GNSS / accelerometer adaptive fusion landslide monitoring method based on variance inflation model

Abstract

The present invention discloses a GNSS / accelerometer adaptive fusion landslide monitoring method based on a variance inflation model, including installing a GNSS antenna and an accelerometer to form a rigid body structure, calculating the Allan variance and calibrating the acceleration random walk coefficient, constructing the state of the Kalman filter and its covariance time update equation; expanding the accelerometer baseline deviation to a parameter to be estimated, and performing random walk modeling; inputting accelerometer data for state prediction, and searching for GNSS measurement information at the same time according to its timestamp, and using the GNSS-RTK displacement as the measurement information to calculate a high-precision fusion deformation monitoring result. The method loosely couples the two types of observation information through a Kalman filter, and uses a random walk model between epochs to constrain the accelerometer baseline deviation. In addition, a variance inflation model is used to adjust the measurement noise of the GNSS abnormal monitoring data to improve the accuracy and reliability of parameter estimation.

Description

Technical Field

[0001] The present invention belongs to the technical field of geological disaster monitoring and relates to a GNSS / accelerometer adaptive fusion landslide monitoring technology based on a variance inflation model. The technology takes the fields of GNSS monitoring positioning algorithm, accelerometer fusion model, and anti-error algorithm as its practical application background and can be used for high-precision deformation monitoring of landslides under abnormal conditions such as GNSS signal interference and interruption. Background Art

[0002] At present, landslide monitoring methods have developed into a three-dimensional monitoring mode of "air, space, and land". Among them, GNSS, as one of the important ground monitoring equipment, can provide continuous three-dimensional landslide deformation monitoring results with its high precision, all-weather and all-day characteristics. Especially in RTK solution mode, centimeter-level positioning results can be obtained by fixing double difference ambiguity. RTK technology has been widely used in landslide monitoring and has successfully issued warnings many times. However, since GNSS signals will be seriously disturbed by factors such as mountain occlusion and vegetation diffraction, the positioning accuracy is frustrated, and it is difficult to obtain accurate and reliable landslide monitoring results, which can easily lead to false alarms and missed alarms of landslide disaster warnings.

[0003] As an inertial sensor, the working performance of the accelerometer is not affected by the external environment, and it has the characteristics of high short-term accuracy and strong stability. However, such inertial sensors usually have obvious zero bias and random walk characteristics. The error will accumulate over time, resulting in the divergence of displacement estimation results. This phenomenon is particularly obvious in low-cost MEMS accelerometer devices. Therefore, the accelerometer and GNSS can be effectively redundantly complemented. The fusion of the two sensors can obtain more reliable landslide monitoring results, especially in the pre-slip stage, which can accurately identify and verify the instability state of the landslide to ensure the reliability of landslide warning.

[0004] Meng Xiaolin established a bridge monitoring system based on GNSS and MEMS accelerometers in "Design and Implementation of a New System for LargeBridge Monitoring—GeoSHM[J].Sensors, 2018, 18(3):775-." and successfully applied it to bridge monitoring projects at home and abroad, but it paid more attention to the vibration characteristics of the structure.

[0005] Dai Wujiao et al. integrated GPS and accelerometers in “Research on the integration method of GPS and accelerometers in high-rise building vibration monitoring [J]. Vibration and Shock, 2011, 30(7):5.” and proposed a multi-rate robustness model to suppress abnormal phenomena such as gross errors and losses in GPS observations. However, they did not consider the error accumulation that may be caused by acceleration baseline deviation.

[0006] Geng Jianghui et al. in “A new seismogeodetic approach applied to GPS and accelerometer observations of the 2012 Brawley seismic swarm: Implications for earthquake early warning[J]. Geochemistry, Geophysics, Geosystems, 2013, 14(7): 2124-2142.” used a random walk model to model the accelerometer baseline bias and formed a tight combination model with GPS to recover the coseismic deformation displacement of the surface. However, they did not consider the problem of how to accurately estimate the acceleration baseline bias when GNSS anomalies occur.

[0007] The above GNSS / acceleration fusion deformation monitoring studies have not considered abnormal conditions such as diffraction and interruption of GNSS signals in complex environments. Abnormal GNSS measurement information will directly lead to incorrect estimation of accelerometer baseline deviation, and ultimately cause divergence of Kalman filter results. Summary of the invention

[0008] The present invention provides a GNSS / accelerometer adaptive fusion landslide monitoring method which suppresses abnormal GNSS landslide monitoring results through a variance inflation model, thereby solving the problem of unreliable GNSS monitoring in complex environments such as signal shielding and diffraction.

[0009] The technical solution for achieving the purpose of the present invention comprises the following steps:

[0010] 【1】Install and level the accelerometer equipment, and align the three axes to the east-north-sky (ENU) direction. Leave the equipment still for ≥30 minutes, calculate the Allan variance and calibrate the random walk coefficient q=[q x q y q z ];

[0011] 【2】Install the GNSS antenna and accelerometer to form a rigid structure, use the first fixed solution of GPS-RTK to establish the local coordinate system of the ENU station center, and unify it with the accelerometer coordinate system;

[0012] 【3】Initialize the initial value X0 of the Kalman filter’s state vector and the initial value P0 of its covariance matrix;

[0013] 【4】The accelerometer baseline deviation u k Expand to estimate the parameters to be estimated and perform random walk modeling;

[0014] 【5】Construct the state and covariance time update equation of the GNSS / accelerometer fusion Kalman filter;

[0015] 【6】Search for GNSS measurement information at the same time based on the acceleration timestamp of the kth epoch;

[0016] [7] If GNSS measurement information can be found, continue with the following steps; otherwise, return to step [5];

[0017] 【8】 Based on the variance inflation model of abnormal observations, the GNSS-RTK measurement noise is adaptively adjusted to obtain the equivalent measurement noise R k , to reduce the impact of abnormal GNSS measurement information on the fusion results;

[0018] 【9】Kalman filter measurement update;

[0019]

[10] Repeat steps 【5】-【9】, and continue to calculate the state gain value X at time k+1, k+2, k+3... k+ 1X k+2 X k+3 and its covariance matrix P k+1 P k+2 P k+3 , high-precision landslide deformation monitoring results can be obtained.

[0020] Furthermore, the formula for random walk modeling of the accelerometer baseline deviation in step [4] is:

[0021] u k =u k-1 +w k

[0022] Where u k represents the accelerometer baseline deviation at time k, w k represents Gaussian white noise at time k.

[0023] Furthermore, the state and covariance time update equation of the GNSS / accelerometer fusion Kalman filter in step [5] are constructed as follows:

[0024] 【5.1】According to the variable acceleration model, perform state calculation and determine the state transfer matrix A k , construct the state time update equation;

[0025] 【5.2】Calculate the noise matrix Q corresponding to the displacement, velocity and baseline deviation components k ;

[0026] 【5.2.1】Calculate the acceleration noise based on the acceleration random walk coefficient obtained in step 【1】;

[0027] 【5.2.2】According to the error propagation law, the acceleration noise is mapped onto the displacement, velocity and baseline deviation components to obtain the noise matrix Q of the process k ;

[0028]

[0029]

[0030] Where N d N v N u Respectively represent the noise of displacement, velocity and baseline deviation, and the matrix [N d N v N u ] k T Use the character Q k It represents the process noise matrix of Kalman filtering, b k is the error propagation coefficient, q is the random walk coefficient obtained in step [1], and Δt is the accelerometer sampling interval;

[0031] 【5.3】Calculate the covariance of displacement, velocity and baseline deviation components based on the state covariance P at time k-1 k-1 , and with the help of the state transfer matrix A in step [5.1] k and the noise matrix Q in step [5.2.2] k Estimate the state covariance P at time k k,k-1 ;

[0032] 【5.4】According to the state time update equation and covariance, the state and covariance time update equation of the GNSS / accelerometer fusion Kalman filter are obtained;

[0033] Furthermore, in step [8], the GNSS-RTK measurement noise is adaptively adjusted based on the variance inflation model of abnormal observations to obtain the equivalent measurement noise

[0034] The variance inflation model is expressed as follows:

[0035]

[0036] in is the variance inflation factor, are the equivalent variance and covariance respectively. The equivalent measurement noise can be described in matrix form:

[0037]

[0038] The diagonal elements They represent the equivalent variance of GNSS measurement information in the three directions of ENU, and the off-diagonal elements represent the covariance. represents the equivalent covariance of EN in both directions, represents the equivalent covariance of the two directions of EU, Represents the equivalent covariance of NU in two directions.

[0039] Furthermore, the Kalman filter measurement update steps in step [9] are as follows:

[0040] 【9.1】Use GNSS-RTK displacement as measurement information and determine the measurement coefficient matrix H k , construct the measurement equation;

[0041] 【9.2】Calculate high-precision filtering solutions for displacement, velocity, and baseline deviation;

[0042] [9.2.1] Update the state covariance time result obtained in step [5] and the measurement coefficient matrix H obtained in [9.1] k The equivalent measurement noise R obtained by [8] k Calculate the measurement gain matrix K of the Kalman filter k ;

[0043] [9.2.2] The gain matrix K obtained according to step [9.2.1] k , the state time update result and its covariance matrix time update result obtained in step [5], and the measurement vector Z obtained in step [9.1] k and the measurement coefficient matrix H k Calculate the state gain value X after measurement update k and its covariance gain matrix P k .

[0044] Compared with the existing GNSS landslide monitoring technology, the present invention has the following advantages:

[0045] 1. As an inertial sensor, the accelerometer is not affected by the external electromagnetic environment and has high short-term accuracy. Theoretically, the displacement change of the deformation body can be inferred through quadratic integration, which can suppress the low-precision monitoring results of traditional single GNSS deformation monitoring technology due to signal interference; GNSS can obtain the absolute displacement information of the deformation body and effectively avoid the error accumulation caused by the long-term calculation of the accelerometer. The fusion of the two sensors can form a highly robust and continuous landslide monitoring system in the displacement dimension, improving the reliability of the monitoring results.

[0046] Second, the current GNSS / accelerometer fusion technology is mainly used in the field of structural deformation monitoring such as bridges, buildings, and earthquakes, all of which are open environments, and do not consider the adverse effects of complex obstruction environments such as landslides on GNSS monitoring accuracy. The existing fusion method relies on high-precision GNSS monitoring information to estimate the accelerometer baseline deviation, and then obtain accurate accelerometer estimation results. The present invention adopts a variance inflation model to downgrade the abnormal monitoring information of GNSS in complex landslide environments, improves the robustness of the fusion system by adaptively expanding the measurement noise of the Kalman filter, accurately estimates the baseline deviation of the accelerometer per epoch (1Hz), and performs closed-loop correction on the original observation value of the accelerometer to avoid the accumulation of errors of secondary integration, and ensure the reliability of the GNSS / accelerometer fusion landslide deformation monitoring system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flow chart of the method of the present invention;

[0048] Figure 2 It is a photo of the experiment scheme of the present invention on site - schematic diagram of the instrument installation;

[0049] Figure 3 The original observation data of the accelerometer of the present invention at rest (left) and the double logarithmic diagram of the Allan variance (right);

[0050] Figure 4 It is the influence of the interruption duration of the GNSS reference station on the state covariance in the present invention;

[0051] Figure 5 It is the fusion solution result of simulating the stable stage of landslide when the GNSS reference station is interrupted in the present invention;

[0052] Figure 6 It is the fusion solution result of simulating the landslide sliding stage when the GNSS reference station is interrupted in the present invention;

[0053] Figure 7 is the correlation relationship between the signal-to-noise ratio, multipath error and GNSS covariance when the satellite is blocked in the present invention;

[0054] Figure 8 It is the fusion solution result of simulating the stable stage of landslide when satellite is blocked in the present invention;

[0055] Fig. 9 It is the fusion solution result of simulating the landslide sliding stage when the satellite is blocked in the present invention.

[0056] The reference numerals in the figures are: 1- GNSS reference station antenna; 2- GNSS monitoring station antenna; 3- three-axis accelerometer; 4- rigid body structure; 5- three-dimensional deformation simulation platform. DETAILED DESCRIPTION

[0057] The present invention will be further described below in conjunction with the accompanying drawings.

[0058] The idea of ​​the present invention is to first unify the coordinate systems of the GNSS and accelerometer devices, initialize the state of the Kalman filter and its covariance, then construct the Kalman filter time update equation based on the variable acceleration model, and then construct the Kalman filter measurement update equation with the help of GNSS solution information. The measurement noise is adaptively adjusted through the variance inflation model to reduce the contamination degree of the abnormal GNSS measurement information on the Kalman filter, and obtain a high-precision Kalman filter gain result, that is, an accurate GNSS / accelerometer fusion deformation monitoring result.

[0059] Reference Figure 1 The specific implementation steps of the present invention are as follows:

[0060] Step 1: Install the accelerometer device and align its three-axis direction (XYZ) to the east-north-sky (ENU) direction. Leave the device still for ≥30 minutes to obtain the three-axis static observation data of the accelerometer ( Figure 3 Left), and calculate its random walk coefficient q=[q x q y q z ].

[0061] Allan variance is widely used to measure the frequency stability of precision instruments. The static observation data of the three axes of the accelerometer are processed according to the following formula, and the double logarithmic curve of the correlation time-Allan variance is drawn ( Figure 3 right).

[0062]

[0063] where σ 2 (T) is the Allan variance, It represents the average value of the kth group of accelerometer observation data with length T, and N is the number of samples in the accelerometer group.

[0064] The various noise sources of the accelerometer can be obtained through the slope of the double logarithmic curve, where the slope corresponding to the acceleration random walk coefficient is 1. Find a curve with a slope closest to 1 in the double logarithmic curve in the three directions of XYZ, and read its corresponding ordinate to obtain the acceleration random walk coefficient q = [q x q y q z ].

[0065] Step 2: Install the GNSS antenna to form a rigid structure with the accelerometer device. Take the first fixed solution of GNSS-RTK as the origin and establish the East-North-Sky (ENU) station center local coordinate system. The conversion formula is:

[0066]

[0067] Where R2 and R3 are the rotation matrices of the Y and Z axes, (φ,λ) are the geodetic latitude and geodetic longitude respectively, [x0 y0 z0] T is the initial epoch coordinate of the station in the global coordinate reference frame geocentric coordinate system WGS-84, [x i y i z i ] T are the station coordinates of the ith epoch in the WGS-84 coordinate system.

[0068] Step 3: Initialize the initial value X0 of the estimated state vector of the GNSS / accelerometer fusion Kalman filter and the initial value P0 of its covariance matrix, which is expressed as:

[0069]

[0070] Where d0 represents the initial displacement value, v0 represents the initial velocity value, and u0 represents the initial accelerometer baseline deviation value; P d P v P u Respectively represent the covariance matrix corresponding to displacement, velocity and baseline deviation. In the present invention, the initial state value is set to 0, and the covariance value is set to 1.0.

[0071] Step 4: Set the estimated parameter accelerometer baseline deviation u k Expand to estimate the parameters to be estimated and perform random walk modeling according to the following formula:

[0072] u k =u k-1 +w k

[0073] Where u k and u k-1 represents the accelerometer baseline deviation at time k and k-1, w k represents Gaussian white noise at time k.

[0074] Step 5: Construct the time update equation of the state and covariance of the GNSS / accelerometer fusion Kalman filter.

[0075] According to the variable acceleration model, the state is extrapolated (including velocity, displacement and baseline deviation). Then the velocity, displacement and baseline deviation components of the first epoch can be extrapolated based on the initial values ​​set in step 3, respectively, and expressed as follows:

[0076]

[0077] Write the above formula in matrix and vector form:

[0078]

[0079] where d 1,0 Indicates the displacement result of the first epoch calculated based on the initial displacement value d0, v 1,0 Indicates the velocity result of the first epoch calculated based on the initial displacement value v0, u 1,0 It means that the baseline deviation result of the first epoch is calculated according to the initial value u0 of the accelerometer baseline deviation. On this basis, the above formula is rewritten into a general form:

[0080] X k,k-1 =A k X k-1 +B k U k

[0081] U k =a k

[0082] Among them, the subscripts k and k-1 represent the k and k-1 moments respectively, and X k,k-1 A represents the state at time k calculated based on the state at time k-1. k is the state transfer matrix, B k is the control input matrix, U k is the input vector, a k represents the accelerometer measurement value at time k, and Δt represents the accelerometer sampling interval. This formula is the state time update equation of the Kalman filter.

[0083] According to the acceleration random walk coefficient q obtained in step 1, x q y q z ]The acceleration noise variance can be calculated as (qΔt) 2 Since the accelerometer is the only noise source in the state time update, the acceleration noise can be mapped to the displacement, velocity and baseline deviation components according to the error propagation law to construct the process noise matrix:

[0084]

[0085] Where N d Nv N u Represent the noise of displacement, velocity and baseline deviation respectively, and its matrix form [N d N v N u ] T Available characters Q k It means the process noise matrix of Kalman filtering. Since the vector q and the value Δt remain unchanged at each epoch, the process noise matrix Q k Also remains unchanged.

[0086] Based on the initial value P0 of the state covariance in step 3 and the process noise matrix Q1 of the first epoch, the state covariance P of the first epoch can be inferred 1,0 :

[0087]

[0088] Change the subscripts to the common form:

[0089] P k,k-1 =A k P k-1 A k T +Q k

[0090] The subscripts k and k-1 represent the k and k-1 moments respectively, P k,k-1 Represents the state covariance matrix P at k-1 time k-1 The predicted k-time state covariance matrix, A k is the state transfer matrix, Q k is the process noise matrix;

[0091] The final formula can be sorted out to obtain the Kalman filter state and its covariance update equation for one-step prediction of the estimated parameters and their covariance:

[0092]

[0093] Where X k,k-1 and P k,k-1 They represent the results of the acceleration-reckoning Kalman filter state vector and its covariance after time update.

[0094] Step 6: Search for GNSS measurement information at the same time based on the acceleration timestamp of the kth epoch.

[0095] Step 7: If GNSS measurement information can be found, continue with steps 8-10; otherwise, return to step 5.

[0096] Step 8: Adaptively adjust the GNSS-RTK measurement noise based on the variance inflation model of abnormal observations to reduce the impact of abnormal GNSS measurement information on the fusion results. The variance inflation model can be expressed by the following formula:

[0097]

[0098] in is the variance inflation factor, are the equivalent variance and covariance respectively. The equivalent measurement noise can be described in matrix form:

[0099]

[0100] The diagonal elements represent the equivalent variance of the GNSS measurement information in the three directions of ENU, and the off-diagonal elements represent the covariance, such as Represents the equivalent covariance of EN in both directions.

[0101] Step 9: Kalman filter measurement update.

[0102] Construct the GNSS / accelerometer fusion Kalman filter measurement equation. Use the GNSS-RTK displacement as the measurement information to calculate the high-precision fusion solution. The measurement equation can be expressed as follows:

[0103] Z k =H k X k +ε k

[0104] Among them, the measurement vector Z k It only contains the 3D deformation displacement results of GNSS. k_GNSS , H k =[1 0 0] T is the measurement coefficient matrix, ε k is the measurement residual.

[0105] Calculate the measurement gain matrix K of the GNSS / accelerometer fusion Kalman k :

[0106]

[0107] Calculate the high-precision filter gain solution of the GNSS / accelerometer fusion Kalman filter state vector (including landslide deformation displacement, deformation velocity and accelerometer baseline deviation):

[0108]

[0109] Where I is the unit matrix, X k and P kare the gain values ​​of the updated state and its covariance matrix, X k,k-1 and P k,k-1 are the time update results of the state and its covariance matrix, K k is the measurement gain matrix, Z k and H k are the measurement vector and measurement coefficient matrix respectively.

[0110] Step 10: Repeat steps 5-9 to continue calculating the state gain value X at the k+1, k+2, k+3... moments k+1 X k+2 X k+3 and its covariance matrix P k+1 P k+2 P k+3 , high-precision landslide deformation monitoring results can be obtained.

[0111] The effect of the present invention can be illustrated by the following experiments:

[0112] 1. Experimental environment

[0113] In order to analyze and verify the effect of GNSS / accelerometer fusion technology in landslide monitoring, the paper simulated typical GNSS landslide monitoring scenarios with partial loss of GNSS signal.

[0114] Figure 2 A schematic diagram of the equipment layout of the simulation experiment scheme of the present invention is given. In the figure, the GNSS base station antenna 1 is placed on the roof, with a good observation environment, and the distance between it and the GNSS monitoring station antenna 2 is 10m to form a short baseline. The GNSS monitoring station antenna 2 and the three-axis accelerometer 3 are fixedly connected to form a rigid structure 4 using a three-dimensional simulation deformation platform 5 to ensure that both can move in the same direction and magnitude with the simulation platform to simulate the deformation process of the landslide. The receiver can receive GPS / Beidou / GLONASS / Galileo multi-system multi-frequency observation signals, the GNSS receiver data sampling rate is 1s, and the accelerometer data sampling frequency is 0.01s.

[0115] 2. Experimental results

[0116] As shown in Table 1, after the ambiguity is fixed, the monitoring positioning accuracy of GNSS can easily reach the centimeter level. However, in the complex environment of landslides, due to poor communication signals and obstruction by mountain vegetation, GNSS is easily affected by external interference such as reference station interruption and multipath diffraction, resulting in floating point solutions. The solution results usually have errors of tens of centimeters or even meters. The present invention designs static and dynamic simulation experiments to analyze the contribution of the GNSS / accelerometer fusion method in the landslide scenario, targeting the two common GNSS anomalies in landslide monitoring, namely reference station interruption and multipath diffraction.

[0117] Table 1

[0118]

[0119] (1) GNSS base station outage scenario

[0120] Figure 4 It is the effect of the interruption duration of the base station on the state covariance, which reflects that when an interruption occurs in the landslide monitoring operation, the positioning accuracy is degraded, which can easily lead to misjudgment of disaster warnings.

[0121] Figure 5 This is the fusion solution result of the simulated landslide stability stage when the GNSS base station is interrupted (period 1). It can be seen that after the GNSS base station signal is interrupted for 25 seconds, the plane error of the GNSS floating point solution reaches 0.15m, and the elevation error reaches 2m. If the conventional GNSS / accelerometer fusion method is used, anomalies will also occur. However, the GNSS measurement noise is adjusted based on the abnormal observation variance inflation model by the present invention, which well restores the accuracy of the fused solution, and the result is consistent with the actual deformation state.

[0122] Figure 6 This is the fusion solution result of the simulated landslide sliding stage when the GNSS base station is interrupted (period 2). It can be seen that when the GNSS base station signal is interrupted, the GNSS floating-point solution will deviate from the reference true value (with the RTK fixed solution as the reference true value) by tens of centimeters, while the GNSS / accelerometer fusion solution has better consistency with the reference true value.

[0123] (2) Multipath Effect & Satellite Occlusion Scenarios

[0124] Figure 7 It simulates the correlation between the signal-to-noise ratio, multipath error and GNSS covariance when satellite obstruction occurs in the stable stage of the landslide. It can be seen that when the multipath error exceeds 0.5m, the covariance of GNSS in the E, N and U directions is greater than 0.3m.

[0125] Figure 8 It is the fusion solution result of simulating the stable stage of landslide when the GNSS satellite is blocked (period 3). The result uses the variance inflation model to adaptively adjust the measurement noise, and the result is consistent with the actual displacement change.

[0126] Fig. 9This is the fusion solution result of simulating the landslide sliding stage when the GNSS satellite is blocked (period 4). During this period, the satellite blockage is simulated for 15 seconds, and only 4-5 GPS satellites with low signal-to-noise ratio (below 40dB) are retained. The results show that extreme satellite blockage is more likely to cause ambiguity fixation failure. The GNSS floating-point solutions in three directions deviate from the reference true value by up to 1.9m, while the fusion solution has better consistency with the reference true value.

Claims

1. A GNSS / accelerometer adaptive fusion landslide monitoring method based on variance inflation model, characterized in that: The following steps are involved: 【1】Install and level the accelerometer equipment, and align the three axes to the east-north-sky (ENU) direction. Leave the equipment still for ≥30 minutes, calculate the Allan variance and calibrate the random walk coefficient q=[q x q y q z ]; 【2】Install the GNSS antenna and accelerometer to form a rigid structure, use the first fixed solution of GPS-RTK to establish the local coordinate system of the ENU station center, and unify it with the accelerometer coordinate system; 【3】Initialize the initial value X0 of the Kalman filter’s state vector and the initial value P0 of its covariance matrix; 【4】The accelerometer baseline deviation u k Expand to estimate the parameters to be estimated and perform random walk modeling; 【5】Construct the state and covariance time update equation of the GNSS / accelerometer fusion Kalman filter; 【5.1】According to the variable acceleration model, perform state calculation and determine the state transfer matrix A k , construct the state time update equation; 【5.2】Calculate the noise matrix Q corresponding to the displacement, velocity and baseline deviation components k ; 【5.2.1】Calculate the acceleration noise based on the acceleration random walk coefficient obtained in step 【1】; 【5.2.2】According to the error propagation law, the acceleration noise is mapped onto the displacement, velocity and baseline deviation components to obtain the noise matrix Q of the process k ; Where N d N v N u Respectively represent the noise of displacement, velocity and baseline deviation, and the matrix [N d N v N u ] k T Use the character Q k It represents the process noise matrix of Kalman filtering, b k is the error propagation coefficient, q is the random walk coefficient, and Δt is the accelerometer sampling interval; 【5.3】Calculate the covariance of displacement, velocity and baseline deviation components based on the state covariance P at time k-1 k-1 , and with the help of the state transfer matrix A in step [5.1] k and the noise matrix Q in step [5.2.2] k Estimate the state covariance P at time k k,k-1 ; 【5.4】According to the state time update equation and covariance, the state and covariance time update equation of the GNSS / accelerometer fusion Kalman filter are obtained; 【6】Search for GNSS measurement information at the same time based on the acceleration timestamp of the kth epoch; [7] If GNSS measurement information can be found, continue with the following steps; otherwise, return to step [5]; 【8】 Based on the variance inflation model of abnormal observations, the GNSS-RTK measurement noise is adaptively adjusted to obtain the equivalent measurement noise To reduce the impact of abnormal GNSS measurement information on the fusion results; The variance inflation model is expressed as follows: in is the variance inflation factor, are the equivalent variance and covariance respectively. The equivalent measurement noise can be described in matrix form: The diagonal elements They represent the equivalent variance of GNSS measurement information in the three directions of ENU, and the off-diagonal elements represent the covariance. Represent the equivalent covariance of EN in two directions, Represent the equivalent covariance of the two directions of EU, Represent the equivalent covariance of NU in two directions; 【9】Kalman filter measurement update; 【10】Repeat steps 【5】-【9】, and continue to calculate the state gain value X at time k+1, k+2, k+3... k+1 X k+2 X k+3 and its covariance matrix P k+1 P k+2 P k+3 , high-precision landslide deformation monitoring results can be obtained.

2. The GNSS / accelerometer adaptive fusion landslide monitoring method based on variance inflation model according to claim 1 is characterized in that: The formula for random walk modeling of the accelerometer baseline deviation in step [4] is: u k =u k-1 +w k Where u k represents the accelerometer baseline deviation at time k, w k represents Gaussian white noise at time k.

3. The GNSS / accelerometer adaptive fusion landslide monitoring method based on variance inflation model according to claim 1 is characterized in that: The Kalman filter measurement update steps in step [9] are as follows: 【9.1】Use GNSS-RTK displacement as measurement information to determine the measurement vector Z k and the measurement coefficient matrix H k , construct the measurement equation; 【9.2】Calculate high-precision filtering solutions for displacement, velocity, and baseline deviation; [9.2.1] Update the state covariance time result obtained in step [5] and the measurement coefficient matrix H obtained in [9.1] k The equivalent measurement noise R obtained by [8] k Calculate the measurement gain matrix K of the Kalman filter k ; [9.2.2] The gain matrix K obtained according to step [9.2.1] k , the state time update result and its covariance matrix time update result obtained in step [5], and the measurement vector Z obtained in step [9.1] k and the measurement coefficient matrix H k Calculate the state gain value X after measurement update k and its covariance gain matrix P k .

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