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Investigating the accuracy and precision of a kinematics from a clinical grade inertial measurement unit. Aaron Hellem, D.P.T – Mayo Clinic 12042017
Transcript of motusONE - Mayo Clinic - Investigating the accuracy and ... · inertial measurement unit. Aaron...
Investigatingtheaccuracyandprecisionofakinematicsfromaclinicalgradeinertialmeasurementunit.
AaronHellem,D.P.T–MayoClinic
12042017
StatisticalMethods:Rawpositionaldatacollectedfromtheopticalmotioncapturesystem(MACdata)wereupsampledfrom120Hzto1600Hz,andweretransformedintodirectional-cosine-matrices(DCM’s)forninemovementtrialsusinganaxisconventionseeninFigure1.DCMdatawerethentransformedintokinematicsusingeuler-transformationsinabody-fixedrotationorderof“XYZ”.DatawereshiftedsuchthatthepeakofthekinematicmeasureoccurredatthesamesampleforboththeMACandIMUdataofinterest.Followingthis,descriptivestatisticswerecomputedforeachtrial:PearsonCorrelation(R),Root-Mean-SquareError(RMSE),andMeanDifference(Bias).
Figure1-LocalCoordinateSystemConventionForeveryframe,aDCMwascomputedfromtherawTRCdata,byfirstcomputingthreeunitvectorsinEquation’s(1)-(3).
𝑥!"# = !"#!!!,!,!!!"#$!,!,!!"#!!!,!,!!!"#$!,!,!
(1)
𝑦!"# = !"#!,!,!!!!"!!,!,!!!"!,!,!!!!"!!,!,!
(2)
𝑧!"# = 𝑐𝑟𝑜𝑠𝑠(𝑥!"# ,𝑦!"#) (3)
𝑥!"# = 𝑐𝑟𝑜𝑠𝑠(𝑦!"# , 𝑧!"#) (4)
Next,theunitvectorsandconstructedintoa3x3direction-cosinematrixasseeninEquation(4).
𝐷𝐶𝑀 = 𝑥! 𝑥! 𝑥!𝑦! 𝑦! 𝑦!𝑧! 𝑧! 𝑧!
= 𝑅! ∅! 𝑅! ∅! 𝑅! ∅! (5)
TheDCMcanbere-writtenintothematrixmultiplicationof3eulerangles,inabody-fixed“X-Y-Z”rotationorderasseeninEquation(6).
𝐷𝐶𝑀 = 1 0 00 cos (∅!) −sin (∅!)0 sin (∅!) cos ∅!
cos ∅! 0 sin ∅!0 1 0
− sin ∅! 0 cos ∅!
cos ∅! −sin (∅!) 0sin (∅!) cos (∅!) 0
0 0 1 (6)
Thedesiredkinematicscanbecomputedbysolvingfor∅! ,∅! ,𝑎𝑛𝑑 ∅! ,where:
∅! = 𝐵𝑙𝑜𝑐𝑘 𝑃𝑖𝑡𝑐ℎ (𝐹𝑙𝑒𝑥𝑖𝑜𝑛) (7)∅! = 𝐵𝑙𝑜𝑐𝑘 𝑌𝑎𝑤 (𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛) (8)∅! = 𝐵𝑙𝑜𝑐𝑘 𝑅𝑜𝑙𝑙 (𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝐹𝑙𝑒𝑥𝑖𝑜𝑛) (9)
Results:Table1–SummarizedDescriptiveStatisticsTrial R RMSE(deg) Bias(deg)X1 0.999 0.979 0.473X2 0.999 1.888 1.798X3 0.999 2.202 2.123X4 0.998 1.840 1.592X5 0.998 2.285 1.831X6 0.998 2.057 1.726XAVG 0.999 1.875 1.590Y1 0.999 4.782 4.698Y3 0.999 2.994 2.917Y4 0.999 1.045 0.243Y5 0.999 1.392 1.200YAVG 0.999 2.553 2.265Z1 0.999 2.321 -2.165Z4 0.999 1.805 -1.511Z5 0.991 2.631 -2.070Z6 0.999 1.808 -1.594ZAVG 0.997 2.141 -1.835
