This disclosure shows how a
time series of measurements of an evolving
system can be processed to create an “inner”
time series that is unaffected by any instantaneous invertible, possibly
nonlinear transformation of the measurements. An inner
time series contains information that does not depend on the nature of the sensors, which the observer chose to monitor the
system. Instead, it encodes information that is intrinsic to the evolution of the observed
system. Because of its sensor-independence, an inner time series may produce fewer false negatives when it is used to detect events in the presence of sensor drift. Furthermore, if the observed
physical system is comprised of non-interacting subsystems, its inner time series is separable; i.e., it consists of a collection of time series, each one being the inner time series of an isolated subsystem. Because of this property, an inner time series can be used to detect a specific behavior of one of the independent subsystems without using blind
source separation to disentangle that subsystem from the others. The method is illustrated by applying it to: 1) an analytic example; 2) the audio waveform of one speaker; 3) mixtures of audio waveforms of two speakers.