Impact of altitude difference for Local Positioning Systems and compensation with two-stage estimators

In range-based positioning systems, an altitude difference between tag and reference plane causes errors in two- and three-dimensional positioning. We analyze how these errors reduce accuracy of Local Positioning Systems (LPS) and show how compensation of the altitude difference improves performance of positioning. In this paper, we consider the availability of additional altitude information and transform the three-dimensional positioning problem into a two-dimensional problem. We provide algorithms for time-based positioning systems with a two-stage estimator for Two-Way Ranging and Time Difference of Arrival and incorporate additional altitude information. We simulate our approach for altitude difference compensation and provide an evaluation based on a Ultra-Wideband (UWB) radio with ranging capability and a barometric sensor for additional altitude information. A comparison is then made between our approach and standard solutions such as the Extended Kalman filter and the Unscented Kalman filter. Finally, the successful decrease in the positioning error for two- and three-dimensional positioning system, using the system disclosed herein, is illustrated. Based on our analysis, we derive practical solutions to deal with altitude differences for positioning systems.