Fig 1.
The basic process of particle filtering.
Initially, a large number of particles are generated for each entity, with the model projecting the state for the next step. The weight of each particle is determined by the likelihood calculated from observational data. A resampling process based on this likelihood is then conducted to establish the distribution of the predicted state for the next step.
Fig 2.
Integration of particle filters into agent-based simulation.
After particles are generated by the model, they are weighted based on camera-captured inflow data. Agents move to locations that are most likely to be visited at time t in both the model and the real world.
Fig 3.
Three types of incompleteness in current people flow measurement techniques.
Fig 4.
Comparison of ground truth and simulated transition tendencies in case 1.
(a) Ground truth values of the OD (Origin-Destination) matrix. The axis values represent store numbers, with the vertical axis indicating the store of departure and the horizontal axis indicating the arrival store. (b) Estimated values based on data assimilation. The axis values represent store numbers, with the vertical axis indicating the store of departure and the horizontal axis indicating the arrival store. (c) Comparison of the top 20 most frequent three-store transition sequences from ground truth and estimated. The horizontal axis numbers represent the ranking of transition frequency, and the vertical axis shows their frequencies.
Fig 5.
Comparison of the ground truth OD matrices (upper) and the simulated OD matrices (lower) for each attribute, along with the combined OD matrix, in Case 2.
(a) OD matrix for attribute 1 (ground truth, upper; simulated, lower). (b) OD matrix for attribute 2 (ground truth, upper; simulated, lower). (c) OD matrix for attribute 3 (ground truth, upper; simulated, lower). (d) OD matrix for attribute 4 (ground truth, upper; simulated, lower). (e) Combined OD matrix (ground truth, upper; simulated, lower). The OD matrices from (a) to (d) are derived from data assimilation, utilizing inflow count data that can distinguish between attributes. The color bar represents the transition count between stores.
Fig 6.
Ground truth OD matrix and estimated OD matrices for different methods in case 3.
(a) Ground truth OD matrix. (b) Estimated OD matrix for baseline sampling. (c) Estimated OD matrix for VAE. (d) Estimated OD matrix for ensemble Kalman filter. (e) Estimated OD matrix for particle filter. The color bar represents the transition count between stores.
Table 1.
Quantitative comparison of estimation methods in Case 3. The table shows absolute error (raw transition counts), Jensen–Shannon divergence (JSD), and Recall@K (K = 5, 10, 20). Lower error and JS divergence, and higher Recall@K, indicate closer agreement with observations.
Fig 7.
Comparison of the frequency of three-store transition sequences in Case 3.
The figure shows the average counts of the top-20 transition sequences (among three stores) from ground truth and estimated by each method (Baseline, VAE, EnKF, PF). The horizontal axis corresponds to the rank of transition sequences in the ground truth data, and the vertical axis shows the average frequency across iterations.