Grid-Coded Retrieval-Augmented Generation with Hybrid Retrieval for Minute-Level Aircraft Trajectory Prediction

Ultra-short-term (1–5 min) tactical trajectory prediction underpins air traffic conflict detection, yet deep learning models such as long short-term memory (LSTM), gated recurrent unit (GRU) and multilayer perceptron (MLP) networks lack an aviation spatial inductive bias, fit sparse grid-transition samples poorly, and in the small-sample setting studied here incur position errors an order of magnitude larger than trivial baselines. Retrieval-augmented generation (RAG) is a natural remedy, replacing parametric fitting with non-parametric retrieval of historical flight priors and requiring no retraining. Existing RAG schemes nevertheless break down on gridded airspace: character-hash encoding of grid identifiers discards spatial semantics, so adjacent grids are treated as unrelated, and the transition prior of the current grid is often missed, while stochastic vector search offers no recall guarantee, so such a miss silently collapses the prediction to persistence. This paper therefore proposes RAG-Hybrid, a grid-coded dual-path framework in which a deterministic breadth-first search (BFS) lookup reconstructs the local transition subgraph of the current grid from the knowledge base, spatially aware FAISS (Facebook AI Similarity Search) retrieval draws on a training-free focal-weighted Gaussian grid vectorisation, and Laplace smoothing with global-Markov weighting calibrates the resulting transition matrix. The evaluation uses Automatic Dependent Surveillance–Broadcast (ADS-B) trajectories from 62 test flights over a 0.25° × 0.25° grid covering Central–South China, and reports 1 min to 5 min horizons. On this test set, the framework holds single-step Top-1 at 0.7097, identical to a leakage-free global-Markov baseline and within one standard error of the trivial persistence predictor (0.7581), while raising Top-3 and Top-5 at the +1 min horizon from 0.9355 to 0.9839. A constant-velocity dead-reckoning baseline attains the highest point accuracy at this horizon (Top-1 0.8065, MAE 4.90 km) but returns a single cell, so the framework exceeds it on Top-5 by 0.1774. The one component effect that this study resolves statistically is the deterministic lookup channel at the far end of the horizon: removing it cuts the pooled five-step Top-5 hit rate from 0.7452 to 0.6516 and the +5 min Top-5 hit rate from 0.5645 to 0.3710.