Math help: calibrating adxl375

[Vindhyachal.Takniki]

I have to 12 point calibration of adxl375. I have attached a datasheet of the method. Page 7 shows the equation 1 which i have to solve.

It has 12 known.

We keep sensor in six different poisition, each generate 3 set of equations to fit in the matrix. Equations arre below. I have filled value of Ax,Ay,Az:

How to solve that in labview??

/* +z axis */
a11*30 + a12*50 + a13*2548 + o1 = 0
a21*30 + a22*50 + a23*2548 + o2 = 0
a31*30 + a32*50 + a33*2548 + o3 = 1

/* -z axis */
a11*20 + a12*10 + a13*980+ o1 = 0
a21*20 + a22*10 + a23*980 + o2 = 0
a31*20 + a32*10 + a33*980 + o3 = -1

/* +y axis */
a11*30 + a12*1911 + a13*50 + o1 = 0
a21*30 + a22*1911 + a23*50 + o2 = 1
a31*30 + a32*1911 + a33*50 + o3 = 0

/* -y axis */
a11*20 + a12*49 + a13*10+ o1 = 0
a21*20 + a22*49 + a23*10 + o2 = -1
a31*20 + a32*49 + a33*10 + o3 = 0

/* +x axis */
a11*2303 + a12*30 + a13*50 + o1 = 1
a21*2303 + a22*30 + a23*50 + o2 = 0
a31*2303 + a32*30 + a33*50 + o3 = 0

/* -x axis */
a11*392 + a12*20 + a13*10+ o1 = -1
a21*392 + a22*20 + a23*10 + o2 = 0
a31*392 + a32*20 + a33*10 + o3 = 0

[GerdW]

Hi Vindhy,

to solve this:

you might use the basic "Solve Linear Equations" function:

Adding the ACC_x0 vector should be easy as last step…

[Vindhyachal.Takniki]

1. I have made a equation as in attached excel file. Equation has 18 varaibles.

2. Then I took 6 readings from adxl375 which in turn form 18 equations. 

Equations are in matrix form in block diagram of labview program attached. 

3. I am getting error: 20001;  The matrix is rank deficient

4. I don't know why this error. i have 18 equations & 18 variables.

5. With error, I still get values in "Solution matrix" in front panel. These values when i put back in equation , I got result as in "AxB" in front panel.

These values are almost matching result. So not a problem at this stage.

I want to know is there any more aggressive method to get exact results.

[Vindhyachal.Takniki]

Edit: Excel file contain the matrix formed

[Vindhyachal.Takniki]

I have been able to do 12 & 15 point calibration both.

I have also attached example for anyone reference.

Solution matrix contain the unknown found.

AxB matrix contain values found in solution matrix to equations.

results are good.

Query:

Find data AxB is very accurate according to my need.

But still values are off a bit.

Is there any more aggressive method to find exact solution?