Hybrid N4SID-PEM-GBDT identification for small unmanned helicopter modeling

Purpose This study aims to improve the dynamic modelling accuracy of small unmanned helicopters with multi-input multi-output behaviour, strong coupling, and nonlinear flight characteristics. Existing linear identification methods can capture dominant dynamics but have limited ability to represent nonlinear residual effects caused by aerodynamic coupling and unmodelled disturbances. Design/methodology/approach A three-stage numerical algorithms for subspace state space system identification–prediction error method–gradient boosting decision tree (N4SID-PEM-GBDT) hybrid identification framework is proposed. First, N4SID is used to establish a linear state-space model and extract the dominant system dynamics. Next, prediction error method (PEM) is applied to refine the linear model parameters, thereby obtaining an improved benchmark model. Finally, causal time-series features are constructed from the optimized residuals, and gradient boosting decision tree (GBDT) is employed to learn nonlinear residual compensation for the pitch-rate and roll-rate channels. Findings Time-domain validation using an independent dataset demonstrated that the proposed N4SID-PEM-GBDT framework achieved an R2 of 0.9112 and a root mean square error (RMSE) of 3.4518. Compared with N4SID and N4SID-PEM, the proposed method increased the average R2 by 13.17 and 8.15 percentage points, respectively, while reducing the average RMSE by 33.61% and 26.37%, respectively. Furthermore, compared with N4SID-PEM-RNN, N4SID-PEM-extreme gradient boosting (XGBoost) and N4SID-PEM- Gaussian Process (GP), the proposed method reduced the average RMSE by 4.71%, 6.57% and 8.19%, respectively. These results demonstrate that the proposed method further reduces prediction errors on independent test data while retaining the ability of the linear state-space model to capture the dominant system dynamics. Originality/value This study integrates subspace identification, prediction error optimization, and GBDT-based residual learning into a unified hybrid framework, providing an effective approach for high-precision modelling of strongly coupled small unmanned helicopter systems.