GNSS positioning slow fault detection method based on residual error-SVR regression

Abstract

A GNSS positioning slowly-varying fault detection method based on residual-SVR regression comprises the steps that an observation information sequence is acquired based on a Kalman filter, and a covariance matrix of the observation information sequence is calculated; accumulating multi-step information through a sliding window, and constructing chi-square statistics; based on the fault-free data, constructing a training set by taking an innovation sequence as input and chi-square statistics as output, and generating an innovation-statistics mapping function; and fitting a normal slope threshold value based on an SVR predicted value, carrying out least square fitting on an observation statistic curve by sliding a window in real time, and judging whether to start a slow change fault alarm or not. According to the method, the residual error sequence is directly used as model input, and the dynamic chi-square statistical magnitude is used for replacing a traditional dichotomy label, so that the detection delay is reduced; an SVR detection model based on grid search and cross validation collaborative optimization is utilized, and an optimal parameter combination of a minimum mean square error (MSE) is screened through logarithm uniform sampling, interval linear sampling and five-fold cross validation, so that the average absolute error of slowly varying fault detection is reduced.

Description

Technical Field

[0001] The present invention relates to a GNSS positioning slowly varying fault detection method based on residual-SVR regression, and belongs to the technical field of satellite positioning. Background Art

[0002] Currently, the detection of slowly varying global navigation satellite system (GNSS) faults (such as satellite clock drift and multipath accumulation error) faces the following limitations: the geometric distribution-based RAIM algorithm is insensitive to continuous small changes; the Kalman filter relies on linear assumptions and exact state equations, making it difficult to model nonlinear, slowly varying processes; and while deep learning methods (such as LSTM) can capture time series features, they require massive fault samples and are computationally complex, making them difficult to meet the real-time requirements of scenarios such as aviation. In contrast, support vector regression (SVR) directly models nonlinear characteristics using kernel functions (such as RBFs), enabling the construction of high-precision prediction models with only a small amount of normal data. Its ε-insensitive band design adaptively filters out GNSS environmental noise, while also enabling dynamic threshold adjustment through sliding window residual statistics (such as the mean ±3σ).

[0003] In fault detection of integrated navigation systems, traditional methods often face the problem of balancing detection efficiency and accuracy, which is manifested in the following technical bottlenecks: (1) Insufficient adaptability of input feature redundancy and output statistics: Existing methods often use multi-sensor raw data (such as accelerometer and gyroscope outputs) or high-order fusion features (such as attitude angle error and velocity residual) as the input of the fault detection model, resulting in high feature dimension and heavy computational load. In addition, most solutions directly use binary classification labels (normal / faulty) as model output, lacking the ability to quantitatively evaluate fault intensity and making it difficult to meet the progressive decision-making requirements required for slow-changing fault detection. For example, although neural network-based classifiers can handle complex features, they have high inference latency (>50ms) and cannot output fault confidence in real time; (2) Coarse model parameter optimization and limited generalization performance: Traditional support vector regression (SVR) methods often rely on empirical parameters (such as penalty factor C, kernel function bandwidth γ) or local grid search in fault detection, resulting in significant prediction deviations in dynamic noise environments. Especially when the sensor noise distribution changes suddenly due to environmental interference, the fixed parameter model is prone to the phenomenon of too tight threshold (high false alarm rate) or too loose threshold (high missed detection rate); (3) Insufficient real-time detection in dynamic scenes: the existing residual analysis method needs to simultaneously calculate the multi-dimensional state estimation error (such as position, velocity, and attitude residuals) and generate statistics through complex hypothesis tests (such as generalized likelihood ratio test), resulting in a single detection time of more than 100ms, which is difficult to meet the real-time requirements of highly dynamic scenes (such as drone obstacle avoidance). In addition, the traditional chi-square test is only used as a posterior verification method and is not deeply coupled with the machine learning model, making it impossible to achieve end-to-end adaptive threshold adjustment. Summary of the Invention

[0004] The present invention provides a GNSS positioning slowly varying fault detection method based on residual-SVR regression. This method has low input feature dimension and small computational load, can achieve continuous quantized output of fault intensity, and reduces detection delay. It has strong generalization performance for the characteristics of slowly varying faults and meets the real-time detection requirements of highly dynamic scenarios.

[0005] To achieve the above object, the present invention provides a GNSS positioning slowly varying fault detection method based on residual-SVR regression, comprising the following steps:

[0006] S1. Obtain observation innovation sequence based on Kalman filter (EKF) and calculate its covariance matrix; accumulate multi-step innovations through sliding window, construct chi-square statistics, and quantify fault distribution characteristics;

[0007] S2. Based on fault-free data, a training set is constructed with the innovation sequence as input and the chi-square statistic as output. The radial basis function is used to optimize the SVR parameters through grid search combined with five-fold cross validation to generate the innovation-statistic mapping function.

[0008] S3. Fit the normal slope threshold based on the SVR prediction value, and use the real-time sliding window least squares to fit the observation statistic curve. If the slope exceeds the threshold range for multiple consecutive times, a slow-changing fault alarm is triggered.

[0009] Furthermore, the specific process of S1 is as follows:

[0010] S1.1. Define the state vector of the GNSS positioning system. The state vector contains the position error components δp corresponding to the three orthogonal directions of east (E), north (N), and sky (U) respectively. e ,δp n ,δp u and the velocity error component δv e ,δv n ,δv u and the receiver clock deviation δt clk and its drift rate δt drift ;

[0011] The dynamic evolution model of the clock bias characterizes the cumulative error characteristics of the receiver clock, and its expression is:

[0012] Among them, k represents the discrete time index of the current moment, Indicates the clock drift at the previous time k-1, Δ t is the filtering period, w t is the clock noise that obeys Gaussian distribution, is the noise variance, reflecting the stability of the clock crystal;

[0013] S1.2. Define the state transfer matrix Used to predict the state quantity at the next moment, its position and velocity block matrix is: Δt∈[10ms,100ms];

[0014] S1.3, based on the extended Kalman filter EKF framework, calculate the actual pseudo-range observation value Z k and the predicted value H k X k / k-1 The residual r k , Z k is the actual pseudorange observation vector, ρ M is the pseudorange measurement value of the Mth visible satellite; is the state prediction vector, x r 、y r 、z r is the receiver position, v x 、v y 、v z is the receiver speed, δt clk is the receiver clock deviation, δt drift is the receiver drift rate; H k is the measurement matrix; the measurement matrix H k Each row of corresponds to the geometric relationship of a visible satellite, and its elements are determined by the geometric partial derivatives of the satellite and receiver positions, expressed as: in, represents the partial derivative of the pseudorange of the i-th satellite with respect to the three-dimensional position of the receiver, where 1 and 0 correspond to the observation coefficients of the clock bias and drift rate, respectively;

[0015] S1.4, update the residual covariance matrix, the residual covariance matrix V k By the prediction covariance matrix P k / k-1 and the observation noise matrix R k The update formula for joint calculation is: Among them, P k / k-1 =φP k-1 Φ T +Q is the state prediction covariance matrix, P k-1 It is the state estimation covariance matrix at the k-1 moment, which indicates the confidence of the system state at the previous moment. In the state prediction covariance calculation: P k / k-1 =ΦP k-1 Φ T +Q, Φ represents the state transfer matrix, Q represents the process noise covariance;

[0016] is the process noise covariance matrix, and They represent the process noise variance of position and velocity, respectively, reflecting the uncertainty of the system model; is the process noise variance of the receiver clock bias, is the process noise variance of the clock drift rate;

[0017] Observation noise matrix is a diagonal matrix whose elements represents the pseudorange measurement noise variance of the i-th satellite, which is calculated in real time by the satellite signal quality assessment module;

[0018] S1.5. Construct a sliding window chi-square statistic. To enhance the sensitivity to slow-varying faults, a sliding window is used to accumulate multi-step residual information and construct a dynamic chi-square statistic: r i represents the residual vector at time step i, V i Residual r i The covariance matrix of the window length m=[T resp / Δt]∈[5,15], response time T resp ∈[0.5s,1.5s], the statistic follows a chi-square distribution with m degrees of freedom.

[0019] Furthermore, the specific process of S2 is as follows:

[0020] S2.1. Construct a training set and collect historical residual sequences under fault-free conditions. As input, the corresponding chi-square statistic As the output, a regression training set is constructed, where d = dim (r k ) is the residual dimension (equal to the number of visible satellites), n ≥ 1000 is the sample size to ensure the generalization ability of the model;

[0021] S2.2. Define the model structure and adopt the support vector regression SVR model. Its mapping function is: Among them, the kernel function is the radial basis function RBF, γ>0 is the bandwidth parameter, which controls the decay rate of similarity between samples; α i , is the Lagrange multiplier, b is the bias term, and is solved by the optimization algorithm;

[0022] S2.3, parameter joint optimization, through grid search traversal bandwidth parameter γ and penalty factor C candidate space: γ∈{10 -3 ,10 -2 ,0.1,1,10,10 2 ,10 3}, C∈{0.1,1,10,100}, the search range covers the feature space mapping from sparse to dense, ensuring the robustness of the model in complex noise environments;

[0023] S2.4. Cross-validation mechanism: 50% time series cross-validation is used, and the objective function is the weighted sum of the mean square error (MSE) and the detection delay time: Score = 0.6 × MSE + 0.4 × T detect , the calculation formula of MSE is: n val Indicates the number of samples in the validation set.

[0024] Furthermore, the specific process of S3 is as follows:

[0025] S3.1. Statistical sequence for SVR prediction Perform a 5th-order polynomial fit: Among them, a0 is the constant term of the polynomial, which represents the value of the fitting curve at t=0, a1 is the coefficient of the first order term, which represents the linear rate of change of the fitting curve, a2 is the coefficient of the second order term, which represents the quadratic curvature of the fitting curve, a3 is the coefficient of the third order term, which represents the cubic curvature of the fitting curve, a4 is the coefficient of the fourth order term, which represents the fourth curvature of the fitting curve, and a5 is the coefficient of the fifth order term, which represents the fifth curvature of the fitting curve. The fifth-order polynomial can effectively approximate the nonlinear change trend of the statistic while avoiding overfitting caused by high-order terms.

[0026] S3.2. Calculate the instantaneous slope and take the derivative of the fitting curve to obtain the instantaneous slope function: This function quantifies the rate of change of the statistic over time and provides a dynamic threshold benchmark for fault detection;

[0027] S3.3. Determine the confidence interval and calculate the slope mean μ based on historical normal data s and standard deviation σ s , determine the 99% confidence interval: [s min ,s max ]=[μ s -2.576σ s ,μ s +2.576σ s ], where 2.576 is the quantile of the standard normal distribution at the 99% confidence level;

[0028] S3.4, outlier elimination, in the preprocessing stage, eliminate the values ​​that meet the conditions |s i -μ s |>3σ s Abnormal samples to avoid interference of extreme values ​​on threshold calculation;

[0029] S3.5. In the sliding window [k-L+1, k], where L≤m, use the weighted least squares method to fit the slope of the current statistic: Weight w i and statistical variance Inversely proportional to ensure that high confidence data dominates the fitting; variance is the square of the standard deviation, Among them, n val is the number of samples in the validation set, is the observed value of each data point, is the mean of the observations;

[0030] S3.6, define the binary event sequence {E k}: This sequence is used to mark whether the slope at each moment is outside the normal range; if it is outside the normal range, it is recorded as 1, and if it is within the normal range, it is recorded as 0;

[0031] S3.7, continuous over-limit judgment, triggers an alarm when over-limit events are detected three times in a row, namely: This judgment condition effectively distinguishes slow-changing faults from instantaneous interferences through the continuous deviation characteristics of the slope of the cumulative statistics.

[0032] Continuous over-limit determination distinguishes slowly varying faults from transient disturbances by observing the persistent deviation of the slope of the cumulative statistic. Specifically, the trigger condition for continuous over-limit determination is three consecutive detections of a slope outside the normal range, which is an over-limit event. This method is effective in distinguishing slowly varying faults from transient disturbances for the following reasons:

[0033] Characteristics of slowly varying faults: Slowly varying faults are usually manifested as a slow and continuous deviation of the slope of a statistical quantity from the normal range. Since this deviation is gradually accumulated, the slope is likely to continue to exceed the normal range in multiple consecutive tests.

[0034] Characteristics of transient interference: Transient interference usually manifests itself as a sudden deviation in the slope of a statistic, but this deviation is usually short-lived and will not last.

[0035] Therefore, in multiple consecutive tests, the slope of the transient interference may exceed the normal range only once or twice, but is unlikely to exceed it three times in a row.

[0036] The system effectively distinguishes between the persistent deviations of slowly varying faults and the brief deviations of transient disturbances. Specifically, a slowly varying fault, due to the persistent deviation of its slope, is likely to exceed the normal range three times in a row, triggering an alarm. A transient disturbance, due to the typically brief deviation of its slope, is unlikely to exceed the normal range three times in a row, thus reducing the possibility of false alarms.

[0037] S3.8, false alarm rate control, the false alarm rate is calculated as: P false =α 3 =10 -6 ,α=0.01, assuming that the false alarm probability of a single limit violation is 1% and the joint probability of three consecutive independent limit violations is 10 -6 , then the security requirements are met.

[0038] Under no-fault conditions, the real-time slope s obs Normal distribution: Among them, μ s is the mean of the historical normal slope, σ s The 99% confidence interval for the normal slope is set to:

[0039] [s min ,s max ]=[μ s -z 0.995 σ s ,μ s +z 0.995 σ s ];

[0040] Among them, z 0.995 =2.576 is the 99% quantile of the standard normal distribution. The probability of one-sided excess is: α = P(s obs >s max )=P(s obs <s min )=0.5%;

[0041] The total probability of exceeding the limit is: α total =1% (i.e. 0.5% + 0.5%);

[0042] According to the DO-178C Level A standard (aviation-grade reliability requirements), the maximum allowable false alarm rate for critical systems is:

[0043] P false ≤10 -9 / hour, through α and P false The relationship between the minimum number of consecutive limit violations N is determined min :

[0044] If α=1%, P false =10 -6 →N min =3;

[0045] Therefore, for the GNSS / INS integrated navigation system, the combination of α = 1% and N = 3 can balance the real-time performance (detection delay ≤ 1.5s) and safety (P false =10 -6), meeting DO-178CLevelB requirements.

[0046] The present invention avoids the computational complexity of high-order features by directly using the residual sequence as the model input, replaces the traditional binary classification label with a dynamic chi-square statistic, achieves continuous quantitative output of fault intensity, and significantly reduces detection latency. The SVR detection model based on grid search and cross-validation collaborative optimization is used to design a parameter search space for slowly varying fault characteristics. Logarithmic uniform sampling is used to match the low-frequency characteristics of slowly varying signals. Interval linear sampling is used to balance the model's sensitivity to small residual fluctuations and significant faults. Five-fold cross-validation is used to screen the optimal parameter combination that minimizes the mean square error (MSE). This solves the prediction bias problem caused by traditional empirical parameters and reduces the mean absolute error of slowly varying fault detection. The present invention has strong generalization performance and meets the real-time detection requirements for highly dynamic scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the workflow of the method of the present invention;

[0048] Figure 2 (a) and (b) are the RMSE comparison diagrams of the LSTM model training set and test set in the embodiment;

[0049] Figure 3 (a) and (b) are the RMSE comparison diagrams of the LSSVM model training set and test set in the embodiment;

[0050] Figure 4 (a) and (b) are RMSE comparison diagrams of the model training set and test set based on the present invention in the embodiment;

[0051] Figure 5 (a) is a diagram showing the chi-square statistic and the threshold value of the AIME algorithm in the embodiment, and (b) is a diagram showing the normal slope range and the actual slope predicted by the model on which the present invention is based. DETAILED DESCRIPTION

[0052] The present invention will be further described below with reference to the accompanying drawings.

[0053] like Figure 1 As shown in FIG, a GNSS positioning slowly varying fault detection method based on residual-SVR regression includes the following steps:

[0054] S1. Obtain observation innovation sequence based on Kalman filter (EKF) and calculate its covariance matrix; accumulate multi-step innovations through sliding window, construct chi-square statistics, and quantify fault distribution characteristics;

[0055] S2. Based on fault-free data, a training set is constructed with the innovation sequence as input and the chi-square statistic as output. The radial basis function is used to optimize the SVR parameters through grid search combined with five-fold cross validation to generate the innovation-statistic mapping function.

[0056] S3: Fit the normal slope threshold based on the SVR prediction value, and use the real-time sliding window least squares to fit the observation statistic curve. If the slope exceeds the threshold range for three consecutive times, a slow-changing fault alarm is triggered.

[0057] Example: To verify the superiority of the GNSS positioning slowly varying fault detection method based on grid search optimized support vector regression (GS-SVR) proposed in the present invention, two sets of systematic experiments were conducted to comprehensively evaluate its model generalization ability and detection timeliness, and compared and analyzed with mainstream algorithms.

[0058] The first set of experiments compared the predictive performance of different regression models. Using historical residual sequences collected by a GNSS receiver in a fault-free state as input, the experiments trained the LSTM, LSSVM, and GS-SVR models proposed in this paper, using the root mean square error (RMSE) as the core evaluation metric.

[0059] The LSTM model showed a low RMSE (1.8341 meters) on the training set, but its test set error increased significantly to 3.2687 meters, with an overfitting rate of up to 78.1%, indicating that its ability to model the non-stationary time series characteristics of GNSS slowly varying faults is limited and it is difficult to adapt to dynamic noise interference. Figure 2 As shown in (a) and (b) in the figure, the RMSE of the training set and test set of the LSTM model are significantly different, revealing its insufficient generalization ability.

[0060] Although the LSSVM model achieved a low error of 0.8339 meters on the training set, the RMSE on the test set rose to 3.5809 meters, with an overfitting rate exceeding 300%, further exposing the inherent defect of the fixed parameter model in terms of sensitivity to data distribution. Figure 3 As shown in (a) and (b), the training set error of LSSVM is extremely low, while the test set error fluctuates violently, verifying that it is heavily dependent on the distribution of training data.

[0061] Through grid search optimization and five-fold cross-validation mechanism, the present invention achieved RMSE of 1.8632 meters and 1.3544 meters on the training set and test set respectively, with an overfitting rate of only 27.3%, showing excellent generalization ability. Figure 4 As shown in (a) and (b), the errors of the training set and the test set of the present invention are both in a reasonable range, and the difference is minimal, proving its anti-overfitting property. This advantage comes from the global optimization of the regularization parameter C and the bandwidth parameter γ by grid search (C∈{0.1, 1, 10, 100}, γ∈{10-3 , 10 -2 , 0.1, 1}), combined with the correction of data bias by cross-validation, the model remains robust in a noisy environment.

[0062] The second set of experiments focused on fault detection timeliness, comparing the response speed of the proposed method with that of the traditional Adaptive Iterative Least Squares (AIME) algorithm in a slowly varying fault scenario. The experiment injected a slowly varying fault (initial deviation 0.1 meter, slope 0.1 meter / second, duration 100 seconds) with a linearly increasing amplitude over time into the GNSS pseudorange observations, and recorded the time to first alarm for both methods.

[0063] The AIME algorithm relies on the threshold judgment mechanism of the chi-square test statistic, which requires sufficient accumulation of residual deviations to trigger an alarm. As a result, it detects the fault at 82.6 seconds, when the fault amplitude has accumulated to 5.26 meters, which is seriously lagging behind the actual fault development process. Figure 5 As shown in (a), the chi-square statistic of AIME (blue curve) takes a long time to accumulate before it exceeds the threshold (gray dotted line).

[0064] The GNSS positioning slowly varying fault detection method based on residual-SVR regression of the present invention calculates the slope of the chi-square test statistic curve after the fault is injected in real time and compares it with the slope range predicted based on historical normal data. It detects that the slope exceeds the normal range within 62 seconds. At this time, the fault amplitude is only 3.2 meters, which is 24.9% earlier than AIME. Figure 5 As shown in (b), the normal slope range is determined by the 99% confidence interval of the historical data ([s min ,s max ]=μ s ±2.576σ s ), while the actual slope after fault injection significantly deviates from this range after 62 seconds, demonstrating the present invention's ability to discern slowly changing trends. This discrepancy stems from the real-time sliding window fitting strategy: a weighted least squares method with a window length of L = 5 is used to calculate the instantaneous slope of the current residual sequence and compare it with the normal range of the prediction model to enable early fault identification.

[0065] Combining two sets of experiments, we show that this method achieves comprehensive improvements in GNSS slowly varying fault detection performance by integrating parameter optimization, dynamic thresholding, and real-time slope monitoring. In terms of model generalization, the RMSE on the test set is reduced by 58.6% and 62.2% compared to LSTM and LSSVM, respectively, effectively overcoming the overfitting problem. In terms of detection timeliness, the alarm response speed is improved by 24.9% compared to AIME. These characteristics make it particularly suitable for highly dynamic GNSS / INS integrated navigation systems, providing accurate and reliable fault detection capabilities for scenarios such as drones and autonomous driving. Figures 2 to 4The algorithm comparison results are intuitively displayed, further demonstrating the effectiveness of the present invention. Experimental data shows that the present invention significantly outperforms traditional methods in both fault detection accuracy and response speed in complex noisy environments, providing high reliability for GNSS positioning systems.

[0066] In addition, the present invention can be used not only for single systems such as GPS, GLONASS, BDS and GALILEO, but also for combined positioning of different satellite systems and inertial systems, and has a wide range of applications.

Claims

1. A GNSS positioning slowly varying fault detection method based on residual-SVR regression, characterized in that: The steps include: S1. Obtain observation innovation sequence based on Kalman filter (EKF) and calculate its covariance matrix; accumulate multi-step innovations through sliding window, construct chi-square statistics, and quantify fault distribution characteristics; S2. Based on fault-free data, a training set is constructed with the innovation sequence as input and the chi-square statistic as output. The radial basis function is used to optimize the SVR parameters through grid search combined with five-fold cross validation to generate the innovation-statistic mapping function. S3. Fit the normal slope threshold based on the SVR prediction value, and use the real-time sliding window least squares to fit the observation statistic curve. If the slope exceeds the threshold range for multiple consecutive times, a slow-changing fault alarm is triggered.

2. The GNSS positioning slowly varying fault detection method based on residual-SVR regression according to claim 1 is characterized in that: The specific process of S1 is as follows: S1.

1. Define the state vector of the GNSS positioning system. The state vector contains the position error components δp corresponding to the three orthogonal directions of east, north and sky. e ,δp n ,δp u and the velocity error component δv e ,δv n ,δv u and the receiver clock deviation δt clk and its drift rate δt drift ; The dynamic evolution model of the clock bias characterizes the cumulative error characteristics of the receiver clock, and its expression is: Among them, k represents the discrete time index of the current moment, Indicates the clock drift at the previous time k-1, Δ t is the filtering period, w t is the clock noise that obeys Gaussian distribution, is the noise variance, reflecting the stability of the clock crystal; S1.

2. Define the state transfer matrix Used to predict the state quantity at the next moment, its position and velocity block matrix is: Δt∈[10ms,100ms]; S1.3, based on the extended Kalman filter EKF framework, calculate the actual pseudo-range observation value Z k and the predicted value H k X k / k-1 The residual r k , Z k is the actual pseudorange observation vector, ρ M is the pseudorange measurement value of the Mth visible satellite; is the state prediction vector, x r 、y r 、z r is the receiver position, v x 、v y 、v z is the receiver speed, δt clk is the receiver clock deviation, δt drift is the receiver drift rate; H k is the measurement matrix; the measurement matrix H k Each row of corresponds to the geometric relationship of a visible satellite, and its elements are determined by the geometric partial derivatives of the satellite and receiver positions, expressed as: in, represents the partial derivative of the pseudorange of the i-th satellite with respect to the three-dimensional position of the receiver, where 1 and 0 correspond to the observation coefficients of the clock bias and drift rate, respectively; S1.4, update the residual covariance matrix, the residual covariance matrix V k By the prediction covariance matrix P k / k-1 and the observation noise matrix R k The update formula for joint calculation is: Among them, P k / k-1 =ΦP k-1 Φ T +Q is the state prediction covariance matrix, P k-1 is the state estimation covariance matrix at time k-1, which indicates the confidence of the system state at the previous moment. In the state prediction covariance calculation: P k / k-1 =ΦP k-1 Φ T +Q, Φ represents the state transfer matrix, Q represents the process noise covariance; is the process noise covariance matrix, and They represent the process noise variance of position and velocity, respectively, reflecting the uncertainty of the system model; is the process noise variance of the receiver clock bias, is the process noise variance of the clock drift rate; Observation noise matrix is a diagonal matrix whose elements represents the pseudorange measurement noise variance of the i-th satellite, which is calculated in real time by the satellite signal quality assessment module; S1.

5. Construct a sliding window chi-square statistic. To enhance the sensitivity to slow-varying faults, a sliding window is used to accumulate multi-step residual information and construct a dynamic chi-square statistic: r i represents the residual vector at time step i, V i Residual r i The covariance matrix of the window length m=[T resp / Δt]∈[5,15], response time T resp ∈[0.5s,1.5s], the statistic follows a chi-square distribution with m degrees of freedom.

3. The GNSS positioning slowly varying fault detection method based on residual-SVR regression according to claim 1 is characterized in that: The specific process of S2 is as follows: S2.

1. Construct a training set and collect historical residual sequences under fault-free conditions. As input, the corresponding chi-square statistic As the output, a regression training set is constructed, where d = dim (r k ) is the residual dimension, n ≥ 1000 is the sample size; S2.

2. Define the model structure and adopt the support vector regression SVR model. Its mapping function is: Among them, the kernel function is the radial basis function RBF, γ>0 is the bandwidth parameter, which controls the decay rate of similarity between samples; α i , is the Lagrange multiplier, b is the bias term, and is solved by the optimization algorithm; S2.3, parameter joint optimization, through grid search traversal bandwidth parameter γ and penalty factor C candidate space: γ∈{10 -3 ,10 -2 ,0.1,1,10,10 2 ,10 3 }, C∈{0.1,1,10,100}, the search range covers the feature space mapping from sparse to dense; S2.

4. Cross-validation mechanism: 50% time series cross-validation is used, and the objective function is the weighted sum of the mean square error (MSE) and the detection delay time: Score = 0.6 × MSE + 0.4 × T detect , the calculation formula of MSE is: n val Indicates the number of samples in the validation set.

4. The GNSS positioning slowly varying fault detection method based on residual-SVR regression according to claim 1 is characterized in that: The specific process of S3 is as follows: S3.

1. Statistical sequence for SVR prediction Perform a 5th-order polynomial fit: Wherein, a0 is the constant term of the polynomial, which represents the value of the fitting curve at t=0; a1 is the coefficient of the first order term, which represents the linear rate of change of the fitting curve; a2 is the coefficient of the second order term, which represents the quadratic curvature of the fitting curve; a3 is the coefficient of the third order term, which represents the cubic curvature of the fitting curve; a4 is the coefficient of the fourth order term, which represents the fourth curvature of the fitting curve; a5 is the coefficient of the fifth order term, which represents the fifth curvature of the fitting curve; S3.

2. Calculate the instantaneous slope and take the derivative of the fitting curve to obtain the instantaneous slope function: S3.

3. Determine the confidence interval and calculate the slope mean μ based on historical normal data s and standard deviation σ s , determine the confidence interval: [s min ,s max ]=[μ s -2.576σ s ,μ s +2.576σ s ], where 2.576 is the quantile of the standard normal distribution at the confidence level; S3.4, outlier elimination, in the preprocessing stage, eliminate the values ​​that meet the conditions |s i -μ s |>3σ s Abnormal samples to avoid interference of extreme values ​​on threshold calculation; S3.

5. In the sliding window [k-L+1, k], where L≤m, use the weighted least squares method to fit the slope of the current statistic: Weight w i and statistical variance Inversely proportional to ensure that high confidence data dominates the fitting; variance is the square of the standard deviation, Among them, n val is the number of samples in the validation set, is the observed value of each data point, is the mean of the observations; S3.6, define the binary event sequence {E k }: This sequence is used to mark whether the slope at each moment is outside the normal range; if it is outside the normal range, it is recorded as 1, and if it is within the normal range, it is recorded as 0; S3.7, continuous over-limit judgment, triggers an alarm when over-limit events are detected three times in a row, namely: This judgment condition effectively distinguishes slow-changing faults from instantaneous interferences through the continuous deviation characteristics of the slope of the cumulative statistics. S3.8, false alarm rate control, the false alarm rate is calculated as: P false =α 3 =10 -6 ,α=0.01, assuming that the false alarm probability of a single limit violation is 1%, and the joint probability of three consecutive independent limit violations is 10 -6 , then the security requirements are met.

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