The very accurate time-of-arrival (TOA) extraction is significantly impacted by the complicated space-time structure of the civil aviation S-mode transponder signal, which is also vulnerable to neighboring electromagnetic interference and transmission link nonlinearities. Based on the air-time structure and spectral analysis of the civil aviation S-mode transponder signal, a quasi-S-mode signal definition model is proposed to simplify the pulse structure of the S-mode signal, and a simplified Volterra level model is constructed based on the quasi-S-mode signal, the kernel function of the inversion constraints of the weak nonlinear system characteristics. Simulation results show that the kernel function gain multiplier of the simplified Volterra level model based on the quasi-S-mode signal is not less than 27 times. Finally, the quasi-S-mode recovery of an interfered S-mode signal with a measured signal-to-noise ratio of about 13 dB is achieved by using a combination of the 3rd-order simplified Volterra level model and spectral compensation at high sub-frequency points, and the waveform recovery error of about 1.54% is obtained with the computation of about 8.8% of the standard S-mode signal model. Additionally, the accuracy of the recovered signal is improved by more than 73% over the TOA extracted from the disturbed signal. Consequently, the reduced Volterra level model of quasi-S-mode signal based on kernel function constraints has significant theoretical significance for improving localization accuracy and accurately estimating the arrival time of S-mode signals in civil aviation.

To improve the wide area multilateration (WAM) accuracy when receiving S-mode baseband signals with low signal-to-noise ratio (SNR), a joint time of arrival (TOA) estimation algorithm based on non-coherent integration was proposed.According to the correlation characteristics of target reply signals during the beam scanning dwell time of the secondary surveillance radar (SSR), a low SNR baseband pulse signal rising edge estimation method with a four-pulse matched filter and amplitude squared operation and accumulation was proposed, which effectively improved the TOA estimation accuracy of S-mode baseband signals with a low SNR ranging from −15 dB to 5 dB. The Monte Carlo simulation results show that the root mean square error (RMSE) of TOA estimation by using the joint algorithm is less than 25 ns for S-mode signals with a low SNR ranging from −15 dB to 5 dB. For non-ideal S-mode baseband signals, when the SNR is as low as −15 dB, the TOA estimation accuracy of the joint algorithm after the non-coherent integration of five pulses can reach 22.245 ns, which is much better than the WAM requirement.