Optimizing Sensor Number and Placement for Accurate and Robust Center of Pressure Estimation on Instrumented Insoles

Smart insoles equipped with pressure sensor matrices are increasingly used for gait analysis, yet high-density arrays compromise battery life and data throughput. This study aims to identify the optimal sparse sensor layout required to accurately estimate the Center of Pressure (CoP) by analyzing the trade-off between sensor number, spatial placement, and reconstruction error. Plantar pressure data were collected from twelve healthy participants walking at a self-selected speed using 16-sensor connected insoles. A combinatorial algorithm evaluated all 216-1 possible sensor combinations to minimize the Root Mean Square Error (RMSE) in the antero-posterior, medio-lateral, and global Euclidean directions. Results reveal a non-linear convergence of accuracy that depends on the spatial axis. For longitudinal and global progression, a clear inflection point achieving sub-centimetric accuracy (RMSE < 5 mm) is reached at seven sensors. In contrast, medio-lateral tracking shows its largest discrete error reduction at five sensors, followed by gradual improvements at higher densities. Anatomical frequency analysis highlights distinct spatial requirements: the posterior heel is consistently selected for medio-lateral accuracy, while the lateral arch and metatarsal regions are critical for longitudinal progression. These findings suggest that while a minimum of seven strategically placed sensors enables robust CoP tracking across all spatial axes, optimal hardware design should remain task-specific. This work provides a data-driven framework for the development of energy-efficient wearable gait monitoring systems.