@ARTICLE{Duda_Krzysztof_Vehicle_2024,
 author={Duda, Krzysztof and Marszalek, Zbigniew},
 volume={vol. 31},
 number={No 4},
 pages={781–796},
 journal={Metrology and Measurement Systems},
 howpublished={online},
 year={2024},
 publisher={Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation},
 abstract={Inductive loop (IL) sensors are permanently installed in road to create output signals for the evaluation of vehicle magnetic profiles (VMPs) as vehicles pass over them. VMPs are acquired using a multi-frequency impedance measurement (MFIM) system equipped with advanced electronic, signal processing, and data management capabilities. Vehicle speed is calculated by measuring the time shift (delay, lag) between VMPs obtained from two distant IL sensors. The cross-correlation sequence (CCS) estimate is a widely accepted method for estimating time shifts that are integer multiples of the sampling period, i.e., the time resolution of the CCS is limited by the sampling period. In this paper, we present a fully operational MFIM system equipped with two wide and two slim IL sensors.We apply the Discrete Fourier Transform (DFT) to estimate fractional time shifts, i.e. we obtain a time resolution higher than the sampling period. Field measurement signals demonstrate that the proposed application of the DFT for fractional shift estimation offers higher accuracy, lower computational complexity, and better noise immunity compared to the CCS-based estimation. For shortduration signals, the DFT-based shift estimation is unbiased, while the CCS is a biased time-shift estimator.},
 title={Vehicle speed determination with inductive-loop technology and fast and accurate fractional time delay estimation by DFT},
 type={Article},
 URL={http://czasopisma.pan.pl/Content/134230/09_2k.pdf},
 doi={10.24425/mms.2024.152048},
 keywords={cross-correlation sequence, discrete Fourier Transform, fractional delay FIR filter, fractional shift estimation, inductive loop, multi-frequency impedance measurement, time shift, vehicle magnetic profile},
}