how do I calibrate an accelerometer?

I am trying to calibrate a sensor. could somebody please help me find the values of theta xy, yx, yz, zx. or explain how to derive it. I have converted the raw values to g. you will see in the plot that the sqrt of x^2 + y^2 +z^2 is deviating quite a bit at some points.

clc
clear all
close all

% min max value
Mx_min = 27681;
Mx_max = 38526;
My_min = 27361;
My_max = 38388;
Mz_min = 27428;
Mz_max = 38539;

% scale value
Sx = 1/((Mx_max - Mx_min)/2);
Sy = 1/((My_max - My_min)/2);
Sz = 1/((Mz_max - Mz_min)/2);

% offset value
Bx = ((Mx_min * Sx) + (Mx_max * Sx)) /2
By = ((My_min * Sy) + (My_max * Sy)) /2
Bz = ((Mz_min * Sz) + (Mz_max * Sz)) /2

% theta
xy = 0;
yx = 0;
yz = 0;
zx = 0;
xz = (Mz_max - Mz_min) / (Mx_max - Mx_min);
zy = (Mz_max - Mz_min) / (My_max - My_min);

[V]=[-Sx, 0 , 0; 0, Sy, 0; 0, 0, -Sz;];
[B]=[Bx;-By;Bz;];

A = [27681,32967,32466;28803,29427,32348;32152,27448,32091;36084,28375,31847;38375,31952,31716;37481,36112,31824;34044,38281,32093;30030,37343,32380;27790,33916,32485;31414,30822,28580;30261,30797,28707;32275,29657,28526;34751,30315,28352;35988,32417,28280;35510,34827,28373;33417,36208,28565;31008,35662,28729;29654,33615,28772;33041,33380,27479;33171,33336,27450;32839,33538,27479;32427,33469,27512;32103,33124,27532;32189,32623,27515;32606,32347,27477;33073,32474,27440;33256,32886,27428;35032,35777,29465;36054,35727,29232;33385,37146,29464;30389,36294,29679;28796,33732,29729;29296,30551,29713;31775,28755,29481;34983,29252,29241;37012,32059,29171;36392,36286,33219;37360,36478,33094;33715,38385,33367;29929,37275,33607;27804,33893,33684;28453,29919,33550;31632,27487,33217;35787,28044,32948;38466,31662,32885;34996,35487,37249;36188,34945,37140;33946,36334,37263;31298,35673,37381;29830,33456,37373;30245,30704,37223;32341,29091,37017;35116,29449,36870;36925,31813,36858;33453,32468,38511;33388,32320,38508;33618,32341,38492;33759,32530,38492;33611,32763,38517;33481,32801,38528;33356,32725,38533;33306,32609,38529;33214,32506,38527;31528,30272,36910;30466,30074,37006;32845,28810,36800;35646,29586,36661;37181,32143,36666;36524,35016,36832;33996,36569,37052;31150,35837,37206;29603,33356,37206;30650,29510,33291;28830,29357,33457;32223,27361,33172;36213,28316,32914;38526,31943,32879;37608,36153,33034;34161,38334,33230;30084,37397,33521;27806,33924,33656;27682,32965,32471;28803,29437,32315;32156,27455,32052;36094,28393,31809;38381,31998,31710;37464,36140,31845;34028,38293,32145;30013,37335,32420;27787,33896,32489;31398,30881,28546;30309,30803,28674;32306,29669,28510;34743,30320,28348;36005,32390,28294;35521,34817,28376;33410,36198,28560;30995,35647,28729;29642,33580,28781;33047,33348,27474;33179,33293,27448;32852,33502,27476;32439,33437,27506;32115,33099,27534;32200,32601,27515;32605,32306,27483;33079,32427,27446;33269,32842,27430;35105,35649,29371;36080,35711,29243;33388,37150,29473;30381,36294,29692;28779,33705,29747;29354,30565,29641;31807,28792,29427;34965,29291,29199;36952,32052,29113;36165,36416,33224;37351,36489,33081;33696,38387,33387;29918,37262,33621;27790,33820,33685;28518,29810,33531;31655,27484,33273;35807,28054,33011;38470,31666,32913;35348,35057,37134;36271,35033,37038;33970,36384,37218;31348,35736,37367;29889,33550,37406;30290,30826,37313;32365,29226,37146;35098,29574,36988;36887,31894,36919;33480,32607,38519;33392,32407,38517;33626,32442,38505;33772,32630,38499;33618,32871,38519;33487,32910,38528;33360,32836,38536;33312,32722,38539;33203,32624,38537;31652,30322,36960;30462,30160,37065;32892,28893,36892;35737,29743,36746;37152,32266,36719;36503,35102,36807;33982,36645,36989;31165,35913,37160;29632,33438,37226;30546,29501,33354;28835,29358,33480;32234,27364,33268;36219,28320,33033;38526,31952,32909;37607,36154,33005;34122,38339,33285;30050,37368,33557;27803,33903,33663;27682,32953,32460;28814,29418,32317;32162,27450,32065;36094,28388,31824;38374,31972,31708;37470,36126,31827;34036,38283,32099;30023,37338,32374;27793,33913,32476;31312,30856,28588;30282,30782,28701;32289,29654,28525;34753,30311,28356;36028,32400,28309;35530,34851,28398;33421,36226,28585;30985,35676,28755;29615,33592,28810;33050,33369,27479;33177,33294,27448;32853,33501,27477;32440,33440,27509;32109,33097,27534;32187,32591,27518;32605,32311,27482;33077,32431,27446;33258,32846,27432;35177,35623,29398;36068,35667,29203;33394,37109,29425;30399,36268,29645;28800,33710,29724;29294,30524,29738;31789,28713,29529;35004,29219,29291;37025,32038,29194;36007,36517,33238;37365,36472,33076;33720,38388,33338;29941,37284,33584;27803,33889,33692;28509,29834,33578;31661,27480,33286;35819,28059,33018;38469,31673,32921;35488,34989,37114;36241,35098,37025;33973,36412,37199;31349,35761,37354;29835,33581,37363;30244,30819,37280;32350,29196,37116;35118,29546,36956;36936,31903,36873;33462,32625,38523;33401,32467,38521;33632,32486,38506;33773,32673,38501;33624,32904,38519;33495,32948,38528;33366,32874,38538;33318,32759,38535;33228,32656,38537;]
A = transpose(A);

for i=1:225
NEW(:,i) = (V * [ A(1,i); A(2,i); A(3,i);]) + B;
end

NEW = transpose(NEW);
for i=1:225
NEW(i,4) = sqrt( NEW(i,1)^2 + NEW(i,2)^2 + NEW(i,3)^2);
ROT(i,1) = atan2(NEW(i,2),NEW(i,1));
ROT(i,2) = radtodeg(-ROT(i,1));
INC(i,1) = atan(sqrt(NEW(i,1)^2 + NEW(i,2)^2 )/NEW(i,3));
INC(i,2) = radtodeg(INC(i,1));

if INC(i,2) < 0 
    INC(i,2) = INC(i,2) + 180;
else
    INC(i,2) = INC(i,2);
end

if ROT(i,2) < 0
    ROT(i,2) = ROT(i,2) + 360;
else
    ROT(i,2) = ROT(i,2);
end

end

plot(NEW,'DisplayName','NEW','YDataSource','NEW');figure(gcf);
hold on
legend('X','Y','Z','sqrt(X^2 + Y^2 + Z^2)');

[Star Strider]

I suspect a lot of us here are not familiar with accelerometers, and especially with what ‘theta xy, yx, yz, zx’ are. If you can describe what they are, we might be able to suggest ways for you to approach your problem.

[Rolfe Dlugy-Hegwer]

What is the application? For example:

• Working with normal gravity to determine which way is up.
• Measuring acceleration under more extreme conditions.

Do you know, based on the datasheet, if the accelerometer response is sufficiently linear for your requirements? Or, does your calibration procedure need to correct for non-linearity?

[Rolfe Dlugy-Hegwer]

Q: Rolfe: Have you seen "MEMS Accelerometer Calibration using Gauss Newton Method" on File Exchange?

A: Rafael: I have tried the program and using my measured data. I keep getting problems with the matrix saying its close to singularity. and the result does not converge.

Answer 1

[Jean Lambert Kubwimana]

Did you find any answer to this question? Your code is confusing and hard to follow. For example, after you transpose NEW, your the rest of the code is not being used in the calculation of x,y, and z! If you have found the answer please update us!