Trilateration in Robotic Sensing Study Notes FL2010 CrossCorrelation(what is)

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Range Estimation

The first part of locating the target is to know how far it is from the anchor nodes (speakers). When a chirp is emitted by the speaker, it takes time for it to travel to the microphone. Because of this, the microphone will, in theory, hear the same signal as the speaker emitted, just delayed by the time it takes the sound wave to propagate. We use a method called cross correlation to yield this delay, then we multiply the delay by the speed of sound to calculate the distance from speaker to microphone.

An excellent explanation of range estimation and cross correlation can be found in this report by Joshua York.

Cross Correlation

Cross Correlation is a mathematical tool used to evaluate the similarity of two signals f and g. f is shifted x units and then multiplied by the unaltered g. The area under this product curve is evaluated as a function h(x). If f and g vary only by a delay and are otherwise the same signal, then the x value which maximizes h is equal to that delay. In our scenario, g is the known signal emitted by the speakers and f is the signal received by the microphone. Assuming negligible noise, the signals are the same excepting a delay. This delay is proportional to the distance between the microphone and speaker because sound moves at a constant speed. To estimate that range, then, we apply cross correlation to the signals f and g and multiply the resulting delay by the speed of sound (c).