Effective Trajectory Imputation using Simple Probabilistic Language Models

Trajectory data collected by GPS has found many critical applications. Unfortunately, most trajectory datasets have missing data due to technical problems or due to the sampling strategy used. Trajectory imputation is the task of filling in the gaps in actual trajectories by computing points that fit "naturally" within existing trajectories. Considering that both trajectories and natural language are essentially sequences of symbols, we explore the use of probabilistic language models for trajectory imputation. Using a grid-based representation of the space, and not considering the underlying road network, we convert trajectory points into tokens corresponding to the grid cell where they appear and train models of different sizes. We report experiments on a real dataset of over 500,000 taxi trips, showing that we can accurately fill gaps of up to 2km between GPS observations with 83% precision. These results are comparable to approaches using much more computationally demanding Large Language Models based on transformers. We discuss why transformers are overkill for the task through experiments that show that trajectory data does not exhibit very long dependencies, as is the case with natural language.