Field Calibration of Inertial Measurement Units

for Miniature Unmanned Aircraft

J. Grauer,∗ J. Conroy,† J. Hubbard,‡ J. Humbert,§ and D. Pines¶

Department of Aerospace Engineering, University of Maryland, College Park, MD, 20742

Modern avionics equipment typically includes measurements from magnetometers, ac-celerometers, and gyroscopes, which can be combined in attitude filters and state observersto provide information on the vehicle configuration, velocity, and acceleration. While vitalfor state estimation and feedback control, sensors used on miniature aircraft, constrainedby payload capacity, are based on microelectromechanical systems and are of lower qualitythan full scale counterparts. This work presents a low cost, batch procedure for calibratinginertial sensors on miniature aircraft immediately before takeoff, so that accurate measure-ments are available for real-time applications. The routine requires a single maneuver toexcite the sensors, and can be implemented in full form on a ground station computer, oras a lower fidelity version in onboard microprocessor software. An experiment is presentedto validate the accuracy of the calibration procedure.

Nomenclature

a acceleration vectorcov covariancee orthonormal frame vectorg gravitational constanth magnetic field vectorI identity matrixJ rotational Jacobian matrixJ cost functionNp number of data pointsNo number of outputsn measurement noise vectorR rotation matrixr position vectorS skew operatorTIC Theil inequality coefficientt timeV measurement noise covariancev translational velocity vectorX regressor matrixy predicted model outputz measurement vector

ε, δ quaternion vector and scalar partsη orientation vectorθ model parameter vectorΛ, λ, b scale factor and bias calibrationsν model residual vectorσ standard deviationφ, θ, ψ Euler anglesω rotational velocity vector

Subscriptsd digitized integer measurementx, y, z orthonormal frame projections

SuperscriptsB body frameI inertial frameS sensor frameT matrix transpose˙ time derivativeˆ estimated value

∗Graduate Student, Department of Aerospace Engineering, Member AIAA.†Graduate Student, Department of Aerospace Engineering, Member AIAA.‡Langley Distinguished Professor, Department of Aerospace Engineering, Associate Fellow AIAA.§Assistant Professor, Department of Aerospace Engineering, Member AIAA.¶Assistant Professor, Department of Aerospace Engineering, Member AIAA.

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I. Introduction

Avionics packages have at their core an inertial measurement unit (IMU), which typically contains orthog-onal triads of magnetometers, accelerometers, and gyroscopes. These sensors provide vital information

about the dynamic state of the aircraft and can be processed directly using non-parametric attitude filtersor in tandem with other sensors using model-based state observers. These sensors are often of high qualityon full scale aircraft, having low noise levels and slow drift rates, facilitating for example the integration ofgyroscope signals for estimating the aircraft orientation. Miniature aircraft however have relatively smallpayload capacities which necessitate the use of sensors based on microelectromechanical systems (MEMS).To a larger extent than the full scale counterparts, MEMS sensors have significant noise levels, temperaturedependencies, and stochastic calibration parameters.

The importance of high-quality inertial measurements in numerous applications has led to significantefforts in the literature to determine accurate calibration parameters, for both MEMS and conventionalsensors. For example Crassidis1 and Thienel2 both adopted real-time adaptive methods for estimating bias,scale factor, and alignment errors for spacecraft magnetometers and gyroscopes, respectively, to correctfor miscalibrations obtained from ground-based experiments. For MEMS gyroscopes and accelerometers,ground-based experiments are best performed on a rate table in a thermally-isolated environment whereangular velocity and temperature may be accurately prescribed for temperature-compensated calibrations.There are however instances when simpler calibration methods are desired, such as when there is a lack oftime to perform the lengthy calibrations, or when the necessary equipment is not available.

This paper outlines an extensible procedure for determining constant bias and scale factor calibrationsfor magnetometers, accelerometers, and gyroscopes from simple excitations without the use of additionalequipment. This method is well suited for field calibration, which can be performed before or during flighttesting to capture any effects of sensor aging, avionics warming, and ambient heating. Additionally thisapproach provides a simple method for checking a priori calibrations or more complicated algorithms. Avariety of algorithms may be used in the procedure, allowing for example least-squares solutions to beimplemented in onboard software to maximize computation speed, or alternatively iterative solutions to becomputed in batch computation to maximize accuracy. This paper is hereafter organized beginning withan overview of the aircraft configuration and an introduction to inertial measurements. The calibrationprocedure is then presented. The method is applied to data obtained with an avionics unit and validatedagainst measurements supplied by a visual positioning system.

II. Inertial Measurements

A generic aircraft, idealized as a single rigid body, is shown in Figure 1. An inertial reference frameKI = {exI , eyI , ezI} is fixed at an arbitrary point CI on the surface of the Earth with orthonormal unitvectors pointing north, east, and down. A second coordinate frame KB = {exB , eyB , ezB} is fixed to theaircraft center of mass CB with the axes pointing out the nose, starboard wing, and underside. With respectto the inertial frame, the body frame has a Cartesian position r and orientation η. The orientation isinitially parameterized in terms of Euler angles φ, θ, ψ for physical intuition and so that simple attitudeapproximations may be presented. To avoid non-physical singularities, a quaternion

η =

[ε

δ

]=

[χ sin(γ/2)cos(γ/2)

](1)

is later used, where γ is the rotation angle about the Euler axis χ.3 The orientation-dependent matrix RBI isused to rotate quantities from the inertial frame to the body frame. The vehicle also has translational velocityv and rotational velocity ω. The sensor package is installed at a point CS with axes KS = {exS , eyS , ezS}rotated by the constant matrix RBS relative to the body axes. The calibration method presented in thiswork assumes perfect knowledge of the sensor orientation, which simplifies the analysis and is an acceptableassumption given a careful installation. If needed, the current analysis may be extended to include alignmentcorrections.

Magnetometers measure the projections of the local magnetic field vector upon its axes hS = [hSx , h

Sy , h

Sz ]T

and can be used to provide orientation information. While the magnetic field of the Earth changes with bothtime and space,4 it can be assumed stationary during flights of miniature unmanned air vehicles, which aretypically for short distances and periods of time. In addition to measurement noise, signals are corrupted

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Figure 1. Aircraft and sensor configuration.

by hard iron and soft iron errors.5 Hard iron errors are created by the presence of additional magneticfields near the magnetometer and effect the bias calibration. Soft iron errors are augmentations to the scalefactors as a result of induced magnetic fields from nearby objects. For these reasons magnetometers shouldbe calibrated in the vicinity of the flight test while inside the vehicle, and should be installed as far away aspossible from onboard DC motors. For small bank and pitch angles, the approximation

ψ̂ = − arctan(hB

y /hBx

)(2)

can be used to approximate the heading angle.Accelerometers measure the projections of the local accelerations aS = [aS

x , aSy , a

Sz ]T on the sensor axes.

These measurements are typically corrected to the aircraft center of mass to remove additional accelerationdue to rotation using6

aB = RBSaS + (1/g)[(ωB)T (ωB)I− (ωB)(ωB)T − S(ω̇B)

]rSB (3)

where S(.) is the matrix form of the cross product operator. Angular acceleration is not typically measured,but good estimates can be obtained using smoothed local differentiation of the angular rate measurements.7

Proceeding this correction, measured accelerations are composed of effects due to gravity and translation.Accelerometers have high bandwidths and usually require filtering to remove high frequency noise. In appli-cations where vehicle experiences small translational accelerations compared to gravity, the approximations

φ̂ = + arcsin(aBy )

θ̂ = − arcsin(aBx )

(4)

can be used to estimate the bank and pitch angles of the aircraft.Gyroscopes measure the rotational velocity projections on the sensing axes ωS = [ωS

x , ωSy , ω

Sz ]T . The

MEMS realizations of gyroscopes are typically very noisy and have bias calibrations which exhibit randomwalk. While orientation estimates can be obtained by numerically integrating these signals, error drift ratesare relatively high and prohibit these estimates from being used directly in applications such as attitudeestimation.

III. Calibration Procedure

For a constant temperature, MEMS inertial sensors typically have linear calibration curves. Assumingadditive noise, the postulated sensor model for a vector observation z in the body frame is

zB = ΛzBd + b + n. (5)

The term Λ = diag(λx, λy, λz) is a diagonal matrix of scale factors for the measurement projections. Theterm zB

d is the digital word representing the measurement produced by an analog to digital converter, orrecorded from a sensor over an RS-232, SPI, or I2C bus. For example, a 16-bit analog to digital converterwould output an integer between 0 and 65535. The term b is a vector representing the bias calibration forthe measurement, and the term n represents random measurement noise.

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A block diagram of the calibration procedure is shown in Figure 2. The magnetometer and accelerometermay be calibrated independent of the gyroscope. These calibrated sensors may then be used to estimate theorientation of the host vehicle. Orientation is related to the rotational velocity through the kinematic differ-ential equations for a rigid body, which can be used to solve for the gyroscope calibration coefficients. Theapproach is modular in that a variety of algorithms exist for parameter estimation and attitude estimation,and may be chosen per the design requirements of the application to for instance improve computation timeor parameter accuracy. Relatively short segments of data are needed for this calibration method; the datashown later in this work used three roll/pitch/yaw doublets.

   

InertialMeasurement

Unit

MagnetometerCalibration Attitude

EstimationAccelerometer

Calibration

GyroscopeCalibration

Figure 2. Calibration procedure block diagram.

Magnetometer calibration often leverages the fact that calibrated signals produce a sphere at the originwith a radius equal to the strength of the local magnetic field. Calibrated accelerometer signals also producecentered spheres in the absence of translational accelerations, and so the same techniques can be used tocalibrate both sensors. Sources of error translate the center, stretch the principle axes, and rotate the shapein three dimensions, producing an ellipsoid. Sensor calibrations are extracted by fitting an ellipsoid to thedata and relating the quadric coefficients to the gain and bias parameters of Equation 5. Estimating thecalibration constants is formally a nonlinear estimation problem which typically requires an iterative solver.Gebre-Egzaiber has contributed several solutions to this problem, two of which involve a linear least-squaressolution followed by a Kalman filter,5 and a total least-squares solution.8 Both methods have already beenshown to produce good results. A similar algorithm has been adopted in this paper, based on the work ofLi,9 which solves the quadric equation

θ1z2x + θ2z

2y + θ3z

2z + 2θ4zyzz + 2θ5zxzz + 2θ6zxzy + 2θ7zx + 2θ8zy + 2θ9zz + θ10 = 0 (6)

for the ellipsoid parameters θ by performing a constrained Eigenvalue analysis. The first three coefficientsdetermine the lengths of the principle axes, the second three coefficients determine the rotation of theellipsoid, the third three coefficients determine the offset of the ellipsoid, and the last coefficient scales theparameters. As noted by Gebre-Egzaibher,5 the rotations of the ellipsoid are small in aircraft applicationsand the terms multiplying θ4, θ5, and θ6 can be set to zero. Once the ellipsoid parameters are estimated,the gains and biases of Equation 5 for the magnetometer and accelerometer can be written

λx = f/[(1/θ1)(θ27/θ1 + θ28/θ2 + θ29/θ3 − θ10/θ1)]1/2

λy = f/[(1/θ2)(θ27/θ1 + θ28/θ2 + θ29/θ3 − θ10/θ2)]1/2

λz = f/[(1/θ3)(θ27/θ1 + θ28/θ2 + θ29/θ3 − θ10/θ3)]1/2

(7)

bx = f(θ7/θ1)/[(1/θ1)(θ27/θ1 + θ28/θ2 + θ29/θ3 − θ10/θ1)]1/2

by = f(θ8/θ2)/[(1/θ2)(θ27/θ1 + θ28/θ2 + θ29/θ3 − θ10/θ2)]1/2

bz = f(θ9/θ3)/[(1/θ3)(θ27/θ1 + θ28/θ2 + θ29/θ3 − θ10/θ3)]1/2

(8)

respectively, where f is the vector field strength. This method produces an accurate, non-iterative solutionat expense of computing an Eigensystem for what reduces to a 3x3 matrix. One major disadvantage of thismethod over other methods is that the statistics of the gain and bias parameters, often used to judge thequality of the estimate, are not readily available.

The next step in the process is to use the calibrated magnetometer and accelerometer signals to producean estimate of the vehicle orientation. Originally posed as Wahba’s problem,10 estimating vehicle attitude

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based on vector observations has since had many solutions,11 any of which may be implemented in this step.In this work, the QUaternion ESTimator (QUEST) algorithm12 was chosen, which solves for the rotationmatrix which minimizes the cost function

J(RBI) =12

Ns∑i=1

wi‖zB −RBIf I‖2 (9)

for an arbitrary number Ns ≥ 2 of sensors, where zB is the measured observation, f I is the known vectorexpressed in the inertial frame, and wi is a weighting coefficient. The references for the magnetic andgravitational fields are typically north and down, respectively, although these may be chosen arbitrarily underthe constraint that they are non-collinear. A unit quaternion may then be extracted from the estimatedrotation matrix.13

The last step in the process is to calibrate the gyroscopes. Given orientation estimates, uncalibratedgyroscope measurements, and the rotational kinematic differential equations, the problem of determiningthe gyroscope calibration constants reduces to performing a kinematic consistency analysis.14 Substitutingthe measurement model of Equation 5, the rotational kinematic equations are written

η̇ = JIB(ΛωωBd + bω + nω) (10)

where JIB is an orientation-dependent Jacobian matrix, and where the QUEST estimates of the orientationare substituted in a certainty-equivalence fashion. The quaternion form of the Jacobian matrix in Equation 10is written

JIB =12

[δI + S(ε)−εT

]. (11)

The equations may also be cast using Euler angles, but this choice places constraints on the pitch angleexcursions and requires the evaluation of trigonometric functions, which is an expensive task for micropro-cessors.

Parameter estimation techniques may then be employed to estimate the gyroscope calibration constants.In this paper a two-step approach using the equation-error and output-error methods is adopted.7,15 Theequation-error method uses Equation 10 directly, where quaternion rates are obtained using a local smoothingdifferentiation method on the orientation estimates. Since there are four kinematic equations, four sets ofparameters can be estimated. It was found that using only the equation for the scalar portion of thequaternion resulted in a good fit of all the axes. The least-squares solutions of the gyroscope parametersand statistics are

θω =(XT X

)−1XT δ̇ (12)

cov(θω) = σ2ω(XT X)−1 (13)

whereθω = [ λωx λωy λωz bωx bωy bωz ]T (14)

X = [ −ε1ωdx −ε2ωdy −ε3ωdz −ε1 −ε2 −ε3 ]T (15)

and where σω is the gyroscope measurement noise. This method however assumes perfect knowledge of thegyroscope measurements and the quaternion derivatives, which may be justified if quantization effects aresmall, signal to noise ratios are high, and the attitude estimates are accurate. The output-error method,implemented with the MATLAB R©16 toolbox SIDPAC,14,17 is used to iteratively refine the estimates byintegrating Equation 10 and matching the orientation data.

IV. Results

An experiment was performed to test the calibration routine. A custom avionics package,18 constructedfor use with miniature aircraft and shown in Figure 3, was used to obtain inertial measurements. The IMUintegrated in this unit is the MAG3 by MEMSense,19 which houses orthogonal triads of MEMS magnetome-ters, accelerometers, and gyroscopes. Outputs are analog signals, band-limited by the manufacturer to 50 Hz.Additional outputs of the gyroscope signal references are provided, allowing for differential measurements tobe taken to mitigate random walk in the voltage reference. Temperature measurements are available, but

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are not used. Output signals are quantized by a set of 16-bit analog to digital converters at a rate of 185Hz and are stored to a removable memory card. The IMU orientation is aligned with the avionics board, sothat the sensor axes are considered coincident with the body axes. A visual positioning system (VPS)20 wasemployed to obtain high fidelity data with which to compare results. The avionics package was fitted withnumerous retro-reflective markers. Six cameras situated in the laboratory recorded the planar appearanceof these markers on their individual image planes, from which spatial measurements of the marker locationswere collectively estimated. Knowledge of the avionics board geometry and the placement of the markersallowed for the estimation of the position and orientation of the avionics, which were computed at 350 Hz.The avionics data were interpolated to 350 Hz to match the visual data. The data sets were synchronizedin time by cross-correlating the orientation estimates from QUEST and the visual data to find the relativetime lag. A fixed-weight smoothing algorithm21 was used to remove noise from the data without introduc-ing phase shifts. A typical laboratory setup is shown in Figure 4, where a helicopter test vehicle, trackingcameras, and the dedicated processing computer are visible. Hardware specifications are given in Table 1,where the specified units are used consistently throughout this work.

(a) obverse (b) reverse

Figure 3. Avionics package.

Figure 4. Typical laboratory setup, showing test vehicle, tracking cameras, and processing equipment.

The sensing elements were excited by performing a sequence of roll/pitch/yaw rotational doublets threetimes, during which the avionics package recorded inertial measurements and the visual tracking systemrecorded position and orientation. The unprocessed sensor data is shown in Figure 5. Calibrations for themagnetometer and accelerometer tabulated in Tables 2 and 3, and illustrated in Figure 6. Only a smallportion of the ellipsoids are measured during a roll/pitch/yaw doublet, however these ranges were found tobe sufficient for this study. The noise in the acceleration sphere is caused by the presence of translationalaccelerations in the maneuver.

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Table 1. Hardware specifications.

Measurement Symbol Sensor Range Resolution Variance UnitTime t Oscillator - 25.600 · 10−6 - s

Magnetic Field hS Magnetometer ±3.1667 48.319 · 10−6 34.043 · 10−6 normRotational Velocity ωS Gyroscope ±5.2360 0.1598 · 10−3 0.0183 · 10−0 rad/sLinear Acceleration aS Accelerometer ±98.100 3.8769 · 10−3 2.4594 · 10−3 m/s2

Orientation η VPS - - 0.8781 · 10−9 rad

0 10 20 30 402.5

3.5

4.5

time (s)

mag

neto

met

er(c

ount

s·1

04)

0 10 20 30 402.8

3.3

3.8

time (s)

acce

lero

met

er(c

ount

s·1

04)

0 10 20 30 402

3.5

5

time (s)

gyro

scop

e(c

ount

s·1

04)

1

0 10 20 30 40−1.5

0

1.5

time (s)

orie

ntat

ion

(rad

)

Figure 5. Unprocessed data measured from the avionics package and visual positioning system.

−1

0

1

−1

0

1

−1

0

1

hBx

hBy

hB z

(a) magnetic sphere

−10

0

10

−10

0

10−10

0

10

aBx

aBy

aB z

(b) gravitational sphere

Figure 6. Magnetometer and accelerometer calibrations.

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Table 2. Magnetometer calibration parameters.

Parameter Estimateθ θ̂

λhx+0.1603 · 10−3

λhy +0.1433 · 10−3

λhz+0.1633 · 10−3

bhx−6.1665 · 10+0

bhy −5.1183 · 10+0

bhz+5.4719 · 10+0

Table 3. Accelerometer calibration parameters.

Parameter Estimateθ θ̂

λax+4.9070 · 10−3

λay +3.3580 · 10−3

λaz+3.5924 · 10−3

bax−0.1533 · 10+3

bay −0.1145 · 10+3

baz+0.1207 · 10+3

Estimates of the orientation measured by the visual tracking system and predicted by the QUEST algo-rithm are shown in Figure 7. For clarity the QUEST results plotted have been decimated to approximately9 Hz. The Theil inequality coefficient

TIC =

√(1/NoNp)(z− y)T (z− y)√

(1/NoNp)yT y +√

(1/NoNp)zT z∈ [0, 1] (16)

provides a normalized fit metric, where Np is the number of data points, No is the number of outputs, zare the measurements, and y are the model outputs. A value of zero indicates a perfect fit and a valueof unity indicates the worst fit. The QUEST estimates of the orientation had a TIC value of 0.0352 withthe measured orientation with the VPS, indicating a very close fit. The QUEST estimates over-predict thepositive peak amplitudes for ε3 at approximately 10 seconds and 20 seconds into the data. The visual dataalso appears to provide poor measurements of the ε1 and ε2 variables at approximately 35 seconds into thedata, which appears to be errors in the VPS estimates, due to the most planar distribution of markers onthe avionics hardware.

0 10 20 30 40−0.6

0

0.6

time (s)

ε 1

0 10 20 30 40−0.6

0

0.6

time (s)

ε 2

0 10 20 30 40−0.6

0

0.6

time (s)

ε 3

1

0 10 20 30 400.8

1

1.2

time (s)

δ

VPS QUEST

Figure 7. Orientation estimates.

The gyroscope calibration results are shown in Table 4. The equation-error fits are shown in Figure 8 andhad a TIC value of 0.1617 indicating a good agreement. All the quaternion rates match consistently, andsome of the larger amplitudes were slightly underestimated by the method. The output-error fits are shownin Figure 9 and had a TIC value of 0.1459, again indicating a good fit to the data. All of the orientation

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parameters were noticeably under-predicted by the output-error method. Interestingly the output-error fitwas slightly better to the quaternion measurements than the equation-error fit to the quaternion rates, asmeasured by the TIC metric. The estimated calibration parameters given in Table 4 are in good agreementbetween the two sets of estimates. With the exception of the rolling velocity channel, standard errors weresignificantly smaller for the output-error method.

0 10 20 30 40−1.5

0

1.5

time (s)

ε̇ 1

0 10 20 30 40−1.5

0

1.5

time (s)

ε̇ 2

0 10 20 30 40−1.5

0

1.5

time (s)

ε̇ 3

1

0 10 20 30 40−0.5

0

0.5

time (s)

δ̇

data model

Figure 8. Equation-error model fit to the QUEST quaternion rate estimates.

0 10 20 30 40−1

0

1

time (s)

ε 1

0 10 20 30 40−1

0

1

time (s)

ε 2

0 10 20 30 40−1

0

1

time (s)

ε 3

1

0 10 20 30 400

0.6

1.2

time (s)

δ

data model

Figure 9. Output-error model fit to the QUEST quaternion estimates.

The calibration constants resulting from the equation-error and output-error analyses were applied tothe quantized gyroscope signals and are plotted along with body-fixed rotational velocities, derived from

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Table 4. Gyroscope calibration estimates and standard errors.

Parameter Equation-Error Output-Errorθ θ̂ ± σ(θ̂) θ̂ ± σ(θ̂)λωx

+0.2221 · 10−3 ± 5.7803 · 10−6 +0.2219 · 10−3 ± 23.331 · 10−6

λωy +0.2899 · 10−3 ± 13.218 · 10−6 +0.2888 · 10−3 ± 0.1786 · 10−6

λωz+0.3794 · 10−3 ± 15.939 · 10−6 +0.3766 · 10−3 ± 0.2510 · 10−6

bωx+7.0283 · 10−0 ± 0.1845 · 10−0 +7.0283 · 10−0 ± 0.7389 · 10−0

bωy −9.6219 · 10−0 ± 0.4431 · 10−0 −9.6219 · 10−0 ± 0.0068 · 10−0

bωz−11.728 · 10−0 ± 0.5015 · 10−0 −11.728 · 10−0 ± 0.0065 · 10−0

the VPS data, in Figure 10. Similar to the model fits used in the parameter estimation, the calibratedgyroscopes fit well but slightly under-predict the amplitudes. The equation-error and output-error resultshave TIC values of 0.2111 and 0.2042, indicating better fits when the output-error can be used after anequation-error analysis.

0 10 20 30 40−4

0

4

ωB x

(rad

/s)

0 10 20 30 40−4

0

4

ωB y

(rad

/s)

0 10 20 30 40−4

0

4

time (s)

ωB z

(rad

/s)

1

VPS equation-error output-error

Figure 10. Visual and calibrated avionics estimates of the body-fixed rotational velocity.

V. Conclusions

This paper presented a calibration procedure which can be used to calibrate inertial measurement unitswithout the use of additional equipment. This method may be used for calibrating sensors on the ground orduring flight testing, and can be used to obtain quick calibration estimates or to check a priori calibrations.The method is modular and allows for the implementation of different algorithms to tailor the software tothe application requirements.

Calibration of magnetometers and accelerometers adopted an ellipsoid fitting algorithm presented in thecomputer vision literature. The calibrated magnetometers and accelerometers were then combined with theQUEST algorithm to produce orientation estimates. Finally a two-step approach using the equation-error

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and output-error methods was used with the rigid body kinematic equation to calibrate the gyroscope.Generally the sensors were calibrated well, indicating that this method performs well. The method is

serial in nature, so good estimates must be determined at each step or the error will compound, which isseen by the increasing TIC value of the estimates as the steps are performed. A set of three roll/pitch/yawdoublets of modest amplitude were seen to be sufficient for estimating the curvature of the magnetometerand accelerometer ellipsoids. Larger amplitudes would facilitate better results, and are possible due to theoptional quaternion parameterization of the orientation. Large amplitudes may be a problem in flight testinghowever, as large pitch excursions create translational accelerations, which bias the accelerometer calibrationparameters. However, this procedure is expected to work well in a variety of applications.

VI. Acknowledgements

The authors would like to thank the the University of Maryland, the National Institute of Aerospace,and the NASA Langley Research Center for their support in this research. Experiments were conducted atthe University of Maryland in the Autonomous Vehicle Laboratory. Conversations with Eugene Morelli atthe NASA Langley Research Center are acknowledged and appreciated. Additionally the authors would liketo thank the members of the Morpheus Laboratory and Autonomous Vehicle Laboratory for their continuedsupport and guidance.

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