How can I approximate the accurate sensor readings given readings from noisy sensors? I have five sensors measuring the same quantities (temperature, humidity, barometric pressure) at the same time. I also have reference measurements (from much more accurate sensors). 
What is the appropriate approach to validate the output of the five sensors in terms of how well they agree with each other and with the reference measurements? 
I have zero statistical background, only a problem to solve!
 A: I would use the reference measurements to calibrate the other sensors' biases:
$$x_{ij}=s_{i}+\mu_j+\varepsilon_{ij},$$
where $x_{ij}$ - measured value from sensor $j$, $s_{i}$ - true value, $\mu_j$ - bias and $\varepsilon_{ij}$ - random error.
We don't know the true value $s_i$, but we can use the reference sensors $r$ assuming they have no bias and small errors $u$:
$$r_{i}=s_{i}+u_{i}$$
Plug one equation to another, and take the expectation:
$$\mu_j = E[x_{ij}-r_{i}]\approx \frac 1 n \sum_{i=1}^n x_{ij}-r_{i}$$
Once you know the bias, you can use it to get the best measurement estimate:
$$\hat s_i=\frac 1 m \sum_{j=1}^m x_{ij}-\mu_j$$
You can get more sophisticated but you need to keep the focus on what matters most. Your main issue is the bias, once you figure out how to deal with it, the stochastic errors will be averaged out by multiple sensor measurements. Consider a case where all sensors have the same bias: $\mu_j=\mu$
This is the worst case scenario, and you have no way to correct it without the reference sensors, unlike the stochastic errors that will be reduced or eliminated by repeated measurements.
A: It sounds like your question is something like, how can I approximate the accurate sensor readings given my noisy sensors. Which, if that's true, you really need to rewrite your question as it is rather confusing. @Aksakal's answer would give you a way of seeing what the bias of each sensor is, but I don't really see how that helps you.
One simple method would be linear regression: Assume the errors are independent in time and then try to predict the correct sensor values as a linear combination of your noisy ones. 
My second suggestion would be to use the fact that you have a ground truth sensor to fit the parameters of a Kalman filter and use that.
