Application of Bayes’ Rule in Positioning
The article discusses various positioning technologies, including using conditional probability to calculate Bayesian positioning and determine the dependency between signal indicators and locations.
Over the years, various localization technologies have been used to determine locations of people and devices in an absolute or relative sense. Relative positioning methods determine a location relative to another one in a local coordinate framework, while absolute positioning techniques fix an absolute location in a specific coordinate framework.
Various positioning technologies share an intrinsic characteristic that a positioning solution is resolved by using the dependency between spatial locations and a set of physical observables. The dependency may be expressed in the form of either a deterministic function model or a probabilistic model. A deterministic model expresses the dependency between locations and observables in a closed-form function, while a probabilistic model defines the dependency between locations and observables in the Bayesian sense.
An example of Bayesian positioning is to use various signals of opportunity (SOOP) — signals not originally intended for positioning and navigation. They include RF signals, such as those of cellular telephone networks, digital television, frequency modulation broadcasting, wireless local area networks, and Bluetooth, as well as naturally occurring signals such as the Earth’s magnetic field and the polarized light from the sun. Indicators of these signals, such as signal strengths and signal quality, are dependent on locations in the Bayesian sense. The dependency between signal indicators and locations is expressed in a probabilistic model:
where signifies a dependency between a set of physical signals and locations, Idenotes indicators of SOOP signals, L denotes location, and P(i|l) is the probability that signal indicators (i) are observed at location (l).
I think this is an interesting article that is relevant to conditional probability using Bayes’ Rule, which is what we have discussed in class. Using various signals of opportunity to navigate and position is an application of Bayes’ Rule because the indicators of the signals are dependent on locations.
Source article: Testing the feasibility of positioning using ambient light http://gpsworld.com/innovation-a-bright-idea/