Look into the area called sensor fusion for algorithms and things.

There are multiple ways people do this. For example, you could use something like factor analysis, where the factor loadings onto the latent "true" signal/factor are fixed based on what you (presumably) know about the empirical reliability/error variance and (potentially) bias in each observed signal. Then you do your modeling with the inferred latent "true" signal. See the second example here to see that sort of approach in the context of a gaussian process model.