An Optimization Method for Indoor Trajectory Estimation from Spatially Sparse and Noisy Beacon Data

Analyzing trajectory data within buildings provides valuable insights for enhancing environmental design and habitability. To gain a comprehensive understanding of how architectural structures affect human behavior, it is necessary to collect extensive spatial-temporal trajectory data from various building types. Therefore, we need methods that can precisely estimate trajectories using sensors that are easy to install. However, indoor location sensor data tends to be both sparse and noisy. Conventional route estimation models face difficulty in effectively applying to this situation. Our study aims to obtain detailed, temporally, and spatially rich trajectory data from this compromised sensor information. We achieve this by interpreting trajectories as continuous stay points. To facilitate this, we introduce a building corridor network that conceptualizes buildings as a series of points. This network enables the consideration of stay point relationships and those between stay points and responding beacons over the full data length. Routes are inferred using a sequence estimation model applied to this network. This approach employs spring dynamics, which balance the resistance to staying with the attraction to specific beacons. Their competing forces are modeled as a mathematical optimization problem, balancing the costs of both travel and beacon. The travel cost controls the relationship between the stay points at each time, while the beacon cost forms the framework to fit the reaction of the beacons. To evaluate the accuracy of this estimation method, experiments are performed. The evaluation experiment compares the trajectory paths estimated by our model using the obtained beacon responses with the actual walking paths. Notably, our model can deduce a trajectory of 131 points from only 15 beacons with, an accuracy rate of 87%. Our method presents a promising avenue for capturing extensive route data.