This paper shows how time-dependent sensory data from an evolving stimulus can be blindly rescaled in a nonlinear time-dependent fashion to create a time series of stimulus representations that are invariant under any unknown invertible transformation of the sensory data. These representations are invariant, because they encode "inner" properties of the time series of stimulus configurations themselves. This means that any two devices, possibly equipped with significantly different sensors, will create the same rescaled representation of an evolving stimulus, as long as they are sensitive to the same internal degrees of freedom of the stimulus. Such sensor-independent stimulus representations will also be unaffected by a wide variety of processes that invertibly remap sensor states, including: (i) altered performance of a device's detector; (ii) changes in the observational environment external to the sensory device and the stimulus; and (iii) certain modifications of the presentation of the stimuli themselves. In an intelligent sensory device, this kind of representation "engine" could function as a "front end" that passes rescaled sensor state representations to the device's pattern analysis module. Because the effects of many extraneous observational conditions have been "filtered out" of these representations, it would not be necessary to recalibrate the device's detectors or to retrain its pattern analysis module in order to account for these factors.