In sensing applications, sensors cannot always measure the latent quantity ofinterest at the required resolution, sometimes they can only acquire a blurredversion of it due the sensor's transfer function. To recover latent signalswhen only noisy mixed measurements of the signal are available, we propose theGaussian process mixture of measurements (GPMM), which models the latent signalas a Gaussian process (GP) and allows us to perform Bayesian inference on suchsignal conditional to a set of noisy mixture of measurements. We describe howto train GPMM, that is, to find the hyperparameters of the GP and the mixingweights, and how to perform inference on the latent signal under GPMM;additionally, we identify the solution to the underdetermined linear systemresulting from a sensing application as a particular case of GPMM. The proposedmodel is validated in the recovery of three signals: a smooth synthetic signal,a real-world heart-rate time series and a step function, where GPMMoutperformed the standard GP in terms of estimation error, uncertaintyrepresentation and recovery of the spectral content of the latent signal.
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