Statistical method for determining the location of a mobile device

1. Non-transitory computer-readable media having computer-executable instructions embodied thereon that, when executed, enable a computing device to perform a method of facilitating a location-based service for use by a mobile-device, the method comprising:

among a set of base stations that make up a portion of a wireless-telecommunications-network, wherein a location of each base station in the set is known, and wherein each base station has a signal-to-noise-and-interference ratio (SINR) above a predetermined minimum SINR such that each base station provides signal coverage to a first geographical area such that a mobile-device in the first geographical area is capable of communicating with the telecommunications-network via the each base station;

for a first base station in the set, the first base station having a directional antenna, considering a.) an angle between an azimuth of the first base station and the first geographical area, and b.) a beamwidth of the directional antenna of the first base station, determining a joint probability that the SINR of the first base station is greater than a first threshold SINR above the predetermined minimum SINR and the SINRs from neighboring base stations within the set of base stations are less than a second threshold SINR above the predetermined minimum SINR such that the first base station provides a level of signal coverage to the first geographical area that would enable a first mobile-device in the first geographical area to communicate with the wireless-telecommunications-network;

determining a density of possible locations that the first mobile-device may be within the first geographical area, the density based on a Bayesian probability conditioned on the first mobile device being covered by the first base station;

approximating a position of the first mobile-device based on the density of possible locations; and

facilitating the location-based service for use by the first mobile-device based on the position.

2. The Non-transitory computer-readable media of claim 1 , wherein the density is based at least in part on a distribution of estimated distances from the first mobile-device to the first base station, the estimated distances derived from the time it takes for a signal to pass from the first base station to the first mobile-device and back to the first base station.

3. The Non-transitory computer-readable media of claim 2 , wherein an actual distance from the first mobile-device to the first base station is within the distribution of estimated distances.

4. The media of claim 1 , wherein the location-based service is a closest-business locator service.

5. The Non-transitory computer-readable media of claim 1 , wherein the probability is further determined as a function of factors including one or more of a fading factor, a noise factor, a downlink power factor, a total downlink power factor, and an interference factor.

6. The Non-transitory computer-readable media of claim 1 , wherein the position of the first mobile-device is further approximated based on a maxima of the density of possible locations, wherein the maxima of the density of possible location indicates a set of probable locations based on the density.

7. The Non-transitory computer-readable media of claim 6 , wherein the position of the first mobile-device is further approximated by calculating an arithmetic mean of the set of probable locations.

8. Non-transitory computer-readable media having computer-executable instructions embodied thereon that, when executed, enable a computing device to perform a method of facilitating a location-based service for use by a mobile-device, the method comprising:

among a set of base stations that make up a portion of a wireless-telecommunications-network, wherein a location of each base station in the set is known, and wherein each base station has a signal-to-noise-and-interference ratio (SINR) above a predetermined minimum SINR such that each base station provides signal coverage over a first geographical area such that a mobile-device in the first geographical area is capable of communicating with the telecommunications-network via the each base station;

for a first base station in the set, the first base station having an omni-directional antenna, determining a joint probability that the SINR of the first base station is greater than a first threshold SINR above the predetermined minimum SINR and the SINRs from neighboring base stations within the set of base stations are less than a second threshold SINR above the predetermined minimum SINR such that the first base station is providing a level of signal coverage to the first geographical area that would enable a first mobile-device in the first geographical area to communicate with the wireless-telecommunications-network;

determining a density of possible locations that the first mobile-device may be within the first geographical area, the density based on a Bayesian probability conditioned on the first mobile-device being covered by the first base station, and further wherein the density is based at least in part on a distribution of estimated distances from the first mobile-device to the first base station;

based on the density, approximating a position of the first mobile-device; and

facilitating the location-based service for use by the first mobile-device based on the position.

9. The Non-transitory computer-readable media of claim 8 , wherein the probability is further determined as a function of factors including one or more of a fading factor, a noise factor, a downlink power factor, a total downlink power factor, an interference factor, and a path-loss factor.

10. The Non-transitory computer-readable media of claim 8 , wherein the facilitating includes providing the position to a location-based service operating on the first mobile-device.