How can I auto determine the IR channel component in the RGB channel with RGB-IR sensor?

Question

In the RGB-IR raw data, bayer array is R, IR, G, B. In the day, IR channel will influence RGB channel, also RGB channel will influence IR channel too. So that the result image's color will incorrect.

My algorithm is:

1. read raw data
2. IR interpolation
3. IR subtraction
4. white balance
5. demosaic.

But in step (3) IR subtraction, I use the following formula：

R_real equal (R - a * IR_R), 
G_real equal (G - b * IR_G), 
B_real equal (B - c * IR_B). 

I try to manually adjustment to get correct para a, b and c with above picture. But in different environment, R, G, B, IR channel component will change.

Can someone help tell me how to get para a, b and c automatically? when environment change, the para a, b and c can adjustment automatically by algorithm. Or help provide some related literatures?

Thanks for your help.