How to combine the responses of two sensors? I have two sets of responses from two different sensors. In each set, the first column is distance measured in feet, and the second column is the response of the sensor. Sensor A has response values in the 10-20 range, with very low variance, and Sensor B has responses in the 50-1000 range, with higher variance, over and beyond the fact that the values are of another order of magnitude. Another important issue is that the sensors fire at different, irregular rates, so the sampling rates do not match up between the sensors.
I would like to combine the data from the two sensors into one plot that reflects the confidence I have that something was sensed, based on the two responses. I am not trying to prove correlation between the two sensors; I expect them to be highly correlated. What sort of tools should I use to explore this data?
 A: You may want to have a look on Dempster-Shafer theory. This framework has been investigated for merging information coming from sensors, for instance you can have a look at the following papers: 


*

*Information fusion and evidential grammars for object class
segmentation

*Information Fusion on Oversegmented Images:
An Application for Urban Scene Understanding
A: Being sensed is a binary outcome. The sensors' distance from target is a covariate that determine the outcomes.  Logistic regression is one way to model this.  The model would look like a smooth 2-dimensional surface over the x-y plane where x and y represent the respective sensor's distance from the target, with the height being the logit of p where p is the probability that the target is sensed (I am assuming that the definition of target being detected is that at least one of the sensors detects it).
There are other possibilities of modeling a binary outcome, probit analysis is one alternative for example.  The choice will depend on what modeling assumptions you think are reasonable.
