High-speed train state acquisition method based on high-order extended Kalman filter

Abstract

The invention provides a high-speed train state acquisition method based on a high-order extended Kalman filter. The method comprises the following steps: establishing dynamic models of a train in different running states; constructing an extended Kalman filter state estimation error covariance matrix of the train after the dynamic models of the train in different running states are utilized; and establishing system models of different running states in the running process of the high-speed train, and acquiring the state information of the high-speed train according to the state estimation error covariance matrix of the extended Kalman filter of the train and the system models. According to the method, deep dynamic analysis is carried out on different running states (such as acceleration, air braking and adhesion braking) of the train, complex dynamic behaviors of the train in the states can be better captured, and the adaptability and reliability of a positioning system under various running conditions are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of train positioning, and in particular to a high-speed train state acquisition method based on a high-order extended Kalman filter. Background Art

[0002] In high-speed railway systems, accurate speed measurement and positioning of trains are key technologies to ensure safe operation of trains and improve transportation efficiency. In train positioning and speed measurement technology, accurate train dynamics modeling is the basis for achieving high-precision estimation. Most existing studies use linear dynamic models, which are simplified train dynamics and are usually used in scenarios with low speed or approximately uniform speed. In this scenario, the dynamic behavior of the train can be considered linear, and the changes in the system state can be described by linear equations. The linear dynamic model is simple to calculate, but it is difficult to accurately describe the actual dynamic characteristics of the train when it is traveling at high speed or non-uniform speed. Some studies use a multi-body dynamic model of the train, that is, each component of the train is regarded as an independent rigid body, and the interaction between them is simulated through connecting elements such as joints, springs and damping. This method can describe the complex dynamic behavior of the train under different operating conditions in detail and is one of the most accurate train dynamics modeling methods currently available. However, its computational complexity is high and its real-time performance is poor.

[0003] The accuracy of train dynamics modeling has a direct impact on the effectiveness of train positioning and speed measurement. Traditional linear or low-order nonlinear models are difficult to fully capture the complex dynamic behavior of high-speed trains, and existing high-precision modeling methods such as multi-body dynamics models have high accuracy but high computational complexity and are difficult to meet real-time requirements.

[0004] At present, the train positioning methods in the prior art mainly include ground signal-based positioning and satellite-based positioning. However, these methods have some limitations in practical applications: the coverage of the ground signal positioning system is limited, and the positioning accuracy will be affected in areas where the signal is weak or blocked. Satellite signals are easily blocked in environments such as tunnels and urban canyons, resulting in increased positioning errors. In addition, the update frequency of satellite positioning is low, and for high-speed moving trains, the real-time performance and accuracy are also insufficient. In order to overcome these problems, researchers have begun to use filtering technology that integrates multiple sensor information in recent years to improve the accuracy of train speed measurement and positioning. Among them, EKF (Extended Kalman Filter) is a commonly used method. EKF can improve the positioning accuracy to a certain extent by linearizing the nonlinear system. However, the traditional EKF only performs a first-order Taylor expansion on the nonlinear function, and its accuracy is still limited when dealing with high-speed motion and complex dynamic environments. In order to solve this problem, many researchers have proposed improved methods.

[0005] The disadvantages of the train positioning method in the prior art include:

[0006] Limited handling of complex dynamic behaviors: The dynamic model of high-speed trains is highly nonlinear and complex, especially when accelerating, decelerating, traveling on curves, and subject to external interference (such as wind, slope changes, etc.). Linear or low-order nonlinear models in the existing technology are difficult to accurately describe these complex dynamic behaviors, resulting in the accumulation of estimation errors, which affects the stability and reliability of the overall system.

[0007] Insufficient positioning accuracy: The traditional Kalman filter for nonlinear systems only performs finite-order Taylor expansion when processing nonlinear systems, ignoring high-order nonlinear information, resulting in low filtering accuracy. Especially in high-speed motion and complex dynamic environments, errors accumulate quickly.

[0008] Poor algorithm robustness: Positioning methods based on ground and satellite signals perform poorly in environments with signal obstruction, reflection, and interference, such as tunnels, urban canyons, and other areas, where positioning accuracy and reliability are significantly reduced.

[0009] The contradiction between real-time performance and computational complexity: Although some improved positioning methods, such as particle filtering (PF) or hybrid modeling methods, perform well in dealing with nonlinear systems, their computational complexity is high, especially in high-speed train scenarios with high real-time requirements, and it is difficult to meet the rapid response requirements. At the same time, the high computational burden of these methods increases hardware requirements and system costs. Summary of the invention

[0010] An embodiment of the present invention provides a high-speed train state acquisition method based on a high-order extended Kalman filter to achieve effective acquisition of the high-speed train state.

[0011] In order to achieve the above object, the present invention adopts the following technical scheme.

[0012] A high-speed train positioning method based on a complex nonlinear dynamic model, comprising:

[0013] Establish dynamic models of trains under different operating conditions;

[0014] After utilizing the dynamic model of the train under different operating states, constructing an extended Kalman filter state estimation error covariance matrix of the train;

[0015] A system model of different operating states during the operation of a high-speed train is established, and the state information of the high-speed train is obtained according to the extended Kalman filter state estimation error covariance matrix of the train and the system model.

[0016] Preferably, the establishment of the dynamic model of the train under different operating conditions includes:

[0017] 1. Train braking model:

[0018]

[0019] Where v(t+1) and v(t) are the speeds of the train at time t+1 and time t, respectively, and the variables are adhesion and air braking force. p (v(t),s) is the running resistance, T is the sampling time, s is the current position of the train, M A is the mass of train passengers, w(t) is the random disturbance of train speed caused by external factors;

[0020] Running resistance C p (v(t)) is composed of basic resistance C1(v(t)) and additional resistance C2(s), namely:

[0021] C p (v(t),s)=C1(v(t))+C2(s)

[0022] The basic resistance R1(vt) is positively correlated with the train running speed vt, expressed as:

[0023] C1(v(t))=M A ×(c0+c1(t)+c2v 2 (t)×g×10 -3 )

[0024] Where c0 is the rolling resistance coefficient, c1 is other mechanical resistance coefficients, which are proportional to the train speed v, C2(s) is the air resistance coefficient, which is proportional to the square of the train speed, and c represents the combined resistance of slopes, curves and tunnels;

[0025] A(u) and B r are adhesion braking force and air braking force respectively, g is the gravity acceleration coefficient, adhesion braking force A(u) is the combined influence of train wheel-rail adhesion coefficient u and train weight M A for:

[0026] A(u)=uM A g

[0027] Air brake force B r Affected by several brake performance parameters, namely:

[0028]

[0029] Where d is the diameter of the brake cylinder, r is the friction radius of the brake disc, R c is the diameter of the train wheel, N A is the total number of brake pads;

[0030] 2. Traction / cruise / glide model:

[0031]

[0032] F Tr (v(t)) is the traction force, and its expression is as follows:

[0033]

[0034] 3. Speed ​​sensor model:

[0035] The train speed measurement system consists of many sensors that generate counting pulses when the gear plate rotates on each pitch. tacho It consists of one pitch and the wheel diameter is R c , if in the time interval T tacho Received within p tacho pulse, the train speed measured by Doppler is:

[0036]

[0037] Doppler radar measures train speed based on the Doppler effect. The relative speed between the train and the track is calculated based on the frequency difference between the transmitted wave and the ground reflected wave. Suppose the number of radar pulses per kilometer is: N dopp , if the train is in time interval T dopp Received within p dopp pulse, the train speed measured by Doppler is:

[0038]

[0039] Combined with the train braking model shown in the above formula, the state space model of wheel Hall sensor speed measurement is expressed as:

[0040]

[0041] Similarly, the state space model of Doppler radar is:

[0042]

[0043] Where e1(t) and e2(t) are sensor measurement errors;

[0044] The train operation observation model is:

[0045]

[0046] Among them, f(·) is the nonlinear state function of the train under different operating modes, and h(·) is the linear measurement function of different speed sensors.

[0047] Preferably, the method of constructing an extended Kalman filter state estimation error covariance matrix by utilizing the dynamic model of the train under different operating states includes:

[0048] The extended Kalman filter filtering method includes two stages: prediction stage and update stage.

[0049] Prediction stage: Based on the dynamic analysis of high-speed trains and the observation sensor equations, a system model in which the state of the high-speed train is nonlinear and the observation is linear during operation is obtained. The system model includes the train braking model, speed sensor model, traction / cruise / sliding model and train operation observation model:

[0050] x(k+1)=f(x(k))+w(k)

[0051] y(k+1)=H(k+1)x(k+1)+v(k+1)

[0052] Where f(·) is a nonlinear state function with arbitrary order continuous differentiability, H(k+1) is the measurement transfer matrix; x(k) is the n-dimensional state vector, w(k) is the n-dimensional state model modeling error vector, y(k+1) is the m-dimensional measurement value vector, h(x(k+1) is the m-dimensional measurement function vector, and v(k+1) is the m-dimensional measurement model modeling error vector;

[0053] Known conditions: the estimated value of the original state at time k and the estimated error covariance matrix

[0054]

[0055] in, is the estimated value of the original state at time k, is the estimated error covariance matrix of the original state at time k;

[0056] By first obtaining the high-order feature estimation information of the state at time k

[0057]

[0058] in

[0059]

[0060]

[0061]

[0062] in, is the original estimation error The l-order Kronecker set of For l-order The estimated value of For l-order The estimated error covariance matrix of ;

[0063] is the original estimation error The l-th order Kronnick product of;

[0064] Establish a high-precision high-order extended Kalman filter based on high-order characteristics to estimate the state of such nonlinear systems

[0065]

[0066]

[0067] Among them, r represents the r-order Taylor expansion approximation of the nonlinear state model, is the state estimation value at the next moment, P(k+1|k+1) is the state estimation error covariance matrix at the next moment;

[0068] Assume that, using the nonlinear state model at Performing Taylor expansion of order i=2,3,…,l, we have obtained

[0069]

[0070] Further recursion yields:

[0071]

[0072] First, based on the linear state model The l-order Taylor expansion of

[0073]

[0074] Among them, x l (k+1) is the state value, is the one-step prediction value, is the one-step prediction error value;

[0075] Get the one-step prediction estimate based on the l-order Taylor expansion of the nonlinear state model

[0076]

[0077] One-step forecast estimate error value

[0078]

[0079] One-step forecast estimate error value

[0080]

[0081] Among them, x l (k+1), and P xx,l The subscript "l" of (k+1|k) and (k+1|k) indicates that the nonlinear state model is used in the The l-order Taylor expansion of is obtained;

[0082]

[0083] Furthermore, the nonlinear shape model is Perform a (l+1)th order Taylor expansion

[0084]

[0085] in

[0086]

[0087] Substituting the above formula into the linear measurement model, we have

[0088]

[0089] Among them, y(k+1) is the measured value, A (i) (k) is the Jacobian matrix corresponding to the Taylor expansion; after merging similar items, the identified quantity is The measurement equations are:

[0090]

[0091] in

[0092]

[0093] In the above formula

[0094]

[0095]

[0096] in, is the observation value in the constructed new observation equation, is the estimated value of the new observation noise constructed, is the estimated error covariance matrix of the constructed new observation noise;

[0097] Using the least squares method for equation (), we have

[0098]

[0099] Calculate the expected value of the

[0100]

[0101] Calculate the expected estimated error value of the measured quantity

[0102]

[0103] Calculate the expected estimation error covariance matrix of the measured

[0104]

[0105] So far, we have obtained

[0106]

[0107] in, is the l+1 order state estimation error value, is the expected estimated value of the quantity being measured,

[0108] is the expected estimation error of the measured quantity, is the expected estimation error covariance matrix of the measured

[0109] Update phase:

[0110] Based on the r-order Taylor expansion

[0111]

[0112] One-step state forecast estimate

[0113]

[0114] One-step state prediction estimation error value

[0115] One-step state prediction estimation error covariance matrix

[0116] There is a one-step measurement prediction estimate based on the measurement equation

[0117]

[0118] One-step measurement prediction estimate error value

[0119]

[0120] Calculate the Extended Kalman Filter state estimation error

[0121] and measurement values ​​directly and decomposed

[0122]

[0123] Using the orthogonal principle

[0124]

[0125] Get the extended Kalman filter gain matrix K r Solving equations for (k+1)

[0126]

[0127] Solving the above equations, we can get the extended Kalman filter gain matrix K r The analytical expression of (k+1):

[0128]

[0129] Among them, the cross-covariance matrix of the state prediction estimation error and the measurement prediction estimation error is:

[0130]

[0131] The autocovariance matrix of the measurement prediction estimation error is:

[0132]

[0133] Based on the formula

[0134]

[0135] Get the estimated state value of the train at the next moment;

[0136] Calculate the high-order extended Kalman filter state estimation error covariance matrix:

[0137]

[0138] The extended Kalman filter state estimation error covariance matrix of the train is obtained as:

[0139]

[0140] Preferably, the establishing of the system model of different operating states during the operation of the high-speed train, and obtaining the high-speed train state information according to the extended Kalman filter state estimation error covariance matrix of the train and the system model, comprises:

[0141] A dynamic model of the high-speed train is established according to the actual motion state of the high-speed train, the dynamic model is used as the state equation of the entire high-speed train operation system, a mathematical model is established with the measurement data obtained by sensors on the high-speed train and on the trackside, the mathematical model is used as the observation equation of the entire high-speed train operation system, and a system model of the high-speed train operation system is obtained according to the state equation and the mathematical model of the high-speed train operation system;

[0142] The extended Kalman filter state estimation error covariance matrix is ​​applied to the system model of the high-speed train operation system. By performing Taylor expansion on the nonlinear state equation, high-order nonlinear information is obtained to obtain the state estimation prediction value of the train at the current moment, which includes the train speed estimation value and the displacement estimation value. The state estimation prediction value at the current moment is substituted into the measurement equation, and the state estimation value of the train at the next moment is obtained with the help of the measurement equation. The estimation value at the next moment is then substituted back into the Kalman filter update formula. The above steps are repeated to obtain the train speed estimation value and displacement estimation value at the next moment. This cycle is repeated to obtain the estimated values ​​of the train speed and position of the entire process.

[0143] It can be seen from the technical solutions provided by the above-mentioned embodiments of the present invention that the method of the embodiments of the present invention enhances the processing capability of complex dynamic behaviors: by conducting in-depth dynamic analysis of different operating states of the train (such as acceleration, air braking, adhesion braking, etc.), the model of the present invention can better capture the complex dynamic behaviors of the train under these states, thereby improving the adaptability and reliability of the positioning system under various operating conditions.

[0144] Improve positioning accuracy: By establishing a nonlinear dynamic model of high-speed trains and combining it with a high-order extended Kalman filter algorithm, a more accurate state estimation is performed using the system's high-order nonlinear information, thereby significantly improving the positioning and speed measurement accuracy of high-speed trains, especially in complex nonlinear environments.

[0145] Enhance algorithm robustness: Combined with the under-measured least squares algorithm, the system's robustness in various complex environments is improved to ensure that high-precision positioning information can still be provided under harsh external environmental conditions.

[0146] Optimize computing efficiency: While ensuring high accuracy, optimize the algorithm structure, reduce computational complexity, improve the real-time performance of filtering, and meet the real-time positioning requirements of high-speed trains.

[0147] Additional aspects and advantages of the present invention will be given in part in the following description, which will become obvious from the following description, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0148] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0149] Figure 1 A processing flow chart of a high-speed train state acquisition method based on a high-order extended Kalman filter provided in an embodiment of the present invention;

[0150] Figure 2 A displacement change curve under train dynamics modeling provided by an embodiment of the present invention;

[0151] Figure 3 A speed variation curve under train dynamics modeling provided by an embodiment of the present invention;

[0152] Figure 4 A flowchart of a high-precision fusion positioning method for a high-speed train using a high-order extended Kalman filter based on a complex nonlinear dynamic model provided by an embodiment of the present invention;

[0153] Figure 5 A high-speed train application scenario of a high-speed train high-order extended Kalman filter high-precision fusion positioning method based on a complex nonlinear dynamic model provided by an embodiment of the present invention;

[0154] Figure 6 A framework diagram of a high-precision fusion positioning method for high-speed trains using a high-order extended Kalman filter based on a complex nonlinear dynamic model provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0155] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0156] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when the present invention refers to an element being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be an intermediate element. In addition, the "connection" or "coupling" used herein may include wireless connection or coupling. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items.

[0157] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0158] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.

[0159] Since estimation algorithms such as Kalman filters rely on system models and observation models to predict and update state estimates, if the model is inaccurate, the prediction and update steps of the filter will be affected, thereby reducing the accuracy of the estimation. Therefore, in order to improve the overall estimation accuracy, the present invention first establishes a system model of different operating states during the operation of a high-speed train. The operating states of a high-speed train can be roughly divided into traction, cruising, coasting and braking. Traction refers to the speed of the train being increased by the influence of traction. When cruising, the train maintains its speed under the action of traction or braking force and resistance, while when coasting, the traction and braking force of the train are zero, and the train is only affected by the running resistance. Finally, braking is a situation where the train speed decreases only under the action of braking force. On this basis, according to the traction requirements of the train in different operating modes, traction, cruising and coasting are regarded as one model type, and braking is regarded as another model type. Considering the different braking characteristics of the train on dry and wet tracks, the existing braking model is further improved. The influence of adhesion coefficient and adhesion braking force on the braking performance of the train is analyzed.

[0160] The processing flow of a high-speed train state acquisition method based on a high-order extended Kalman filter provided by an embodiment of the present invention is as follows: Figure 1 As shown, the processing steps include the following:

[0161] Step S10: Establishing a dynamic model of the train under different operating conditions.

[0162] Step S20: After using the dynamic model of the train under different operating states, construct an extended Kalman filter state estimation error covariance matrix.

[0163] Step S30: Establish a system model of different operating states during the operation of the high-speed train, and use the extended Kalman filter state estimation error covariance matrix to measure the speed and position the high-speed train.

[0164] Specifically, the above step S10 includes:

[0165] 1. Train braking model:

[0166]

[0167] Where v(t+1) and v(t) are the speeds of the train at time t+1 and time t, respectively, and the variables are adhesion and air braking force. p (v(t),s) is the running resistance, T is the sampling time, s is the current position of the train, M A is the passenger mass of the train, and w(t) is the random disturbance of the train speed caused by external factors.

[0168] The running resistance C p (v(t)) is composed of basic resistance C1(v(t)) and additional resistance C2(s), namely:

[0169] C p (v(t),s)=C1(v(t))+C2(s)

[0170] The basic resistance R1(vt) is positively correlated with the train running speed vt, usually expressed as:

[0171] C1(v(t))=M A ×(c0+c1v(t)+c2v 2 (t)×g×10 -3 )

[0172] Where c0 is the rolling resistance coefficient, c1 is the other mechanical resistance coefficient, which is proportional to the train speed v, and C2(s) is the air resistance coefficient, which is proportional to the square of the train speed. Their values ​​are usually set heuristically. c represents the combined resistance of slopes, curves and tunnels.

[0173] Among them, A(u) and B rThe adhesion braking force A(u) is jointly affected by the train wheel-rail adhesion coefficient u and the train weight M. A ,for

[0174] A(u)=uM A g

[0175] Where g is the gravitational acceleration coefficient, 9.8m / s2.

[0176] In the above formula, the wheel-rail adhesion coefficient decreases as the train speed decreases. Their mutual relationship is affected by the track surface. Taking the train braking process as an example, when the train moves from dry track to wet track, the adhesion coefficient decreases significantly, the train system tends to lock and slip, and the air braking force acting on the wheels is difficult to stop the train. In this case, the system cannot accurately obtain the real-time status of the train, increasing the risk of train operation.

[0177] Air brake force B r Affected by several brake performance parameters, namely:

[0178]

[0179] Where d is the diameter of the brake cylinder, r is the friction radius of the brake disc, R c is the diameter of the train wheel, N A is the total number of brake pads. These parameters can be directly measured by conventional methods and remain unchanged during the operation of the train. Therefore, these parameters are regarded as constants in the calculation of the present invention. The additional parameter η in the above formula is the transmission efficiency of the main brake device, γ B is the braking ratio. is the friction coefficient of the train brake disc, which depends on the working conditions of the train and the material of the brake disc. Pre is the air pressure in the brake cylinder. During the actual emergency braking process of the train, the entire air pressure will be released.

[0180] 2. Traction / cruise / glide model:

[0181]

[0182] Among them, F Tr (v(t)) is the traction force, which can be adjusted in real time according to the actual operation conditions. The specific operation mode of the model is determined by the traction force, and its expression is as follows:

[0183]

[0184] 3. Speed ​​sensor model:

[0185] The train speed measurement system consists of many sensors, such as inertial navigation unit (INS), tachometer, Doppler radar and global positioning system (GPS). Taking the CTCS3.300T train control system as an example, the current multi-sensor system architecture consists of a combination of two tachometers and two tachometers. Specifically, when the gear plate rotates on each pitch, a counting pulse is generated. tacho It consists of one pitch and the wheel diameter is R c If in the time interval T tacho Received within p tacho pulse, the train speed measured by Doppler is:

[0186]

[0187] It should be noted that the tachometer is affected by the adhesion condition of the track surface. When the train is idling or slipping, the tachometer has a greater impact on the measurement accuracy.

[0188] Therefore, Doppler radar measures the speed of the train based on the Doppler effect. The relative speed between the train and the track is calculated based on the frequency difference between the transmitted wave and the ground reflected wave. Assume that the number of radar pulses per kilometer is: N dopp If in the time interval T dopp Received within p dopp pulse, the train speed measured by Doppler is:

[0189]

[0190] Doppler radar is not affected by wheel spin, slip and wheel diameter changes. However, it is generally more susceptible to interference than a tachometer.

[0191] Combined with the train braking model shown in the above formula, the state space model of wheel Hall sensor speed measurement can be expressed as:

[0192]

[0193] Similarly, the state space model of Doppler radar is:

[0194]

[0195] Where e1(t) and e2(t) are sensor measurement errors.

[0196] In summary, the train operation observation model can be uniformly rewritten as:

[0197]

[0198] Among them, f(·) is the nonlinear state function of the train under different operating modes, and h(·) is the linear measurement function of different speed sensors.

[0199] Specifically, the above step S20 includes:

[0200] The processing process of the extended Kalman filter filtering method of the embodiment of the present invention mainly includes two stages: a prediction stage and an update stage.

[0201] Prediction stage: Assume that the present invention has obtained a system model in which the state of the high-speed train is nonlinear and the observation is linear according to the dynamic analysis of the high-speed train and the observation sensor equation. The system model includes the train braking model, speed sensor model, traction / cruise / sliding model and train operation observation model obtained in step S10 above:

[0202] x(k+1)=f(x(k))+w(k)

[0203] y(k+1)=H(k+1)x(k+1)+v(k+1)

[0204] Where f(·) is a nonlinear state function with arbitrary order continuous differentiability, H(k+1) is the measurement transfer matrix, x(k) is the n-dimensional state vector, w(k) is the n-dimensional state modeling error vector, y(k+1) is the m-dimensional measurement value vector, h(x(k+1) is the m-dimensional measurement function vector, and v(k+1) is the m-dimensional measurement modeling error vector.

[0205] Known conditions: the estimated value of the original state at time k and the estimated error covariance matrix

[0206]

[0207] in, is the estimated value of the original state at time k, is the estimated error covariance matrix of the original state at time k.

[0208] The present invention aims to estimate the information of the high-order characteristics of the state at time k by first obtaining

[0209]

[0210] in

[0211]

[0212]

[0213]

[0214] in, is the original estimation error The l-order Kronecker set of For l-order The estimated value of For l-order The estimated error covariance matrix of .

[0215] is the original estimation error The l-th order Kronecker product of .

[0216] Establish a high-precision high-order extended Kalman filter based on high-order characteristics to estimate the state of such nonlinear systems

[0217]

[0218] Among them, r represents the r-order Taylor expansion approximation of the nonlinear state model. is the state estimation value at the next moment, and P(k+1|k+1) is the state estimation error covariance matrix at the next moment.

[0219] Assume that, using the nonlinear state model at Performing Taylor expansion of order i=2,3,...,l, we have obtained

[0220]

[0221] Further recursion to obtain

[0222]

[0223] To this end, the present invention firstly has a linear state model based on The l-order Taylor expansion of

[0224]

[0225] Among them, x l (k+1) is the state value, is the one-step prediction value, is the one-step prediction error value.

[0226] Get the one-step prediction estimate based on the l-order Taylor expansion of the nonlinear state model

[0227]

[0228] One-step forecast estimate error value

[0229]

[0230] One-step forecast estimate error value

[0231]

[0232] Among them, xl (k+1), and P xx,l The subscript "l" of (k+1|k) and (k+1|k) indicates that the nonlinear state model is used in the It is obtained by the l-order Taylor expansion of .

[0233]

[0234] Furthermore, the nonlinear shape model is Perform a (l+1)th order Taylor expansion

[0235]

[0236] in

[0237]

[0238] Substituting the above formula into the linear measurement model, we have

[0239]

[0240] Among them, y(k+1) is the measured value, A (i) (k) is the Jacobian matrix corresponding to Taylor expansion. After merging similar items, the identified quantity is The measurement equations are:

[0241]

[0242] in

[0243]

[0244]

[0245]

[0246] In the above formula

[0247]

[0248]

[0249] in, is the observation value in the constructed new observation equation, is the estimated value of the new observation noise constructed, is the estimated error covariance matrix of the constructed new observation noise.

[0250] Using the least squares method for equation (), we have

[0251]

[0252] Calculate the expected value of the

[0253]

[0254] Calculate the expected estimated error value of the measured quantity

[0255]

[0256] Calculate the expected estimation error covariance matrix of the measured

[0257]

[0258] So far, the present invention has obtained

[0259]

[0260] in, is the l+1 order state estimation error value, is the expected estimated value of the quantity being measured,

[0261] is the expected estimation error of the measured quantity, is the expected estimation error covariance matrix of the measured

[0262] Update phase:

[0263] Based on the r-order Taylor expansion

[0264]

[0265] One-step state forecast estimate

[0266]

[0267] One-step state prediction estimation error value

[0268] One-step state prediction estimation error covariance matrix

[0269] There is a one-step measurement prediction estimate based on the measurement equation

[0270]

[0271] One-step measurement prediction estimate error value

[0272]

[0273] Calculate high-precision EKF state estimation error

[0274] and measurement values ​​directly and decomposed

[0275]

[0276] Using the orthogonal principle

[0277]

[0278] The present invention obtains the EKF gain matrix K r Solving equations for (k+1)

[0279]

[0280] Solving the above equations, we get the EKF gain matrix K r The analytical expression of (k+1)

[0281]

[0282] Among them, the cross-covariance matrix of the state prediction estimation error and the measurement prediction estimation error is

[0283]

[0284] The autocovariance matrix of the measurement prediction estimation error is:

[0285]

[0286] Based on the formula

[0287]

[0288] The estimated state value at the next moment can be obtained.

[0289] Finally, the high-order extended Kalman filter state estimation error covariance matrix is ​​calculated:

[0290]

[0291] Therefore, the high-precision EKF state estimation error covariance matrix is ​​obtained

[0292]

[0293] So far, the present invention has completed the design of a high-precision EKF for estimating nonlinear states and linear measurement systems based on high-order characteristics.

[0294] Specifically, the above step S30 includes: establishing a dynamic model of the high-speed train according to the actual motion state of the high-speed train, using the dynamic model as the state equation of the entire high-speed train operation system, establishing a mathematical model with the measurement data obtained by sensors on the high-speed train and on the trackside, and using the mathematical model as the observation equation of the entire high-speed train system. According to the state equation and mathematical model of the high-speed train operation system, the system model of the high-speed train operation system is obtained, and the extended Kalman filter state estimation error covariance matrix proposed in the present invention is applied to the system model of the high-speed train operation system, and the state estimation values ​​of the high-speed train at different times, that is, the displacement estimation value and the speed estimation value, can be obtained, that is, the position and speed of the high-speed train can be accurately estimated under the condition of external interference.

[0295] The state of a high-speed train includes two indicators: displacement and speed. The state of the train can be set as a state vector, which includes two physical quantities: displacement and speed. By modeling the dynamics of a high-speed train, we have obtained an equation for the change of the state of a high-speed train over time. However, due to the presence of various noises and interferences in the environment where the train is located, the modeling accuracy of the equation will be inaccurate. Therefore, we use Kalman filtering to reduce the interference of the environmental noise on the train state estimation. The specific process is to perform Taylor expansion on the nonlinear state equation to obtain high-order nonlinear information, obtain a more accurate one-step prediction value of the state estimation, and bring the prediction value into the measurement equation. With the help of the measurement equation, the state estimation value at the next moment is obtained, that is, the train speed estimation value and displacement estimation value at the next moment, and then bring the estimation value at this moment back to the Kalman filter update formula. Repeat the above steps to obtain the train speed estimation value and displacement estimation value at the next moment. Repeat this cycle to obtain the train speed and position estimation value of the entire process.

[0296] Figure 2 and Figure 3 is the state change curve of the high-speed train after dynamic modeling. Figure 2 and Figure 3 It can be seen that the train operation is weakly nonlinear. The present invention takes into account the influence of multiple resistances such as friction, air resistance, and additional force of curves during the train operation, and obtains a more accurate train operation status curve, which can greatly reduce the error of the estimation algorithm in the cycle process, thereby achieving higher accuracy.

[0297] Figure 4 It is an algorithm flow chart of the high-order extended Kalman filter algorithm of the present invention, such as Figure 4As shown, after the system state model and initial state are input into the algorithm, the nonlinear state equation in the system is first Taylor expanded, and then brought into the observation equation and the known terms and unknown terms are separated and moved to form a new observation equation. By applying the under-measured least squares algorithm to the observation equation, the estimated values ​​of the high-order terms of the Taylor expansion can be calculated, and then the nonlinear state equation is expanded to a higher order again. By repeating the above operations, the infinite order information of the theoretical nonlinear function can be obtained, thereby obtaining higher estimation accuracy.

[0298] Figure 5 This is an application scenario diagram of the high-order extended Kalman filter algorithm of the present invention, that is, assuming that a high-speed train runs on a straight high-speed railway, multiple wireless radio heads, sensors and other observation equipment are arranged in a zigzag shape on the trackside, and the train can exchange information with the wireless radio heads and Doppler radars through communication equipment. The observation information of different observation equipment and the state information of the train are input into the high-order extended Kalman filter algorithm to obtain the real-time estimation value of the train position and speed.

[0299] Figure 6 The framework diagram of applying the high-order extended Kalman filter algorithm to the high-speed train system. The high-speed train has multiple operating states, so the train is modeled separately according to the different motion states, and then different observation instruments such as sensors, Doppler radars, and train tachometers are modeled. An accurate high-speed train operation system model can be obtained, and the high-order extended Kalman filter algorithm can be applied to this system model.

[0300] In summary, the embodiments of the present invention have the following advantages in terms of high-speed train speed measurement and positioning:

[0301] Enhanced processing capabilities for complex dynamic behaviors: Existing train dynamic models are usually simplified linear or low-order nonlinear models, which make it difficult to accurately capture the complex dynamic behaviors of high-speed trains under different operating conditions, especially when track irregularities and external interference exist. Positioning accuracy will be affected. By establishing a more accurate nonlinear dynamic model, the present invention can fully capture the motion characteristics of high-speed trains under various dynamic conditions. Combined with the HEKF algorithm, this model significantly improves the system's ability to handle complex dynamic behaviors, thereby improving positioning accuracy and system robustness.

[0302] The positioning accuracy is significantly improved: When dealing with nonlinear systems, the traditional extended Kalman filter (EKF) algorithm only uses the first-order Taylor expansion for linearization, which leads to large estimation errors in complex nonlinear environments and makes it difficult to meet the needs of high-precision positioning of high-speed trains. By introducing the high-order extended Kalman filter (HEKF) algorithm, the present invention can utilize the high-order nonlinear information of the system and significantly improve the positioning and speed measurement accuracy. This improvement enables the present invention to maintain high-precision state estimation under various operating conditions (such as acceleration, deceleration, constant speed, etc.), especially under high-speed or complex nonlinear conditions.

[0303] Comprehensive performance advantages: Existing technologies often have a trade-off between accuracy, real-time performance, and complexity. For example, the high-precision particle filter algorithm has a bottleneck in computational complexity, and the simple linearization method is fast in calculation but lacks accuracy. Through the innovative high-order extended Kalman filter algorithm and nonlinear dynamic modeling, the present invention has excellent performance in positioning accuracy, real-time performance, computational efficiency, and environmental adaptability, achieving comprehensive performance optimization and meeting the multiple requirements of high-speed train positioning.

[0304] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0305] It can be known from the description of the above implementation methods that those skilled in the art can clearly understand that the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention or certain parts of the embodiments.

[0306] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The device and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0307] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A high-speed train positioning method based on a complex nonlinear dynamic model, characterized in that: include: Establish dynamic models of trains under different operating conditions; After utilizing the dynamic model of the train under different operating states, constructing an extended Kalman filter state estimation error covariance matrix of the train; A system model of different operating states during the operation of a high-speed train is established, and the state information of the high-speed train is obtained according to the extended Kalman filter state estimation error covariance matrix of the train and the system model.

2. The method according to claim 1, characterized in that The said establishing the dynamic model of the train under different running states includes:

1. Train braking model: Where v(t+1) and v(t) are the speeds of the train at time t+1 and time t, respectively, and the variables are adhesion and air braking force. p (v(t),s) is the running resistance, T is the sampling time, s is the current position of the train, M A is the mass of train passengers, w(t) is the random disturbance of train speed caused by external factors; Running resistance C p (v(t)) is composed of basic resistance C1(v(t)) and additional resistance C2(s), namely: C p (v(t),s)=C1(v(t))+C2(s) The basic resistance R1(vt) is positively correlated with the train running speed vt, expressed as: C1(v(t))=M A ×(c0+c1v(t)+c2v 2 (t)×g×10 -3 ) Where c0 is the rolling resistance coefficient, c1 is other mechanical resistance coefficients, which are proportional to the train speed v, C2(s) is the air resistance coefficient, which is proportional to the square of the train speed, and c represents the combined resistance of slopes, curves and tunnels; A(u) and B r are adhesion braking force and air braking force respectively, g is the gravity acceleration coefficient, adhesion braking force A(u) is the combined influence of train wheel-rail adhesion coefficient u and train weight M A for: A(u)=uM A g Air brake force B r Affected by several brake performance parameters, namely: Where d is the diameter of the brake cylinder, r is the friction radius of the brake disc, R c is the diameter of the train wheel, N A is the total number of brake pads; 2. Traction / cruise / glide model: F Tr (v(t)) is the traction force, and its expression is as follows:

3. Speed ​​sensor model: The train speed measurement system consists of many sensors that generate counting pulses when the gear plate rotates on each pitch. tacho It consists of one pitch and the wheel diameter is R c , if in the time interval T tacho Received within p tacho pulse, the train speed measured by Doppler is: Doppler radar measures train speed based on the Doppler effect. The relative speed between the train and the track is calculated based on the frequency difference between the transmitted wave and the ground reflected wave. Suppose the number of radar pulses per kilometer is: N dopp , if the train is in time interval T dopp Received within p dopp pulse, the train speed measured by Doppler is: Combined with the train braking model shown in the above formula, the state space model of wheel Hall sensor speed measurement is expressed as: Similarly, the state space model of Doppler radar is: Where e1(t) and e2(t) are sensor measurement errors; The train operation observation model is: Among them, f(·) is the nonlinear state function of the train under different operating modes, and h(·) is the linear measurement function of different speed sensors.

3. The method according to claim 1, characterized in that The method of constructing an extended Kalman filter state estimation error covariance matrix by utilizing the dynamic model of the train under different operating states includes: The extended Kalman filter filtering method includes two stages: prediction stage and update stage. Prediction stage: Based on the dynamic analysis of high-speed trains and the observation sensor equations, a system model in which the state of the high-speed train is nonlinear and the observation is linear during operation is obtained. The system model includes the train braking model, speed sensor model, traction / cruise / sliding model and train operation observation model: x(k+1)=f(x(k))+w(k) y(k+1)=H(k+1)x(k+1)+v(k+1) Where f(·) is a nonlinear state function with arbitrary order continuous differentiability, H(k+1) is the measurement transfer matrix; x(k) is the n-dimensional state vector, w(k) is the n-dimensional state model modeling error vector, y(k+1) is the m-dimensional measurement value vector, h(x(k+1) is the m-dimensional measurement function vector, and v(k+1) is the m-dimensional measurement model modeling error vector; Known conditions: the estimated value of the original state at time k and the estimated error covariance matrix in, is the estimated value of the original state at time k, is the estimated error covariance matrix of the original state at time k; By first obtaining the high-order feature estimation information of the state at time k in in, is the original estimation error The l-order Kronecker set of For l-order The estimated value of For l-order The estimated error covariance matrix of ; is the original estimation error The l-th order Kronnick product of; Establish a high-precision high-order extended Kalman filter based on high-order characteristics to estimate the state of such nonlinear systems Among them, r represents the r-order Taylor expansion approximation of the nonlinear state model, is the state estimation value at the next moment, P(k+1|k+1) is the state estimation error covariance matrix at the next moment; Assume that, using the nonlinear state model at Performing Taylor expansion of order i=2,3,…,l, we have obtained Further recursion yields: First, based on the linear state model The l-order Taylor expansion of Among them, x l (k+1) is the state value, is the one-step prediction value, is the one-step prediction error value; the one-step prediction estimate based on the l-order Taylor expansion of the nonlinear state model is obtained One-step forecast estimate error value One-step forecast estimate error value Among them, x l (k+1), and P xx,l The subscript "l" of (k+1|k) and (k+1|k) indicates that the nonlinear state model is used in the The l-order Taylor expansion of is obtained; Furthermore, the nonlinear shape model is Perform a (l+1)th order Taylor expansion in Substituting the above formula into the linear measurement model, we have Among them, y(k+1) is the measured value, A (i) (k) is the Jacobian matrix corresponding to Taylor expansion; After merging similar items, the identified quantity The measurement equations are: in In the above formula in, is the observation value in the constructed new observation equation, is the estimated value of the new observation noise constructed, is the estimated error covariance matrix of the constructed new observation noise; Using the least squares method for equation (), we have Calculate the expected value of the Calculate the expected estimated error value of the measured quantity Calculate the expected estimation error covariance matrix of the measured So far, we have obtained in, is the l+1 order state estimation error value, is the expected estimated value of the quantity being measured, is the expected estimation error of the measured quantity, The expected estimation error covariance matrix of the measured object is updated in the following phase: Based on the r-order Taylor expansion One-step state forecast estimate One-step state prediction estimation error value One-step state prediction estimation error covariance matrix There is a one-step measurement prediction estimate based on the measurement equation One-step measurement prediction estimate error value Calculate the Extended Kalman Filter state estimation error and measurement values ​​directly and decomposed Using the orthogonal principle Get the extended Kalman filter gain matrix K r Solving equations for (k+1) Solving the above equations, we can get the extended Kalman filter gain matrix K r The analytical expression of (k+1): Among them, the cross-covariance matrix of the state prediction estimation error and the measurement prediction estimation error is: The autocovariance matrix of the measurement prediction estimation error is: Based on the formula Get the estimated state value of the train at the next moment; Calculate the high-order extended Kalman filter state estimation error covariance matrix: The extended Kalman filter state estimation error covariance matrix of the train is obtained as:

4. The method according to claim 3, characterized in that The establishment of a system model for different operating states during the operation of a high-speed train, and obtaining high-speed train state information according to the extended Kalman filter state estimation error covariance matrix of the train and the system model, includes: A dynamic model of the high-speed train is established according to the actual motion state of the high-speed train, the dynamic model is used as the state equation of the entire high-speed train operation system, a mathematical model is established with the measurement data obtained by sensors on the high-speed train and on the trackside, the mathematical model is used as the observation equation of the entire high-speed train operation system, and a system model of the high-speed train operation system is obtained according to the state equation and the mathematical model of the high-speed train operation system; The extended Kalman filter state estimation error covariance matrix is ​​applied to the system model of the high-speed train operation system. By performing Taylor expansion on the nonlinear state equation, high-order nonlinear information is obtained to obtain the state estimation prediction value of the train at the current moment, which includes the train speed estimation value and the displacement estimation value. The state estimation prediction value at the current moment is substituted into the measurement equation, and the state estimation value of the train at the next moment is obtained with the help of the measurement equation. The estimation value at the next moment is then substituted back into the Kalman filter update formula. The above steps are repeated to obtain the train speed estimation value and displacement estimation value at the next moment. This cycle is repeated to obtain the estimated values ​​of the train speed and position of the entire process.

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