A method and system for modeling dynamic safety gap of maglev train tracking operation

Abstract

The application discloses a kind of maglev train tracking operation dynamic safety interval modeling method and system, it is related to data analysis technical field, the method includes: based on traction characteristic model, brake characteristic model and motion resistance model constructs longitudinal dynamics model to construct discretization state transition model;Based on discretization state transition model determines current priori estimation and Jacobian matrix, to determine current time priori covariance in this way;Based on current time priori covariance calculation Kalman gain, to and current priori estimation determine target posterior covariance matrix;Based on target posterior covariance matrix extraction diagonal line element to construct target confidence interval, to determine the lower bound of car position confidence interval and uncertainty allowance in this way;Calculate rear car brake distance;Based on rear car brake distance, the lower bound of car position confidence interval and uncertainty allowance constructs time-varying safety constraint to calculate dynamic safety interval.The application improves the reliability of dynamic safety interval calculation.

Description

Technical Field

[0001] This invention relates to the field of data analysis technology, and in particular to a method and system for modeling dynamic safety distances during maglev train tracking. Background Technology

[0002] Maglev trains utilize electromagnetic force for vehicle levitation and guidance, and are driven by linear motors. In train tracking and control, to ensure operational safety, the following train must maintain a sufficient safety distance from the preceding train to avoid rear-end collisions. Therefore, calculating the safety distance is one of the core functions of the train operation control system. However, the traditional model used to calculate the safety distance treats the position and speed of the preceding train as precisely known quantities, ignoring the inherent measurement noise and errors of the maglev train's non-contact speed measurement and positioning system under conditions of strong magnetic fields, low speeds, and complex tracks. This model uses a fixed empirical value as a safety margin, which cannot be dynamically adjusted according to the strength of actual perceived uncertainty. When the actual measurement error is small, this fixed margin is too large, leading to unnecessary resource waste; when the actual measurement error is large, this fixed margin may be insufficient, failing to cover the uncertainty range of the preceding train's true position, thus creating safety hazards.

[0003] Meanwhile, the minimum tracking distance calculated by traditional models depends only on the current speed of the following vehicle and preset fixed parameters. Its output is a fixed value that monotonically changes with speed, or a discrete value given by a lookup table. This model cannot respond to the following time-varying factors: the real-time noise level of the speed measurement and positioning system; the dynamic changes in estimation uncertainty caused by the operating state of the preceding vehicle; and the differentiated impact of different track sections on speed measurement and positioning accuracy. Therefore, the safety boundary of traditional models is static or quasi-static, lacking the ability to adapt in real-time to the time-varying uncertainties of the operating environment. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art. This invention provides a method and system for modeling dynamic safety distances for maglev train tracking operations. It provides dynamic boundaries with clear probabilistic meaning, and the dynamic safety distance is adjusted in real time according to the estimation uncertainty, avoiding overly conservative or unsafe conditions caused by fixed margins.

[0005] To address the aforementioned technical problems, this invention provides a method for modeling dynamic safety distances during maglev train tracking operations, the method comprising: A traction characteristic model, a braking characteristic model, and a motion resistance model of a maglev train are constructed. A longitudinal dynamic model is constructed based on the traction characteristic model, the braking characteristic model, and the motion resistance model. A discretized state transition model is constructed based on the longitudinal dynamic model. The current prior estimate and Jacobian matrix are determined based on the discretized state transition model, and the prior covariance at the current time is determined based on the Jacobian matrix. The Kalman gain is calculated based on the prior covariance at the current time, and the target posterior covariance matrix is ​​determined based on the current prior estimate and the Kalman gain. Based on the target posterior covariance matrix, diagonal elements are extracted, and a target confidence interval is constructed based on the diagonal elements. Based on the target confidence interval, the lower bound of the confidence interval for the position of the preceding vehicle and the uncertainty margin are determined. The current operating speed and maximum service braking deceleration of the following vehicle in the maglev train are obtained, and the braking distance of the following vehicle is calculated based on the current operating speed and maximum service braking deceleration. Time-varying safety constraints are constructed based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the uncertainty margin, and dynamic safety distances are calculated based on the time-varying safety constraints.

[0006] Optionally, the construction of the traction characteristic model, braking characteristic model, and motion resistance model of the maglev train, and the construction of a longitudinal dynamic model based on the traction characteristic model, braking characteristic model, and motion resistance model, and the construction of a discretized state transition model based on the longitudinal dynamic model, includes: The traction characteristic model of the maglev train is constructed based on piecewise polynomials, and the expression of the traction characteristic model is as follows:

[0007] in, is the traction force for the maglev train, and v is the speed of the maglev train; Obtain the mass of the maglev train and the proportional coefficients related to the characteristics of the maglev train and its braking system, and construct a braking characteristic model based on the maglev train mass and proportional coefficients. The expression of the braking characteristic model is as follows:

[0008] in, For the braking force of the train, Where M is the proportionality coefficient, v is the mass of the maglev train, and v is the speed of the maglev train. The air resistance, magnetic resistance, onboard linear generator resistance, gradient resistance, curve resistance, and electromagnetic eddy current resistance experienced by the maglev train during operation on the line are obtained. Based on these factors, a motion resistance model is constructed. The expression for the motion resistance model is as follows: , in, For total resistance, For air resistance, For magnetic resistance, For the resistance of the vehicle-mounted linear generator, Add resistance to the ramp, Add resistance to the curve. This is electromagnetic eddy current resistance; A longitudinal dynamics model is constructed based on the aforementioned traction characteristic model, braking characteristic model, and motion resistance model. The expression for the longitudinal dynamics model is as follows: , Where v is the speed of the maglev train, x is the distance traveled by the maglev train, t is the travel time of the maglev train, M is the mass of the maglev train, and a is the acceleration of the maglev train. For the traction force of the maglev train, For the braking force of the train, Total resistance; Based on the aforementioned longitudinal dynamics model, a discretized state transition model is obtained. The expression of the discretized state transition model is as follows: , in, Let f be the state vector determined by the longitudinal dynamics model, and let f() be the nonlinear state transition function. Let be the state vector of the train at the previous moment. To control the input, This is process noise.

[0009] Optionally, determining the current prior estimate and Jacobian matrix based on the discretized state transition model, and determining the prior covariance at the current time based on the Jacobian matrix, includes: Obtain the posterior estimate and control input of the maglev train at the previous moment, and determine the current prior estimate based on the discretized state transition model using the posterior estimate and control input of the maglev train at the previous moment. Linearization is performed based on the discretized state transition model to obtain the Jacobian matrix. The prior covariance at the current time is then calculated from the Jacobian matrix.

[0010] Optionally, the expression for the prior covariance at the current time is: , in, Let the prior covariance be at the current moment. For Jacobian matrices, Let T be the posterior covariance of the previous time step, T be the transpose operation, and Q be the process noise covariance matrix.

[0011] Optionally, the step of calculating the Kalman gain based on the prior covariance at the current time, and determining the target posterior covariance matrix based on the current prior estimate and the Kalman gain, includes: Obtain the observation matrix, and calculate the Kalman gain based on the observation matrix and the prior covariance at the current time. The expression for the Kalman gain is as follows: , in, For Kalman gain, Let T be the prior covariance at the current moment, and T be the transpose operation. R is the observation matrix, and R is the observation noise covariance matrix; Based on the current prior estimate and Kalman gain, the state estimate is updated to obtain the target posterior covariance matrix. The expression for the target posterior covariance matrix is ​​as follows: , in, Let I be the target posterior covariance matrix, and let I be the identity matrix. For Kalman gain, For the observation matrix, Let be the prior covariance at the current moment.

[0012] Optionally, the expression for the target confidence interval is: , in, The target confidence interval, This is the posterior location estimate; 1.96 is the 97.5th percentile of the standard normal distribution. It is a diagonal element.

[0013] Optionally, the expression for the braking distance of the rear vehicle is: , in, This is the braking distance of the following vehicle. At the current running speed, This is the maximum commonly used braking deceleration.

[0014] Optionally, the step of constructing time-varying safety constraints based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the uncertainty margin, and calculating the dynamic safety distance based on the time-varying safety constraints, includes: Based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the position of the rear vehicle, safety constraints are determined, and the expression for the safety constraints is: , in, For the position of the rear vehicle, This is the braking distance of the following vehicle. This is the lower bound of the confidence interval for the position of the vehicle ahead. Based on the uncertainty margin, the security constraints are organized to obtain time-varying security constraints; The traditional minimum spacing is determined, and the expression for the traditional minimum spacing is: , in, For traditional minimum spacing, For the total length of the train, Minimum parking clearance This refers to the braking distance of the vehicle behind. Based on the time-varying safety constraints, a time-varying uncertainty safety tracking margin is determined, and a dynamic safety distance is calculated based on the uncertainty safety tracking margin and the traditional minimum spacing. The expression for the dynamic safety distance is: , , in, For dynamic safety spacing, For traditional minimum spacing, To provide a safety margin for uncertainty tracking, It is a diagonal element.

[0015] Optionally, the expression for the time-varying security constraint is: , in, This is the posterior location estimate. This is the braking distance of the following vehicle. For the position of the rear vehicle, It is a diagonal element.

[0016] In addition, the present invention also provides a dynamic safety distance modeling system for maglev train tracking operation, the system comprising: Model building module: used to build traction characteristic model, braking characteristic model and motion resistance model of maglev train, and to build longitudinal dynamic model based on the traction characteristic model, braking characteristic model and motion resistance model, and to build discretized state transition model based on the longitudinal dynamic model; Prior covariance module: used to determine the current prior estimate and Jacobian matrix based on the discretized state transition model, and to determine the prior covariance at the current time based on the Jacobian matrix; Covariance matrix module: used to calculate the Kalman gain based on the prior covariance at the current time, and to determine the target posterior covariance matrix based on the current prior estimate and the Kalman gain; Condition determination module: used to extract diagonal elements based on the target posterior covariance matrix, construct a target confidence interval based on the diagonal elements, and determine the lower bound and uncertainty margin of the confidence interval for the position of the preceding vehicle based on the target confidence interval; Rear vehicle braking distance module: used to obtain the current operating speed and maximum service braking deceleration of the rear vehicle in the maglev train, and calculate the braking distance of the rear vehicle based on the current operating speed and maximum service braking deceleration; Dynamic safety distance module: used to construct time-varying safety constraints based on the braking distance of the following vehicle, the lower bound of the confidence interval of the position of the preceding vehicle, and the uncertainty margin, and to calculate the dynamic safety distance based on the time-varying safety constraints.

[0017] In this embodiment of the invention, a traction characteristic model, a braking characteristic model, and a motion resistance model of a maglev train are constructed. A longitudinal dynamic model is constructed based on the traction characteristic model, the braking characteristic model, and the motion resistance model. A discretized state transition model is constructed based on the longitudinal dynamic model. The constructed model is highly matched with the actual dynamic characteristics of the maglev train, avoiding estimation deviations caused by model mismatch. Based on a discretized state transition model, the current prior estimate and Jacobian matrix are determined, and the prior covariance at the current time is determined based on the Jacobian matrix. The Kalman gain is calculated based on the current prior covariance, and the target posterior covariance matrix is ​​determined based on the current prior estimate and Kalman gain. Diagonal elements are extracted from the target posterior covariance matrix, and a target confidence interval is constructed based on these elements. The lower bound of the preceding vehicle's position confidence interval and the uncertainty margin are determined based on the target confidence interval. The braking distance of the following vehicle is calculated based on the current operating speed and maximum common braking deceleration of the following vehicle in the maglev train. Time-varying safety constraints are constructed based on the following vehicle's braking distance, the lower bound of the preceding vehicle's position confidence interval, and the uncertainty margin. Dynamic safety clearance is calculated based on these time-varying safety constraints. This explicitly quantifies the uncertainty of the preceding vehicle's state perception and transforms it into a calculable and executable safety constraint. The dynamic safety clearance is adjusted in real time according to the estimated uncertainty, avoiding overly conservative or undersafe conditions caused by fixed margins. Simultaneously, the target confidence interval improves tracking efficiency and provides a dynamic boundary with clear probabilistic meaning for multi-objective collaborative optimization, overcoming the limitations of traditional binary safety constraints. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1This is a flowchart illustrating the dynamic safety distance modeling method for maglev train tracking operation in an embodiment of the present invention. Figure 2 This is a flowchart illustrating a method for modeling dynamic safety distances during maglev train tracking in another embodiment of the present invention. Figure 3 This is a schematic diagram of the structural composition of the dynamic safety distance modeling system for maglev train tracking operation in an embodiment of the present invention; Figure 4 This is a schematic diagram of the longitudinal force on a maglev train in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Example 1 Please see Figure 1 , Figure 1 This is a flowchart illustrating the dynamic safety distance modeling method for maglev train tracking operation in an embodiment of the present invention. The method includes: S11: Construct traction characteristic model, braking characteristic model and motion resistance model of maglev train, and construct longitudinal dynamic model based on the traction characteristic model, braking characteristic model and motion resistance model, and construct discretized state transition model based on the longitudinal dynamic model; In the specific implementation of this invention, a traction characteristic model of the maglev train is constructed based on piecewise polynomials; the mass of the maglev train and the proportional coefficients related to the characteristics of the maglev train and braking system are obtained, and a braking characteristic model is constructed based on the mass of the maglev train and the proportional coefficients; the air resistance, magnetic resistance, on-board linear generator resistance, gradient additional resistance, curve additional resistance, and electromagnetic eddy current resistance experienced by the maglev train when running on the line are obtained, and a motion resistance model is constructed based on the air resistance, magnetic resistance, on-board linear generator resistance, gradient additional resistance, curve additional resistance, and electromagnetic eddy current resistance; a longitudinal dynamic model is constructed based on the traction characteristic model, braking characteristic model, and motion resistance model; the longitudinal dynamic model is discretized to obtain a discretized state transition model, which provides a model basis for accurately predicting train motion and supports subsequent uncertainty quantification and safety constraint generation.

[0022] S12: Determine the current prior estimate and Jacobian matrix based on the discretized state transition model, and determine the prior covariance at the current time based on the Jacobian matrix; In the specific implementation of this invention, the posterior estimate and control input of the maglev train at the previous moment are obtained, and the current prior estimate is determined based on the discretized state transition model using the posterior estimate and control input of the maglev train at the previous moment; the discretized state transition model is linearized to obtain the Jacobian matrix, and the prior covariance at the current moment is calculated using the Jacobian matrix, providing the necessary statistical characteristics for subsequent reasonable fusion of measurement information and quantification confidence interval.

[0023] S13: Calculate the Kalman gain based on the prior covariance at the current time, and determine the target posterior covariance matrix based on the current prior estimate and the Kalman gain; In the specific implementation of this invention, the observation matrix is ​​obtained, and the Kalman gain is calculated based on the observation matrix and the prior covariance at the current time. The state estimate is updated based on the current prior estimate and the Kalman gain to obtain the target posterior covariance matrix. The posterior covariance matrix is ​​the direct basis for constructing the safety confidence interval, ensuring that the subsequent safety margin is neither too aggressive nor too conservative.

[0024] S14: Extract the diagonal elements based on the target posterior covariance matrix, construct the target confidence interval based on the diagonal elements, and determine the lower bound of the confidence interval for the position of the preceding vehicle and the uncertainty margin based on the target confidence interval; In the specific implementation of this invention, diagonal elements are extracted based on the target posterior covariance matrix, and a target confidence interval is constructed based on the diagonal elements. The lower bound and uncertainty margin of the preceding vehicle position confidence interval are determined based on the target confidence interval, avoiding underestimation of the actual interval due to positioning noise or communication delay, and significantly enhancing tracking safety.

[0025] S15: Obtain the current operating speed and maximum service braking deceleration of the following vehicle in the maglev train, and calculate the braking distance of the following vehicle based on the current operating speed and maximum service braking deceleration; In the specific implementation of this invention, the current operating speed and maximum service braking deceleration of the following vehicle in the maglev train are obtained, and the braking distance of the following vehicle is calculated based on the current operating speed and maximum service braking deceleration, so as to provide sufficient data support for subsequent time-varying safety constraints.

[0026] S16: Construct time-varying safety constraints based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the uncertainty margin, and calculate the dynamic safety distance based on the time-varying safety constraints.

[0027] In the specific implementation of this invention, safety constraints are determined based on the braking distance of the following vehicle, the lower bound of the confidence interval of the position of the preceding vehicle, and the position of the following vehicle. These safety constraints are then processed based on the uncertainty margin to obtain time-varying safety constraints. A traditional minimum clearance is determined. A time-varying uncertainty safety tracking margin is determined based on the time-varying safety constraints, and a dynamic safety clearance is calculated based on the uncertainty safety tracking margin and the traditional minimum clearance. The safety clearance is no longer a fixed value or a simple function of the following vehicle's speed, but rather dynamically adjusted in real time to follow the uncertainty of the preceding vehicle's state estimation. In areas with strong electromagnetic interference or under low-speed operating conditions, the safety clearance automatically increases to compensate for perceived uncertainty. Under good observation conditions, the safety clearance automatically decreases to release line capacity.

[0028] In this embodiment of the invention, a traction characteristic model, a braking characteristic model, and a motion resistance model of a maglev train are constructed. A longitudinal dynamic model is constructed based on the traction characteristic model, the braking characteristic model, and the motion resistance model. A discretized state transition model is constructed based on the longitudinal dynamic model. The constructed model is highly matched with the actual dynamic characteristics of the maglev train, avoiding estimation deviations caused by model mismatch. Based on a discretized state transition model, the current prior estimate and Jacobian matrix are determined, and the prior covariance at the current time is determined based on the Jacobian matrix. The Kalman gain is calculated based on the current prior covariance, and the target posterior covariance matrix is ​​determined based on the current prior estimate and Kalman gain. Diagonal elements are extracted from the target posterior covariance matrix, and a target confidence interval is constructed based on these elements. The lower bound of the preceding vehicle's position confidence interval and the uncertainty margin are determined based on the target confidence interval. The braking distance of the following vehicle is calculated based on the current operating speed and maximum common braking deceleration of the following vehicle in the maglev train. Time-varying safety constraints are constructed based on the following vehicle's braking distance, the lower bound of the preceding vehicle's position confidence interval, and the uncertainty margin. Dynamic safety clearance is calculated based on these time-varying safety constraints. This explicitly quantifies the uncertainty of the preceding vehicle's state perception and transforms it into a calculable and executable safety constraint. The dynamic safety clearance is adjusted in real time according to the estimated uncertainty, avoiding overly conservative or undersafe conditions caused by fixed margins. Simultaneously, the target confidence interval improves tracking efficiency and provides a dynamic boundary with clear probabilistic meaning for multi-objective collaborative optimization, overcoming the limitations of traditional binary safety constraints.

[0029] Example 2 Please see Figure 2 , Figure 2 This is a flowchart illustrating a method for modeling dynamic safety distances during maglev train tracking, according to another embodiment of the present invention. The method includes: S201: Construct a traction characteristic model, a braking characteristic model, and a motion resistance model for a maglev train, and construct a longitudinal dynamic model based on the traction characteristic model, braking characteristic model, and motion resistance model, and construct a discretized state transition model based on the longitudinal dynamic model; In the specific implementation of this invention, the construction of the traction characteristic model, braking characteristic model, and motion resistance model of the maglev train, and the construction of a longitudinal dynamic model based on the traction characteristic model, braking characteristic model, and motion resistance model, and the construction of a discretized state transition model based on the longitudinal dynamic model, includes: constructing the traction characteristic model of the maglev train based on a piecewise polynomial, wherein the expression of the traction characteristic model is:

[0030] in, is the traction force for the maglev train, and v is the speed of the maglev train; Obtain the mass of the maglev train and the proportional coefficients related to the characteristics of the maglev train and its braking system, and construct a braking characteristic model based on the maglev train mass and proportional coefficients. The expression of the braking characteristic model is as follows:

[0031] in, For the braking force of the train, Where M is the proportionality coefficient, v is the mass of the maglev train, and v is the speed of the maglev train. The air resistance, magnetic resistance, onboard linear generator resistance, gradient resistance, curve resistance, and electromagnetic eddy current resistance experienced by the maglev train during operation on the line are obtained. Based on these factors, a motion resistance model is constructed. The expression for the motion resistance model is as follows: , in, For total resistance, For air resistance, For magnetic resistance, For the resistance of the vehicle-mounted linear generator, Add resistance to the ramp, Add resistance to the curve. This is electromagnetic eddy current resistance; A longitudinal dynamics model is constructed based on the aforementioned traction characteristic model, braking characteristic model, and motion resistance model. The expression for the longitudinal dynamics model is as follows: , Where v is the speed of the maglev train, x is the distance traveled by the maglev train, t is the travel time of the maglev train, M is the mass of the maglev train, and a is the acceleration of the maglev train. For the traction force of the maglev train, For the braking force of the train, Total resistance; Based on the aforementioned longitudinal dynamics model, a discretized state transition model is obtained. The expression of the discretized state transition model is as follows: , in, Let f be the state vector determined by the longitudinal dynamics model, and let f() be the nonlinear state transition function. Let be the state vector of the train at the previous moment. To control the input, This is process noise.

[0032] Specifically, the maglev train uses a short-stator linear induction motor as its traction power source. The stator of the motor is located at the bottom of the vehicle body, while the rotor is laid on the track. Based on the traction characteristic curve of the maglev train under load conditions, a piecewise polynomial fitting method is used to obtain the functional relationship between traction force and speed. That is, a traction characteristic model of the maglev train is constructed based on the piecewise polynomial. The expression of the traction characteristic model is as follows:

[0033] in, v is the traction force (kN) for the maglev train, and v is the speed of the maglev train. ).

[0034] During operation, the switching of braking modes is typically determined based on the speed of the maglev train. When the speed exceeds a set threshold, the system prioritizes electric braking; when the speed drops below this threshold, it switches to mechanical braking to ensure reliable stopping of the maglev train. The electro-hydraulic braking process of the maglev train exhibits significant time lag, making modeling the braking dynamics challenging. Therefore, it is necessary to obtain the maglev train's mass and a proportionality coefficient related to the maglev train's braking system characteristics. This proportionality coefficient is used when the train speed is below 5 km / h, at which point electric braking disengages, and the system engages mechanical braking. The braking force is controlled by a constant torque based on the train's total mass to ensure smooth low-speed stopping. A braking characteristic model is constructed based on the maglev train's mass and the proportionality coefficient. The expression for this braking characteristic model is as follows:

[0035] in, The braking force of the train (kN). The proportionality constant is M, where M is the mass of the maglev train (kg), and v is the speed of the maglev train (kg). ).

[0036] The air resistance, magnetic resistance, onboard linear generator resistance, gradient resistance, curve resistance, and electromagnetic eddy current resistance experienced by the maglev train during operation on the track are obtained. Air resistance, magnetic resistance, onboard linear generator resistance, and electromagnetic eddy current resistance during braking are considered the basic resistances, while gradient resistance and curve resistance are considered additional resistances. A motion resistance model is constructed based on these factors, and its expression is as follows: , in, For total resistance, For air resistance, For magnetic resistance, For the resistance of the vehicle-mounted linear generator, Add resistance to the ramp, Add resistance to the curve. This is electromagnetic eddy current resistance.

[0037] The dynamic model of a maglev train is the fundamental basis for calculating the train's speed curve and for analyzing train control strategies to achieve operational optimization goals. This paper analyzes the dynamic model and traction and braking characteristics of a maglev train, considering the characteristics of the maglev line. The resultant force acting on the maglev train during operation consists of traction force, braking force, and train running resistance. The longitudinal force diagram of the maglev train is shown below. Figure 4 As shown. Based on Newton's second law, a longitudinal dynamics model is constructed based on the traction characteristic model, braking characteristic model, and motion resistance model. The expression of the longitudinal dynamics model is: , Where v is the speed of the maglev train, x is the distance traveled by the maglev train, t is the travel time of the maglev train, M is the mass of the maglev train, and a is the acceleration of the maglev train. For the traction force of the maglev train, For the braking force of the train, This represents the total resistance.

[0038] To accommodate the digital computation of the Kalman Filter (KF), the longitudinal dynamics model is discretized, and a state vector is defined. ,in For location, Let T be the velocity and T be the transpose operation. Based on the longitudinal dynamics model, discretization is performed to obtain a discretized state transition model. The expression of the discretized state transition model is as follows: , in, Let f be the state vector determined by the longitudinal dynamics model, and also represent the state vector of the maglev train at the k-th discrete time. f() is the nonlinear state transition function. Let be the state vector of the train at the previous moment. To control the input, This is process noise.

[0039] S202: Obtain the posterior estimate and control input of the maglev train at the previous moment, and determine the current prior estimate based on the discretized state transition model using the posterior estimate and control input of the maglev train at the previous moment; In the specific implementation of this invention, the posterior estimate and control input of the maglev train at the previous moment are obtained, and the current prior estimate is determined based on the posterior estimate and control input of the maglev train at the previous moment using the discretized state transition model. That is, at each sampling time k, based on the posterior estimate and control input of the previous moment, the prior estimate of the current moment is calculated through the state transition model. The expression of the current prior estimate is: , in, For the current prior estimate, This is the posterior estimate from the previous time step. This is the control input from the previous moment.

[0040] S203: Linearize the discretized state transition model to obtain the Jacobian matrix, and calculate the prior covariance at the current time based on the Jacobian matrix; In the specific implementation of this invention, the discretized state transition model is linearized to obtain the Jacobian matrix. The calculation of the prior covariance matrix requires linearization of the nonlinear state transition function, that is, in... At this point, perform a first-order Taylor expansion on f: , in, This is the posterior estimate from the previous time step. Let be the train's state vector at the previous moment; The Jacobian matrix is ​​defined according to the first-order Taylor expansion. Since the state vector is two-dimensional, the Jacobian matrix is ​​a 2×2 matrix, where the Jacobian matrix is:

[0041] in, The first row and first column of the Jacobian matrix. This indicates that the partial derivative of the current position prediction with respect to the previous position is 1. This means that the position error from the previous moment is propagated to the current position prediction at a 1:1 ratio (ignoring the effects of acceleration changes); (First row, second column) This indicates the sensitivity of the current position to the velocity at the previous moment; second row, first column. This means that in the basic model, speed prediction does not directly depend on the position at the previous moment (unless the track gradient or curve drag varies with position). In more complex models, if drag is a function of position... If the function is a function of gradient resistance (e.g., gradient resistance varies with mileage), then this term is non-zero. For a straight road model, this term is 0; (Row 2, Column 2) It indicates the sensitivity of the current velocity to the velocity at the previous moment.

[0042] The prior covariance at the current time is obtained by calculating the Jacobian matrix. The expression for the prior covariance at the current time is: , in, Let the prior covariance be at the current moment. For Jacobian matrices, Let T be the posterior covariance of the previous time step, T be the transpose operation, and Q be the process noise covariance matrix. The process noise covariance matrix needs to be pre-calibrated according to the uncertainty of the maglev train dynamics model (e.g., by minimizing the root mean square error (RMSE) through grid search).

[0043] S204: Obtain the observation matrix and calculate the Kalman gain based on the observation matrix and the prior covariance at the current time. In a specific implementation of this invention, an observation matrix is ​​obtained, and the Kalman gain is calculated based on the observation matrix and the prior covariance at the current time. The expression for the Kalman gain is as follows: , in, For Kalman gain, Let T be the prior covariance at the current moment, and T be the transpose operation. R is the observation matrix, and R is the observation noise covariance matrix. The observation noise covariance matrix reflects the measurement uncertainty of the velocity positioning system.

[0044] S205: Update the state estimate based on the current prior estimate and Kalman gain to obtain the target posterior covariance matrix; In the specific implementation of this invention, the state estimate is updated based on the current prior estimate and the Kalman gain to obtain the target posterior covariance matrix, and the state estimate is updated according to the Kalman gain: , in, For posterior state estimation, For the current prior estimate, For Kalman gain, These are actual observed values. For the observation matrix, the posterior covariance matrix is ​​updated to obtain the target posterior covariance matrix, which is expressed as follows: , in, Let I be the target posterior covariance matrix, and let I be the identity matrix. For Kalman gain, For the observation matrix, Let be the prior covariance at the current moment.

[0045] S206: Extract the diagonal elements based on the target posterior covariance matrix, construct the target confidence interval based on the diagonal elements, and determine the lower bound of the confidence interval for the position of the preceding vehicle and the uncertainty margin based on the target confidence interval; In the specific implementation of this invention, diagonal elements are extracted based on the target posterior covariance matrix, that is, diagonal elements corresponding to the positional state are extracted from the target posterior covariance matrix. A target confidence interval is constructed based on these diagonal elements, that is, a 95% confidence interval for the true position of the preceding vehicle is determined according to the diagonal elements. The expression for the target confidence interval is: , in, The target confidence interval, This is the posterior location estimate; 1.96 is the 97.5th percentile of the standard normal distribution. It is a diagonal element.

[0046] Based on the target confidence interval, determine the lower bound of the confidence interval for the position of the preceding vehicle and the uncertainty margin. (Lower bound of the confidence interval for the position of the preceding vehicle) Upper bound of the confidence interval for the position of the preceding vehicle Uncertainty margin .

[0047] S207: Obtain the current operating speed and maximum service braking deceleration of the following vehicle in the maglev train, and calculate the braking distance of the following vehicle based on the current operating speed and maximum service braking deceleration; In the specific implementation of this invention, the current operating speed and maximum service braking deceleration of the following vehicle in the maglev train are obtained, and the braking distance of the following vehicle is calculated based on the current operating speed and maximum service braking deceleration. The braking distance of the following vehicle is the minimum physical distance required for the following vehicle to brake from the current speed to a stop. The expression for the braking distance of the following vehicle is: , in, This is the braking distance of the following vehicle. At the current running speed, This is the maximum commonly used braking deceleration.

[0048] S208: Construct time-varying safety constraints based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the uncertainty margin, and calculate the dynamic safety distance based on the time-varying safety constraints.

[0049] In a specific implementation of this invention, the step of constructing time-varying safety constraints based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the uncertainty margin, and calculating the dynamic safety distance based on the time-varying safety constraints, includes: determining safety constraint conditions based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the position of the rear vehicle. The expression for the safety constraint conditions is: , in, For the position of the rear vehicle, This is the braking distance of the following vehicle. This is the lower bound of the confidence interval for the position of the vehicle ahead. Based on the uncertainty margin, the security constraints are organized to obtain time-varying security constraints; The traditional minimum spacing is determined, and the expression for the traditional minimum spacing is: , in, For traditional minimum spacing, For the total length of the train, Minimum parking clearance This refers to the braking distance of the vehicle behind. Based on the time-varying safety constraints, a time-varying uncertainty safety tracking margin is determined, and a dynamic safety distance is calculated based on the uncertainty safety tracking margin and the traditional minimum spacing. The expression for the dynamic safety distance is: , , in, For dynamic safety spacing, For traditional minimum spacing, To provide a safety margin for uncertainty tracking, It is a diagonal element.

[0050] Furthermore, the expression for the time-varying security constraint is: , in, This is the posterior location estimate. This is the braking distance of the following vehicle. For the position of the rear vehicle, It is a diagonal element.

[0051] Specifically, in actual tracking control or multi-objective optimization, the actual position of the preceding vehicle cannot be directly used. To ensure safety, a conservative estimate is adopted: the lower boundary of the confidence interval of the preceding vehicle's position is taken as the most unfavorable position of the preceding vehicle. Let the position of the following vehicle be... Based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the position of the rear vehicle, safety constraints are determined, and the expression for the safety constraints is: , in, For the position of the rear vehicle, This is the braking distance of the following vehicle. This represents the lower bound of the confidence interval for the preceding vehicle's position. The safety constraint is that the difference between the following vehicle's current position and the smallest possible position of the preceding vehicle (95% confidence lower bound) must be at least equal to the following vehicle's physical braking distance. Introducing a probabilistic safety boundary into the modeling of safe distances for maglev trains allows safety constraints to no longer rely on empirical guesses but rather on quantifiable uncertainties. Simulations show that this confidence interval achieves 96.8% actual coverage of the preceding vehicle's true position, close to the theoretical value, proving the effectiveness of the probabilistic guarantee.

[0052] Based on the aforementioned uncertainty margin, the security constraints are rearranged to obtain time-varying security constraints, which are then substituted into... We can obtain: Finally, after simplification, the final expression for the time-varying safety constraint is: , in, This is the posterior location estimate. This is the braking distance of the following vehicle. For the position of the rear vehicle, The elements are diagonal. Their physical meaning is: the actual position of the following train must be preceded by an additional buffer amount equal to the "estimated position of the preceding train + braking distance of the following train," and this buffer amount is dynamically equal to the uncertainty half-width of the current state estimate. This constraint can be directly embedded into the multi-objective optimization problem of train tracking control as a time-varying safety constraint.

[0053] The traditional minimum spacing is determined, and the expression for the traditional minimum spacing is: , in, For traditional minimum spacing, For the total length of the train, Minimum parking clearance This is the braking distance of the vehicle behind.

[0054] Based on the time-varying safety constraints, a time-varying uncertainty safety tracking margin is determined, and a dynamic safety distance is calculated based on the uncertainty safety tracking margin and the traditional minimum spacing. The expression for the dynamic safety distance is: , , in, For dynamic safety spacing, For traditional minimum spacing, To provide a safety margin for uncertainty tracking, This is a diagonal element. It's important to note that... It is time-varying based on time-varying safety constraints, and it dynamically adjusts as the covariance of the KF estimate changes: when the speed measurement and positioning accuracy is high and the estimation uncertainty is small, Automatic reduction; when electromagnetic interference is strong and observation noise is high, Automatically increases the safety distance. This makes the safety distance no longer a fixed value or a simple function of the following vehicle's speed, but a dynamic adjustment based on the uncertainty of the preceding vehicle's state estimation in real time. In areas with strong electromagnetic interference or under low-speed operating conditions, the safety distance automatically increases to compensate for perceived uncertainties. Under good observation conditions, the safety distance automatically decreases to release line capacity.

[0055] To verify the effectiveness of the above method, the following simulation experiment was designed: Experimental setup: Real Automatic Train Operation (ATO) data (total duration 507 seconds, covering all operating conditions including start-up, acceleration, deceleration, and stopping) from a medium-low speed maglev line was used as the actual trajectory of the preceding train. Gaussian white noise (standard deviation 0.5m) was superimposed on the position data of the actual trajectory to generate simulated speed and positioning observations. KF parameters were set: process noise covariance. Optimize using a grid search (to minimize RMSE), and take the known variance (0.5²) of the observation noise covariance; run KF confidence interval mixture estimation to calculate the 95% confidence interval for each time step. Calculate the coverage index to verify if it is close to 95%; simulate following vehicle tracking to compare the tracking margin of the dynamic safety distance of this invention with that of the traditional fixed distance model.

[0056] Experimental results: The RMSE estimated by KF is significantly lower than that of the direct observation. The actual coverage of the location confidence interval to the real location reaches 96.8%, close to the theoretical 95%. In six independent simulations, the tracking margin (actual distance minus dynamic safety distance) of the method of this invention is always positive (17~20m), while the traditional method shows a negative margin (-25~-28m), indicating that the traditional method actually intrudes into the risk area.

[0057] In this embodiment of the invention, a traction characteristic model, a braking characteristic model, and a motion resistance model of a maglev train are constructed. A longitudinal dynamic model is constructed based on the traction characteristic model, the braking characteristic model, and the motion resistance model. A discretized state transition model is constructed based on the longitudinal dynamic model. The constructed model is highly matched with the actual dynamic characteristics of the maglev train, avoiding estimation deviations caused by model mismatch. Based on a discretized state transition model, the current prior estimate and Jacobian matrix are determined, and the prior covariance at the current time is determined based on the Jacobian matrix. The Kalman gain is calculated based on the current prior covariance, and the target posterior covariance matrix is ​​determined based on the current prior estimate and Kalman gain. Diagonal elements are extracted from the target posterior covariance matrix, and a target confidence interval is constructed based on these elements. The lower bound of the preceding vehicle's position confidence interval and the uncertainty margin are determined based on the target confidence interval. The braking distance of the following vehicle is calculated based on the current operating speed and maximum common braking deceleration of the following vehicle in the maglev train. Time-varying safety constraints are constructed based on the following vehicle's braking distance, the lower bound of the preceding vehicle's position confidence interval, and the uncertainty margin. Dynamic safety clearance is calculated based on these time-varying safety constraints. This explicitly quantifies the uncertainty of the preceding vehicle's state perception and transforms it into a calculable and executable safety constraint. The dynamic safety clearance is adjusted in real time according to the estimated uncertainty, avoiding overly conservative or undersafe conditions caused by fixed margins. Simultaneously, the target confidence interval improves tracking efficiency and provides a dynamic boundary with clear probabilistic meaning for multi-objective collaborative optimization, overcoming the limitations of traditional binary safety constraints.

[0058] Example 3 Please see Figure 3 , Figure 3 This is a schematic diagram of the structural composition of the dynamic safety distance modeling system for maglev train tracking operation in an embodiment of the present invention. The system includes: Model building module 31: used to build the traction characteristic model, braking characteristic model and motion resistance model of the maglev train, and to build a longitudinal dynamic model based on the traction characteristic model, braking characteristic model and motion resistance model, and to build a discretized state transition model based on the longitudinal dynamic model; Prior covariance module 32: used to determine the current prior estimate and Jacobian matrix based on the discretized state transition model, and to determine the prior covariance at the current time based on the Jacobian matrix; Covariance matrix module 33: used to calculate the Kalman gain based on the prior covariance at the current time, and to determine the target posterior covariance matrix based on the current prior estimate and the Kalman gain; Condition determination module 34: used to extract diagonal elements based on the target posterior covariance matrix, construct a target confidence interval based on the diagonal elements, and determine the lower bound of the confidence interval for the position of the preceding vehicle and the uncertainty margin based on the target confidence interval; Rear vehicle braking distance module 35: used to obtain the current operating speed and maximum service braking deceleration of the rear vehicle in the maglev train, and calculate the braking distance of the rear vehicle based on the current operating speed and maximum service braking deceleration; Dynamic safety distance module 36: used to construct time-varying safety constraints based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle and the uncertainty margin, and to calculate the dynamic safety distance based on the time-varying safety constraints.

[0059] In the specific implementation of this invention, the specific implementation methods of the system items can be referred to the implementation methods of the above-mentioned method items, and will not be repeated here.

[0060] In this embodiment of the invention, a traction characteristic model, a braking characteristic model, and a motion resistance model of a maglev train are constructed. A longitudinal dynamic model is constructed based on the traction characteristic model, the braking characteristic model, and the motion resistance model. A discretized state transition model is constructed based on the longitudinal dynamic model. The constructed model is highly matched with the actual dynamic characteristics of the maglev train, avoiding estimation deviations caused by model mismatch. Based on a discretized state transition model, the current prior estimate and Jacobian matrix are determined, and the prior covariance at the current time is determined based on the Jacobian matrix. The Kalman gain is calculated based on the current prior covariance, and the target posterior covariance matrix is ​​determined based on the current prior estimate and Kalman gain. Diagonal elements are extracted from the target posterior covariance matrix, and a target confidence interval is constructed based on these elements. The lower bound of the preceding vehicle's position confidence interval and the uncertainty margin are determined based on the target confidence interval. The braking distance of the following vehicle is calculated based on the current operating speed and maximum common braking deceleration of the following vehicle in the maglev train. Time-varying safety constraints are constructed based on the following vehicle's braking distance, the lower bound of the preceding vehicle's position confidence interval, and the uncertainty margin. Dynamic safety clearance is calculated based on these time-varying safety constraints. This explicitly quantifies the uncertainty of the preceding vehicle's state perception and transforms it into a calculable and executable safety constraint. The dynamic safety clearance is adjusted in real time according to the estimated uncertainty, avoiding overly conservative or undersafe conditions caused by fixed margins. Simultaneously, the target confidence interval improves tracking efficiency and provides a dynamic boundary with clear probabilistic meaning for multi-objective collaborative optimization, overcoming the limitations of traditional binary safety constraints.

[0061] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include: read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk, etc.

[0062] Furthermore, the above provides a detailed description of the dynamic safety distance modeling method and system for tracking and operating maglev trains provided by the embodiments of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for modeling dynamic safety distances during maglev train tracking operation, characterized in that, The method includes: A traction characteristic model, a braking characteristic model, and a motion resistance model of a maglev train are constructed. A longitudinal dynamic model is constructed based on the traction characteristic model, the braking characteristic model, and the motion resistance model. A discretized state transition model is constructed based on the longitudinal dynamic model. The current prior estimate and Jacobian matrix are determined based on the discretized state transition model, and the prior covariance at the current time is determined based on the Jacobian matrix. The Kalman gain is calculated based on the prior covariance at the current time, and the target posterior covariance matrix is ​​determined based on the current prior estimate and the Kalman gain. Based on the target posterior covariance matrix, diagonal elements are extracted, and a target confidence interval is constructed based on the diagonal elements. Based on the target confidence interval, the lower bound of the confidence interval for the position of the preceding vehicle and the uncertainty margin are determined. The current operating speed and maximum service braking deceleration of the following vehicle in the maglev train are obtained, and the braking distance of the following vehicle is calculated based on the current operating speed and maximum service braking deceleration. Time-varying safety constraints are constructed based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the uncertainty margin, and dynamic safety distances are calculated based on the time-varying safety constraints.

2. The method for modeling dynamic safety distances for maglev train tracking operation according to claim 1, characterized in that, The process involves constructing traction characteristic models, braking characteristic models, and motion resistance models for a maglev train, and based on these models, constructing a longitudinal dynamic model. Based on the longitudinal dynamic model, a discretized state transition model is then constructed, including: The traction characteristic model of the maglev train is constructed based on piecewise polynomials, and the expression of the traction characteristic model is as follows: in, is the traction force for the maglev train, and v is the speed of the maglev train; Obtain the mass of the maglev train and the proportional coefficients related to the characteristics of the maglev train and its braking system, and construct a braking characteristic model based on the maglev train mass and proportional coefficients. The expression of the braking characteristic model is as follows: in, For the braking force of the train, Where M is the proportionality coefficient, v is the mass of the maglev train, and v is the speed of the maglev train. The air resistance, magnetic resistance, onboard linear generator resistance, gradient resistance, curve resistance, and electromagnetic eddy current resistance experienced by the maglev train during operation on the line are obtained. Based on these factors, a motion resistance model is constructed. The expression for the motion resistance model is as follows: ， in, For total resistance, For air resistance, For magnetic resistance, For the resistance of the vehicle-mounted linear generator, Add resistance to the ramp, Add resistance to the curve. This is electromagnetic eddy current resistance; A longitudinal dynamics model is constructed based on the aforementioned traction characteristic model, braking characteristic model, and motion resistance model. The expression for the longitudinal dynamics model is as follows: ， Where v is the speed of the maglev train, x is the distance traveled by the maglev train, t is the travel time of the maglev train, M is the mass of the maglev train, and a is the acceleration of the maglev train. For the traction force of the maglev train, For the braking force of the train, Total resistance; Based on the aforementioned longitudinal dynamics model, a discretized state transition model is obtained. The expression of the discretized state transition model is as follows: ， in, Let f be the state vector determined by the longitudinal dynamics model, and let f() be the nonlinear state transition function. Let be the state vector of the train at the previous moment. To control the input, This is process noise.

3. The method for modeling dynamic safety distances for maglev train tracking operation according to claim 1, characterized in that, The step of determining the current prior estimate and Jacobian matrix based on the discretized state transition model, and determining the prior covariance at the current time step based on the Jacobian matrix, includes: Obtain the posterior estimate and control input of the maglev train at the previous moment, and determine the current prior estimate based on the discretized state transition model using the posterior estimate and control input of the maglev train at the previous moment. Linearization is performed based on the discretized state transition model to obtain the Jacobian matrix. The prior covariance at the current time is then calculated from the Jacobian matrix.

4. The method for modeling dynamic safety distances for maglev train tracking operation according to claim 3, characterized in that, The expression for the prior covariance at the current moment is: ， in, Let the prior covariance be at the current moment. For Jacobian matrices, Let T be the posterior covariance of the previous time step, T be the transpose operation, and Q be the process noise covariance matrix.

5. The method for modeling dynamic safety distances for maglev train tracking operation according to claim 1, characterized in that, The step of calculating the Kalman gain based on the prior covariance at the current time, and determining the target posterior covariance matrix based on the current prior estimate and the Kalman gain, includes: Obtain the observation matrix, and calculate the Kalman gain based on the observation matrix and the prior covariance at the current time. The expression for the Kalman gain is as follows: ， in, For Kalman gain, Let T be the prior covariance at the current moment, and T be the transpose operation. R is the observation matrix, and R is the observation noise covariance matrix; Based on the current prior estimate and Kalman gain, the state estimate is updated to obtain the target posterior covariance matrix. The expression for the target posterior covariance matrix is ​​as follows: ， in, Let I be the target posterior covariance matrix, and let I be the identity matrix. For Kalman gain, For the observation matrix, Let be the prior covariance at the current moment.

6. The method for modeling dynamic safety distances for maglev train tracking operation according to claim 1, characterized in that, The expression for the target confidence interval is: ， in, The target confidence interval, This is the posterior location estimate; 1.96 is the 97.5th percentile of the standard normal distribution. It is a diagonal element.

7. The method for modeling dynamic safety distances for maglev train tracking operation according to claim 1, characterized in that, The expression for the braking distance of the rear vehicle is: ， in, This is the braking distance of the following vehicle. At the current running speed, This is the maximum commonly used braking deceleration.

8. The method for modeling dynamic safety distances during maglev train tracking operation according to claim 1, characterized in that, The process of constructing time-varying safety constraints based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the uncertainty margin, and calculating the dynamic safety distance based on the time-varying safety constraints, includes: Based on the braking distance of the rear vehicle, the lower bound of the confidence interval of the position of the front vehicle, and the position of the rear vehicle, safety constraints are determined, and the expression for the safety constraints is: ， in, For the position of the rear vehicle, This is the braking distance of the following vehicle. This is the lower bound of the confidence interval for the position of the vehicle ahead. Based on the uncertainty margin, the security constraints are organized to obtain time-varying security constraints; The traditional minimum spacing is determined, and the expression for the traditional minimum spacing is: ， in, For traditional minimum spacing, For the total length of the train, Minimum parking clearance This refers to the braking distance of the vehicle behind. Based on the time-varying safety constraints, a time-varying uncertainty safety tracking margin is determined, and a dynamic safety distance is calculated based on the uncertainty safety tracking margin and the traditional minimum spacing. The expression for the dynamic safety distance is: ， ， in, For dynamic safety spacing, For traditional minimum spacing, To provide a safety margin for uncertainty tracking, It is a diagonal element.

9. The method for modeling dynamic safety distances for maglev train tracking operation according to claim 8, characterized in that, The expression for the time-varying security constraint is: ， in, This is the posterior location estimate. This is the braking distance of the following vehicle. For the position of the rear vehicle, It is a diagonal element.

10. A dynamic safety distance modeling system for tracking and operating maglev trains, characterized in that, The system includes: Model building module: used to build traction characteristic model, braking characteristic model and motion resistance model of maglev train, and to build longitudinal dynamic model based on the traction characteristic model, braking characteristic model and motion resistance model, and to build discretized state transition model based on the longitudinal dynamic model; Prior covariance module: used to determine the current prior estimate and Jacobian matrix based on the discretized state transition model, and to determine the prior covariance at the current time based on the Jacobian matrix; Covariance matrix module: used to calculate the Kalman gain based on the prior covariance at the current time, and to determine the target posterior covariance matrix based on the current prior estimate and the Kalman gain; Condition determination module: used to extract diagonal elements based on the target posterior covariance matrix, construct a target confidence interval based on the diagonal elements, and determine the lower bound and uncertainty margin of the confidence interval for the position of the preceding vehicle based on the target confidence interval; Rear vehicle braking distance module: used to obtain the current operating speed and maximum service braking deceleration of the rear vehicle in the maglev train, and calculate the braking distance of the rear vehicle based on the current operating speed and maximum service braking deceleration; Dynamic safety distance module: used to construct time-varying safety constraints based on the braking distance of the following vehicle, the lower bound of the confidence interval of the position of the preceding vehicle, and the uncertainty margin, and to calculate the dynamic safety distance based on the time-varying safety constraints.

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