Reliable dynamic monitoring of bridges with integrated GPS and BeiDou

: GPS (Global Positioning System) in recent years has been widely used for the measurement of deflections of bridges. However, due to multipath and satellite signal obstructions, caused by towers, cables and passing vehicles, the reliability of deformation monitoring with GPS is still a problem. Recent research with respect to multi-GNSS (Global Navigation Satellite System) technology, though, have proved to enhance satellite visibility and availability for positioning, navigation and timing (PNT) for users. Its benefits involving application in bridge monitoring are still rarely studied. In this paper, we propose a composite strategy where integrated GPS and BDS (BeiDou Navigation Satellite System) dual-frequency carrier phase data processing is carried out to improve the reliability of bridge monitoring with GNSS measurements. In addition, SNR (signal-to-noise ratio) based stochastic model and post-fit residual editing strategies are utilized to enhance the reliability further. In a group of fixed point experiments, improvements of 20% to 30% in precision were achieved with the integrated GPS and BDS compared to GPS-only results. Based on the real GPS and BDS measurements collected on the Baishazhou Yangtze River Bridge in China, we assessed the performance of the proposed method. In the vibration experiment, no apparent effects on natural frequencies identification were found by introducing BDS into the solution at ideal observation environment. However, the combined GPS and BDS results seem to be much more promising, with lower background noise. Meanwhile, the integrated GPS and BDS data processing with post-fit residual editing and SNR-based stochastic model strategies can effectively deal with satellite signal obstruction and the influence of multipath effect to attain reliable dynamic deformation monitoring information for bridges.


Introduction
Global Positioning System (GPS) as a technique that was developed from 1970s, has gradually become a major means used in structural bridge deformation monitoring in recent years, due to its continuous, all-weather, automated and highly accurate measurement services. With the continuous development of hardware and software, especially the increasing sampling rate, GPS begins to show its unique advantages in the aspect of the bridge dynamic monitoring (Meng et al. 2007). In the last years, a large number of achieves on deformation monitoring of structural bridges using GPS has Multipath effect and signal diffraction results from obstructions can also degrade the precision and accuracy of GPS or produce unreliable and even failure of monitoring results, and can adversely affect the ambiguities resolution in data processing (Wang et al. 2017). Some literatures reported using fusion of GPS and GLObal NAvigation Satellite System (GLONASS) data could enhance the number of tracking satellites and geometry, and using sidereal filter or analogous methods could deal with multipath. Nevertheless, due to the frequency division multiple access (FDMA) signal mode of GLONASS system, the ambiguity of GLONASS is difficult to be fixed (Li and Zhang 2014). The dynamic multipath caused by passing vehicles cannot be eliminated by a sidereal filter or other types of digital filters (Moschas and Stiros 2014). In case of severe multipath, the ambiguity parameters tend to be fixed to wrong integer values, which will probably induce biases in the monitoring results. The large noise, at the same time, can over flood the true movement and limit the GPS vibration monitoring in model frequencies identification. Hence, these issues are still critical in dynamic deformation monitoring of the bridge with GPS.
Fortunately, except for the GPS and GLONASS system, BeiDou Navigation Satellite System (BDS) and Galileo (satellite navigation) are in the process of providing global coverage services.
Better signal quality, similar Code division multiple access (CDMA) mode and different constellations provided by BDS and Galileo can be a way to enhance satellite visibility and availability for positioning, navigation and timing (PNT) for users (Yang et al. 2011).
BDS is a global satellite navigation system, which is independently developed, deployed, and operated by China and still in progress until to 2020 (Yang et al. 2011;Shi et al. 2012). Up to now, there are 23 satellites in BDS constellation and it is capable of providing PNT services in Asia-Pacific Region. Three constellation types of BDS satellites are considered, including Geostationary Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO). The geodetic reference system used by BDS is the China Geodetic Coordinate System 2000 (CGCS2000), and its definition is: the origin is located at the mass center of the earth, the Z-axis is in the direction of the IERS Reference Pole (IRP), the X-axis is directed to the intersection of IERS reference meridian (IRM) and the plane passing through the origin and normal to the Z-axis. The Yaxis, together with Z-axis and X-axis, constitutes a right-handed orthogonal coordinate system. It is an earth-centered earth-fixed (ECEF) system. The origin of the CGCS2000 system is also the geometric center of the CGCS2000 ellipsoid, and the Z-axis coincides with the semi-minor axis of the CGCS2000 ellipsoid. The parameters of the CGCS2000 ellipsoid and WGS-84 (World Geodetic System 1984) are as Table 1. As can be seen, only is slight different between the two ellipsoids. According to Gao et al. (2012), the differences of between the two ellipsoids can be ignored for short baseline RTK positioning, and the coordinate difference between BDS and GPS systems can be neglected.

Observation model
In the most general terms of using GPS or BDS for SHM of bridges, monitoring stations located at the feature points of bridges, and one or more reference stations are set at stable points, not far from the bridge. In operation, these stations receive the satellite signal simultaneously and the data processing software will process the data in real-time. In GPS or BDS observations, as pseudorange is easily contaminated by multipath and hardware delays, biases are significant.
Therefore, in our data processing module, we only use the dual-frequency carrier phase observations.
The pseudorange observations are used to calculate the receiver clock error in the stage of getting satellite positions and cycle slip detection (Liu 2013). For a satellite i observed by receiver p , the dual-frequency GPS or BDS phase observation model can be presented as follows: 1, 1, where L is the carrier phase observation;  is the geometric distance between satellite i and receiver p ; c is the speed of light; p dt and i dt are the clock errors of receiver and satellite, respectively; Since the baselines are usually short (usually < 5 km), double difference (DD) method can eliminate the satellite-dependent terms (such as satellite clock offsets, receiver clock errors and carrier phase hardware delay) and the distance-dependent terms (such as tropospheric and ionospheric delay). Then, with reference station q and pivot satellite j , the DD models can be read: where  operator represents the two-station DD between two observed satellites. For the purpose of fast ambiguity fixing, the ambiguity parameters of second frequency (N2) can be represented as the combination of first frequency (N1) ambiguity and wide-lane (WL) ambiguity After the linearization and considering Eq. (3), Eq. (2) is reorganized in matrix form as ij pq  is the geometric distance calculated by provided stations' initial coordinates and l  is the Observations minus Computations (OMC) terms of dual-frequencies, X denotes the baseline component parameters. G is the corresponding geometry matrices containing the satellite-to-receiver unit vector.
As for GPS and BDS system, they both apply CDMA technology. The model described above is available for the two GNSS systems. Let SG and SC denote the number of GPS and BDS satellites that are tracked by the two receivers. Since GPS and BDS do not share common frequencies, the where 2 e denotes the two vectors of ones. (5) is assumed as a zero-mean Gaussian noise with the covariance matrix lb Q Q Q 

Stochastic model
 is the oneway covariance for carrier phase observations.
In GNSS data processing, elevation-dependent stochastic models are often used to weight undifferenced phase noise. It assumes the effects of multipath as well as atmospheric errors are elevation-dependent. However, in bridge monitoring, the serious multipath and signal diffraction effect often occurred even in high elevation satellites, due to the obstructions, such as towers, cables and passing vehicles, around the antenna. Fortunately, the power of a GNSS signal is a measurement of its quality. One way of expressing the GNSS signal power, used by most receiver brands, is the carrier-to-noise power-density ratio (C/N0). It is the ratio of the signal carrier to noise power in a 1-Hz bandwidth Hartinger and Brunner 1999). The SNR-based weight scheme (i.e. SIGMA-∆ model) is reasonable for the one-way carrier phase observations. Therefore, in order to reduce the influence of high multipath effect, the one-way covariance can be calculated as: where the factor C consists of the carrier loop noise bandwidth and a conversion term from cycle 2 to mm 2 . In this paper, for first frequency C = 0.00224 m 2 and second frequency C = 0.00077 m 2 , as mentioned in Dai (2008). Normally, the value of 0  is selected to 3 mm for GPS and BDS carrier phase observations (Amiri-Simkooei and Tiberius 2007).

Parameter estimation
A Kalman filter is applied for parameter estimation in this study, because it is efficient and suitable for real-time positioning with a large number of states and observations. The state vector k X contains coordinates of monitoring station and the ambiguity parameters at epoch k . Based on the cooperative dynamic model, the matrix form of the system state equation is given by is the state transition matrix. In this paper, it is an identity matrix.
F is the coefficient matrix of system noise, and k w is the system noise vector.
Because the pseudorange measurements are not used in this paper, the prior covariance matrix constraints for the coordinate and ambiguity parameters, must be given, that is where p  is the initial prior standard deviation for baseline component parameters. Normally, the initial position of monitoring station is set to its approximate coordinate. The initial prior standard deviation should be set according to the accuracy of the approximate coordinate. The initial values of ambiguity parameters were zero and the initial prior standard deviations were set to 100 cycles, assuming the large number part of ambiguities had been removed by Geometry-Free (GF) and Melbourne-Wübbena (MW) combinations (Chen 1998).

Ambiguity fixing strategy and post-fit residual editing
After parameter estimating with a Kalman filter, the coordinate parameters with float ambiguities can be obtained. Then the least-squares ambiguity decorrelation adjustment (LAMBDA) method will be applied to fix the ambiguities (Teunissen, 1995). Since the long wavelength for WL ambiguities, in this paper, the GPS and BDS WL ambiguities will be fixed together forward and then the N1 ambiguities. In order to ensure the ambiguity resolution (AR) reliability, the solved integer ambiguities will be validated with the well-known ratio test. The threshold is set to 2.0 as many scholars did.
However, during the data processing, the multipath effect resulting from passing vehicles and stay-cables may be serious in some cases. The ambiguities may pass the ratio test and be fixed to an incorrect integer value. In this case, we will get the wrong baseline estimation. In this paper, a post-fit residual editing strategy is employed to test the validity of the fixed ambiguities. If the postfit residuals after ambiguity resolution surpass 0.35 (empirical value), the corresponding ambiguities will be set to unfixed and reprocess the data at current epoch (Deng et al. 2014).
Beside the method mentioned previously, additional processing options should be taken care are listed in Table 2. Table 2 Additional data processing models and strategies used in this paper.

Options Processing Strategy
Ephemeris GPS and BDS broadcast ephemeris

Ambiguity resolution performance analysis
In this section, a group of GPS and BDS data collected from two short baselines formed by a  It shows that the percentage of epochs with correctly resolved WL and NL ambiguities are all around 95% when the threshold is set to 2. The GPS+BDS system is slightly higher than the BDSonly and GPS-only counterparts. Meanwhile, over 90% epochs whose WL ambiguity ratio is greater than 5 and 10 for BDS-only and GPS+BDS systems. However, the GPS-only system shows a slightly lower percentage. After WL ambiguities are correctly resolved, approximately 90% epochs can fix the NL ambiguities with a high ratio value. Therefore, for short baselines, if there are no obvious shelters around the station, GPS and BDS ambiguities can be easily fixed, with about 95% single-epoch ambiguity success rate for ratio threshold of 2.

Precision analysis
As a matter of fact, in GPS and BDS data processing, once the ambiguities are reliably fixed, the integer ambiguities will be passed to the following epochs until the cycle slip occurs. Then, the fixed solutions are achieved. Fig 3 presents Table 3. From STD values, the precision of BDS-only results is worse than that of GPS-only, and the GPS+BDS results show the highest precision, with better than 2 mm in horizontal component and 5 mm in vertical component, and compared with GPS-only results, the precision is improved by about 20%-30% in all directions. As known, the precision improvement is profit from more observations and the enhancement of satellite geometry.   It should be noticed that, the observed satellite numbers for GPS and BDS are at the same level during the whole day. However, BDS shows a higher PDOP value than GPS.

Bridge experiments and results analysis
The GNSS observations used in this paper were collected from the Baishazhou Yangtze River  hours. The sampling rate for each site is set to 10 Hz and the elevation cutoff angle is 10°. The details of the monitoring stations are given in Table 4.

Vibration monitoring
In dynamic monitoring of bridges, deflections and modal frequencies of the middle span and Hanyang Wuchang supporting towers are important parameters for cable-stayed or suspension bridges. In this paper, two stations were mounted at the both side of the middle span (S012 and S035) and another two located at top of the towers (S023 and S029). To validate the performance of the method proposed above in vibration monitoring, we used the GNSSDEM software to process the data of BDS-only, GPS-only, and GPS+BDS separately of the four stations for one hour (12:00-13:00, September 27 th 2016). Before the data processing, GAMIT software was applied to obtain the initial coordinate of the reference station. The initial coordinates of monitoring stations were then calculated by code differential positioning with the code measurements of the reference station and monitoring stations.
Since the baseline is short, the accuracy of code differential positioning can achieve to decimeter level. However, the monitoring stations are always moving, and always within 5 m. Then, we set the initial prior standard deviation of the coordinate of monitoring stations to 5 m.

Availability and reliability
As mentioned in Section 1, towers, intensive cables and passing vehicles beside the monitoring stations can obstruct GNSS signals. The obstructions mainly cause severe multipath effect, signal diffraction and satellite exclusion, which will adversely affect the performance of GNSS deformation monitoring in the aspect of availability and reliability. In this section, an example of obstruction test will be given to validate the performance of the proposed method. As previously discussed, the multipath effect and signal diffraction could also be severe in bridge monitoring environment. Fig 11 presents   / sin ( ) mm   (13) where m is set to 3 mm and  is elevation angle. Therefore, we know that the contribution of BDS can increase the satellite visibility and enhance the satellite geometry. The availability and reliability of bridge monitoring at obstruction environment can be effectively improved with SNR stochastic model and the post-fit residual editing procedure.

Conclusions
In this study, in order to improve the reliability of GNSS-based bridge monitoring technology, an integrated GPS and BDS data processing method with specific strategies, such as SNR-based stochastic model and post-fit residual editing procedure, was proposed. At a group of fixed points, the ambiguity resolution and precision performance of the proposed method were assessed. The ambiguity success fixing rate of GPS-only, BDS-only and GPS+BDS data can achieve to approximately 95% within only one epoch when there are no shelters around the stations. Compared with GPS-only results, an improvement of 20% to 30% in precision can be achieved with GPS+BDS data. Based on the real bridge monitoring data, the proposed method was assessed. The results indicate that, the introduction of BDS into the solution has little effect on natural frequencies identification at ideal observation environment. However, the combined GPS and BDS results seem to be much more promising, with lower background noise. Meanwhile, integrated GPS and BDS data processing with the SNR-based stochastic model and post-fit residual editing strategies can effectively deal with the satellite signal obstruction and the influence of multipath effect on ambiguity resolution, to attain reliable dynamic deformation monitoring information for bridges.