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.

This paper proposes a physics-informed identification framework for the spatial and dynamic responses of dual-element pyroelectric infrared (PIR) sensors using variable circular-aperture excitation. The dynamic half is carried through to experimental identification, while the spatial half is carried only to the reference-pose location, so the joint estimation is proposed rather than demonstrated. The spatial response is modeled as a bipolar differential kernel composed of a pose-dependent optical mapping, an optical envelope with a spatial scale factor, two smoothed rectangular sensing-element footprints, and a small antisymmetric residual correction. Sinusoidal modulation of the aperture radius leads to a complex first-harmonic frequency-domain model relating the measured response to aperture radius, modulation amplitude, pose setting, and excitation frequency. Rather than being assumed, the dynamic structure is identified from a 40-point frequency sweep spanning 0.0999 to 4.0453 Hz. A compact two-time-constant differentiating model leaves a root-mean-square log-magnitude error of 15.1%, with a maximum log-magnitude deviation of 48.4% (62% in relative amplitude). A structure with two zeros at the origin and four poles reproduces the same measurement to 0.71% root-mean-square. Its poles are an underdamped complex pair at 0.2126 Hz with damping ratio 0.899 and real poles at 0.5023 Hz and 2.9672 Hz. The additional zero and pole are tentatively attributed to the AC-coupled conditioning stage. Evaluated at this identified operating point, the scaled Jacobian of the dynamic block is full column rank with cond(J_s) = 75.8, and Cramér–Rao bounds agree with residual-bootstrap intervals to within ten per cent on every parameter. A greedy D-optimal selection retains 61.6% of the information of the full sweep from ten frequencies, whereas the originally proposed excitation grid attains only 13.8% because it does not sample the band containing the identified pole pair. Restoring the excitation phase reference increases the Fisher determinant by a factor of 130. A structured estimation procedure is also formulated, in which the residual coefficients are updated through a regularized linear least-squares subproblem within a staged optimization exploiting the disparate conditioning of the spatial and dynamic blocks. It has not yet been executed on a joint aperture–pose–frequency data set.