Mud pulse measurement-while-drilling technology is a core key technology for real-time dynamic transmission of downhole engineering parameters and formation geological parameters, providing real-time data support for drilling geosteering, dynamic optimization of drilling operation parameters, and efficient development of oil and gas resources. However, the drilling fluid transmission channel has long been subject to superimposed interference from periodic pump noise and broadband random noise, which can easily obscure weak effective downhole pressure pulse signals, reduce pulse signal identification accuracy and telemetry data decoding reliability, and constrain the field application effectiveness of measurement-while-drilling systems. To address the technical deficiencies of traditional single filtering algorithms under complex drilling conditions such as pump frequency fluctuations and low signal-to-noise ratios, including insufficient noise suppression and susceptibility of effective signals to distortion and damage, this article proposes a multi-stage combined filtering algorithm for mud pulse signal processing. The algorithm adopts a hierarchical and progressive denoising architecture. Firstly, a bandpass filter is used for signal preprocessing to remove low-frequency baseline drift and high-frequency random noise from the signal. Secondly, based on real-time pump rotational speed information, a cascaded notch filter is constructed to dynamically track and suppress the fundamental frequency of the pump body and interference from its various harmonics. Finally, a correlated matched filter is introduced to enhance the detailed features of the pulse signal and improve pulse signal detection precision and identification accuracy. Field drilling test results show that in a 4 000 m deep well drilling test, the decoded sequence of the algorithm is highly consistent with the actual encoding, and the bit error rate was reduced is 2.1%. The algorithm can effectively filter out pump noise line-spectrum interference and clearly extract pulse signals. In the time-varying and non-stationary complex noise environment of drilling sites, the algorithm exhibits excellent robustness, can improve the data transmission reliability of mud pulse telemetry systems, and has high engineering application value and promotion prospects.