A High-Frequency Vibration Error Compensation Method for Terahertz SAR Imaging Based on Short-Time Fourier Transform

High-frequency vibration error of a moving radar platform easily introduces a non-negligible phase of periodic modulation in radar echoes and greatly degrades terahertz synthetic aperture radar (THz-SAR) image quality. For solving the problem of THz-SAR image-quality degradation, the paper proposes a multi-component high-frequency vibration error estimation and compensation approach based on the short-time Fourier transform (STFT). To improve the robustness of the method against noise effects, STFT is used to extract the instantaneous frequency (IF) of a high-frequency vibration error signal, and the vibration parameters are coarsely obtained by the least square (LS) method. To reduce the influence of the STFT window widths, a method based on the maximum likelihood function (MLF) is developed for determining the optimal window width by a one-dimensional search of the window widths. In the case of high noise, many IF estimation values seriously deviate from the true ones. To avoid the singular values of IF estimation in the LS regression, the random sample consensus (RANSAC) is introduced to improve estimation accuracy. Then, performing the STFT with the optimal window width, the accurate vibration parameters are estimated by LS regression, where the singular values of IF estimation are excluded. Finally, the vibration error is reconstructed to compensate for the non-negligible phase of the platform-induced periodic modulation. The simulation results prove that the error compensation method can meet THz-SAR imaging requirements, even at a low signal-to-noise ratio (SNR).

Vibration Error Correction for the FOGs-Based Measurement in a Drilling System Using an Extended Kalman Filter

Fiber-optic gyroscopes (FOGs)-based Measurement While Drilling system (MWD) is a newly developed instrument to survey the borehole trajectory continuously and in real time. However, because of the strong vibration while drilling, the measurement accuracy of FOG-based MWD deteriorates. It is urgent to improve the measurement accuracy while drilling. Therefore, this paper proposes an innovative scheme for the vibration error of the FOG-based MWD. Firstly, the nonlinear error models for the FOGs and ACCs are established. Secondly, a 36-order Extended Kalman Filter (EKF) combined with a calibration method based on 24-position is designed to identify the coefficients in the error model. Moreover, in order to obtain a higher accurate error model, an iterative calibration method has been suggested to suppress calibration residuals. Finally, vibration experiments simulating the drilling vibration in the laboratory is implemented. Compared to the original data, compensated the linear error items, the error of 3D borehole trajectory can only be reduced by a ratio from 10% to 34%. While compensating for the nonlinear error items of the FOG-based MWD, the error of 3D borehole trajectory can be reduced by a ratio from 44.13% to 97.22%. In conclusion, compensation of the nonlinear error of FOG-based MWD could improve the trajectory survey accuracy under vibration.

Simultaneous Time-Varying Vibration and Nonlinearity Compensation for One-Period Triangular-FMCW Lidar Signal

Frequency modulation continuous wave (FMCW) Lidar inevitably suffers from vibration and nonlinear frequency modulation, which influences the ranging and imaging results. In this paper, we analyze the impact of vibration error coupled with nonlinearity error on ranging for FMCW Lidar, and propose a purely theoretical approach that simultaneously compensates for time-varying vibration and nonlinearity in one-period triangular FMCW (T-FMCW) signals. We first extract the localized characteristics of dechirp signals in time-frequency domain by using a second-order synchro-squeezing transform (second-order SST), and establish an instantaneous ranging model based on second-order SST which can characterize the local distributions of time-varying errors. Second, we estimate the nonlinearity error by using time-frequency information of an auxiliary channel and then preliminarily eliminate the error from the instantaneous measurement range. Finally, we construct a particle filtering (PF) model for T-FMCW using the instantaneous ranging model to compensate for the time-varying vibration error and the residual nonlinearity error, and calculate the range of target by using triangular symmetry relations of T-FMCW. Experimental tests prove that the proposed method can accurately estimate the range of target by compensating for the time-varying vibration and the nonlinearity errors simultaneously in one-period T-FMCW signal.

The Accuracy of the Navigational Accelerometer with a Nonlinear Metrological Model in Operating Conditions

A mathematical model of the error of the navigational accelerometer caused by the nonlinearity of its metrological model, taking into account the influence of vibration, was developed. The method of experimental estimation of the vibration error based on the developed model was proposed. The main idea of the method is to evaluate parameters of the developed model during static tests in the terrestrial gravitational field and to calculate error according to the specific vibration characteristics – the amplitude in the case of harmonic vibration profile or the frequency band and the power spectral density in the case of random vibration. The effectiveness of the proposed method has been tested using three types of navigation accelerometers in comparison with the results of classical dynamic testing in various vibration conditions (harmonic, white noise, etc.).

A Novel High-Frequency Vibration Error Estimation and Compensation Algorithm for THz-SAR Imaging Based on Local FrFT

Compared with microwave synthetic aperture radar (SAR), terahertz SAR (THz-SAR) is easier to achieve ultrahigh-resolution image due to its higher frequency and shorter wavelength. However, higher carrier frequency makes THz-SAR image quality very sensitive to high-frequency vibration error of motion platform. Therefore, this paper proposes a novel high-frequency vibration error estimation and compensation algorithm for THz-SAR imaging based on local fractional Fourier transform (LFrFT). Firstly, the high-frequency vibration error of the motion platform is modeled as a simple harmonic motion and THz-SAR echo signal received in each range pixel can be considered as a sinusoidal frequency modulation (SFM) signal. A novel algorithm for the parameter estimation of the SFM signal based on LFrFT is proposed. The instantaneous chirp rate of the SFM signal is estimated by determining the matched order of LFrFT in a sliding small-time window and the vibration acceleration is obtained. Hence, the vibration frequency can be estimated by the spectrum analysis of estimated vibration acceleration. With the estimated vibration acceleration and vibration frequency, the SFM signal is reconstructed. Then, the corresponding THz-SAR imaging algorithm is proposed to estimate and compensate the phase error caused by the high-frequency vibration error of the motion platform and realize high-frequency vibration error estimation and compensation for THz-SAR imaging. Finally, the effectiveness of the novel algorithm proposed in this paper is demonstrated by simulation results.