Research on Velocity Measurement Method of Targets Inside Tubular Structures Based on STFrFT-IG

To address the critical issues in target velocity measurement inside tubular structures using microwave interferometers—including low signal-to-noise ratio (SNR) of microwave interference echo signals and severe degradation of measurement accuracy induced by harsh working environments such as strong interference, intense vibration and heavy impact—this paper proposes a signal processing method for in-tubular-structure velocity measurement based on the short-time fractional Fourier transform (STFrFT) and information geometry (IG). First, the echo signals acquired by the microwave interferometer are preprocessed via trend term elimination and wavelet denoising. Subsequently, the STFrFT is adopted for time-frequency analysis. Instantaneous frequencies of targets inside the tubular cavity are extracted by means of parabolic interpolation and frequency tracking techniques, and the initial velocity of the in-cavity targets is calculated in accordance with the Doppler principle. Furthermore, the time-frequency amplitude spectrum obtained from STFrFT is mapped into a probability distribution, and the extracted trend term of radar echoes is taken as the reference distribution. An optimized algorithm framework is constructed based on the Kullback-Leibler (KL) divergence and Fisher information matrix. The natural gradient descent algorithm is utilized to iteratively calibrate the initial velocity curve of targets within the tubular structure, ultimately realizing high-precision velocity measurement of internal targets. Results of both simulation experiments and measured signal processing demonstrate that the proposed method achieves superior time-frequency resolution and anti-interference capability under low-SNR conditions compared with conventional short-time Fourier transform (STFT) and Wigner-Ville distribution (WVD) algorithms. In simulation environments with an SNR of −10 dB, the mean absolute error and standard deviation of the proposed algorithm are reduced by 26.7% and 26.4%, respectively, relative to the standalone STFrFT method. Moreover, the practical velocity measurement accuracy inside actual tubular structures exceeds 0.030%. This work provides a methodological reference for measuring motion parameters of targets inside tubular structures under complex harsh environments.