# Obtaining n values from n-1 sensors

As the questions states, lets consider we have 3 gas sensors giving me data for:

• A
• B
• C

Note that only sensors for A and B give absolute values, yet we need the absolute values for all four species:

• A
• B
• C
• D

Where the sum of the four gases are 1: A + B + C + D = 100%.

Where should I start solving this problem from? How can the general case be described mathematically?

EDIT: As a real-world example, lets consider that:

Edit:

My objective is to obtain fairly accurate air composition, based on the assumption that the air around us is composed only of oxygen, nitrogen, carbon dioxide and pollutants respectively. Therefore, if we know the volume composition of 3 of the above species, we will have the forth: which is where the title of this question comes from.

By absolute, I am referring to the fact that it is zero-referenced and is independent or other values. I'm sorry if this caused confusion.

• Can you please edit your question for clarity? As it stands now, it is not exactly clear what you are asking. Also, is it possible to make it a bit more specific? What are sensors A,B,C and what exactly is the desired outcome that results as a sum of the A,B,C,D sensors? – A_A Oct 24 '16 at 8:52
• We have three gas sensors named GSensorA, GSensorB and GSensorC which measure the amount of species A, B and C respectively. The sum of species A, B, C and D is 100%. I'm looking a way to express this mathematically (neural networks?). – salehgeek Oct 24 '16 at 9:13
• The absolute value of amount is amount, because an "amount" must be nonnegative. If it can be negative you must call it something else. Why don't you have access to |C|? – Olli Niemitalo Oct 24 '16 at 9:48
• Thank you. If the sum of A,B,C,D is 100% and they are supposed to analyse the gas content of a set volume, then $A+B+C+D=100$ and so $A$ should account for $0.25$ of the total. Why neural networks? I am also seconding Olli Niemitalo's question. Can you please talk a little bit more about the application? I don't object to Neural Networks :) But at the same time, I struggle to understand the sort of difficulty that would call for their use in this case. – A_A Oct 24 '16 at 10:14
• @OlliNiemitalo Only GSensorA and GSensorB give a absolute value (percentage of gas content in a set volume). GSensorC can only state if the gas content is more or less than a standard value. – salehgeek Oct 24 '16 at 10:31