Ultrasonic locationing using only time difference of arrival measurements

A system for ultrasonic locationing using only time difference of arrival measurements, the system comprising:

• an ultrasonic receiver including four microphones, three of the microphones disposed on a periphery of a housing, and a fourth centrally-positioned microphone between the other three microphones, the ultrasonic receiver operable to receive an ultrasonic signal from an ultrasonic emitter within an environment;
• and
• a controller communicatively coupled to the receiver and operable to:
• a) establish only time difference of arrival measurements of the ultrasonic signal at each of the four microphones,
• b) assume an arbitrary flight time for the ultrasonic signal in order to obtain three respective flight distances of the ultrasonic signal for each of the three microphones,
• c) calculate an intersection point of three spheres defined by three radii equal to the three flight distances,
• d) calculate a distance from the intersection point to the centrally-positioned microphone,
• e) subtract the distance from a test distance corresponding to a sum of the arbitrary flight time plus the time difference of arrival measurement for the centrally-positioned microphone to establish an test error, and
• f) repeat steps b) through e), searching different arbitrary flight times along a straight line through the centrally-positioned microphone and intersection point until the test error is less than an accuracy threshold, indicating an actual location of the emitter.