Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated 'total entropy' associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.
Trilateration calculations are affected by errors in distance measurements from the set of fixed points to the object of interest. When these errors are systemic, each distinct set of fixed points can be said to exhibit a unique set noise. For ultra-wideband (UWB) indoor position tracking, the set of fixed points is a set of sensors measuring the distance to a tracked tag. In this paper we develop a noise model for this sensor set noise, along with a particle filter that uses our set noise model. We test our methods on a real UWB system. Our methods showed an approximately 15% improvement in accuracy over the raw measurements.
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