Application and Optimization of Wavelet Transform Filter for North-Seeking Gyroscope Sensor Exposed to Vibration

1. Introduction

A gyro total station (gyrotheodolite) is a north-seeking instrument that combines a gyroscope sensor and total station (theodolite), which can measure true geographical azimuths in narrow spaces where satellite signals cannot be received [ 1 2 ]. The technology of the north-seeking gyroscope is widely used in the fields of breakthrough measurement of super-long tunnels, indoor positioning systems and quick orientation of mobile missile sites [ 3 5 ].

During orientation measurement in a tunnel, gyro data are not only affected by the constant and random drift errors of the sensor but also the external environmental factors, such as blasting, construction vibration, air draft-induced vibration of passing vehicles [ 6 7 ], magnetic field interference, and changes in temperature, humidity and air pressure [ 8 9 ]. These interference factors (especially physical vibration) cause abnormalities of the gyro signal, which contains significant non-stationary noise, leading to distortion of the orientation results [ 10 ].

The wavelet transform (WT) proposed by Morlet is a signal analysis and filtering method with high resolution in both the time and frequency domains [ 11 ], which has applicability in processing non-linear and non-stationary data. The basic idea is to use a window function to construct a basis function for orthogonal transformation [ 12 ]. The signal is decomposed into a series of wavelet coefficients, including high-frequency and low-frequency coefficients, by choosing an appropriate wavelet function. The high-frequency coefficients are limited according to the corresponding threshold criteria, and then reconstructed with low-frequency coefficients to achieve the purpose of de-noising and correction [ 13 14 ]. With the development of the WT filter, the application field has been greatly expanded to include biomedicine [ 15 17 ], geophysics [ 18 19 ], image processing [ 20 21 ], tracking detection [ 22 24 ], and feature extraction [ 25 27 ]. The wavelet filter also has precedents for signal processing of gyroscope sensors of the strapdown inertial navigation system (SINS) used for attitude determination, such as the fiber optic gyroscope (FOG) [ 28 29 ] and micro electro mechanical system (MEMS) gyroscopes [ 30 31 ], for which good application results have been achieved in previous studies [ 32 35 ]. However, the widely-used suspension tape gyroscope sensor is limited by the tracking north-seeking mode of collecting scattered points, which cannot easily simulate the changeable environment in real-time. Since there are fewer redundant observations of this north-seeking mode, the application effect of the filtering model is not significant [ 10 ].

An innovative new type of north-seeking gyroscope, the magnetic levitation gyroscope (GAT), developed by the Chang’an University and China Space Age Electronics 16th Research Institute in 2008, adopts a magnetic suspension-supporting and non-contact photoelectric technology to measure the true geographical azimuth (the nominal orientation accuracy is 3.5″ in 8 min) [ 36 ]. The GAT has the capacity to dynamically record large amounts of north-seeking parameters in real-time, which allows monitoring of a changing environment (40,000 groups of observed signals per orientation result). It is possible to optimize the non-stationary gyro data with modern filtering technology and extract the effective components from the noisy signals, thus improving the north-seeking orientation accuracy [ 37 ]. Since 2008, the GAT has been widely used in several major underground engineering projects in China and provided reliable orientation checks for the breakthrough of the tunnels, such as in the cases of the Qinghai–Tibet Railway Tunnel [ 38 ], the Hanjiang River Diversion to Weihe River Qinling Water Conveyance Tunnel [ 39 ], and the Immersed Tunnel of the Hong Kong-Zhuhai-Macao Bridge [ 10 ].

However, there are some problems in the application of the WT filter to GAT data correction and de-noising: (1) The filters applicable for FOG and MEMS have less effect on the application of the GAT since their observed signal distribution characteristics are different [ 10 ]. (2) Some researchers suggested that the optimal decomposed level is 5 for the gyro signal [ 40 ], while others considered that the decomposed level of 10 is a better choice [ 28 42 ], but the reasons for these choices were not given. Practices indicated that WT filtering for GAT cannot provide a good de-noising effect with these decomposed levels [ 37 ]. (3) Several previous studies used computer-simulated signals to verify the effect of the filtering model, which lacked verification by actual observed data. Metrics such as signal-to-noise ratio, mean square error, smoothness and correlation coefficient are often used to evaluate the quality of the filtering model [ 35 ], while less attention has been paid to investigating the relationship between the variation of these metrics and the wavelet decomposed level.

To solve the above problems and improve the robustness and environmental adaptability of the GAT exposed to vibration, based on the WT and time-frequency analysis theory [ 11 ], a filter adapting to GAT data was designed. In our research the observed signals of the GAT were collected under the conditions of wind-induced vibration and ground vibration caused by vehicles passing. By comparing the difference between the filtered (and unfiltered) orientation results and the relative true north azimuth (high-precision Global Navigation Satellite System (GNSS) baseline established in the experimental area, with an orientation accuracy better than 0.5″), we determined the optimal wavelet decomposed level suitable for GAT data affected by different environmental factors, and a field experiment was carried out to verify the feasibility of our study.