Improved variable step adaptive filtering algorithm and its application in time delay estimation for continuous wave dual-sensor pulse signals

Abstract

Continuous wave mud pulse transmission is crucial for wireless logging, but surface pump noise disrupts upstream mud pulses, hindering downhole information extraction. At a theoretical level, the dual-sensor differential denoising approach is an excellent technology for suppressing pump noise, but precisely identifying the time delay, which has a considerable impact on the denoising effect, remains a challenge. This paper provides an improved variable step-size adaptive time delay estimation method TVSS-LMSTDE to address this issue. Iteration time regulates the change in step size. The preset adjustment principle states that modifying parameters ζ and γ controls the learning features of step size. A series of stable and erratic dual-sensor continuous wave mud pulse signals interfered by various noise intensities are created in the simulation, and the performance of three different variable step-size technologies—error-oriented, nonlinear relationship, and iterative time regulation—in terms of convergence speed, estimation stability, and calculation amount are compared and analyzed. The results show that the iterative time regulation technique produces a minimal mean square error in time delay estimate, with generally steady estimation and excellent accuracy. When applied to hydraulic cycle tests, the technique accurately gets the time delay value of dual-sensor signals, giving critical support for the successful recovery of mud pulse data severely disrupted by pump noise.