Evaluation of Correlation-Based Methods for Time Period Estimation in Vehicle Speed Measurement Using Pyroelectric Infrared Sensors

Accurate time period estimation (TPE) between sensor signals is essential for vehicle speed measurement in intelligent transportation systems (ITSs). In this context, we focus on time period estimation using signals acquired from a dual pyroelectric infrared (PIR) sensor setup. To estimate the time period between these signals, this paper analyzes and compares two correlation-based methods—conventional cross-correlation (CCF) and Hilbert transform-enhanced cross-correlation (CCFHT). An analytical framework is developed to quantify the bias and variance of each method under practical conditions, including sensor mismatch and noise. The PIR sensor signals are modeled based on their dynamic response characteristics, enabling theoretical analysis supported by simulations and field experiments. Results show that although both methods yield negligible bias under ideal conditions, CCFHT significantly reduces estimation variance in noisy or mismatched scenarios. These findings confirm the advantages of CCFHT for achieving robust and precise vehicle speed estimation using low-cost PIR sensor systems, and provide insights into practical deployment within ITSs.