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