CN110203254A - The safety detection method of Kalman filter in train positioning system - Google Patents

Abstract

The invention relates to a safety detection method of a Kalman filter in a train positioning system. The method comprises the following steps: 1) performing fault diagnosis on the sensor; Kalman filter equation to obtain the positioning result of the train; 3) carry out the Kalman filter divergence test, the track electronic map auxiliary inspection and the second axle sensor auxiliary inspection to the train positioning result; 4) after passing the inspection, calculate the final result of the train positioning result Locate the location and safety interval; 5) Design a fault tree based on the above calculation process, and analyze the safety of the train system. Compared with the prior art, the present invention provides a system-level fault tree analysis method for train positioning, which has the advantages of reliability, stability, safety and the like.

Description

Safety Detection Method of Kalman Filter in Train Positioning System

technical field

The invention relates to the fields of data fusion, data verification and fault tree analysis, in particular to a safety detection method of a Kalman filter in a train positioning system.

Background technique

At present, with the development of Beidou satellite positioning system, the combined train positioning system based on GNSS, wheel speed sensor, and track electronic map is gradually becoming mature. Compared with the traditional train positioning system, this positioning system has the advantages of high positioning accuracy, low dependence on trackside equipment, continuous positioning, etc., and is very suitable for positioning of low-density lines. However, the satellite-based positioning system also has inherent deficiencies. Its positioning is easily affected by environmental factors. The risk of space signal availability caused by factors such as signal shielding, signal interference, and multipath effects may bring safety risks, especially under viaducts. Or in tunnels, GNSS positioning is often invalid. Therefore, it is necessary to use multiple sensors for combined positioning to meet the requirements of accuracy and stability.

The Kalman filter is widely used in the processing of multi-sensor positioning data, especially for the combined positioning of GNSS, IMU and wheel speed sensors. However, the current domestic GNSS-based train positioning technology is still in the stage of research and development and experimental verification, and there is no mature research on the analysis of system stability and safety. Domestic universities have given a unit-level fault tree analysis method, but for combination Localization, especially the safety system based on multi-sensor combination positioning of Kalman filter, lacks an effective method for system fault tree analysis.

Contents of the invention

The object of the present invention is to provide a safety detection method of a Kalman filter in a train positioning system in order to overcome the above-mentioned defects in the prior art.

The purpose of the present invention can be achieved through the following technical solutions:

A safety detection method of a Kalman filter in a train positioning system, wherein the sensors in the train positioning system include GNSS, an electronic track map, a first axle sensor and a second axle sensor, and the fault detection method of the combined train positioning system Include the following steps:

S1: Carry out fault diagnosis on the first axle sensor, the second axle sensor, GNSS and track electronic map, if there is no fault, go to S2; otherwise, end;

S2: Based on the speed measurement data of the first axle sensor, GNSS positioning data and track electronic map data, the extended Kalman filter equation is used to obtain the positioning result of the train, and S3 is performed;

S3: Perform a Kalman filter divergence test on the train positioning result obtained in S2, if it is determined that the train positioning result does not diverge, then proceed to S4, otherwise it is determined that the Kalman filter is divergent, and the filtering result is not currently used;

S4: Project the train positioning result obtained in S2 to the track electronic map data to obtain the lateral deviation; set the track electronic map detection threshold, if the lateral deviation is less than the track electronic map detection threshold, go to S5, otherwise it is determined that the Kalman filter error exceeds Poor, the filtering result is not currently used;

S5: Project the train positioning result obtained in S2 to the track electronic map data, and obtain the positioning mileage according to the time period; set the detection threshold of the wheel axle sensor, if in each time period, the difference between the positioning mileage and the distance measured by the second wheel axle sensor is less than Wheel axle sensor detection threshold, then go to S6, otherwise it is determined that the Kalman filter error is out of tolerance, and the filter result is not currently used;

S6: determine that the current Kalman filter result is available, and use the current Kalman filter to obtain the current safe positioning interval;

S7: Design the fault tree of the combined train positioning system based on Kalman filter, and analyze the safety of the train system.

Preferably, the specific process of the step S2 includes:

S201: Obtain the actual transverse coordinate, longitudinal coordinate, transverse velocity, longitudinal velocity, transverse acceleration and longitudinal acceleration of the train at time k;

S202: According to the speed measurement data of the first axle sensor and the track electronic map data, obtain the lateral velocity and longitudinal velocity detected by the train k time; according to the GNSS positioning data and the track electronic map data, obtain the transverse coordinate and longitudinal coordinate detected by the train k time;

S203: Obtain the lateral state space and longitudinal state space of the train based on the data obtained in S201; obtain the lateral measurement space and longitudinal measurement space of the train based on the data obtained in S202;

S204: Based on the transverse state space, longitudinal state space, transverse measurement space and longitudinal measurement space of the train, the extended Kalman filter equation is used to obtain the transverse and longitudinal information sequence of the train, that is, the positioning result of the train.

Preferably, in the step S203, the expression of the lateral state space X _e (k) is:

X _e (k) = [d _e (k), v _e (k), a _e (k)]

In the formula, d _e (k) is the actual lateral coordinate of train k at time k, v _e (k) is the actual lateral velocity of train k at time k, and a _e (k) is the actual lateral acceleration of train k at time k;

The expression of the longitudinal state space X _n (k) is:

X _n (k) = [d _n (k), v _n (k), a _n (k)]

In the formula, d _n (k) is the actual longitudinal coordinate of train k at time k, v _n (k) is the actual longitudinal velocity of train k at time k, and a _n (k) is the actual longitudinal acceleration of train k at time k;

The expression of the lateral measurement space Z _e (k) is:

In the formula, is the horizontal coordinate measured by GNSS at time k of the train, is the lateral velocity measured by the first axle sensor at train k moment;

The expression of the longitudinal measurement space Z _n (k) is:

In the formula, is the longitudinal coordinate measured by GNSS at time k of the train, is the longitudinal velocity measured by the first axle sensor of the train at time k.

Preferably, in the step S204, the expression of the extended Kalman filter equation is:

X(k)＝A·X(k-1)+B·U+W(k)

Z(k)＝H·X(k)+V(k)

In the formula, X(k) is the state space of the train at time k, A is the state transition matrix, U is the acceleration after input smoothing, B is the acceleration transfer matrix, W is the system noise, Z(k) is the measurement of the train at time k space, H is the measurement matrix, and V is the measurement noise.

Preferably, in the step S3, the specific process of the Kalman filter divergence test includes:

S301: Use the variance inequality criterion to test the horizontal and vertical positioning results of the train respectively, and if they meet, go to S302; otherwise, judge as divergence;

The expression of the variance inequality criterion is:

In the formula, V _k is the innovation sequence at time k, r≥1 is the reserve coefficient, P _k is the variance matrix of the innovation sequence at time k,

S302: Use the error inequality criterion to test the horizontal and vertical positioning results of the train respectively, and if they meet, go to S303; otherwise, judge as divergence;

The expression of the error inequality criterion is:

In the formula, is the measurement error of the innovation sequence at time k, ||Z _min || is the preset measurement error limit;

S303: Using the covariance modulus inequality criterion to test the horizontal and vertical positioning results of the train respectively, if they meet, it is judged to be non-divergent; otherwise, it is judged to be divergent;

The expression of the covariance modular inequality criterion is:

||P _k ||≤||P _min ||

In the formula, ||P _k || is the modulus of the covariance matrix of the innovation sequence at time k, and ||P _min || is the threshold of the pre-set covariance modulus.

Preferably, in the step S4, the expression for setting the detection threshold of the track electronic map is:

In the formula, σ ^kalman is the standard deviation of Kalman filter positioning, and λ is the threshold coefficient.

Preferably, the λ is 4-4.2 according to the map accuracy.

Preferably, in the step S5, the expression for setting the detection threshold of the wheel axle sensor is:

In the formula, is the detection threshold of the second axle sensor within the ΔT time period, is the standard deviation of the second axle sensor within Δd mileage difference, is the standard deviation of Kalman filter positioning within Δd mileage difference;

The expression of the difference between the positioning mileage of each time period and the distance measured by the second axle sensor is:

In the formula, d is the mileage, is the detection mileage of the second axle sensor within the ΔT time period, is the positioning mileage of the Kalman filter innovation sequence within the ΔT time period, is all the detected mileage of the second axle sensor before the current T time, is all the detected mileage of the second wheel axle sensor before the current T time period ΔT, Locate mileages for all Kalman filters before the current time T, Locate mileages for all Kalman filters before the current T time period ΔT.

Preferably, in the step S6, the expression for calculating the current safe positioning interval U _safe is:

U _safe ＝[d _kalman -ησ _kalman -β,d _kalman +ησ _kalman +β]

In the formula, σ _kalman is the variance of Kalman filter innovation sequence positioning mileage, η is the multiple of σ _kalman amplification, β is selected according to the characteristics of the original data, and 1 to 1.5 times σ ^map is taken, where σ ^map represents the orbit electronic map Data precision.

Compared with the prior art, the present invention has the following advantages:

(1) The present invention has introduced the inspection of system safety on the basis of the Kalman filter algorithm of the combined train positioning system, has determined the safety interval of the train positioning result and the fault tree of the Kalman filter system, and can improve the Kalman filter algorithm The accuracy of the calculated train positioning results, the safety of judging the train positioning results, and the analysis of the cause of the fault for the unsafe train positioning results, and the detection of faults have the advantages of high reliability, high safety, and high availability.

(2) The present invention first judges the operating state of the sensor to ensure that the Kalman filter condition is met, which improves the stability of the present invention.

(3) The present invention has carried out self-divergence inspection, track electronic map auxiliary inspection and second axle sensor auxiliary inspection independent of filtering result three kinds of inspection means to the result of Kalman filtering, ensures the reliability of positioning result by multi-level mode.

(4) The present invention provides the fault tree of the combined train positioning system, realizes the monitoring of the train running state and the actual effect mode, can carry out quantitative analysis to the system, improves the stability and safety of the system, because of its quantifiable representation The reliability and error of the positioning system greatly improves the availability of the train system based on satellite positioning.

Description of drawings

Fig. 1 is a schematic diagram of the safety analysis principle of the Kalman filter of the present invention;

Fig. 2 is the schematic diagram of horizontal and vertical Kalman filter and track of the present invention;

Fig. 3 is the overall flow chart that safety analysis is carried out to Kalman filter result in embodiment 1 of the present invention;

Fig. 4 is the fault tree of the combined train positioning system based on Kalman filtering in the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is carried out on the premise of the technical solution of the present invention, and detailed implementation and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.

Example 1

In this embodiment, the sensors in the combined train positioning system include GNSS, track electronic map, first axle sensor and second axle sensor that are independent of each other.

The flowchart of the safety detection method of the Kalman filter in the train positioning system of this embodiment is shown in FIG. 1 . Firstly, it is judged whether the current Kalman filter condition is satisfied according to the current sensor running status. Then combined with the track electronic map, the first wheel axle sensor data and the GNSS output results, the eastward and northward Kalman filters were respectively established to obtain the filtering results in the two directions. Then, the diagnosis of the Kalman filter result is carried out, including the self-divergence test of the Kalman filter, the auxiliary test of the track electronic map, and the auxiliary test of the second axle sensor independent of the filter result. Finally, according to each operating state and failure mode, the fault tree of the train safety positioning system based on Kalman filtering is constructed. The specific process is shown in Figure 3, including:

1. Sensor fault diagnosis

S101: Carry out fault diagnosis on the first axle sensor and the second axle sensor, and obtain the operating state S _odo of the axle sensor.

S102: Carry out fault diagnosis on GNSS to obtain the current GNSS running state S _GNSS .

S103: When both the S _odo and the S _GNSS show no fault, proceed to the subsequent steps. Otherwise, it is determined that the current moment does not meet the conditions for using the Kalman filter.

2. Establish the Kalman filter equation to realize the filtering process

Along the east and north directions of the train positioning, Kalman filter equations based on GNSS, the first axle sensor, and track electronic map are respectively established, specifically including the following steps:

S201: According to the current position of the train, combined with the track electronic map information and the speed measurement result of the first axle sensor, obtain the eastward speed of the train at time k and north speed

S202: According to the GNSS measurement results, obtain the east and north coordinates at time k and

S203: Describe the eastward and northward state spaces at time k as 3-dimensional vectors X _e (k) and X _n (k), respectively, and the measurement space as 2-dimensional vectors Z _e (k) and Z _n (k). Where X _e (k) = [d _e (k), v _e (k), a _e (k)], X _n (k) = [d _n (k), v _n (k), a _n (k )], where d, v, a represent the train position, train speed and train acceleration respectively, and the subscripts e and n represent the east direction and north direction respectively. Survey space 2D vector for easting and northing

S204: Use the extended Kalman filter equation X(k)=A X(k-1)+B U+W(k) for east and north respectively, Z(k)=H X(k)+V (k), obtain the position of train k time Among them, A is the state transition matrix, U is the acceleration after input smoothing, W is the system noise, H is the measurement matrix, and V is the measurement noise.

3. Kalman filter divergence test

Kalman filter divergence test, specifically includes the following steps

S301: Judging whether the eastward and northward Kalman filters satisfy the inequality criterion Among them, V _k is the innovation sequence at time k, and r≥1 is the reserve coefficient. P _k is the variance matrix of the innovation sequence at time k,

S302: Set the measurement error limit ||Z _min ||, and calculate whether the estimated error is within a certain range, that is, whether the eastward and northward filtering are satisfied in is the estimated measurement error.

S303: Set the threshold ||P _min || of the covariance modulus, and judge whether the modulus of the covariance matrix is smaller than the set threshold, that is, whether the eastward and northward filters satisfy ||P _k ||≤||P _min | |.

S304: If the filtering result satisfies all the inequalities in S301 to S303, the Kalman filtering divergence test is passed, and the subsequent steps are continued; otherwise, it is determined that the Kalman filtering is divergent, and the filtering result is not currently used.

4. Orbit map-assisted Kalman filter result inspection

The principle of orbit map-assisted Kalman filtering result inspection is shown in Figure 2, which specifically includes the following steps:

S401: The positioning result calculated in step S204 Projected onto the orbit map to calculate the lateral bias.

S402: Setting a map detection threshold Among them, σ ^kalman is the standard deviation of Kalman filter positioning, and λ is the threshold coefficient, which is 4 to 4.2 according to the map accuracy. when When the test passes and proceed to the next step. Otherwise, it is determined that the Kalman filter error is out of tolerance, and the filter result is not currently used.

5. Second axle sensor auxiliary filter result inspection

The second axle sensor auxiliary filter result inspection independent of the Kalman filter includes the following steps:

S501: Using S204, calculate the positioning result of the train at each time And project it on the track map to get the train positioning mileage d _kalman .

S502: Calculate the difference between the measurement distance of the second wheel axle sensor and the Kalman filter positioning mileage in a series of ΔT time periods

S503: Set the detection threshold corresponding to each ΔT period When the average is satisfied If the time test passes, otherwise it is judged that the Kalman filter error is out of tolerance, and the filter result is not currently used.

6. Establish a safe positioning interval

When the foregoing tests all pass, it is determined that the current Kalman filtering result is available. The variance σ _kalman of the mileage d _kalman projected onto the orbit by the Kalman filter is amplified by η times, and properly compensated by β to obtain the current safe positioning interval [d _kalman -ησ _kalman -β,d _kalman +ησ _kalman +β], Among them, η is 6; β is selected according to the characteristics of the original data. It can be 1 to 1.5 times σ ^map , where σ ^map represents the map accuracy.

7. Establish the fault tree of the combined train positioning system based on Kalman filter

According to the judgment steps of 1 to 5 above, the fault tree of the designed Kalman filter system is shown in Figure 4.

8. Fault detection

Based on the safety interval of the train positioning result, it is judged whether the positioning result is safe. If it is not safe, the cause of the train fault is obtained from the fault tree of the combined train positioning system based on Kalman filter, so as to detect the fault; if it is safe, no Fault.

specific embodiment

Taking tram as an example below, in conjunction with Fig. 1-4, the inventive method is described in detail:

Step 1: First judge whether the status of the wheel speed sensors A and B, the GNSS receiver is good, and whether the route map is successfully loaded. If OK, go to step 2, otherwise switch to the backup system;

Step 2: Combining the speed measurement data of the wheel sensor A, the route map data and the GNSS positioning data, use the Kalman filter method to calculate the position and obtain the positioning result;

Step 3: Carry out security analysis on the positioning results. First, judge whether the noise of the measurement results is less than a certain threshold. If it is less than a certain threshold, go to step 4. Otherwise, Kalman filtering is not used, and the positioning interval is calculated by interval fusion;

Step 4: Further judge whether the measurement error is less than a certain threshold, if it is less than a certain threshold, enter step 5, otherwise do not use Kalman filter, and use interval fusion to calculate the positioning interval;

Step 5: Determine whether the threshold of the covariance modulus is less than a certain threshold, and if it is less, proceed to step 6, otherwise Kalman filtering is not used, and the positioning interval is calculated by interval fusion;

Step 6: Map the results obtained by the Kalman filter to the line map, and calculate whether the lateral deviation is less than the threshold set according to the map accuracy, and if it is less, go to step 7, otherwise, do not use the Kalman filter, and use interval fusion to calculate the positioning interval;

Step 7: Combining the speed measurement data of the wheel sensor B, the route map data and the GNSS positioning data, use the Kalman filter method to calculate the position, obtain the positioning result, and project it into the route map, and then go to step 8;

Step 8: Determine whether the deviation between the measurement data of the wheel sensor B and the result obtained by the Kalman filter is less than the detection threshold, and if so, proceed to step 9, otherwise, do not use the Kalman filter, and use interval fusion to calculate the positioning interval;

Step 9: Give the safety interval of the positioning result, that is, the variance σ _kalman of d _kalman is enlarged by 6 times, and an appropriate compensation of 1 is given to obtain the current safe positioning interval [d _kalman -6σ _kalman -1,d _kalman +6σ _kalman +1] ;

Step 10: According to steps 1 to 8, the fault tree of the Kalman filter system can be obtained through analysis, and the safety analysis of the train system can be performed.

The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make many modifications and changes according to the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art shall be within the scope of protection defined by the claims.

Claims (9)

1. The sensor 1. safety detection method of Kalman filter in a kind of train positioning system, in the train positioning system Including GNSS, orbital electron map, the first axle sensor and the second axle sensor, which is characterized in that the train combination The fault detection method of positioning system the following steps are included:

   S1: fault diagnosis is carried out to the first axle sensor, the second axle sensor, GNSS and orbital electron map, all without reason When barrier, S2 is carried out；Otherwise terminate；

   S2: measurement data, GNSS location data and orbital electron map datum based on the first axle sensor utilize expansion card Graceful filtering equations obtain the positioning result of train, carry out S3；

   S3: it to S2 train positioning result obtained, carries out Kalman filtering diverging and examines, if it is decided that go out train positioning result It does not dissipate, then carries out S4, otherwise determine Kalman filtering diverging, do not use filter result currently；

   S4: S2 train positioning result obtained is projected into orbital electron map datum, obtains lateral deviation；Set track electricity Sub- map detection threshold value carries out S5 if lateral deviation is less than orbital electron map detection threshold value, otherwise determines Kalman's filter Wave error is overproof, does not use filter result currently；

   S5: projecting to orbital electron map datum for S2 train positioning result obtained, obtains positioning mileage according to the time period；If Fixed wheel axle sensor detection threshold value, if in each period, positioning mileage and the measurement of the second axle sensor being small apart from its difference In axle sensor detection threshold value, then S6 is carried out, otherwise determines that Kalman Filter Residuals are overproof, do not use filter result currently；

   S6:；Determine that current Kalman filtered results are available, obtains current safety using current Kalman filtering and position section；

   S7: designing the fault tree of the train integrated positioning system based on Kalman filtering, carries out safety point to train system Analysis.
2. 2. the safety detection method of Kalman filter, feature in a kind of train positioning system according to claim 1 It is, the detailed process of the step S2 includes:

   S201: obtain train k moment actual lateral coordinates, longitudinal coordinate, lateral velocity, longitudinal velocity, transverse acceleration and Longitudinal acceleration；

   S202: the cross detected according to the measurement data of the first axle sensor and orbital electron map datum, acquisition train k moment To speed and longitudinal velocity；According to GNSS location data and orbital electron map datum, obtains the transverse direction that the train k moment is detected and sit Mark and longitudinal coordinate；

   S203: being based on S201 data obtained, obtains transverse state space, the longitudinal direction state space of train；Based on S202 institute The data of acquisition obtain the cross measure space and longitudinal measurement space of train；

   S204: transverse state space, longitudinal state space, cross measure space and longitudinal measurement space based on train utilize Extended Kalman filter equation obtains the horizontal and vertical information sequence of train, the i.e. positioning result of train.
3. 3. the safety detection method of Kalman filter, feature in a kind of train positioning system according to claim 2 It is, in the step S203, transverse state space X_e(k) expression formula are as follows:

   X_e(k)=[d_e(k),v_e(k),a_e(k)]

   In formula, d_eIt (k) is train k moment actual lateral coordinates, v_eIt (k) is train k moment actual lateral velocity, a_e(k) it is Train k moment actual transverse acceleration；

   The longitudinal direction state space X_n(k) expression formula are as follows:

   X_n(k)=[d_n(k),v_n(k),a_n(k)]

   In formula, d_nIt (k) is train k moment actual longitudinal coordinate, v_nIt (k) is train k moment actual longitudinal velocity, a_n(k) it is Train k moment actual longitudinal acceleration；

   The cross measure space Z_e(k) expression formula are as follows:

   In formula,For train k moment GNSS measurement lateral coordinates,For the first axle sensor of train k moment The lateral velocity of measurement；

   Longitudinal measurement space Z_n(k) expression formula are as follows:

   In formula,For train k moment GNSS measurement longitudinal coordinate,For the first axle sensor of train k moment The longitudinal velocity of measurement.
4. 4. the safety detection method of Kalman filter, feature in a kind of train positioning system according to claim 2 It is, in the step S204, the expression formula of Extended Kalman filter equation are as follows:

   X (k)=AX (k-1)+BU+W (k)

   Z (k)=HX (k)+V (k)

   In formula, X (k) is the state space at train k moment, and A is state-transition matrix, and U is to input smoothed out acceleration, and B is Acceleration transfer matrix, W are system noise, and Z (k) is the measurement space at train k moment, and H is calculation matrix, and V is measurement noise.
5. 5. the safety detection method of Kalman filter, feature in a kind of train positioning system according to claim 1 It is, in the step S3, the detailed process that Kalman filtering diverging is examined includes:

   S301: using inequality of variance criterion, the positioning result horizontal and vertical to train is tested respectively, if meeting into Row S302；Otherwise, it is determined that for diverging；

   The expression formula of the inequality of variance criterion are as follows:

   In formula, V_kFor the innovation sequence at k moment, r >=1 is reserve factor, P_kFor the variance matrix of k moment innovation sequence,

   S302: using Error Inequation criterion, the positioning result horizontal and vertical to train is tested respectively, if meeting into Row S303；Otherwise, it is determined that for diverging；

   The expression formula of the Error Inequation criterion are as follows:

   In formula,For the measurement error of k moment innovation sequence, | | Z_min| | it is limited for preset measurement error；

   S303: using covariance modular inequality criterion, the positioning result horizontal and vertical to train is tested respectively, if meeting, Then it is judged to not dissipating；Otherwise, it is determined that for diverging；

   The expression formula of the covariance modular inequality criterion are as follows:

   ||P_k||≤||P_min||

   In formula, | | P_k| | it is the mould of k moment innovation sequence covariance matrix, | | P_min| | it is the threshold of preset covariance mould Value.
6. 6. the safety detection method of Kalman filter, feature in a kind of train positioning system according to claim 1 It is, in the step S4, the expression formula of orbital electron map detection threshold value basis of design are as follows:

   In formula, σ^kalmanPoor for Kalman filtering localization criteria, λ is threshold coefficient.
7. 7. the safety detection method of Kalman filter, feature in a kind of train positioning system according to claim 5 It is, precision takes 4~4.2 to the λ according to the map.
8. 8. the safety detection method of Kalman filter, feature in a kind of train positioning system according to claim 1 It is, in the step S5, the expression formula of axle sensor detection threshold value basis of design are as follows:

   In formula,For the detection threshold value of the second axle sensor in Δ T time section,For the second wheel shaft in Δ d mileage difference The standard deviation of sensor,It is poor for Kalman filtering localization criteria in Δ d mileage difference；

   The positioning mileage of each period and the second axle sensor measure the expression formula apart from its difference are as follows:

   In formula, d is mileage,For the detection mileage of the second axle sensor in Δ T time section,For Δ T time section The positioning mileage of interior Kalman filtering innovation sequence,For in all detections of the second axle sensor before the current T moment Journey,For all detection mileages of the second axle sensor before current T moment Δ T time section,For the current T moment Before all Kalman filterings position mileage,It is fixed for Kalman filtering all before current T moment Δ T time section Position mileage.
9. 9. the safety detection method of Kalman filter, feature in a kind of train positioning system according to claim 1 It is, in the step S6, current safety positions section U_safeThe expression formula of calculating are as follows:

   U_safe=[d_kalman-ησ_kalman-β,d_kalman+ησ_kalman+β]

   In formula, σ_kalmanThe variance of mileage is positioned for Kalman filtering innovation sequence, η is by σ_kalmanThe multiple of amplification, β is according to original Beginning data characteristics etc. is chosen, and 1~1.5 times of σ is taken^map, wherein σ^mapIndicate orbital electron map datum precision.