Mathematical Requirements and Options
Mathematics serves for everything that cannot be covered by physics approaches. The assumption that a most qualified electro technical approach solves all problems arising from measurement is naïve and does not lead to sufficient results. At least thriving for best performance only at the expense of electronics is not an economized approach.
An operationally sufficient locating system will balance benefit and effort. Measurement and estimate shall take motion into account. This must not include the measuring of motion itself, but proper assessment of current and past motion to estimates. All estimate approximating the real location of the target is determined on the basis of a statistical model for the observed stochastic processes. Such model and estimation will use the set of observed propagation parameters. Some calibration data may serve as a basis for a statistical model of the propagation parameters. Such calibration is performed versus a spatial distribution of radio energy and with aspect to a known spatial distribution of corresponding targets. Other passive objects affecting propagation interfere with wireless operation and measurement.
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“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)