Probabilistic Localization With Gateway Location Errors and Multiple Transmissions.

This paper investigates the effect of uncertainty in the positions of a set of spatially separated receivers (gateways) that are used to localize a device (target) that transmits a burst signal intermittently. Such systems have applications in radar, sonar and wireless sensor networks, and have been extensively studied, at least in the context of point estimation. This paper extends the limited work on region estimation to include the effect of uncertainty in the locations of the gateways on the probability that the target is in a specified region. Specifically, this paper extends previous work that found the a posteriori probability density function (pdf) of the target’s coordinates from estimates of the times the transmitted message arrives at the receivers (ToAs) under the assumption the positions of the gateways were known exactly. The expression for the a posteriori pdf is redeveloped to include the uncertainty in the measurement of the receivers’ positions. Three practical scenarios are considered: (i) the target transmits a single message and the gateways measure the ToAs as well as their own positions, (ii) the target transmits multiple messages and the gateways measure the ToAs as well as their own positions upon each reception, and (iii) the target transmits multiple messages and the gateways measure the ToAs upon each reception, but the positions of the gateways are measured once, at the time of installation. Various numerical examples are given to corroborate, provide insights, and illustrate the utility of the obtained results.