Optimal Indoor Positioning, Trajectory Reconstruction and Localisation with Uncertainty Control using Radio-Frequency Measurements

This thesis addresses the problem of target positioning and localization using Radio Frequency (RF) based measurements and using a variety of modulation including Time of Arrival (ToA), Phase of arrival (PoA) and Received Strength Indicator of RF signals (RSSI). Starting from finding the planar coordinates of a device from a collection of ranging measurements using weighted least square (WLS) methods, we explore the dependency of the solution uncertainty from the geometric configuration of anchors and then develop solutions that compensate for the effects of geometry and reduce the positioning uncertainty to a value close to the Cramer–Rao Lower Bound (CRLB), a measure which is then used in the proceeding chapters for developing optimal anchor configurations for positioning problem with guaranteed estimation uncertainties. The findings in the positioning part are also used to address the limitations of initializing Ultra-Wideband (UWB) anchors through a random trajectory. This is done by studying the dual of the positioning problem addressed in the first part, that is incorporating CRLB as a measure of optimality to design a trajectory that minimizes the uncertainty of anchor initialization. We finally close the positioning part of the thesis by studying the range and bearing measurements provided by radar sensors for people tracking and positioning in indoor environments. Taking into account the target dynamics, in the second part of the thesis we present observabilty analysis and localization for non-holonomic robots, using a combination of onboard sensors and range-only anchors. By using a discrete-time formulation of the system’s kinematics, we identify the geometric conditions that make the system globally observable and thereby derive the observability-based filter (ObF) to outperform the limitations of the classic Bayesian filters. We then use the implications of this analysis to design an active control and optimal path-planning strategy with guaranteed maximum observability. We close this part of the thesis by investigating localization in presence of intermittent measurements and discuss how the observability of a trajectory can be quantified by the condition number of the system matrix, a subject related to the maneuvers executed by the robot and to the sampling time used to collect the measurements. Eventually, in the last part of this thesis, we address the localization in presence of offset and ambiguities in measurements. First, we show that, while using range-only measurements corrupted with offset, the trajectories can be observed and the offset can be estimated in a finite number of steps. Next, we present an approach to resolve the ambiguity of rang-only measurements obtained from RSSI values at the Ultra-High Frequency (UHF) band by proposing an optimization algorithm that merges RFID and odometry data to reconstruct the entire robot trajectory. Finally, we present a solution to resolve the ambiguity of the RFID signal phase and reconstruct the robot trajectory through sensor fusion and using UHF-RFID passive tags.