Technical Report, University of Bristol, UK, 2010

[14] XSENS Technologies, "MTi 1-series IMU, VRU and AHRS," MTi 1-series leaflet, 2018

[15] Winer, Kris, "MPU6050: Affordable 9 DoF Sensor Fusion," GitHub repository wiki, Jan.29, 2016, Retrieved from https://github.com/kriswiner/MPU6050/wiki/Affordable-9-DoF-Sensor-Fusion

[16] Wikipedia contributors. "Flight dynamics," Wikipedia, The Free Encyclopedia, Retrieved Feb.18, 2019 from https://en.wikipedia.org/wiki/Flight_dynamics

[17] x-io Technologies, "Open source IMU and AHRS algorithms," Jul. 31, 2012, Retrieved fromhttp://x-io.co.uk/open-source-imu-and-ahrs-algorithms/

[18] Winer, Kris, "Hardware Sensor Fusion Solutions," GitHub repository wiki, Jul. 28, 2015,Retrieved from https://github.com/kriswiner/MPU6050/wiki/Hardware-Sensor-Fusion-Solutions

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[19] Varesano, Fabio, "Initial implementation of a 9 DOM/DOF MARG IMU orientation fil-ter with ADXL345, ITG3200 and HMC5843 on Arduino," Varesano.net, May 10, 2011, Re-trieved from http://www.varesano.net/blog/fabio/initial-implementation-9-domdof-marg-imu-orientation-filter-adxl345-itg3200-and-hmc5843-a

[20] Swatch Group, "Combining Sensors Intelligently, LowPower Sensor Fusion," Retrieved on Feb. 18, 2019 fromhttp://www.swatchgroup.com/en/group_profile/innovation_powerhouse/the_internet_of_things_overview/combining_sensors_intelligently_low_power_sensor_fusion

[21] EM Microelectronic, EM7180SFP – Sensor Fusion, Retrieved Feb. 18, 2019 fromhttps://www.emmicroelectronic.com/product/sensor-fusion/em7180sfp

[22] Winer, Kris, "Ultimate Sensor Fusion Solution – MPU9250," Tindie product page, Retrievedon Feb. 18, 2019 from https://www.tindie.com/products/onehorse/ultimate-sensor-fusion-solution/

[23] Winer, Kris, "F. Magnetometer and Accelerometer Calibra-tion," GitHub repository wiki, Apr. 16, 2017, Retrieved fromhttps://github.com/kriswiner/EM7180_SENtral_sensor_hub/wiki/F.–Magnetometer-and-Accelerometer-Calibration

[24] Winer, Kris, "Simple and Effective Magnetometer Calibration," GitHub repository wiki,Aug 14, 2017, Retrieved from https://github.com/kriswiner/MPU6050/wiki/Simple-and-Effective-Magnetometer-Calibration

[25] Freescale Semiconductor, "Calibrating an eCompass in the Presence of Hard- and Soft-IronInterference," Application Note AN4246, Rev 4.0

[26] Cai, Yongyao, et al., "Magnetometer basics for mobile phone applications," Electronic Products,Feb. 2012

[27] True North Technologies, "Optimizing Performance," Retrieved Feb. 18, 2019 fromhttps://www.tntc.com/optimizing-performace-true-north-technologies-electronic-compasses/

[28] Stancin, Sara and Saso Tomazic. "Time- and Computation-Efficient Calibration of MEMS 3DAccelerometers and Gyroscopes," Sensors, vol. 14, no. 8, 2014

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