Multivariable measurement sensor fault-tolerant control method based on spatiotemporal redundancy data reconstruction

Abstract

The application discloses a kind of multivariate measurement sensor fault-tolerant control methods based on spatiotemporal redundancy data reconstruction, it is applicable to intelligent driving vehicle sensor abnormal or suffers physical attack scene.The application first constructs vehicle three-dimensional position, velocity, acceleration multivariate state model and multisource heterogeneous sensor observation model, clear measurement and state mapping relationship;Secondly based on state time evolution and sensor space observation correlation, construct spatiotemporal redundancy description model, quantify consistency and combine threshold value to identify abnormality;Again rely on redundancy data driven state estimation model, abnormality determination is converted into continuous credibility weight, reconstructs key state quantity and generates virtual measurement information set;Finally, combined with adaptive weight distribution and feedback control constructs fault-tolerant control law, and verifies closed-loop stability through Lyapunov function.The application adopts credibility weighting and virtual measurement compensation double mechanism, avoids single sensor failure risk, improves system adaptability and safe operation ability.

Description

Technical Field

[0001] This invention belongs to the field of intelligent driving and multi-sensor fault-tolerant control technology, specifically involving a multivariable measurement sensor fault-tolerant control method based on spatiotemporal redundant data reconstruction. It involves spatiotemporal redundancy modeling of multi-source sensors, abnormal state judgment, credibility weight modeling, vehicle state reconstruction and closed-loop fault-tolerant control technology, which is applicable to the state estimation and stability control of autonomous vehicles in scenarios of sensor anomalies, failures or physical attacks. Background Technology

[0002] As intelligent driving technology evolves towards higher levels of autonomous driving, vehicle perception systems integrate six types of heterogeneous sensors, including LiDAR, cameras, millimeter-wave radar, and inertial measurement units. Through multi-source data fusion, they achieve high-precision perception of the vehicle's own state and its surrounding environment. As the core component of the perception system, the measurement accuracy and operational reliability of sensors directly determine the safety of the intelligent driving system.

[0003] In complex driving environments, sensors are susceptible to adverse weather, physical obstruction, electromagnetic interference, or malicious attacks, resulting in abnormal situations such as measurement drift, data loss, or even complete failure. Existing intelligent driving sensor fault-tolerant control methods mainly have the following shortcomings: (1) The anomaly judgment dimension is singular, relying mainly on the sensor's own measurement noise or threshold comparison, failing to fully utilize the spatiotemporal correlation between multiple sensors, which easily leads to misjudgment or omission, resulting in incorrect system decisions and safety risks; (2) The state reconstruction robustness is insufficient, with some methods directly eliminating abnormal sensor data, resulting in reduced system information redundancy, making it difficult to achieve stable state estimation when multiple sensors are abnormal at the same time; (3) The coupling degree between fault-tolerant control and state estimation is low, with traditional methods separating anomaly judgment, state reconstruction, and control input calculation, failing to construct a closed-loop optimization mechanism, making it difficult to adapt to the dynamic changes of sensor anomalies; (4) The uncertainty of virtual measurement is not considered, with some methods generating virtual measurements through state estimation to replace abnormal sensor outputs, but failing to quantify the reduction in the credibility of virtual measurements, resulting in potential risks to control input.

[0004] To address the aforementioned issues, there is an urgent need to propose a fault-tolerant control method based on the spatiotemporal redundancy characteristics of multiple sensors. This method achieves accurate anomaly detection by constructing a spatiotemporal redundancy metric model, reconstructs the vehicle state based on credibility weighting, and designs a fault-tolerant control law in conjunction with closed-loop stability constraints. This will improve the robustness and safety of the intelligent driving system under sensor anomaly scenarios.

[0005] The multivariable measurement sensor fault-tolerant control method proposed in this invention, based on spatiotemporal redundant data reconstruction, constructs a quantified redundancy model by mining the continuous evolution characteristics of multiple sensors in the time dimension and the observation correlation in the spatial dimension, thereby achieving accurate identification of sensor anomalies. The discrete anomaly judgment results are transformed into continuous reliability weights to avoid information loss caused by directly eliminating abnormal sensors. By combining recursive estimation and virtual measurement compensation, a closed-loop system of "anomaly judgment - state reconstruction - fault-tolerant control - stability verification" is formed, providing a highly reliable fault-tolerant control solution for intelligent driving vehicles. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of inaccurate anomaly detection, unstable state reconstruction, disconnect between control and estimation, and unclear risks of virtual measurement in existing intelligent driving sensor fault-tolerant control methods, and to propose a multivariable measurement sensor fault-tolerant control method based on spatiotemporal redundant data reconstruction.

[0007] To achieve the above objectives, this invention provides a fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction. Its key feature is that it is applied to a multi-sensor system of an intelligent driving vehicle, enabling vehicle stability control in the event of sensor malfunction or failure. Specifically, it includes the following steps: Step 1) Multivariable system and multi-sensor measurement modeling: A multivariable system state model and a multi-sensor measurement model for the vehicle are constructed. Three types of state variables are defined in the three-dimensional space of the vehicle: position, velocity, and acceleration. The mapping relationship between the measurement output of each sensor and the system state is established. The observation characteristics of the vehicle state by the multi-source sensors are described, providing a standardized mathematical basis for subsequent spatiotemporal redundancy modeling.

[0008] The specific method in step 1) is as follows: Step 1.1) Based on the kinematic and dynamic characteristics of intelligent driving vehicles operating in complex environments, construct a unified multivariable system state description model to characterize the real physical operating state of the vehicle in three-dimensional space, and define the vehicle at time... The true state vector is:

[0009] in, This represents the spatial position components of the vehicle in the global coordinate system; This represents the vehicle's velocity component in the corresponding direction; Represents the acceleration components of the vehicle; Step 1.2) Establish a unified multi-sensor measurement model for the different measurement methods of the above state variables by the vehicle-mounted multi-source sensors; assume that there are a total of The heterogeneous sensor, the first Each sensor at time The measurement output is expressed as:

[0010] in, For the first Measurement vectors of each sensor This is the corresponding nonlinear measurement function, used to describe the mapping relationship between the vehicle's actual state and the sensor measurement space. This is a measurement of the noise term, used to characterize the inherent uncertainties of the sensor and the effects of external interference; By performing a first-order approximation on the above nonlinear measurement model, which satisfies the linearization condition or is located near a local operating point, we obtain the linear observation expression:

[0011] in, For the first The measurement matrix corresponding to each sensor is used to characterize the sensor's sensitivity to the observation of each component in the system state.

[0012] Step 2) Construction and quantification of spatiotemporal redundancy relationships among multi-source sensors: Based on the continuous evolution characteristics of vehicle state over time and the spatial correlation of different sensors, a spatiotemporal redundancy model of multi-source sensors is constructed. The degree of sensor measurement redundancy is quantitatively described by temporal prediction consistency and cross-sensor spatial consistency.

[0013] The specific method in step 2) is as follows: Based on the multivariable system state model and multi-sensor measurement model constructed in step 1), in order to support state reconstruction and fault-tolerant control under abnormal sensor conditions, the redundancy relationship of different sensors in the time and space dimensions is further characterized. By introducing time-series prediction consistency and cross-sensor spatial consistency constraints, a quantifiable and determinable spatiotemporal redundancy description model is constructed. Step 2.1) In the time dimension, utilizing the continuous evolution characteristics of vehicle state between adjacent time points, construct a system state time prediction model:

[0014] in, For a moment The predicted value of the prior state. The result of the state estimation at the previous moment. This is the system state transition matrix, used to describe the motion evolution of the vehicle per unit time. Based on the time-predicted state, construct the first Prediction residuals of each sensor over time:

[0015] in, It represents the deviation between the actual measured value of the sensor and the predicted state over time, and is used to reflect the degree of consistency of the sensor in the time dimension; Step 2.2) In the spatial dimension, considering the cross-observation or equivalent mapping relationship between different sensors for the same physical state variable, a cross-sensor spatial consistency constraint is introduced for any two sensors. and Construct spatial mapping residuals:

[0016] in, This is a spatial mapping matrix used to describe the sensor. The measurement results are sent to the sensor Equivalent transformation relationships in the measurement space; Step 2.3) To achieve a unified quantification of spatiotemporal redundancy, temporal redundancy measurement indicators and spatial redundancy measurement indicators are defined respectively:

[0017]

[0018] in, This represents the L2 norm operation. The smaller the index value, the higher the consistency between the sensor measurement results and the time prediction model or spatial redundancy constraints.

[0019] Step 3) Sensor anomaly determination based on spatiotemporal redundancy consistency: Based on the spatiotemporal redundancy relationship model, the deviation between the measurement results of each sensor and the time prediction model and spatial redundancy constraints is calculated to form a comprehensive anomaly judgment index. Based on the preset threshold, the current state of the sensor is judged to be abnormal, providing a clear criterion for subsequent credibility assessment.

[0020] The specific method in step 3) is as follows: Based on the quantitative modeling of the spatiotemporal redundancy relationship of multi-source sensors, in order to identify faults, drifts or abnormal attack behaviors that occur in the sensors during operation, it is necessary to determine the measurement consistency of each sensor in real time. This step is based on temporal redundancy consistency and spatial redundancy consistency to build a unified sensor anomaly detection and judgment mechanism. First, regarding the consistency of a single sensor's performance in the time dimension, based on the temporal redundancy residual obtained in step 2... Construct time consistency metrics:

[0021] in, For the first The covariance matrix of the sensor measurement noise is used to characterize the statistical characteristics of the sensor under normal operating conditions; this index is used to measure the degree of deviation between the sensor's current measurement and its time prediction result. Secondly, regarding the consistency of sensor performance in the spatial dimension, based on the spatial redundancy residuals defined in step 2), Construct spatial consistency indicators:

[0022] in, The covariance matrix of the spatial mapping residuals is used to describe the sensor. With sensors Spatial consistency statistical characteristics under normal conditions; Furthermore, to comprehensively reflect the consistency level of the sensor in both time and space, a third... Comprehensive anomaly detection index for each sensor:

[0023] in, and These are the weighting coefficients for temporal consistency and spatial consistency, respectively. Indication and Sensors A set of sensors with spatial redundancy; Finally, the comprehensive anomaly detection index is compared with the preset threshold to complete the determination of the sensor's abnormal state.

[0024] in, Indicates the first Each sensor at time It was determined to be an abnormal state. This indicates that the sensor is in normal working condition. The anomaly detection threshold is related to the sensor type and noise characteristics; Through the above steps, a sensor anomaly determination mechanism based on spatiotemporal redundancy consistency was realized, providing a clear criterion basis for subsequent sensor reliability assessment, redundant data screening, state reconstruction, and fault-tolerant control.

[0025] Step 4) Sensor credibility assessment and weight modeling: The discrete anomaly determination results are transformed into continuous confidence weights to quantitatively evaluate the reliability of the measurement information of each sensor and construct an effective sensor set for subsequent processing.

[0026] The specific method in step 4) is as follows: Based on the completion of the abnormal state determination of multi-source sensors, in order to avoid the system information being insufficient or the estimation being unstable due to the direct elimination of abnormal sensors, this step introduces a sensor reliability evaluation mechanism, which transforms the abnormal determination result into a continuously adjustable reliability weight for subsequent spatiotemporal redundant data reconstruction and fault-tolerant control. First, based on the comprehensive anomaly judgment index obtained in step 3). , construct the first The original confidence function for each sensor:

[0027] in, This represents the sensor's initial confidence level at the current moment. This is the credibility decay coefficient, used to adjust the impact of anomaly level on the rate of credibility decline; this function ensures that when sensor measurements deviate significantly from spatiotemporal redundancy constraints, their credibility automatically decreases. Secondly, combined with anomaly detection flags The original credibility is corrected to distinguish between obvious anomalies and minor deviations:

[0028] in, The corrected credibility weight. This is the anomaly penalty coefficient, used to further suppress the sensor's influence on system estimation when an abnormal state is determined. To ensure the consistency and numerical stability of multi-source sensor weights during the fusion and reconstruction process, the confidence levels of all sensors are normalized.

[0029] in, Represents the normalized confidence weights, satisfying ; Furthermore, an effective sensor set is constructed based on the magnitude of the confidence weights:

[0030] in, The minimum confidence threshold is used to filter out sensor data that contributes very little to the reconstruction of the system state. Through the above credibility assessment and weight modeling process, a continuous quantitative description of the reliability of multi-source sensor measurement information is achieved. This enables the system to make full use of the remaining reliable information even when sensors are abnormal or partially fail, providing a stable and controllable input basis for subsequent data reconstruction and state estimation based on spatiotemporal redundancy.

[0031] Step 5) Reconstructing multivariate states based on credibility weighting: Based on the credibility weight, effective sensor measurement data are weighted and fused to construct an equivalent fusion observation model. Spatiotemporal redundant measurement information is used to reconstruct the state of the vehicle multivariable system and obtain the reconstructed state estimation result, which provides the initial state for subsequent recursive estimation updates.

[0032] The specific method in step 5) is as follows: Based on the completion of multi-source sensor credibility assessment and weight modeling, in order to obtain reliable vehicle status information even when some sensors are abnormal or fail, this step uses redundant measurement data from the set of trusted sensors to construct a multivariate state reconstruction model based on credibility weighting, so as to realize the real-time reconstruction of the system state. First, based on the effective sensor set obtained in step 4). The corresponding measurement data are then filtered, and a weighted fusion observation vector is constructed:

[0033] in, Indicates at time The fusion measurement results formed by multiple reliable sensors For the first Normalized confidence weights of each sensor, Its original measurement vector; the fusion process achieves adaptive allocation of the measurement contributions of sensors with different degrees of anomaly through weight adjustment; Secondly, to maintain the consistency of the state reconstruction process in mathematical form, an equivalent fusion measurement matrix is ​​constructed based on the measurement models of each sensor:

[0034] in, This is the fusion measurement matrix, used to describe the mapping relationship between the fusion observation vector and the system state vector; Based on this, a state reconstruction observation model based on spatiotemporal redundant data is established:

[0035] in, To fuse the measurement noise term, its covariance can be expressed as:

[0036] For the first The measurement noise covariance matrix of each sensor; Furthermore, combining the time prediction state obtained in step 2), Construct the least squares estimation form of the reconstructed state:

[0037] in, This represents the reconstructed state estimation result obtained based on spatiotemporal redundant data; Through the above steps, continuous reconstruction of the vehicle's multivariable state using reliable redundant measurement information is achieved under sensor malfunction conditions, providing a stable and reliable state input for subsequent state estimation updates, virtual measurement generation, and fault-tolerant control law design.

[0038] Step 6) Reconstructing the recursive state estimation update: By combining the vehicle system dynamic model, the reconstructed state is recursively estimated and updated to form a vehicle state estimation result with continuity and convergence, thus suppressing the impact of measurement uncertainty on system stability.

[0039] The specific method in step 6) is as follows: After completing the multivariate state reconstruction based on credibility weighting, in order to achieve continuous estimation and error suppression of vehicle state over time, this step introduces a recursive state estimation mechanism to predict and correct the system state, thereby improving the stability and real-time performance of state estimation. First, based on the dynamic characteristics of the vehicle system, a state prediction model is constructed, and the state estimate of the previous moment is extrapolated over time:

[0040] in, For a moment The predicted value of the prior state. For a moment The reconstruction state estimation results, This is the system state transition matrix; Simultaneously, the state estimation error covariance is predicted and updated:

[0041] in, For the prediction error covariance matrix, Let be the error covariance matrix of the previous time step. The system process noise covariance matrix; Secondly, based on the equivalent fusion observation model constructed in step 5), a state correction process is introduced; the recursive estimation gain matrix is ​​calculated:

[0042] in, For the state estimation gain matrix, and These are the fusion measurement matrix and its noise covariance, respectively. Based on the estimated gain, the system state is corrected and updated:

[0043] in, This is the recursively updated system state estimate; Simultaneously, the state estimation error covariance is updated:

[0044] in, It is the identity matrix; Through the above recursive estimation and update process, continuous and stable estimation of the multivariable state of the vehicle is achieved by using spatiotemporal redundancy to reconstruct observations under the condition of sensor anomaly or partial failure, providing a high-confidence state basis for subsequent virtual measurement generation and fault-tolerant control input calculation.

[0045] Step 7) Virtual Measurement Generation and Expansion Measurement Set Construction: For abnormal or malfunctioning sensors, corresponding virtual measurement information is generated based on the vehicle state obtained by recursion estimation. This virtual measurement information, together with the real measurements from valid sensors, constitutes an extended measurement set, maintaining the integrity of the system's measurement structure.

[0046] The specific method in step 7) is as follows: After completing the recursive state estimation update based on the reconstructed observation model, in order to avoid measurement channel interruption, system structure degradation or unusable control law due to sensor abnormality or failure, this step constructs a virtual measurement noise model based on the current state estimation result and performs equivalent compensation for the measurement information of abnormal sensors. First, regarding the first condition that was determined to be abnormal in step 3), One sensor (i.e.) Using the system state estimation results obtained in step 6 Generate the corresponding equivalent virtual measurement values:

[0047] in, This represents a virtual measurement vector used to replace the output of an abnormal sensor. This is the measurement matrix corresponding to the sensor; Secondly, to characterize the uncertainty introduced by virtual measurement relative to real measurement, a virtual measurement noise model is introduced, whose covariance is defined as:

[0048] in, For the first The measurement noise covariance matrix of each sensor under normal operating conditions. This is the uncertainty amplification factor, used to reflect the degree of reduction in reliability of virtual measurements compared to real measurements; Furthermore, virtual measurements are organized in a unified manner with valid real measurements at the current moment to construct an extended measurement set:

[0049] in, This represents an extended set of measurements that includes both real and virtual measurements. Correspondingly, an extended measurement noise covariance matrix is ​​constructed:

[0050] Used to uniformly describe measurement uncertainty in subsequent state updates or control calculations; Through the above virtual measurement generation and compensation modeling process, the measurement information structure is continuously maintained in the event of sensor abnormality or failure. This enables the system to stably transition to fault-tolerant operation mode without changing the overall estimation and control framework, providing complete measurement input conditions for subsequent fault-tolerant control law design and closed-loop stability analysis.

[0051] Step 8) Fault-tolerant control input calculation: A fault-tolerant control law is constructed based on the extended measurement set and vehicle state estimation results. The control input is adaptively adjusted according to the overall reliability level of the available measurement information to obtain the fault-tolerant control input of the vehicle.

[0052] The specific method in step 8) is as follows: After completing the virtual measurement generation and constructing the extended measurement set, in order to ensure that the vehicle can still maintain stable operation in the event of sensor malfunction or partial failure, this step constructs a fault-tolerant control input calculation method based on the recursive state estimation results and extended measurement information to realize real-time correction of vehicle control quantities. First, define the vehicle at time. Control target state vector:

[0053] in, This represents the expected reference values ​​for the vehicle's current position and speed, two key state variables. Based on the system state estimate obtained in step 6) Construct the control state error vector:

[0054] in, A state selection matrix is ​​used to extract key state components involved in control from the complete state vector; Secondly, to reduce the indirect impact of abnormal sensors on control input, a control weight adjustment factor based on sensor reliability is introduced:

[0055] in, This represents the current system credibility adjustment factor; Based on this, a fault-tolerant control law is constructed:

[0056] in, For the vehicle's control input vector, A pre-designed control gain matrix is ​​used to map state errors into control variables; Furthermore, to suppress the impact of virtual measurement uncertainty on the control input, a control input smoothing term is introduced:

[0057] in, The fault-tolerant control input for the final output. To control the smoothing coefficient; Through the above steps, fault-tolerant control input adaptive calculation based on extended measurement and reconstructed state information is realized under the condition of sensor abnormality or failure, so that the vehicle control system can still maintain a continuous, stable and controllable operating state even when the information is incomplete.

[0058] Step 9) Verification of stability constraints and control effects of the closed-loop system: Stability constraints are applied to the closed-loop system after the introduction of fault-tolerant control, and the effect of fault-tolerant control is verified by preset stability judgment indicators to ensure that the vehicle operates stably and controllably under the condition of sensor abnormality or failure.

[0059] The specific method in step 9) is as follows: After completing the calculation of the fault-tolerant control input based on extended measurement and reconstructed state, in order to ensure that the vehicle system still has stable operation capability under the condition of sensor abnormality or partial failure, this step performs stability constraint analysis on the constructed closed-loop control system and gives the judgment conditions for the effectiveness of fault-tolerant control. First, based on the control state error vector defined in step 8). Construct the Lyapunov function of the closed-loop system:

[0060] in, It is a symmetric positive definite matrix used to characterize the energy function of the system state error; Under the fault-tolerant control law, the dynamic error of the closed-loop system can be expressed as:

[0061] in, and These are the state matrix and control input matrix of the vehicle system, respectively. The credibility adjustment factor defined in step 8); Calculating the difference between adjacent time steps for the Lyapunov function yields:

[0062] By selecting the control gain matrix With Lyapunov matrix To satisfy the following inequality constraints:

[0063] in, It is a symmetric positive definite matrix; Then we have:

[0064] This indicates that under sensor malfunction or failure, the closed-loop system error asymptotically converges, and the system remains stable. Furthermore, we define the indicators for judging the effectiveness of fault-tolerant control:

[0065] When the following conditions are met:

[0066] in, The threshold for stability determination To ensure a stable convergence time (in discrete time steps), the fault-tolerant control method is deemed effective under the current abnormal conditions. Through the aforementioned closed-loop stability constraint and effectiveness judgment mechanism, the theoretical integrity of the fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction is verified, ensuring that the method has reliable and stable operation capability under complex and abnormal scenarios.

[0067] Compared with the prior art, the present invention has the following beneficial effects: (1) Accurate anomaly detection: Based on the spatiotemporal dual-dimensional redundancy constraints, a comprehensive index is constructed to break through the limitations of single-dimensional detection and improve the accuracy and reliability of sensor anomaly identification. (2) Stable state reconstruction: By weighted fusion of redundant information based on credibility, information loss caused by directly eliminating abnormal sensors is avoided, and the state can still be stably estimated when multiple sensors are abnormal at the same time. (3) Strong control adaptability: A closed-loop control system is constructed to achieve dynamic adaptation between state estimation and control input. (4) High system robustness: Virtual measurement compensation and stability constraints are combined to reduce the impact of sensor anomalies on the system. (5) Good engineering practicality: No additional hardware redundancy is required, it is compatible with various intelligent driving multi-sensor systems, and has a wide range of applications.

[0068] In summary, the multivariable measurement sensor fault-tolerant control method based on spatiotemporal redundant data reconstruction provided by this invention can achieve stable vehicle control under abnormal sensor scenarios, provide highly reliable fault-tolerant support for intelligent driving systems, and improve the system's adaptability and safety under complex operating conditions. Attached Figure Description

[0069] Figure 1 This is a flowchart of the method of the present invention.

[0070] This invention discloses a fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction, applicable to the safety control of intelligent driving vehicles under conditions of sensor anomaly, failure, or physical attack. This method achieves continuous correction and stable output of vehicle control inputs by constructing a multi-source sensor spatiotemporal redundancy description model, a redundant data-driven state estimation model, and an adaptive weight allocation and feedback control strategy. It does not rely on a single sensor, thus improving the robustness and safety of intelligent driving systems in complex environments. The invention is described in detail below with specific implementation steps.

[0071] Step 1): Modeling the state and multi-sensor measurement model of a multivariable system.

[0072] This step clarifies the mapping relationship between the vehicle's physical state and sensor measurement outputs by constructing a unified multivariable system state model and a multi-sensor measurement model, laying a mathematical foundation for subsequent spatiotemporal redundancy modeling, anomaly detection, and fault-tolerant control. Specifically, it includes the following: (I) Definition of State Vector for Multivariable Systems To characterize the kinematics and dynamics of intelligent driving vehicles and their actual physical state in three-dimensional space, the true state vector at time t is defined as:

[0073] in: x(t): The true state vector of the vehicle system at time t, which is a 9×1 column vector; x(t),y(t),z(t): Spatial position components of the vehicle along the x, y, and z axes in the global coordinate system; v x (t),v γ (t),v z (t): The velocity components of the vehicle in the x, y, and z axes of the global coordinate system; a x (t),a γ (t),a z (t): The acceleration components of the vehicle in the x, y, and z axes of the global coordinate system; T : Vector transpose operator, converts a row vector into a column vector.

[0074] This state vector covers the key motion parameters required for vehicle control and safety decisions, and is the core input for subsequent state estimation and fault-tolerant control.

[0075] (II) Construction of Multi-Sensor Nonlinear Observation Model

[0076] Suppose the system contains N heterogeneous sensors (LiDAR, camera, millimeter-wave radar, IMU). For each sensor's different measurement methods of vehicle state, a unified nonlinear observation model is established. The measurement output of the i-th sensor at time t is:

[0077] in: i: Sensor number, with a value range of 1, 2, ..., N; z i (t): The measurement vector of the i-th sensor at time t, with dimension m. i ×1(m) i (where is the output dimension of the i-th sensor), and matches the sensor type; h i ( ): The nonlinear measurement function of the i-th sensor, denoted as m. i The ×1 vector value function is used to describe the mapping relationship from the actual state of the vehicle to the sensor measurement space, and is determined by the sensor hardware characteristics and installation parameters. x(t): The true state vector of the vehicle system at time t (9×1 column vector); n i (t): The measurement noise term of the i-th sensor at time t, which is m i A ×1 column vector, following a zero-mean Gaussian distribution, is used to characterize the effects of sensor inherent uncertainties and external environmental interference (such as illumination and electromagnetic interference).

[0078] (III) Linearized Observation Model Approximation

[0079] When the linearization condition is met or the vehicle is operating near a local operating point, the above nonlinear measurement model is approximated by a first-order Taylor expansion to obtain a linear observation expression, which facilitates subsequent matrix operations and model solving:

[0080] in: z i (t): The measurement vector of the i-th sensor at time t (m i (×1 column vector); H i The measurement matrix corresponding to the i-th sensor has a dimension of m. i ×9 (sensor output dimension × state vector dimension) characterizes the sensor's sensitivity to the observation of each component of the system state, determined by the nonlinear function h. i ( The Jacobian matrix at the operating point is determined; x(t): The true state vector of the vehicle system at time t (9×1 column vector); n i (t): The measurement noise term (m) of the i-th sensor at time t. i (×1 column vector), which follows a zero-mean Gaussian distribution.

[0081] Step 2): Construction and quantification of spatiotemporal redundancy relationships among multi-source sensors

[0082] Building upon the modeling in step 1, this step introduces temporal dimension prediction consistency constraints and spatial dimension cross-sensor consistency constraints to construct a quantifiable spatiotemporal redundancy model. This enables accurate characterization of the redundancy level of multi-source sensor measurements, providing a quantitative basis for subsequent anomaly detection. Specifically, this includes the following: By leveraging the continuous evolution characteristics of vehicle states at adjacent time points, a system state time prediction model is constructed to provide a benchmark for time-series redundancy consistency analysis, as detailed below:

[0083] in: - (t): The prior state prediction value at time t, which is a 9×1 column vector, that is, the theoretical state at the current time derived based on the state at the previous time. F(t-1): The system state transition matrix from time t-1 to time t, with a dimension of 9×9, describes the motion evolution of the vehicle per unit time. It is derived from the vehicle dynamics equation and takes into account the influence of two types of motion parameters: vehicle speed and steering angle. (t-1): The posterior state estimation result at time t-1, which is a 9×1 column vector obtained from the preceding recursive estimation process.

[0084] Based on the above prediction model, the time prediction residual of the i-th sensor is constructed to reflect the deviation between the actual measurement and the time prediction state of the sensor:

[0085] in: e i time (t): The time residual vector of the i-th sensor at time t, with dimension m. i ×1, the smaller the residual, the stronger the consistency of the sensor measurement in the time dimension; z i (t): The measurement vector of the i-th sensor at time t (m i (×1 column vector); H i : The measurement matrix (m) corresponding to the i-th sensor i ×9); - (t): The prior state prediction at time t (9×1 column vector).

[0086] Considering the cross-observation characteristics of different sensors for the same physical state variable, a cross-sensor spatial consistency constraint is introduced to construct the spatial mapping residual between any two sensors i and j:

[0087] in: e ij space (t): The spatial residual vector of sensors i and j at time t, with dimension m. i ×1, used to characterize the consistency between the two at the space observation level; i,j: Sensor number, i≠j, value range is 1,2,...,N; z i (t): The measurement vector of the i-th sensor at time t (m i (×1 column vector); T ij The spatial mapping matrix from sensor j to sensor i, with dimension m. i ×m j (Matching the output dimensions of sensors i and j), used to equivalently transform the measurement results of sensor j to the measurement space of sensor i, and is obtained by calibrating the geometric parameters of the sensor installation position and field of view. z j(t): The measurement vector of the j-th sensor at time t (m j (×1 column vector).

[0088] To achieve a unified quantification of spatiotemporal redundancy, based on the aforementioned residual vector, temporal redundancy and spatial redundancy metrics are defined respectively. The vector residuals are then transformed into scalar metrics using L2 norm operations, as detailed below:

[0089]

[0090] in: D i time (t): The time redundancy metric of the i-th sensor at time t, which is a non-negative scalar; D ij space (t): Spatial redundancy measure of sensors i and j at time t, which is a non-negative scalar; 2: The L2 norm operation is used to calculate the Euclidean length of a vector, and the result is a non-negative value; e i time (t): The time residual vector of the i-th sensor at time t (m i (×1 column vector); e ij space (t): Spatial residual vector (m) of sensors i and j at time t i (×1 column vector).

[0091] The smaller the values ​​of the above indicators, the higher the consistency between the sensor measurement results and the time prediction model and spatial redundancy constraints, and the more reliable the redundancy information.

[0092] Step 3): Sensor anomaly determination based on spatiotemporal redundancy consistency

[0093] This step, based on the spatiotemporal redundancy metric constructed in step 2), establishes a comprehensive anomaly detection mechanism to identify sensor malfunctions, drift, or abnormal attack behaviors in real time, providing clear criteria for subsequent credibility assessment and data filtering. Specifically, it includes the following: (I) Construction of Time Consistency Indicators To assess the time consistency performance of a single sensor, a time consistency index is constructed based on the statistical characteristics of measurement noise, as follows: Time Consistency Index:

[0094] in: J itime (t): The time consistency index of the i-th sensor at time t. It is a non-negative scalar that follows a chi-square distribution. The larger the value, the greater the deviation between the sensor measurement and the time prediction result, and the higher the probability of an anomaly. e i time (t): The time residual vector of the i-th sensor at time t (m i (×1 column vector); T : Vector transpose operator, converts a column vector into a row vector; R i The covariance matrix of the noise measured by the i-th sensor, with dimension m. i ×m i , is a symmetric positive definite matrix, obtained by statistical analysis of sensor factory calibration and actual test data, and characterizes the noise distribution characteristics of the sensor under normal operating conditions; R i - ¹: Covariance matrix R i The inverse matrix with dimension m i ×m i Only when R i If it is invertible, it exists (a symmetric positive definite matrix is ​​always invertible).

[0095] (II) Construction of Spatial Consistency Indicators

[0096] To address the spatial consistency performance among sensors, a spatial consistency index is constructed based on the statistical characteristics of spatial mapping residuals, as follows: Spatial Consistency Index:

[0097] in: J ij space (t): Spatial consistency index of sensors i and j at time t, which is a non-negative scalar; e ij space (t): Spatial residual vector (m) of sensors i and j at time t i (×1 column vector); T Vector transpose operator; S ij : The covariance matrix of the spatial mapping residuals between sensors i and j, with dimension m i ×m i , obtained from historical data during normal operation of the sensors, describes the spatial consistency statistical characteristics of sensors i and j under normal conditions; S ij - ¹: Covariance matrix Sij The inverse matrix with dimension m i ×m i symmetric positive definite matrix S ij It is reversible.

[0098] To comprehensively reflect the consistency level of sensors in both time and space, a weighted coefficient is introduced to balance the influence of temporal and spatial characteristics, thus constructing a comprehensive anomaly judgment index for the i-th sensor:

[0099] in: J i (t): The comprehensive anomaly judgment index of the i-th sensor at time t, which is a non-negative scalar; λ t Time consistency weighting coefficient, a non-negative scalar; λ s Spatial consistency weighting coefficient, a non-negative scalar; λ t +λ s =1, which can be adjusted according to the sensor type and application scenario (e.g., for IMUs, which emphasize time consistency, take λ). t >λ s LiDAR emphasizes spatial consistency, so λ is chosen. s >λ t ); J i time (t): The time consistency index of the i-th sensor at time t (a non-negative scalar); ∑: Summation operator, for all j∈N i The items are accumulated; N i The set of sensors that have spatial redundancy with sensor i, determined by the system's sensor layout and observation range, j∈N i Let j be a set N i The elements in the set, where j ≠ i; J ij space (t): Spatial consistency index (non-negative scalar) of sensors i and j at time t.

[0100] (III) Determination of Sensor Abnormal Status

[0101] The comprehensive anomaly detection index is compared with a preset threshold, and the sensor anomaly status detection result is output:

[0102] in: δ i(t): The abnormal state flag of the i-th sensor at time t, which is a binary variable, δ i (t)=1 indicates that the i-th sensor determines an anomaly at time t, δ i (t)=0 indicates normal operation; J i (t): The comprehensive anomaly judgment index (non-negative scalar) of the i-th sensor at time t; Γ i The anomaly detection threshold for the i-th sensor is a non-negative scalar that is related to the sensor type, noise characteristics, and confidence level. It is determined by the chi-square distribution quantile to ensure that the sensor anomaly false detection rate is lower than the preset value during normal operation.

[0103] Step 4): Sensor reliability assessment and weight modeling based on anomaly detection results

[0104] This step transforms discrete anomaly detection results into continuously adjustable reliable weights, constructing a sensor reliability assessment mechanism. This avoids insufficient system information caused by directly eliminating anomalous sensors, providing a reliable weighting basis for subsequent data fusion and state reconstruction. Specifically, it includes the following: (I) Construction of the original credibility function Based on the comprehensive anomaly judgment index J obtained in step 3 i (t), construct the original confidence function for the i-th sensor to achieve a continuous mapping between anomaly level and confidence level:

[0105] in: w i raw (t): The original confidence value of the sensor, ranging from (0,1], J i The smaller (t) is, the closer the confidence level is to 1; α: Reliability decay coefficient, used to adjust the impact of anomaly degree on the rate of reliability decline. The larger α is, the more significant the reliability decline of the anomaly sensor. It is set according to the system's fault tolerance requirements.

[0106] (II) Credibility Weight Correction and Normalization

[0107] Combined with the anomaly detection flag δ i (t) is used to correct the original confidence level and enhance the weight suppression effect of the anomaly sensor:

[0108] in: η: Anomaly penalty coefficient, η∈(0,1), used to further reduce the weight of abnormal sensors and avoid abnormal data from interfering with the system; w i(t): The corrected credibility weight.

[0109] To ensure weight consistency and numerical stability, the confidence levels of all sensors are normalized so that the sum of their weights is 1.

[0110] (III) Construction of an effective sensor set

[0111] Based on the normalized confidence weights, a minimum confidence threshold ε is set to filter out sensor data that contributes very little to the system state reconstruction, thus constructing an effective sensor set:

[0112] Here, ε is the minimum confidence threshold, which is set by the system's requirements for data reliability. It is usually set to 0.05~0.1 to ensure that the sensor data in the effective set has sufficient confidence.

[0113] Step 5): Multivariate state reconstruction based on credibility weighting

[0114] This step utilizes redundant measurement data from the effective sensor set to construct a confidence-weighted state reconstruction model. Even with some sensors malfunctioning or failing, this model enables real-time reconstruction of the vehicle's multivariable state, providing stable input for subsequent recursive estimation. Specifically, it includes the following: (I) Construction of weighted fusion observation vectors and matrices Based on the effective sensor set S obtained in step 4 v (t) and normalized weight w i (t) is used to weight and fuse the effective sensor measurement data to construct a weighted fused observation vector:

[0115] Among them, Z f (t) represents the fusion measurement result at time t. The contribution of sensors with different credibility levels is adaptively adjusted through weight allocation. The higher the credibility of the sensor, the greater its influence on the fusion result.

[0116] An equivalent fusion measurement matrix is ​​constructed accordingly to maintain mathematical consistency in the state reconstruction process:

[0117] Among them, H f (t) is the fusion measurement matrix, which describes the mapping relationship between the fusion observation vector and the system state vector. Its dimension is the same as that of the single sensor measurement matrix.

[0118] (ii) Calculation of noise covariance in fusion measurement

[0119] Based on this, a state reconstruction observation model based on spatiotemporal redundant data is established:

[0120] in: n f (t): The noise term of the fused measurement, whose covariance can be expressed as: ; R i : The measurement noise covariance matrix of the i-th sensor.

[0121] (III) Least Squares State Reconstruction

[0122] Combined with the time prediction state x obtained in step 2 - (t), construct a state reconstruction model based on the least squares criterion, and solve for the optimal reconstruction state:

[0123] Where, x re c (t) represents the system state estimation result obtained based on spatiotemporal redundant data reconstruction. By solving the weighted least squares problem, the influence of measurement noise and abnormal data can be effectively suppressed, ensuring the reliability of the reconstructed state.

[0124] Step 6): Reconstructing the recursive estimation update of the state

[0125] This step introduces a recursive state estimation mechanism to predict and correct the reconstructed state, achieving continuous estimation and error suppression of the vehicle state over time, thus improving the stability and real-time performance of the state estimation. Specifically, it includes the following: (I) Prediction of State and Error Covariance Based on the dynamic characteristics of the vehicle system, the state estimation result of the previous moment is extrapolated to obtain the predicted value of the prior state at the current moment:

[0126] in: - (t): The prior state prediction value at time t, which is a 9×1 column vector, that is, the theoretical state at the current time derived based on the state at the previous time. F(t-1): The system state transition matrix from time t-1 to time t, with a dimension of 9×9, describes the motion evolution of the vehicle per unit time. It is derived from the vehicle dynamics equation and takes into account the influence of motion parameters such as vehicle speed and steering angle. (t-1): The posterior state estimation result at time t-1, which is a 9×1 column vector obtained from the preceding recursive estimation process.

[0127] Simultaneously, the state estimation error covariance is predicted and updated to characterize the uncertainty of the prior state:

[0128] in: P - (t): The prediction error covariance matrix at time t (9×9 dimensions); P(t-1): The posterior state error covariance matrix at time t-1; Q(t-1): The system process noise covariance matrix, which is obtained by statistical analysis of vehicle motion uncertainties (such as changes in road surface friction coefficient).

[0129] (ii) Recursive estimation of gain calculation

[0130] Based on the fusion observation model constructed in step 5), the recursive estimation gain matrix is ​​calculated to balance the effects of prior state uncertainty and measurement uncertainty:

[0131] Where K(t) is the state estimation gain matrix, with dimensions equal to H. f (t) Matching, the gain is determined by the prior error covariance and the fusion measurement noise covariance.

[0132] (III) State and Error Covariance Correction

[0133] Based on the estimated gain, the prior state is corrected to obtain the estimated posterior state of the system.

[0134] Simultaneously, the state estimation error covariance matrix is ​​updated to characterize the uncertainty of the posterior state:

[0135] Where I is the identity matrix (with the same dimension as the state vector), and the corrected error covariance matrix can intuitively reflect the reliability of the current state estimate.

[0136] Step 7): Virtual measurement generation and extended measurement set construction based on recursive estimation results

[0137] This step, based on the recursive state estimation results, constructs a virtual measurement model to perform equivalent compensation for abnormal sensor measurement information, maintaining the integrity of the system's measurement structure and preventing control framework degradation. Specifically, it includes the following: (a) Generation of virtual measurement values For the kth sensor (δ) identified as abnormal in step 3), k (t)=1), using the posterior state estimate obtained in step 6) Generate equivalent virtual measurement values ​​to replace abnormal sensor outputs:

[0138] Among them, H k The measurement matrix corresponding to this abnormal sensor is kept consistent with that during normal operation to ensure a unified spatial mapping relationship between virtual and real measurements.

[0139] (ii) Virtual measurement noise modeling

[0140] Considering the increased uncertainty of virtual measurements compared to real measurements, a virtual measurement noise covariance model is introduced to quantify the degree of confidence reduction:

[0141] in: R k : Measurement noise covariance matrix when the k-th sensor is working normally; β k Uncertainty amplification factor, β k ≥1, the larger the value, the higher the uncertainty of the virtual measurement, and it is set according to the sensor anomaly type (such as complete failure, drift).

[0142] (III) Construction of Extended Measurement Sets

[0143] By unifying virtual measurements with real measurements from effective sensors, an extended measurement set is constructed, maintaining the integrity of the system's measurement channels.

[0144] The corresponding extended measurement noise covariance matrix is ​​constructed as follows:

[0145] Here, diag(·) represents the diagonal matrix construction operation, and the extended matrix can uniformly describe the uncertainty of real and virtual measurements in subsequent control calculations.

[0146] Step 8): Calculation of fault-tolerant control inputs based on extended measurement and reconfiguration state

[0147] This step, based on the extended measurement set and recursive state estimation results, constructs an adaptive fault-tolerant control law to achieve real-time correction of the vehicle control input, ensuring stable system operation under sensor malfunctions. Specifically, it includes the following: (I) Construction of Control State Error Define the vehicle control target state vector at time t, representing the vehicle's desired operating state:

[0148] Where, x r (t) is the target vector composed of the desired position and velocity components, output by the intelligent driving decision layer.

[0149] Based on the posterior system state estimate obtained in step 6) Extract key control state components and construct a control state error vector:

[0150] Where C is the state selection matrix, which is used to extract the three key components involved in control—position, velocity, and acceleration—from the complete state vector, and its dimension matches the target state vector.

[0151] (II) Control weight adjustment and control law construction

[0152] Introducing a control weight adjustment factor based on sensor reliability to quantify the overall reliability level of the available measurement information in the current system:

[0153] Where μ(t)∈(0,1], the closer the value is to 1, the higher the reliability of the system measurement information, and the more the control input can rely on the measurement data.

[0154] Based on the control state error and adjustment factor, a fault-tolerant control law is constructed:

[0155] in: u(t): Vehicle control input vector, including steering angle and acceleration control values; K c The preset control gain matrix is ​​designed using pole placement or LQR methods to ensure the stability of the closed-loop system.

[0156] (iii) Smoothing of control input

[0157] To suppress control input fluctuations caused by virtual measurement uncertainties, a control input smoothing term is introduced to achieve continuous transition of the control quantity:

[0158] in: The fault-tolerant control input for the final output; ρ: Control smoothing coefficient, ρ∈(0,1). The larger the value, the higher the weight of the current control input. It can be adjusted according to the dynamic response requirements of the system.

[0159] Step 9: Verification of Fault-Tolerant Control Closed-Loop Stability Constraints and Control Effect

[0160] This step involves performing a stability analysis on the constructed closed-loop fault-tolerant control system, setting validity criteria to ensure that the vehicle maintains stable and controllable operation even in the event of sensor malfunction or failure. Specifically, it includes the following: (I) Lyapunov stability analysis Based on the control state error vector e defined in step 8) c (t), construct the Lyapunov function of the closed-loop system to characterize the system error energy:

[0161] Among them, P c It is a symmetric positive definite matrix, pre-designed by stability analysis to ensure that the Lyapunov function is a positive definite function.

[0162] Under the fault-tolerant control law, the dynamic equation of the closed-loop system error is:

[0163] Where A and B are the state matrix and control input matrix of the vehicle system, respectively, which are derived from the vehicle dynamics equations.

[0164] Calculating the difference between adjacent time steps for the Lyapunov function yields:

[0165] By selecting a suitable K c With P c This makes the following equation true:

[0166] Among them, Q c It is a symmetric positive definite matrix, at this time <0 indicates that the closed-loop system error asymptotically converges, and the system is stable.

[0167] (II) Determination of the effectiveness of fault tolerance control

[0168] Define indicators for judging the effectiveness of fault-tolerant control, and quantify the system's stable convergence performance:

[0169] Where V(0) is the initial Lyapunov function value, and Φ(t) represents the error energy decay ratio.

[0170] The fault-tolerant control method is considered effective when the following conditions are met:

[0171] in: ξ: Stability threshold, ξ∈(0,1), set by the maximum allowable error energy of the system; T s Stable convergence time is the time from the occurrence of sensor anomaly to the convergence of error to the allowable range, which must meet the real-time requirements of intelligent driving (usually ≤100ms).

[0172] In summary, this invention constructs a complete fault-tolerant control system of "modeling-detection-evaluation-reconstruction-control-verification" through the above 9 steps, realizing the stable operation of intelligent driving vehicles under sensor abnormality scenarios and improving the system's robustness and safety.

Claims

1. A fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction, characterized in that, The steps are as follows: Step 1) Multivariable system and multi-sensor measurement modeling: Based on the kinematic and dynamic characteristics of intelligent driving vehicles, construct a unified multivariable system state model and multi-sensor measurement model, define the core state variables of vehicle three-dimensional spatial position, velocity and acceleration, establish the mapping relationship between the measurement output of each sensor and the system state, and clarify the measurement noise characteristics; Step 2) Construction and Quantification of Spatiotemporal Redundancy Relationship of Multi-Source Sensors: Based on the multivariable system state model and multi-sensor measurement model established in Step 1), the spatiotemporal redundancy relationship model of multi-source sensors is constructed by utilizing the continuous evolution characteristics of vehicle state in the time dimension and the spatial observation correlation of different sensors; through time prediction consistency analysis and cross-sensor spatial consistency analysis, redundancy measurement indexes are defined to quantify the degree of sensor measurement redundancy, forming a quantitative redundancy basis for anomaly judgment and state reconstruction. Step 3) Sensor anomaly determination based on spatiotemporal redundancy consistency: Based on the spatiotemporal redundancy relationship model and redundancy measurement index constructed in Step 2), calculate the deviation between the measurement results of each sensor and the time prediction model and spatial redundancy constraints; construct time consistency index and spatial consistency index, and the two are weighted to form a comprehensive anomaly determination index. By comparing with the preset threshold, the anomaly determination of the current state of the sensor is completed, and the anomaly determination result is output. Step 4) Sensor credibility assessment and weight modeling: Based on the comprehensive anomaly judgment index and anomaly judgment results in Step 3), the discrete anomaly judgment results are transformed into continuous credibility weights; through credibility function construction, anomaly penalty and normalization processing, the reliability of the measurement information of each sensor is quantitatively evaluated, and an effective sensor set Sv(t) is screened and constructed. Step 5) Reconstructing the multivariate state based on credibility weights: Based on the continuous credibility weights and effective sensor set obtained in Step 4), the effective sensor measurement data are weighted and fused to construct an equivalent fusion observation model; combined with the measurement information obtained from the spatiotemporal redundancy relationship model in Step 2), the state of the vehicle multivariate system is reconstructed to obtain the reconstructed state estimation result. Step 6) Reconstructing the recursive estimation update of the reconstructed state: Combining the multivariate system state model in Step 1) with the reconstructed state estimation results in Step 5), a state prediction-correction recursive mechanism is constructed; the recursive estimation update of the reconstructed state is performed to optimize the state estimation results and update the error covariance; Step 7) Virtual Measurement Generation and Extended Measurement Set Construction: For sensors identified as abnormal or failed in Step 3), equivalent virtual measurement information is generated based on the optimized state estimation results in Step 6; a virtual measurement noise model is defined, and the virtual measurements and the effective sensor set Sv(t) in Step 4) together constitute an extended measurement set; Step 8) Fault-tolerant control input calculation: Based on the extended measurement set in Step 7) and the optimized state estimation results in Step 6), combined with the continuous confidence weight in Step 4), a fault-tolerant control law is constructed; the control input is adaptively adjusted according to the overall confidence level of the currently available measurement information, a control smoothing term is introduced to suppress virtual measurement uncertainty, and the vehicle's fault-tolerant control command is output. Step 9) Closed-loop system stability constraints and control effect verification: Based on the fault-tolerant control command in Step 8) and the multivariable system state model of the vehicle in Step 1), a closed-loop control system is constructed; stability constraints are applied to the closed-loop system through Lyapunov stability theory, and a fault-tolerant control effectiveness judgment index is defined to verify the fault-tolerant control effect through the index.

2. The fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 1) is as follows: Step 1.1) Based on the kinematic and dynamic characteristics of intelligent driving vehicles operating in complex environments, construct a unified multivariable system state description model to characterize the real physical operating state of the vehicle in three-dimensional space, and define the vehicle at time... The true state vector is: in, This represents the spatial position components of the vehicle in the global coordinate system; This represents the vehicle's velocity component in the corresponding direction; Represents the acceleration components of the vehicle; Step 1.2) Establish a unified multi-sensor measurement model for the different measurement methods of the above state variables by the vehicle-mounted multi-source sensors; assume that there are a total of The heterogeneous sensor, the first Each sensor at time The measurement output is expressed as: in, For the first Measurement vectors of each sensor This is the corresponding nonlinear measurement function, used to describe the mapping relationship between the vehicle's actual state and the sensor measurement space. This is a measurement of the noise term, used to characterize the inherent uncertainties of the sensor and the effects of external interference; By performing a first-order approximation on the above nonlinear measurement model, which satisfies the linearization condition or is located near a local operating point, we obtain the linear observation expression: in, For the first The measurement matrix corresponding to each sensor is used to characterize the sensor's sensitivity to the observation of each component in the system state.

3. The multivariable measurement sensor fault-tolerant control method based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 2) is as follows: Based on the multivariable system state model and multi-sensor measurement model constructed in step 1), in order to support state reconstruction and fault-tolerant control under abnormal sensor conditions, the redundancy relationship of different sensors in the time and space dimensions is further characterized. By introducing time-series prediction consistency and cross-sensor spatial consistency constraints, a quantifiable and determinable spatiotemporal redundancy description model is constructed. Step 2.1) In the time dimension, utilizing the continuous evolution characteristics of vehicle state between adjacent time points, construct a system state time prediction model: in, For a moment The predicted value of the prior state. The result of the state estimation at the previous moment. This is the system state transition matrix, used to describe the motion evolution of the vehicle per unit time. Based on the time-predicted state, construct the first Prediction residuals of each sensor over time: in, It represents the deviation between the actual measured value of the sensor and the predicted state over time, and is used to reflect the degree of consistency of the sensor in the time dimension; Step 2.2) In the spatial dimension, considering the cross-observation or equivalent mapping relationship between different sensors for the same physical state variable, a cross-sensor spatial consistency constraint is introduced for any two sensors. and Construct spatial mapping residuals: in, This is a spatial mapping matrix used to describe the sensor. The measurement results are sent to the sensor Equivalent transformation relationships in the measurement space; Step 2.3) To achieve a unified quantification of spatiotemporal redundancy, temporal redundancy measurement indicators and spatial redundancy measurement indicators are defined respectively: in, This represents the L2 norm operation. The smaller the index value, the higher the consistency between the sensor measurement results and the time prediction model or spatial redundancy constraints.

4. The fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 3) is as follows: Based on the quantitative modeling of the spatiotemporal redundancy relationship of multi-source sensors, in order to identify faults, drifts or abnormal attack behaviors that occur in the sensors during operation, it is necessary to determine the measurement consistency of each sensor in real time. This step is based on temporal redundancy consistency and spatial redundancy consistency to build a unified sensor anomaly detection and judgment mechanism. First, regarding the consistency of a single sensor's performance in the time dimension, based on the temporal redundancy residual obtained in step 2... Construct time consistency metrics: in, For the first The covariance matrix of the sensor measurement noise is used to characterize the statistical characteristics of the sensor under normal operating conditions; this index is used to measure the degree of deviation between the sensor's current measurement and its time prediction result. Secondly, regarding the consistency of sensor performance in the spatial dimension, based on the spatial redundancy residuals defined in step 2), Construct spatial consistency indicators: in, The covariance matrix of the spatial mapping residuals is used to describe the sensor. With sensors Spatial consistency statistical characteristics under normal conditions; Furthermore, to comprehensively reflect the consistency level of the sensor in both time and space, a third... Comprehensive anomaly detection index for each sensor: in, and These are the weighting coefficients for temporal consistency and spatial consistency, respectively. Indication and Sensors A set of sensors with spatial redundancy; Finally, the comprehensive anomaly detection index is compared with the preset threshold to complete the determination of the sensor's abnormal state. in, Indicates the first Each sensor at time It was determined to be an abnormal state. This indicates that the sensor is in normal working condition. The anomaly detection threshold is related to the sensor type and noise characteristics.

5. The multivariable measurement sensor fault-tolerant control method based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 4) is as follows: Based on the completion of the abnormal state determination of multi-source sensors, in order to avoid the system information being insufficient or the estimation being unstable due to the direct elimination of abnormal sensors, this step introduces a sensor reliability evaluation mechanism, which transforms the abnormal determination result into a continuously adjustable reliability weight for subsequent spatiotemporal redundant data reconstruction and fault-tolerant control. First, based on the comprehensive anomaly judgment index obtained in step 3). , construct the first The original confidence function for each sensor: in, This represents the sensor's initial confidence level at the current moment. This is the credibility decay coefficient, used to adjust the impact of anomaly level on the rate of credibility decline; this function ensures that when sensor measurements deviate significantly from spatiotemporal redundancy constraints, their credibility automatically decreases. Secondly, combined with anomaly detection flags The original credibility is corrected to distinguish between obvious anomalies and minor deviations: in, The corrected credibility weight. This is the anomaly penalty coefficient, used to further suppress the sensor's influence on system estimation when an abnormal state is determined. To ensure the consistency and numerical stability of multi-source sensor weights during the fusion and reconstruction process, the confidence levels of all sensors are normalized. in, Represents the normalized confidence weights, satisfying ; Furthermore, an effective sensor set is constructed based on the magnitude of the confidence weights: in, The minimum confidence threshold is used to filter out sensor data that contributes very little to the reconstruction of the system state.

6. The fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 5) is as follows: Based on the completion of multi-source sensor credibility assessment and weight modeling, in order to obtain reliable vehicle status information even when some sensors are abnormal or fail, this step uses redundant measurement data from the set of trusted sensors to construct a multivariate state reconstruction model based on credibility weighting, so as to realize the real-time reconstruction of the system state. First, based on the effective sensor set obtained in step 4). The corresponding measurement data are then filtered, and a weighted fusion observation vector is constructed: in, Indicates at time The fusion measurement results formed by multiple reliable sensors For the first Normalized confidence weights of each sensor, Its original measurement vector; the fusion process achieves adaptive allocation of the measurement contributions of sensors with different degrees of anomaly through weight adjustment; Secondly, to maintain the consistency of the state reconstruction process in mathematical form, an equivalent fusion measurement matrix is ​​constructed based on the measurement models of each sensor: in, This is the fusion measurement matrix, used to describe the mapping relationship between the fusion observation vector and the system state vector; Based on this, a state reconstruction observation model based on spatiotemporal redundant data is established: in, To fuse the measurement noise term, its covariance can be expressed as: For the first The measurement noise covariance matrix of each sensor; Furthermore, combining the time prediction state obtained in step 2), Construct the least squares estimation form of the reconstructed state: in, This represents the reconstructed state estimation result obtained based on spatiotemporal redundant data.

7. The fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 6) is as follows: After completing the multivariate state reconstruction based on credibility weighting, in order to achieve continuous estimation and error suppression of vehicle state over time, this step introduces a recursive state estimation mechanism to predict and correct the system state, thereby improving the stability and real-time performance of state estimation. First, based on the dynamic characteristics of the vehicle system, a state prediction model is constructed, and the state estimate of the previous moment is extrapolated over time: in, For a moment The predicted value of the prior state. For a moment The reconstruction state estimation results, This is the system state transition matrix; Simultaneously, the state estimation error covariance is predicted and updated: in, For the prediction error covariance matrix, Let be the error covariance matrix of the previous time step. The system process noise covariance matrix; Secondly, based on the equivalent fusion observation model constructed in step 5), a state correction process is introduced; the recursive estimation gain matrix is ​​calculated: in, For the state estimation gain matrix, and These are the fusion measurement matrix and its noise covariance, respectively. Based on the estimated gain, the system state is corrected and updated: in, This is the recursively updated system state estimate; Simultaneously, the state estimation error covariance is updated: in, It is an identity matrix.

8. The fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 7) is as follows: After completing the recursive state estimation update based on the reconstructed observation model, in order to avoid measurement channel interruption, system structure degradation or unusable control law due to sensor abnormality or failure, this step constructs a virtual measurement noise model based on the current state estimation result and performs equivalent compensation for the measurement information of abnormal sensors. First, regarding the first condition that was determined to be abnormal in step 3), One sensor (i.e.) Using the system state estimation results obtained in step 6 Generate the corresponding equivalent virtual measurement values: in, This represents a virtual measurement vector used to replace the output of an abnormal sensor. This is the measurement matrix corresponding to the sensor; Secondly, to characterize the uncertainty introduced by virtual measurement relative to real measurement, a virtual measurement noise model is introduced, whose covariance is defined as: in, For the first The measurement noise covariance matrix of each sensor under normal operating conditions. This is the uncertainty amplification factor, used to reflect the degree of reduction in reliability of virtual measurements compared to real measurements; Furthermore, virtual measurements are organized in a unified manner with valid real measurements at the current moment to construct an extended measurement set: in, This represents an extended set of measurements that includes both real and virtual measurements. Correspondingly, an extended measurement noise covariance matrix is ​​constructed: Used to uniformly describe measurement uncertainty in subsequent state updates or control calculations.

9. The fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 8) is as follows: After completing the virtual measurement generation and constructing the extended measurement set, in order to ensure that the vehicle can still maintain stable operation in the event of sensor malfunction or partial failure, this step constructs a fault-tolerant control input calculation method based on the recursive state estimation results and extended measurement information to realize real-time correction of vehicle control quantities. First, define the vehicle at time. Control target state vector: in, This represents the expected reference values ​​for the vehicle's current position and speed, two key state variables. Based on the system state estimate obtained in step 6) Construct the control state error vector: in, A state selection matrix is ​​used to extract key state components involved in control from the complete state vector; Secondly, to reduce the indirect impact of abnormal sensors on control input, a control weight adjustment factor based on sensor reliability is introduced: in, This represents the current system credibility adjustment factor; Based on this, a fault-tolerant control law is constructed: in, For the vehicle's control input vector, A pre-designed control gain matrix is ​​used to map state errors into control variables; Furthermore, to suppress the impact of virtual measurement uncertainty on the control input, a control input smoothing term is introduced: in, The fault-tolerant control input for the final output. To control the smoothing coefficient.

10. The fault-tolerant control method for multivariable measurement sensors based on spatiotemporal redundant data reconstruction according to claim 1, characterized in that, The specific method in step 9) is as follows: After completing the calculation of the fault-tolerant control input based on extended measurement and reconstructed state, in order to ensure that the vehicle system still has stable operation capability under the condition of sensor abnormality or partial failure, this step performs stability constraint analysis on the constructed closed-loop control system and gives the judgment conditions for the effectiveness of fault-tolerant control. First, based on the control state error vector defined in step 8). Construct the Lyapunov function of the closed-loop system: in, It is a symmetric positive definite matrix used to characterize the energy function of the system state error; Under the fault-tolerant control law, the dynamic error of the closed-loop system can be expressed as: in, and These are the state matrix and control input matrix of the vehicle system, respectively. The credibility adjustment factor defined in step 8); Calculating the difference between adjacent time steps for the Lyapunov function yields: By selecting the control gain matrix With Lyapunov matrix To satisfy the following inequality constraints: in, It is a symmetric positive definite matrix; Then we have: This indicates that under sensor malfunction or failure, the closed-loop system error asymptotically converges, and the system remains stable. Furthermore, we define the indicators for judging the effectiveness of fault-tolerant control: When the following conditions are met: in, The threshold for stability determination To ensure a stable convergence time, the fault-tolerant control method is determined to be effective under the current abnormal conditions.

Images