Determination of Static Orientation Using IMU Data Revision 1

Transcription

1 Determinatin f Static Orientatin Usin IMU Data Revisin 1

2 Determinatin f Static Orientatin frm IMU Accelermeter and Manetmeter Data Intrductin An imprtant applicatin f inertial data is the rientatin determinatin f the device durin static cnditins. This can be accmplished thruh the emetric analsis f the f the accelermeter and manetmeter data. Determinatin f static rientatin usin accelermeter data The rientatin f the device relative t the ravit vectr can be determined accrdin t the fllwin methd frm accelermeter data. The device is assumed t be under static r quasi static (ver lw frequenc) cnditins. The planar prjectins f the ravit vectr make sme set f anles with respect t the primar device aes (Fi. 1.0). As an eample, the anle between the cmpnent f ravit,, and the psitive ais is = Arctan (, ) = tan [eq 1.0] Where the functin Arctan (, ) is the quadrant sensitive (tw-input) frm f the inverse tanent. And likewise, = tan = tan Infrmatin prvided in this dcument is believed t be accurate, hwever it is nt uaranteed. MEMSense reserves the riht t chane prduct specificatins at antime withut ntice

3 + + + Fiure 1.0: Lcal ravit vectr read with respect t the device crdinate sstem Determinatin f static rientatin usin manetmeter data The determinatin f rientatin usin the ravit vectr lends itself immediatel t rientatin relative t earth, since anles calculated accrdin t the abve methd can be used directl t describe the rientatin relative t the hrintal plane r the inclinatin t this plane. The earth manetic field vectr will mst likel nt be pintin radiall twards the earth s center r an ther cnvenient directin. A crdinate transfrmatin ma be utilied t rerient the earth reference manetic field. This is dne nl t cnvenientl interpret the manetmeter data when cmpared t accelermeter data. Reslvin the rientatin f the device via manetic data requires accurate values fr the earth field cmpnents. These are determined either frm actual measurements with a reference manetmeter r b usin a current manetic mdel f the earth field. While mdels can be quite accurate, it is preferred that the earth field is measured directl in the rein where the device is intended t be used. Infrmatin prvided in this dcument is believed t be accurate, hwever it is nt uaranteed. MEMSense reserves the riht t chane prduct specificatins at antime withut ntice

4 Fr eample, the lcal earth field cmpnents (Fi. 2.0) have the fllwin values at sme lcatin: The particular cmpensatin anles are then: and ( ) m = auss m = auss = 8.82 m = auss = = The quantities 90 are knwn as the declinatin and inclinatin f the field respectivel. The anles and ma be subtracted frm manetmeter utput t prduce a manetic field vectr in the same directin as ravit fr desin purpses as in Fi. 3. These values will var with lcatin and time (Fi. 5 and Fi. 6), but frtunatel the earth s manetic field drifts quite slwl, n the rder f ±10-100nT per ear fr each cmpnent. Peridic calibratin can be dne t crrect these chanes. due Nrth H + F due East + cmpensated manetic field M M actual earth field radiall dwn + Fiure 2: Earth Manetic filed crdinate sstem Fiure 3: Simplificatin f manetmeter crdinate sstem thruh cmpensatin Infrmatin prvided in this dcument is believed t be accurate, hwever it is nt uaranteed. MEMSense reserves the riht t chane prduct specificatins at antime withut ntice

5 The rientatin f the device t the lcal earth manetic vectr can be determined in a similar fashin as with the accelermeter data. The planar prjectins f the manetic vectr make anther set f anles with respect t the primar device aes. M = tan m m m m M = tan M = tan m m Where the functin 1 tan is the quadrant sensitive frm f the inverse tanent and m, m and m, are the IMU manetmeter utputs. m m + + M m M + F Fiure 4: Earth manetic field read b device Infrmatin prvided in this dcument is believed t be accurate, hwever it is nt uaranteed. MEMSense reserves the riht t chane prduct specificatins at antime withut ntice

6 Fiure 5.0: Earth Field Declinatin Fiure 6.0: Earth Field Inclinatin Summar This MEMSense technical nte has attempted t eplain cmmn methds used t determine the rientatin f an inertial measurement unit utilied in static and quasi-static cnditins. These methds are the mst basic means fr rientatin determinatin. Much mre sphisticated methds ma be empled thruh hiher level alrithms, such as the Kalman r cmplimentar filters. These filters hwever require a sinificant develpment effrt and time t implement. In man cntrlled applicatins use f the methds described here will suffice. Infrmatin prvided in this dcument is believed t be accurate, hwever it is nt uaranteed. MEMSense reserves the riht t chane prduct specificatins at antime withut ntice