Localization with Multi-Lateration Techniques in Low-Power Wide-Area Networks

Abstract

This thesis concerns the localization of an Internet-of-Things (IoT) target (sensor) that intermittently transmits a signal (message) to an array of spatially separated receivers (gateways). In the setting of primary interest the source’s signal is known to the receivers. The application of primary interest is a target (sensor) transmits a short time duration (burst) signal in a homogeneous line-of-sight environment to gateways that can measure the time of arrivals of the source’s signal subject to suffering zero-mean Gaussian measurement errors. The time when the source emits the signal (i.e., the transmission time) is unknown. However the results can be applied in a wide range of applications.

The problem of localizing a target is approached from a probability density point of view as opposed to the well-explored point estimation point of view. Equations for the joint a posteriori probability density functions (pdfs) of the target’s coordinates in both two-dimensional (2D) and three-dimensional (3D) spaces are developed using the measurements of the times that a transmitted message arrives at the spatially separated gateways. The a posteriori pdfs also take uncertainty, i.e., measurement errors, in the positions of the gateways into account.

The corroboration and utility of the a posteriori pdf are explored through various examples to demonstrate its superiority and usefulness. First, it is shown that the joint a posteriori pdf of the target’s location is not always approximately jointly Gaussian, especially when the target is in close proximity to one of the gateways, or when the gateways are located in close proximity to each other. Next, several examples are provided to examine the effects of the measurement errors in the positions of the gateways to the spread and position of the resulting a posteriori pdfs. These examples also include the incorporation with a priori pdf, especially when the a priori pdf is quite restrictive, which makes the a posteriori pdf very useful in many practical scenarios. Lastly, an improvement of the a posteriori pdf is thoroughly analyzed for a scenario where there are multiple transmissions of the message from a target located at a fixed position.

While intermittently active targets are the rule in the application of primary interest, a chapter is dedicated to targets that transmit a continuous signal that is unknown to the receivers. In a scenario where the transmitted signal is unknown to the receivers, the ToAs can not be estimated, but the time-difference-of-arrivals (TDoAs) can be estimated by time-windowing the continuous signal and cross-correlating the windowed segments. An a posteriori pdf is developed for TDoAs obtained by taking the difference of ToAs. It is shown that this a posteriori pdf does not apply to TDoAs obtained by cross-correlation unless one of the segments being cross-correlated is noise free.