Accelerometer-assisted GNSS method for real-time extraction of dynamic deflection of high-speed railway bridges

Abstract

The present invention discloses a method for extracting the dynamic deflection of a high-speed railway bridge in real time by using an accelerometer to assist GNSS. The method collects multi-system GNSS monitoring data and acceleration data on the high-speed railway bridge, establishes a single-difference residual sequence and a multipath error model, corrects the data of the next multipath repetition cycle, and eliminates the influence of the multipath error on the GNSS positioning result. For the extraction of high- and low-frequency dynamic displacements, correlation analysis is performed through the GNSS displacement sequence and the acceleration displacement sequence to extract the low-frequency displacement component, and finally reconstructs it with the acceleration displacement sequence to obtain the overall dynamic displacement sequence of the high-speed railway bridge. The method effectively improves the GNSS displacement positioning accuracy, and the acceleration data assists the GNSS data to effectively separate the high- and low-frequency displacements of the high-speed railway bridge, so as to obtain a more accurate overall dynamic displacement of the high-speed railway bridge. The method can realize the dynamic displacement monitoring of the high-speed railway bridge in real time, efficiently, and more accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a method for extracting the dynamic deflection of a high-speed railway bridge in real time by using an accelerometer to assist a GNSS. Background Art

[0002] In order to ensure the safe operation of high-speed railways, the entire high-speed railway line adopts a closed driving mode. Bridges account for a large proportion of high-speed railway lines, among which super-large bridges across rivers (railway bridges with a length of more than 500 meters) are key nodes for the safe operation of high-speed railways. These bridges have huge investments and play a vital role in the sustainable development of society and the national economy. The current prominent problem is that many large bridges are built too fast, and the design regulations and their assumed structural design parameters have not been fully and completely checked; in addition, geological disasters frequently occur in some areas, resulting in frequent bridge collapse accidents. Therefore, monitoring the structural health of bridges along the high-speed railway is very important to ensure the safe operation of high-speed railways and feedback bridge design parameters.

[0003] The dynamic deflection of the bridge structure directly reflects the dynamic change of the deflection of the beam under the action of the moving load. Through the dynamic deflection time history curve obtained in the bridge load test, the impact coefficient reflecting the dynamic response of the bridge can be calculated; in the process of implementing bridge health monitoring, the long-term and continuous dynamic deflection change obtained can assist in bridge maintenance and design. Therefore, it is very important to monitor the dynamic deflection deformation of high-speed railway bridges under loads such as high-speed trains, wind, temperature, water flow and even earthquakes. There are many methods for measuring bridge deflection. The precision leveling elevation method uses a level to regularly measure the level elevation of the bridge deck monitoring points, and the elevation change reflects the deflection of the main beam. It has high accuracy, but it has disadvantages such as time-consuming and labor-intensive, interrupting traffic, and poor real-time performance. The connecting pipe deflection monitoring method is based on the principle of the liquid level in the connecting pipe. By monitoring the changes in the liquid level in the connecting pipe, the changes in the bridge deflection are converted. It has the advantages of large monitoring range, high accuracy, and not being affected by the harsh actual environment. It has received widespread attention in recent years, but it has problems such as monitoring lag and poor dynamic performance. The ultra-high precision total station monitoring method uses a motor-driven robot total station to scan the bridge monitoring points in turn to obtain the bridge deformation, which can be used for static and dynamic load detection tests of the bridge. It is applied to the dynamic deflection monitoring of large-span bridges, but has the disadvantages of high cost, great environmental impact, and The laser projection method uses the collimation of the laser to install a target at the monitoring point of the bridge, and calculates the dynamic deflection of the bridge by calculating the coordinates of the laser projection. It has high sampling speed and high monitoring accuracy, but it is easily disturbed by the on-site environment of the bridge, and the cost is high. It must have line of sight, and it is difficult to be widely used in real-time deflection monitoring of large bridges. The ground-based interferometric radar technology developed in recent years can obtain the law of change of dynamic deflection of bridges, but there are still problems such as accuracy limited by conversion models, monitoring limited by line of sight conditions and operating distance, high cost, inability to provide absolute displacement, and discontinuous observation data, making it difficult to use for daily operation monitoring.

[0004] The real-time differential technology of the Global Navigation Satellite System (GNSS) can automatically obtain the dynamic displacement information of deformable bodies in real time and with high accuracy around the clock, without being restricted by line of sight conditions or distance. It has fully demonstrated its great advantages in dynamic deflection monitoring of bridges and is widely used in deformation monitoring of flexible highway bridges such as cable-stayed bridges and suspension bridges.

[0005] Since bridges with high rigidity, such as high-speed railway bridges, have high requirements for the vertical deflection of the beam body, traditional GNSS dynamic positioning technology has problems such as insufficient monitoring accuracy, poor reliability and high cost when monitoring bridges such as high-speed railway bridges. In recent years, some countries have actively promoted the modernization of the Global Positioning System (GPS) and GLONASS systems, and the Galileo system is also actively networking. The BeiDou Navigation System (BDS) has officially provided services to the world at the end of 2018.

[0006] The rapid development of multi-system GNSS and the continuous progress of related GNSS chip and receiver manufacturers have provided favorable conditions for improving GNSS monitoring accuracy and reducing monitoring costs. Therefore, facing the special environment of high-speed railway bridge monitoring, research on accelerometer-assisted GNSS precise relative positioning is carried out to improve the positioning accuracy of GNSS when monitoring the dynamic deflection of high-speed railway bridges. This will not only help promote the widespread application of GNSS in dynamic deformation monitoring of infrastructure such as high-speed railway bridges, provide technical support for the safe operation of high-speed railways, but also promote the widespread application of BDS in the field of infrastructure deformation monitoring, and has broad application prospects.

[0007] In order to ensure the bearing capacity and safety of the bridge structure during operation, it is essential to conduct safety monitoring of the bridge. Therefore, high-precision displacement and frequency information of the bridge is required.

[0008] GNSS systems have been used for bridge health monitoring since the 1990s. During the early monitoring experiments, the monitoring objects were mainly flexible structure bridges such as suspension bridges and cable-stayed bridges. These bridges have the characteristics of large amplitude and low vibration frequency, so the sampling frequency and monitoring accuracy of the GNSS system can fully meet the requirements. With the development of GNSS hardware technology and data processing technology, GNSS positioning accuracy and sampling frequency have been continuously improved, so scholars have begun to seek the application of GNSS technology on rigid structure bridges, such as high-speed railway bridges.

[0009] GNSS technology is not very sensitive to high-frequency vibration displacement of bridges due to its own observation errors and the influence of high-frequency signal noise, but it can play a good integration role through the integration of GNSS technology and accelerometers. Therefore, the fusion system of GNSS technology and accelerometers can theoretically achieve the accuracy and frequency requirements for monitoring high-speed railway bridges.

[0010] At present, a lot of research has been conducted at home and abroad on the application of accelerometer and GNSS fusion system in bridge monitoring. There are two main strategies: (1) using accelerometer as reference value to filter GNSS displacement sequence, and using acceleration displacement as constraint value in GNSS observation value processing; (2) multi-rate Kalman filter based on rigorous mathematical derivation.

[0011] The first method is to use different basis filters to reconstruct displacement with acceleration to extract low-frequency displacement components in GNSS displacement sequences. The main filters used include wavelet transform, empirical mode decomposition and adaptive filtering.

[0012] For GNSS observation technology, multipath error caused by complex bridge environment is a major source of error affecting positioning accuracy. Because the bridge monitoring system mainly uses GNSS relative positioning technology, due to the short limit, by establishing a double difference model, the satellite orbit error, satellite clock error, and receiver clock error can be basically eliminated, and the tropospheric delay error can be greatly reduced.

[0013] Therefore, it is crucial to reduce the impact of multipath error on positioning results. At present, the main methods to reduce multipath error include: signal-to-noise ratio method and sidereal day filtering based on satellite repetition period.

[0014] Therefore, how to adopt appropriate multipath error modeling strategies and how to effectively integrate accelerometer observations and GNSS observations are the key to the effective application of accelerometer / GNSS fusion system in high-speed railway bridge deflection monitoring. Summary of the invention

[0015] In view of the above problems, the present invention proposes a method for extracting the dynamic deflection of a high-speed railway bridge in real time by using an accelerometer to assist GNSS.

[0016] To achieve the purpose of the present invention, a method for extracting the dynamic deflection of a high-speed railway bridge in real time using an accelerometer-assisted GNSS is provided, comprising the following steps:

[0017] S10, collecting GNSS pseudo-range observation values, carrier phase observation values, and Doppler observation values ​​through a GNSS receiver installed on the high-speed railway bridge; and collecting acceleration observation values ​​using an accelerometer sensor;

[0018] S20, calculating a deflection displacement sequence according to the GNSS pseudorange observation value and the carrier phase observation value;

[0019] S30, obtaining the satellite angular velocity at the time of broadcasting each broadcast satellite ephemeris, and calculating the time offset of the repetition period of each broadcast satellite relative to the number of full days of the repetition period according to the satellite angular velocity at the time of broadcasting each broadcast satellite ephemeris;

[0020] S40, constructing a double-difference residual sequence, and reconstructing a single-difference residual sequence using the double-difference residual based on the zero mean assumption;

[0021] S50, using the Kalman filter-RTSS model to extract the multipath error model in the single-difference residual sequence, and correcting the multipath error of the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence;

[0022] S60, extracting low-frequency displacement sequence components in the GNSS displacement sequence by performing correlation analysis on the reconstructed acceleration displacement sequence and the GNSS displacement sequence, and reconstructing the low-frequency displacement components and the acceleration displacement to obtain an overall dynamic displacement sequence.

[0023] In one embodiment, the calculating of the deflection displacement sequence according to the GNSS pseudorange observation value and the carrier phase observation value comprises:

[0024] Substituting the GNSS pseudorange observation value and the carrier phase observation value into the double difference observation model to calculate the deflection displacement sequence; the double difference observation model includes:

[0025]

[0026]

[0027] in, represents the double difference factor, P represents the pseudorange observation value, φ represents the carrier phase observation value, subscript b represents the reference station, subscript r represents the monitoring station, superscript i represents the reference satellite number, superscript j represents the satellite number other than the reference satellite, ρ represents the distance from the satellite to the receiver, λ represents the wavelength of the carrier phase observation value, N represents the integer ambiguity parameter, ε p represents the observation noise of pseudo-range observation value, which has the characteristics of Gaussian white noise, ε φ is the carrier phase observation noise.

[0028] In one embodiment, the obtaining of the satellite angular velocity at the time of broadcasting each broadcast satellite ephemeris, and the calculation of the time offset of the repetition period of each broadcast satellite relative to the number of full days of the repetition period according to the satellite angular velocity at the time of broadcasting each broadcast satellite ephemeris comprises:

[0029] According to the satellite angular velocity correction value corresponding to each broadcast satellite, the satellite angular velocity at the time of broadcasting each broadcast satellite calendar is calculated according to the satellite angular velocity correction value corresponding to each broadcast satellite; the satellite angular velocity at the time of broadcasting the broadcast satellite calendar is: Where GM represents the gravitational constant, Δn represents the satellite angular velocity correction value, and a represents the square of the semi-major axis of the satellite orbit;

[0030] Substitute the satellite angular velocity at the time of each broadcast satellite calendar broadcast into the offset calculation formula to calculate the time offset of the corresponding broadcast satellite repetition period relative to the number of full days of the repetition period; the offset calculation formula includes:

[0031]

[0032] Wherein, ΔT represents the time offset of the broadcast satellite repetition period relative to the number of full days in the repetition period, and d represents the number of full days included in the repetition period.

[0033] In one embodiment, the single-difference residual sequence includes:

[0034]

[0035] in, represents the single difference residual vector of the i-th reference satellite, represents the double difference residual vector of the i-th reference satellite, w i represents the coefficient weight between the i-th reference satellite and the receiver single-difference residual vector; i is an integer greater than or equal to 1 and less than or equal to n, and n is the total number of reference satellites.

[0036] In one embodiment, the Kalman filter-RTSS model is used to extract the multipath error model in the single difference residual sequence, and the multipath error correction is performed on the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence including:

[0037] The multipath error time series MP k As state parameters, the single-difference residual time series As the observed quantity, determine the Kalman filter observation equation and the Kalman filter state equation;

[0038] Step by step filtering the Kalman filter observation equation and the Kalman filter state equation, after completing the k-th step of filtering, smoothing the multipath error time series to obtain a smoothed state phasor;

[0039] According to the time offset ΔT corresponding to each reference satellite calculated by the smoothed state phasor, the corresponding satellite multipath error sequence is time corrected to obtain MP′(t), and the deflection displacement sequence is corrected by the multipath model to obtain the GNSS displacement sequence X(t) gnss .

[0040] In one embodiment, the correlation analysis is performed on the reconstructed acceleration displacement sequence and the GNSS displacement sequence to extract the low-frequency displacement sequence component in the GNSS displacement sequence, and the low-frequency displacement component and the acceleration displacement are reconstructed to obtain the overall dynamic displacement sequence, which includes:

[0041] According to the acceleration observation sequence a k , reconstruct the displacement sequence s k ;

[0042] Perform correlation analysis on the GNSS displacement sequence and the displacement sequence reconstructed by acceleration;

[0043] For the low-frequency displacement sequence S(t a ) low Interpolation is performed to obtain the overall dynamic displacement sequence.

[0044] The above-mentioned accelerometer-assisted GNSS method for extracting the dynamic deflection of the high-speed railway bridge in real time is to collect GNSS pseudo-range observations, carrier phase observations and Doppler observations through the GNSS receiver installed on the high-speed railway bridge, and use the accelerometer sensor to collect acceleration observations. The deflection displacement sequence is calculated according to the GNSS pseudo-range observations and carrier phase observations, and the satellite angular velocity at the time of each broadcast satellite calendar broadcast is obtained. The time offset of the repetition period of each broadcast satellite relative to the number of full days of the repetition period is calculated according to the satellite angular velocity at the time of each broadcast satellite calendar broadcast, and a double-difference residual sequence is constructed. Based on the zero mean assumption, the double-difference residual is used to reconstruct the single-difference residual sequence, and the Kalman filter-RTSS is used. The multipath error model is extracted from the single-difference residual sequence. The multipath error correction is performed on the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence. The low-frequency displacement sequence component in the GNSS displacement sequence is extracted by performing correlation analysis on the reconstructed acceleration displacement sequence and the GNSS displacement sequence. The low-frequency displacement component and the acceleration displacement are reconstructed to obtain the overall dynamic displacement sequence. A more accurate overall dynamic displacement of the high-speed railway bridge can be obtained based on the overall dynamic displacement sequence, which can realize real-time, efficient and more accurate dynamic displacement monitoring of the high-speed railway bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of a method for extracting dynamic deflection of a high-speed railway bridge in real time using an accelerometer-assisted GNSS according to an embodiment;

[0046] Figure 2 It is a flow chart of a method for extracting the dynamic deflection of a high-speed railway bridge in real time using an accelerometer to assist GNSS according to another embodiment. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0048] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0049] refer to Figure 1 As shown, Figure 1 The flowchart of a method for extracting the dynamic deflection of a high-speed railway bridge in real time by using an accelerometer to assist GNSS according to an embodiment includes the following steps:

[0050] S10, collecting GNSS pseudo-range observation values, carrier phase observation values ​​and Doppler observation values ​​through a GNSS receiver installed on the high-speed railway bridge; and collecting acceleration observation values ​​using an accelerometer sensor.

[0051] The above steps can utilize a GNSS receiver monitoring station and an acceleration sensor installed on a high-speed railway bridge to collect observation values, collect GNSS pseudorange observation values, carrier phase observation values ​​and Doppler observation values ​​through a GNSS receiver; and collect acceleration observation values ​​using an accelerometer sensor.

[0052] S20, calculating the deflection displacement sequence according to the GNSS pseudorange observation values ​​and the carrier phase observation values.

[0053] In one embodiment, the calculating of the deflection displacement sequence according to the GNSS pseudorange observation value and the carrier phase observation value comprises:

[0054] Substituting the GNSS pseudorange observation value and the carrier phase observation value into the double difference observation model to calculate the deflection displacement sequence; the double difference observation model includes:

[0055]

[0056]

[0057] in, represents the double difference factor, P represents the pseudorange observation value, φ represents the carrier phase observation value, subscript b represents the reference station, subscript r represents the monitoring station, superscript i represents the reference satellite number, superscript j represents the satellite number other than the reference satellite, ρ represents the distance from the satellite to the receiver, λ represents the wavelength of the carrier phase observation value, N represents the integer ambiguity parameter, ε p represents the observation noise of pseudo-range observation value, which has the characteristics of Gaussian white noise, ε φ is the carrier phase observation noise.

[0058] This embodiment uses a short baseline and double difference observation model for displacement estimation. Because a short baseline is used, the tropospheric delay error and ionospheric error can be ignored; and the double difference observation model can weaken the influence of satellite clock error, receiver clock error, etc. The double difference observation model used is as follows:

[0059]

[0060]

[0061] in represents the double difference factor; P represents the pseudorange observation value; φ represents the carrier phase observation value; subscript b represents the reference station; subscript r represents the monitoring station; superscript i represents the reference satellite number; superscript j represents the satellite number other than the reference satellite; ρ represents the distance from the satellite to the receiver; λ represents the wavelength of the carrier phase observation value; N represents the integer ambiguity parameter; ε p Represents the observation noise of pseudo-range observation value, which has the characteristics of Gaussian white noise; ε φ It is the carrier phase observation value noise and has the characteristics of Gaussian white noise.

[0062] The above double difference model is converted into matrix form as follows:

[0063]

[0064] The coefficients l, m, and n can be obtained according to the linearization of the observation model, and then the double difference model can be solved by the least square method to finally obtain the GNSS displacement sequence. This step is mainly applied to step S50, which is used to process the second-phase GNSS observation data and obtain the second-phase GNSS displacement sequence.

[0065] S30, obtaining the satellite angular velocity at the time of broadcasting each broadcast satellite calendar, and calculating the time offset of the repetition period of each broadcast satellite relative to the number of full days of the repetition period according to the satellite angular velocity at the time of broadcasting each broadcast satellite calendar.

[0066] In one embodiment, the obtaining of the satellite angular velocity at the time of broadcasting each broadcast satellite ephemeris, and the calculation of the time offset of the repetition period of each broadcast satellite relative to the number of full days of the repetition period according to the satellite angular velocity at the time of broadcasting each broadcast satellite ephemeris comprises:

[0067] According to the satellite angular velocity correction value corresponding to each broadcast satellite, the satellite angular velocity at the time of broadcasting each broadcast satellite calendar is calculated according to the satellite angular velocity correction value corresponding to each broadcast satellite; the satellite angular velocity at the time of broadcasting the broadcast satellite calendar is: Where GM represents the gravitational constant, Δn represents the satellite angular velocity correction value, and a represents the square of the semi-major axis of the satellite orbit;

[0068] Substitute the satellite angular velocity at the time of each broadcast satellite calendar broadcast into the offset calculation formula to calculate the time offset of the corresponding broadcast satellite repetition period relative to the number of full days of the repetition period; the offset calculation formula includes:

[0069]

[0070] Wherein, ΔT represents the time offset of the broadcast satellite repetition period relative to the number of full days in the repetition period, and d represents the number of full days included in the repetition period.

[0071] This embodiment uses multi-system GNSS data to analyze the repetition period of different satellite constellations in GEO, IGSO, and MEO orbits; and then studies the satellite-side multipath characteristics of different constellations and different satellite orbits, and calculates the corresponding time offset. Specifically, the time offset of the satellite orbit repetition period of different satellite constellations and different orbits is calculated. In an example, the corresponding calculation process may also include:

[0072] 3.1) Based on the orbital radius and the angular velocity given by the broadcast ephemeris, the satellite angular velocity at each broadcast ephemeris broadcast time can be obtained:

[0073]

[0074] In formula (28), GM = 3.986005 × 10 14 is the gravitational constant, Δn is the satellite angular velocity correction, and a is the square of the semi-major axis of the satellite orbit.

[0075] 3.2) So for a satellite with a repetition period of d days, assuming that it completes k orbits within the repetition period, the time offset of its repetition period relative to the number of full days of the repetition period is:

[0076]

[0077] For satellites in different satellite systems and orbits, the values ​​of d and k are as follows:

[0078]

[0079] S40, constructing a double-difference residual sequence, and reconstructing a single-difference residual sequence using the double-difference residual based on the zero mean assumption.

[0080] In one embodiment, the single-difference residual sequence includes:

[0081]

[0082] in, represents the single difference residual vector of the i-th reference satellite, represents the double difference residual vector of the i-th reference satellite, w i represents the coefficient weight between the i-th reference satellite and the receiver single-difference residual vector; i is an integer greater than or equal to 1 and less than or equal to n, and n is the total number of reference satellites.

[0083] This embodiment constructs a double-difference residual sequence through a period of multi-system GNSS data and a baseline reference value, and reconstructs a single-difference residual sequence using the double-difference residual based on the zero mean assumption. In one example, the process of obtaining the single-difference residual sequence includes:

[0084] 4.1) According to the double-difference pseudorange and carrier phase observation equation:

[0085] y p =A·b+ε p (30)

[0086]

[0087] where y p , denote the double-difference pseudorange observation and the double-difference carrier phase observation respectively, A denotes the baseline vector coefficient matrix, B denotes the double-difference integer ambiguity coefficient matrix, ε p , They represent double difference residual errors respectively. The double difference residual corresponding to the carrier phase observation value can be expressed as:

[0088]

[0089] Where a represents the double difference ambiguity column vector; b represents the double difference position vector, which includes position parameters in three directions in total, which are the three coordinate axis directions of the bridge coordinate system.

[0090] In the case of a short baseline, the double difference residual basically only contains multipath errors, so the multipath error model can be extracted through the double difference residual. However, the multipath model extracted by the double difference residual has the following two disadvantages: first, the change of the reference satellite will make the double difference residual sequence change complex, and it is difficult to correspond to a specific satellite; second, because the repetition period of the two satellites may be different, it is difficult to achieve the establishment process of the double difference residual. Therefore, in order to avoid this problem, the double difference residual needs to be restored to a single difference residual.

[0091] 4.2) The relationship between the single difference residual and the double difference residual is as follows:

[0092]

[0093] Where sd represents the single difference residual vector; dd represents the double difference residual vector, and the number (1, 2...n-1, n) represents the satellite number.

[0094] However, since the coefficient matrix of this formula is a singular matrix, the zero mean assumption is introduced:

[0095] ∑w i ·sd i =0 (34)

[0096] w i =sin 2 θ (35)

[0097] Where θ represents the satellite altitude angle; w i is the coefficient weight corresponding to the single difference residual vector between the i-th satellite and the receiver.

[0098] So the single difference residual solution is:

[0099]

[0100] S50, using the Kalman filter-RTSS model, extracting the multipath error model in the single-difference residual sequence, and performing multipath error correction on the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence.

[0101] In one embodiment, the Kalman filter-RTSS model is used to extract the multipath error model in the single difference residual sequence, and the multipath error correction is performed on the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence including:

[0102] The multipath error time series MP k As state parameters, the single-difference residual time series As the observed quantity, determine the Kalman filter observation equation and the Kalman filter state equation;

[0103] Step by step filtering the Kalman filter observation equation and the Kalman filter state equation, after completing the k-th step of filtering, smoothing the multipath error time series to obtain a smoothed state phasor;

[0104] According to the time offset ΔT corresponding to each reference satellite calculated by the smoothed state phasor, the corresponding satellite multipath error sequence is time corrected to obtain MP′(t), and the deflection displacement sequence is corrected by the multipath model to obtain the GNSS displacement sequence X(t) gnss .

[0105] This embodiment uses the Kalman filter-RTSS model to extract the multipath error model in the single difference residual sequence, and then corrects the multipath error of the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence. In one example, the GNSS displacement sequence X(t) is obtained.gnss The acquisition process may also include:

[0106] 5.1) Multipath error time series MP k As state parameters, the single-difference residual time series As an observation quantity, component Kalman filter observation equation and state equation:

[0107]

[0108] MP k+1 =Γ k MP k +w k (38)

[0109] Then perform Kalman filtering:

[0110]

[0111]

[0112] Measurement Update:

[0113]

[0114]

[0115] P k (+) = P k (-)-K k ·H k ·P k (-) (43)

[0116] 5.2) After completing the k-th step of filtering, the multipath error time series is smoothed by the following steps:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] Finally, the smoothed state phasor is This sequence is also the multipath error model extracted from the single-difference residual, and is also denoted as MP(t).

[0123] 5.3) Then, according to the time offset ΔT corresponding to each satellite calculated in step S20, the corresponding satellite multipath error sequence is time corrected to obtain MP′(t). According to step S20, the GNSS displacement sequence X(t) is calculated. gnss、raw , then for X(t) gnss、raw Perform multipath model correction to obtain the GNSS displacement sequence X(t) gnss .

[0124] S60, extracting low-frequency displacement sequence components in the GNSS displacement sequence by performing correlation analysis on the reconstructed acceleration displacement sequence and the GNSS displacement sequence, and reconstructing the low-frequency displacement components and the acceleration displacement to obtain an overall dynamic displacement sequence.

[0125] In one embodiment, the correlation analysis is performed on the reconstructed acceleration displacement sequence and the GNSS displacement sequence to extract the low-frequency displacement sequence component in the GNSS displacement sequence, and the low-frequency displacement component and the acceleration displacement are reconstructed to obtain the overall dynamic displacement sequence, which includes:

[0126] According to the acceleration observation sequence a k , reconstruct the displacement sequence s k ;

[0127] Perform correlation analysis on the GNSS displacement sequence and the displacement sequence reconstructed by acceleration;

[0128] For the low-frequency displacement sequence S(t a ) low Interpolation is performed to obtain the overall dynamic displacement sequence.

[0129] This embodiment performs correlation analysis on the reconstructed acceleration displacement sequence and the GNSS displacement sequence to extract the low-frequency displacement sequence component in the GNSS displacement sequence; finally, the low-frequency displacement component and the acceleration displacement are reconstructed to obtain the overall dynamic displacement sequence. In an example, the acquisition process of the overall dynamic displacement sequence may also include:

[0130] 6.1) According to the acceleration observation sequence a k , reconstruct the displacement sequence s k , the relationship between the two is as follows:

[0131]

[0132] So we can get the error equation:

[0133]

[0134] Where Δt represents the acceleration data sampling interval; s n represents the displacement of the nth epoch; an Represents the acceleration observation at the nth epoch.

[0135] However, the coefficient matrix of the above error equation is a singular matrix, so according to the Tikhonov regularization principle, the estimation criterion is introduced:

[0136] minΠ(X)=||AX-L|| 2 +λ 2 ||XX * || 2 (51)

[0137] Where X * is the static displacement vector, set to zero vector; λ is the regularization factor; so equation (14) has the following solution:

[0138] X(t) acc =X=(A T A+λ 2 I) -1 A T L (52)

[0139] So we get the displacement sequence X(t) reconstructed by the accelerometer: acc , this sequence is also a high-frequency displacement sequence S(t) high .

[0140] 6.2) Then, the GNSS displacement sequence and the acceleration reconstructed displacement sequence are subjected to correlation analysis. The specific steps are as follows:

[0141] The correlation analysis is performed on the GNSS sequence and accelerometer sequence within each one-minute interval. First, the GNSS displacement sequence X(t 0 ) gnss Bring in the EMD filter and decompose it into several IMFs i (t 0 ) gnss Components and residual terms r n (t 0 ) gnss , if we start at scale k, IMF k (t 0 ) gnss and X(t 0 ) acc When the correlation coefficient approaches 0, the low-frequency displacement sequence can be expressed as:

[0142]

[0143] 6.3) In order to make the accelerometer high-frequency displacement sequence S(t a ) high and GNSS low-frequency displacement S(ta ) low The data sampling rate is kept consistent, and the low-frequency displacement sequence S(t a ) low Interpolation is performed to obtain S′(t a ) low , and finally the overall displacement sequence is obtained. Specifically, the above low-frequency displacement sequence S′(t i ) low It is obtained by eliminating the high-frequency component of GNSS displacement. Because of the influence of high-frequency noise in GNSS signals, GNSS receivers are more sensitive to low-frequency displacement signals. high The sum is the reconstructed acceleration integral displacement X(t) acc The above overall displacement sequence includes:

[0144]

[0145] The above-mentioned accelerometer-assisted GNSS method for extracting the dynamic deflection of the high-speed railway bridge in real time is to collect GNSS pseudo-range observations, carrier phase observations and Doppler observations through the GNSS receiver installed on the high-speed railway bridge, and use the accelerometer sensor to collect acceleration observations. The deflection displacement sequence is calculated according to the GNSS pseudo-range observations and carrier phase observations, and the satellite angular velocity at the time of each broadcast satellite calendar broadcast is obtained. The time offset of the repetition period of each broadcast satellite relative to the number of full days of the repetition period is calculated according to the satellite angular velocity at the time of each broadcast satellite calendar broadcast, and a double-difference residual sequence is constructed. Based on the zero mean assumption, the double-difference residual is used to reconstruct the single-difference residual sequence, and the Kalman filter-RTSS is used. The multipath error model is extracted from the single-difference residual sequence. The multipath error correction is performed on the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence. The low-frequency displacement sequence component in the GNSS displacement sequence is extracted by performing correlation analysis on the reconstructed acceleration displacement sequence and the GNSS displacement sequence. The low-frequency displacement component and the acceleration displacement are reconstructed to obtain the overall dynamic displacement sequence. A more accurate overall dynamic displacement of the high-speed railway bridge can be obtained based on the overall dynamic displacement sequence, which can realize real-time, efficient and more accurate dynamic displacement monitoring of the high-speed railway bridge.

[0146] In one embodiment, the above-mentioned method of accelerometer-assisted GNSS real-time extraction of dynamic deflection of high-speed railway bridge can also refer to Figure 2 As shown, the following steps are included:

[0147] S1. Use the GNSS receiver base station, GNSS receiver monitoring station and acceleration sensor installed on the high-speed railway bridge to collect GNSS base station, monitoring station observation values ​​and acceleration observation values;

[0148] S2. Analyze the repetition period of different satellite constellations in GEO, IGSO and MEO orbits using multi-system GNSS data; then study the satellite-side multipath characteristics of different constellations and different satellite orbits, and calculate the corresponding time offset;

[0149] S3. Construct a double-difference residual sequence through long-term observation of multi-system GNSS data and baseline reference values. Based on the zero mean assumption, reconstruct a single-difference residual sequence using the double-difference residual.

[0150] S4, using the Kalman filter-RTS smoothing model to extract the multipath error model in the single-difference residual sequence, and then correcting the multipath error of the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence;

[0151] S5. By performing correlation analysis on the reconstructed acceleration displacement sequence and the GNSS displacement sequence, the low-frequency displacement sequence component in the GNSS displacement sequence is extracted; finally, the low-frequency displacement component and the acceleration displacement are reconstructed to obtain the overall dynamic displacement sequence. The specific operations are as follows:

[0152] S21. According to the orbital radius and the angular velocity given by the broadcast ephemeris, the satellite angular velocity at each broadcast ephemeris broadcasting time can be obtained:

[0153]

[0154] In formula (55), GM = 3.986005 × 10 14 is the gravitational constant, Δn is the satellite angular velocity correction, and a is the square of the semi-major axis of the satellite orbit.

[0155] S22. For a satellite with a repetition period of d days, assuming that it completes k orbits within the repetition period, the time offset of its repetition period relative to the number of full days of the repetition period is:

[0156]

[0157] For satellites in different satellite systems and orbits, the values ​​of d and k are as follows:

[0158]

[0159] S31, according to the double difference pseudorange, carrier phase observation equation:

[0160] y p =A·b+ε p (57)

[0161]

[0162] where y p , denote the double-difference pseudorange observation and the double-difference carrier phase observation respectively, A denotes the baseline vector coefficient matrix, B denotes the double-difference integer ambiguity coefficient matrix, ε p , They represent double difference residual errors respectively. The double difference residual corresponding to the carrier phase observation value can be expressed as:

[0163]

[0164] In the case of a short baseline, the double difference residual basically only contains multipath errors, so the multipath error model can be extracted through the double difference residual. However, the multipath model extracted by the double difference residual has the following two disadvantages: first, the change of the reference satellite will make the double difference residual sequence change complex, and it is difficult to correspond to a specific satellite; second, because the repetition period of the two satellites may be different, it is difficult to achieve the establishment process of the double difference residual. Therefore, in order to avoid this problem, the double difference residual needs to be restored to a single difference residual.

[0165] The relationship between S32, single-difference residuals, and double-difference residuals is as follows:

[0166]

[0167] However, since the coefficient matrix of this formula is a singular matrix, the zero mean assumption is introduced:

[0168] ∑w i ·sd i =0 (61)

[0169] w i =sin 2 θ (62)

[0170] Where θ represents the satellite altitude angle.

[0171] So the single difference residual solution is:

[0172]

[0173] S41, multipath error time series MP k As state parameters, the single-difference residual time series As an observation quantity, component Kalman filter observation equation and state equation:

[0174]

[0175] MP k+1 =Γ k MP k +w k (65)

[0176] Then perform Kalman filtering:

[0177]

[0178]

[0179] Measurement Update:

[0180]

[0181]

[0182] P k (+) = P k (-)-K k ·H k ·P k (-) (70)

[0183] S42, after completing the k-th step of filtering, smooth the multipath error time series through the following steps:

[0184]

[0185]

[0186]

[0187]

[0188]

[0189] Finally, the smoothed state phasor is This sequence is also the multipath error model extracted from the single-difference residual, and is also denoted as MP(t).

[0190] S43, then according to the time offset ΔT corresponding to each satellite calculated in step 2), the corresponding satellite multipath error sequence is time corrected to obtain MP′(t), and then the second-phase GNSS data is corrected for the multipath model to obtain the GNSS displacement sequence X(t) gnss .

[0191] S51, according to the acceleration observation value sequence a k , reconstruct the displacement sequence s k , the relationship between the two is as follows:

[0192]

[0193] So we can get the error equation:

[0194]

[0195] However, the coefficient matrix of the above error equation is a singular matrix, so according to the Tikhonov regularization principle, the estimation criterion is introduced:

[0196] minΠ(X)=||AX-L|| 2 +λ 2 ||XX * || 2 (78)

[0197] Where X * is the static displacement vector, set to zero vector; λ is the regularization factor; so equation (14) has the following solution:

[0198] X(t) acc =X=(A T A+λ 2 I) -1 A T L (79)

[0199] So we get the displacement sequence X(t) reconstructed by the accelerometer: acc , this sequence is also a high-frequency displacement sequence S(t) high .

[0200] S52, then performing correlation analysis on the GNSS displacement sequence and the displacement sequence reconstructed by acceleration, the specific steps are as follows:

[0201] The correlation analysis is performed on the GNSS sequence and accelerometer sequence within each one-minute interval. First, the GNSS displacement sequence X(t 0 ) gnss Bring in the EMD filter and decompose it into several IMFs i (t 0 ) gnss Components and residual terms r n (t 0 ) gnss , if we start at scale k, IMF k (t 0 ) gnss and X(t 0 ) acc When the correlation coefficient approaches 0, the low-frequency displacement sequence can be expressed as:

[0202]

[0203] S53, in order to make the accelerometer high frequency displacement sequence S (t a ) high and GNSS low-frequency displacement S(t a )low The data sampling rate is kept consistent, and the low-frequency displacement sequence S(t a ) low Interpolation is performed to obtain S′(t a ) low , the final overall displacement sequence is as follows:

[0204]

[0205] This embodiment collects multi-system GNSS monitoring data and acceleration data on the high-speed railway bridge, establishes a single-difference residual sequence through GNSS monitoring data, establishes a multipath error model in the observation value domain, and then corrects the data of the next multipath repetition cycle, eliminating the influence of multipath error on the GNSS positioning result; for the extraction of high and low frequency dynamic displacement, correlation analysis is performed through GNSS displacement sequence and acceleration displacement sequence, and low frequency displacement components are extracted, and finally reconstructed with acceleration displacement sequence to obtain the overall dynamic displacement sequence of the high-speed railway bridge. Compared with the traditional monitoring method, this method has the advantages of automatic data collection, the use of multi-system GNSS data, and the correction of multipath errors, which effectively improves the GNSS displacement positioning accuracy, and the acceleration data assists GNSS data to effectively separate the high and low frequency displacements of the high-speed railway bridge, so as to obtain a more accurate overall dynamic displacement of the high-speed railway bridge. Therefore, this invention can realize the dynamic displacement monitoring of the high-speed railway bridge in real time, efficiently and more accurately.

[0206] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0207] It should be noted that the terms "first\second\third" involved in the embodiments of the present application are only used to distinguish similar objects, and do not represent a specific order for the objects. It is understandable that the specific order or sequence of "first\second\third" can be interchanged where permitted. It should be understood that the objects distinguished by "first\second\third" can be interchanged where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein.

[0208] The terms "including" and "having" and any variations thereof in the embodiments of the present application are intended to cover non-exclusive inclusions. For example, a process, method, device, product, or equipment that includes a series of steps or modules is not limited to the listed steps or modules, but may optionally include steps or modules that are not listed, or may optionally include other steps or modules that are inherent to these processes, methods, products, or equipment.

[0209] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A method for extracting the dynamic deflection of a high-speed railway bridge in real time using an accelerometer-assisted GNSS, characterized in that: The steps include: S10, collecting GNSS pseudo-range observation values, carrier phase observation values, and Doppler observation values ​​through a GNSS receiver installed on the high-speed railway bridge; and collecting acceleration observation values ​​using an accelerometer sensor; S20, calculating a deflection displacement sequence according to the GNSS pseudorange observation value and the carrier phase observation value; S30, obtaining the satellite angular velocity at the time of broadcasting each broadcast satellite ephemeris, and calculating the time offset of the repetition period of each broadcast satellite relative to the number of full days of the repetition period according to the satellite angular velocity at the time of broadcasting each broadcast satellite ephemeris; S40, constructing a double-difference residual sequence, and reconstructing a single-difference residual sequence using the double-difference residual based on the zero mean assumption; S50, using the Kalman filter-RTSS model to extract the multipath error model in the single-difference residual sequence, and correcting the multipath error of the second-phase GNSS monitoring data according to the calculated time offset to obtain the GNSS displacement sequence; S60, extracting a low-frequency displacement sequence component in the GNSS displacement sequence by performing correlation analysis on the reconstructed acceleration displacement sequence and the GNSS displacement sequence, and reconstructing the low-frequency displacement component and the acceleration displacement to obtain an overall dynamic displacement sequence; The Kalman filter-RTSS model is used to extract the multipath error model in the single difference residual sequence, and the multipath error correction is performed on the second-phase GNSS monitoring data according to the calculated time offset, and the GNSS displacement sequence obtained includes: The multipath error time series MP k As state parameters, the single-difference residual time series As the observed quantity, determine the Kalman filter observation equation and the Kalman filter state equation; Step by step filtering the Kalman filter observation equation and the Kalman filter state equation, after completing the k-th step of filtering, smoothing the multipath error time series to obtain a smoothed state phasor; According to the time offset ΔT corresponding to each reference satellite calculated by the smoothed state phasor, the corresponding satellite multipath error sequence is time corrected to obtain MP′(t), and the deflection displacement sequence is corrected by the multipath model to obtain the GNSS displacement sequence X(t) gnss ; The method performs correlation analysis on the reconstructed acceleration displacement sequence and the GNSS displacement sequence, extracts the low-frequency displacement sequence component in the GNSS displacement sequence, reconstructs the low-frequency displacement component and the acceleration displacement, and obtains the overall dynamic displacement sequence, including: According to the acceleration observation sequence a k , reconstruct the displacement sequence s k ; The displacement sequence s reconstructed from the GNSS displacement sequence and acceleration k Conduct correlation analysis; For the low-frequency displacement sequence S(t a ) low Interpolation is performed to obtain the overall dynamic displacement sequence.

2. The method for extracting the dynamic deflection of a high-speed railway bridge using accelerometer-assisted GNSS in real time according to claim 1 is characterized in that: The calculating of the deflection displacement sequence according to the GNSS pseudorange observation value and the carrier phase observation value comprises: Substituting the GNSS pseudorange observation value and the carrier phase observation value into the double difference observation model to calculate the deflection displacement sequence; the double difference observation model includes: in, represents the double difference factor, P represents the pseudorange observation value, φ represents the carrier phase observation value, subscript b represents the reference station, subscript r represents the monitoring station, superscript i represents the reference satellite number, superscript j represents the satellite number other than the reference satellite, ρ represents the distance from the satellite to the receiver, λ represents the wavelength of the carrier phase observation value, N represents the integer ambiguity parameter, ε p represents the observation noise of pseudo-range observation value, which has the characteristics of Gaussian white noise, ε φ is the carrier phase observation noise.

3. The method for extracting the dynamic deflection of a high-speed railway bridge using accelerometer-assisted GNSS in real time according to claim 1 is characterized in that: The obtaining of the satellite angular velocity at the time of broadcasting each broadcast satellite calendar, and the calculation of the time offset of the repetition period of each broadcast satellite relative to the number of full days of the repetition period according to the satellite angular velocity at the time of broadcasting each broadcast satellite calendar comprises: The satellite angular velocity at the time of broadcasting each broadcast satellite calendar is calculated according to the satellite angular velocity correction value corresponding to each broadcast satellite; the satellite angular velocity at the time of broadcasting the broadcast satellite calendar is: Where GM represents the gravitational constant, Δn represents the satellite angular velocity correction value, and a represents the square of the semi-major axis of the satellite orbit; Substitute the satellite angular velocity at the time of each broadcast satellite calendar broadcast into the offset calculation formula to calculate the time offset of the corresponding broadcast satellite repetition period relative to the number of full days of the repetition period; the offset calculation formula includes: Wherein, ΔT represents the time offset of the broadcast satellite repetition period relative to the number of full days in the repetition period, and d represents the number of full days included in the repetition period.

4. The method for extracting the dynamic deflection of a high-speed railway bridge using accelerometer-assisted GNSS in real time according to claim 1, characterized in that: The single-difference residual sequence includes: in, represents the single difference residual vector of the i-th reference satellite, represents the double difference residual vector of the i-th reference satellite, w i Represents the coefficient between the i-th reference satellite and the receiver single-difference residual vector; i is an integer greater than or equal to 1 and less than or equal to n, and n is the total number of reference satellites.

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