Complex analytic signals applied on time delay estimation

Abstract

In this paper, we present the concept of the time delay estimation based on the transformation of real sensor signals into analytic ones. We analyze the differential time delay values obtained using real seismic signals, simulated complex analytic signals and simulated complex analytic signals with real parts coming from real seismic signals. The simulation results indicate that the application of complex analytic signals leads to reliable computation of the differential time delay. The influence of specific signal parameters on spectral coherence threshold in systems for passive localization and proposed methods for lowering the threshold is analyzed. The computation of all differential time delays with respect to the reference sensor (geophone) is based on the application of Generalized Cross-Correlation (GCC) applied on corresponding analytic signals. The difficulties to select a peak of cross-correlation function that corresponds to true differential time delay when dealing with real signals are significantly reduced if GCC is applied on analytic signals. The efficiency of the proposed technique on differential delay estimation is performed on deterministic and real-life signals.U ovom radu je prezentovan koncept izracunavanja diferencijalnog kasnjenja koji je zasnovan na transformaciji realnog senzorskog signala u analiticki. Analizirane su vrednosti dobijenih diferencijalnih kasnjenja za realni seizmicki signal, simulirani kompleksni analiticki signal i simulirani kompleksni analiticki signal ciji realni deo odgovara akviziranom realnom signalu. Simulacioni rezultati pokazuju da se primenom kompleksnog analitickog signala dobijaju pouzdanije vrednosti diferencijalnog kasnjenja. Analiziran je uticaj specificnih parametara signala na prag koherence u sistemima za pasivnu lokalizaciju i preporuceni su metodi za njeno snizavanje. Diferencijalno vreme kasnjenja je odredjeno u odnosu na referentni senzor (geofon) primenom GCC metoda nad analitickim signalima. Poteskoce oko odredjivanja pika kroskorelacione funkcije kod realnih signala, koji odgovara tacnom diferencijalnom kasnjenju, su znatno redukovane primenom GCC metoda nad analitickim signalima. Efikasnost predlozene tehnike je ispitana na deterministickim i realnim signalima.