Trajectory Modeling | Yonghui Liu

Autonomous Traffic Sensor Web (ATSW)

Sun, 11 Oct 2026 00:00:00 +0000

Overview

ATSW is a working local research prototype for exploring how GPS observation decisions affect the movement state available to a receiver. Independent sources replay recorded trajectories and decide when to report a new observation. A web workspace shows the received evidence, movement estimates, forecasts, and reporting decisions as playback advances.

The prototype connects to my research on : selecting or reporting an observation changes the information available for recovering movement. It provides an inspectable setting for studying that relationship.

Implemented

Adaptive reporting: Each source compares its current GPS observation with a local replica of the receiver’s predicted state. A heuristic policy reports significant deviations and periodically refreshes the receiver. Periodic and all-observation policies provide comparison modes.
Receiver-state maintenance: Constant-velocity Kalman prediction and updates, implemented with Stone Soup, maintain each receiver’s position estimate. Delivered GPS observations update the estimate; between reports, the receiver advances by prediction.
Live inspection: The workspace supports playback, pause and single-step controls, per-source decision logs, forecasts, and requests for a source’s next recorded observation.
Historical comparison: An elapsed recorded window can be reduced to selected original observations and reconstructed between them. This branch currently uses a geometric retention baseline and linear interpolation.
Run evidence: A local journal and JSON export record received observations, estimates, and diagnostic events for inspection.

What the Prototype Evaluates

Replay comparisons pair position error with the ratio of delivered GPS observations. The ratio measures report count; network bytes and device energy require separate measurement. Received GPS evidence and predicted or updated state estimates remain distinct in the workspace.

The live receiver uses reported observations. The History view separately accesses an elapsed source recording for retrospective retention and reconstruction comparisons. These two views examine different information conditions.

Recorded sources and their independent receiver states run in one local process. The implemented version uses heuristic reporting, Kalman estimation, and geometric historical reconstruction. Its current scope is recorded GPS replay.

Next Steps

The next stage is to integrate and evaluate compatible learned reporting and recovery modules while preserving the source–receiver information boundary. Live device connections and coordination across sources are further development directions, supported by the observation and command interfaces.

Trajectory Observation–Reconstruction Co-Design

Sun, 08 Mar 2026 00:00:00 +0000

Research Focus

Urban mobility applications use discrete observations to represent continuous movement. Storage and communication constraints limit the observations that can be retained or reported. Which observations are available, and how they are reconstructed, jointly determine the movement information a system can provide.

My doctoral research, Compression–Reconstruction Co-Design for Urban Mobility Trajectories, studies this relationship. The aim is to preserve useful movement information at the resource level a system actually achieves, by considering observation decisions and reconstruction together.

Complementary Research Settings

Completed-trajectory retention: Once a trip is recorded, which observations should be kept under a fixed retained-point budget? Current work examines reconstruction-aware selection and refinement of retained point sets.
Live trajectory reporting: As a trip unfolds, when should a source report a new observation so that a receiver can maintain an accurate movement state? Current work coordinates reporting decisions with the state propagated at the receiver.
Sparse-trajectory reconstruction: How does recoverability change as gaps between available observations grow? This work studies road-consistent reconstruction and the computational cost of recovering long trajectories.

Completed retention can use the full recorded trip; live reporting makes decisions with information available at the current time. These settings share a co-design perspective and are evaluated under their respective information conditions.

Road-network structure and semantics provide another source of information for mobility models. Related work on develops road representations and compatible labels, and examines the value of this context in stated transportation tasks.

Published Studies

Reconstruction capability: reconstructs long trajectories from sparse, noisy GPS observations using progressive skeleton generation and parallel chunk completion. It studies the accuracy and efficiency of recovery across increasing observation intervals. Published in Communications in Transportation Research.
Conditional information value: uses controlled input gating to examine the contributions of historical trajectory, current state, and available goal information to forecasting. It is a supporting information-value study within the wider research program. Published in Knowledge-Based Systems.
Urban context: and study road representations and semantic compatibility across datasets. Published in IEEE ITSC 2025.

From Research to Systems

is a working local prototype for inspecting GPS reporting decisions, receiver estimates, and historical retention. Its recorded-trajectory replay and explicit source–receiver states make the effects of observation decisions visible. The current prototype uses heuristic reporting, Kalman estimation, and a geometric historical baseline; it provides a setting for future evaluation of learned methods.

Across these studies, the shared question is how much useful movement information a reduced observation record can support. Retained-point count and reporting ratio are evaluated alongside movement fidelity, with their resource definitions made explicit.

Sequential decomposition and attribution for trajectory forecasting

Tue, 23 Dec 2025 00:00:00 +0000

Trajectory forecasting models keep getting longer input windows on the assumption that more history means better predictions. In practice that assumption often breaks down: accuracy gains taper off quickly, extra history adds compute cost, and longer windows pull in more noise. SDA is not another forecasting model — it is an evaluation protocol for measuring why a model performs the way it does.

SDA splits any trajectory forecasting input into three interpretable streams and gates them on/off in controlled combinations to measure each one’s standalone value, its marginal contribution on top of the others, and how the streams interact:

Past — the historical trajectory before the current step
Current — the most recent observed state
Prior — an optional destination or goal, when available

Running this protocol on two real-world datasets (Porto taxi, ETH pedestrian) with both an LSTM and a Transformer backbone gives a consistent picture:

Accuracy sensitivity to history length L, across horizons H and both backbones.

Accuracy gains from history saturate after a short window (L*≈6–8 steps) regardless of backbone or prediction horizon.
The Current state alone is already highly informative at short horizons.
A reliable Prior (goal/destination) gives a bigger boost than piling on more history, especially at longer horizons.
Past, Current, and Prior show conditional complementarity — their combined value is not simply additive.

The takeaway for model design: prioritize making good use of the latest state and any available goal information, rather than defaulting to ever-longer observation windows.

Enhanced trajectory reconstruction from sparse and noisy GPS data: A progressive chunked transformer approach

Mon, 01 Dec 2025 00:00:00 +0000

GPS traces collected in the wild are sparse and noisy — long gaps between fixes are the norm, not the exception. Reconstructing a coherent, road-consistent trajectory from such data matters for mobility analysis, transportation planning, and navigation, but the long output sequences involved make it computationally expensive, and autoregressive models tend to accumulate error step by step over a long reconstruction.

ProChunkFormer tackles this with a two-phase, divide-and-conquer strategy instead of decoding the full trajectory one point at a time:

Phase 1 — Skeleton generation. The sparse, low-frequency GPS input and the road network are encoded and decoded into an intermediate, semi-high-frequency “skeleton” of the trajectory (MM-Semi) that already follows the road network.
Phase 2 — Trajectory completion. Conditioned on that skeleton — and optionally on a heuristic shortest-path estimate (Heuristic) computed between each pair of consecutive skeleton points — the remaining trajectory is divided into chunks and reconstructed in parallel with self-attention, rather than autoregressively. Concatenating all the reconstructed chunks gives the final, complete trajectory (MM-Full).

Self-attention is quadratic in the length of the sequence it looks at, but standard autoregressive decoding still ends up cubic in the length of the whole trajectory, because each of its output steps has to attend over an ever-growing context. ProChunkFormer avoids this by sizing each attention pass to a chunk rather than the full trajectory and generating chunks in parallel; the paper’s complexity analysis shows this cuts decoding time by roughly the cube of the number of chunks used, compared with standard autoregressive decoding. On an open-source taxi trajectory dataset, this lets ProChunkFormer match the accuracy of autoregressive transformer baselines while running faster — 13.9%, 16.5%, and 20.7% faster at sampling intervals of 60, 120, and 240 seconds, respectively — with the largest accuracy gains showing up on the hardest cases: long sampling intervals of up to 240 seconds, where it improves accuracy by 23.1%, F1 score by 18.6%, mean absolute error by 22.3%, and road-network error by 25.1% over a standard transformer baseline.

Ground truth versus reconstructed GPS points for the same trip: the standard transformer’s points collapse together in the circled area, while ProChunkFormer — which reconstructs the trajectory in independent, parallel chunks — keeps them spread out along the real route. Map data © OpenStreetMap contributors, licensed under CC BY-SA 2.0.

Adding heuristic guidance — using the shortest path between consecutive skeleton points to help condition each chunk’s reconstruction — speeds up convergence during training and improves accuracy and error metrics in most configurations, though the paper reports a few cases (for example, accuracy at a 120-second sampling interval) where it produces a small decline instead.