Physics-Informed Identification of Spatial and Dynamic Responses of Dual-Element Pyroelectric Infrared Sensors Using Variable Circular-Aperture Excitation

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(Js) = 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.