Let consider a simple equation $$I = \frac{V_1-V_2}{R}$$ with $R = 0.001$ and $V_1, V_2$ around $10\ 000$, while $I$ is around $10$. The problem is $V_1$ and $V_2$ are measured with some small error (compared to $10\ 000$ as nominal value) of around $5$. But this small error will lead to unacceptable big error in $I$, when we get $$I = \frac{V_1-V_2}{R}. $$
How can we solve this problem? when we have $I$, $V_1$ and $V_2$ are continuously changing with time. how we can get a good estimate of $I$ with $V_1$ and $V_2$ measurement. Thank you very much!
What you need to do is measure $V_1-V_2$ directly rather than measuring each separately and subtracting. This is not always possible, but sometimes it is. Think of two cars in neighboring lanes on the freeway traveling at almost the same speed. At one time they are next to each other. $5$ minutes later one is a car length ahead, say $20$ feet for a large one. This tells us that $V_1-V_2$ is about $4 ft/min$ regardless of what $V_1,V_2$ are individually.