CN118953462B - Urban rail locomotive position estimation method considering electrical measurement information - Google Patents
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Abstract
The invention provides a method for estimating the position of a urban rail locomotive taking into account electrical measurement information, which comprises the steps of firstly determining the number of running locomotives between adjacent traction stations according to locomotive section positioning results and constructing traction power supply system circuit equivalent models under different locomotive numbers, then analyzing the multi-equation relation between the locomotive position and each electrical measurement value in a traction power supply system based on circuit theorem to obtain a locomotive position calculation value and supplement the position measurement, then considering the influence of measurement errors and modeling errors, combining the locomotive running process to carry out optimal estimation of the locomotive position by using the urban rail locomotive position estimation method based on robust adaptive Kalman filtering.
Description
Technical Field
The invention relates to the technical field of power system dispatching automation, in particular to a method for estimating the position of a urban rail locomotive, which comprises the power supply of renewable energy sources, in particular to the method for estimating the position of the urban rail locomotive by taking electrical measurement information into account.
Background
At present, the urban rail transit locomotive positioning method adopted in engineering is mainly based on a section positioning mode of the trackside equipment, but is influenced by sampling frequency, the section recognition result has strong hysteresis, the specific position of the locomotive cannot be determined by a specific rule, and the positioning precision is low. The combination positioning method based on multi-sensor data fusion is mostly adopted for locomotive positioning research, but because the urban rail locomotives basically run in special environments such as underground, tunnels and the like, sensor signals are easy to be interfered and shielded to cause signal loss, and the algorithm has great difficulty in practical application. Meanwhile, there is currently no research related to the development of locomotive positioning from the electrical measurement perspective, and in the circuit equivalent model of the traction power supply system, locomotive position mainly affects the resistance value of each branch. Therefore, the position of the locomotive can be effectively obtained by constructing a traction power supply system circuit equivalent model and solving the resistance value of each branch by utilizing the electrical quantity in the system, such as node voltage, feeder line current and the like, and the multi-equation relation can be further deduced and obtained according to the circuit theory. However, due to noise in actual measurement, the solution result is not completely accurate, and further consideration of the processing mode is required.
Disclosure of Invention
The invention provides a urban rail locomotive position estimation method taking electrical measurement information into account, which fully analyzes a multi-coupling relation between electrical measurement and locomotive positions based on circuit constraint and locomotive operation process, further considers measurement and modeling errors, seeks an optimal estimation method of the urban rail locomotive position, can overcome the defect of the lack of developing locomotive positioning from an electrical measurement view, and obtains an effective and practical urban rail locomotive positioning method.
The invention adopts the following technical scheme.
When the urban rail locomotive position estimation model taking the electrical measurement information into account is established, the number of running locomotives among adjacent traction stations is determined according to locomotive section positioning results, traction power supply system circuit equivalent models under different locomotive numbers are constructed, then a multi-equation relation between locomotive positions and electrical measurement values in a traction power supply system is analyzed based on circuit theorem to obtain locomotive position calculation values and serve as supplement of position measurement, then the influences of measurement errors and modeling errors are considered, and the locomotive operation process is combined to carry out optimal estimation of locomotive positions according to the urban rail locomotive position estimation method based on robust adaptive Kalman filtering.
The method comprises the following steps;
step S1, acquiring the number of locomotives between adjacent traction stations based on locomotive section positioning results of trackside equipment based on a shaft counter and a transponder;
s2, constructing traction power supply system circuit equivalent models with different locomotive numbers in intervals by using intervals divided by adjacent traction;
S3, analyzing the correlation between the electric measurement value in the traction power supply system and the locomotive position in the section based on the circuit theory to obtain a locomotive position calculation formula;
S4, constructing a urban rail locomotive position estimation model based on Kalman filtering, and adding the locomotive position calculation value obtained in the step S3 into a measurement value;
S5, considering the influence of measurement errors, identifying and eliminating bad data in the measurement values based on the robust estimation idea, and reducing the influence of low-quality data;
And S6, taking modeling error influence into consideration, constructing a self-adaptive adjustment factor to act on the estimation model, realizing optimal estimation of the locomotive position, and outputting an estimation result.
Step S1 comprises the following steps;
S11, acquiring the section position information of an operating locomotive in a traction power supply system from an automatic locomotive monitoring system in real time;
And step S12, acquiring physical position information of each section and each traction station, and acquiring the number of running locomotives between adjacent traction stations according to the section positions of the locomotives.
The step S2 specifically comprises the following steps:
step S21, regarding both the traction station and the locomotive as power supply nodes, regarding contact networks and steel rails among all nodes as branches, wherein the resistances of all branches are as follows:
formula one;
Wherein R c and R r are branch resistances of the contact net and the rail respectively, R c and R r are resistance values of unit lengths of the contact net and the rail respectively, l is branch length, namely distance between adjacent nodes, and subscript i represents branch number;
And S22, neglecting longitudinal resistance and stray current between the steel rail and the ground, combining R c and R r between adjacent nodes, and further constructing chain circuit models of traction power supply systems under different locomotive numbers.
The step S3 specifically comprises the following steps:
Step S31, utilizing the electric quantity of the traction voltage U tss, the locomotive voltage U train and the feeder line current I, and establishing a multi-coupling relation between the locomotive position and each electric measurement value in the interval according to the circuit theorem, wherein the formula form is as follows:
a second formula;
wherein m is the distance from the locomotive to the traction position of the head end of the section, L is the distance between adjacent traction positions;
Step S32, when one locomotive is arranged in the section in the up-down direction, the position of the up-going locomotive relative to the front end traction station is as follows:
a formula III;
in the formula, U 1、U2、U3、U4 is the voltage of the head-tail traction station and the voltage of the up-down locomotive respectively, and I 1、I2、I3、I4 is the four feeder currents led out by the head-tail traction station;
Step S33, similar to the above case, the number of remaining locomotives in the interval is added or deleted, and the feeder current is unchanged.
The step S4 specifically comprises the following steps:
Step S41, taking a state variable x and a measurement z as follows:
Wherein m is the position vector of all locomotives, v is the speed vector of all locomotives, z m,mea is the position sensor measurement vector of all locomotives, and z v,mea is the speed measurement vector of all locomotives;
step S42, the state transition equation and the measurement equation are expressed as the following formulas:
Wherein, I and 0 are an identity matrix and a zero matrix respectively; The method comprises the steps of determining a time interval, wherein a is an acceleration measurement vector of all locomotives, F, B is a state transition matrix and a control matrix respectively, u is a control vector, H is a measurement matrix, corresponding elements of the matrix are 1 and the rest are 0 when only equivalent measurement is performed on locomotive state information which is the same as state quantity description, the corresponding elements are a sparse matrix, w and v respectively represent process noise and measurement noise and are Gaussian white noise which meets the conditions that the mean value is zero and the covariance is Q and R respectively, and subscript t represents time;
step S43, a position estimation model based on Kalman filtering comprises two steps of prediction and updating, wherein the two steps are expressed as follows:
in the formula, Respectively representing a predicted value vector, a predicted error covariance matrix and a state transition covariance matrix; And P represents an estimated value vector and an estimated error covariance matrix respectively, R represents a measurement error covariance matrix, and K represents a Kalman gain matrix.
The step S5 specifically comprises the following steps:
step S51, measuring residual error vector at any moment as V, measuring weight matrix as B, and equivalent weight matrix as The measurements are independent of each other, and have:
wherein n represents the number of measurement values, ω i represents an equivalent weight, which can be determined by an equivalent weight function, and IGGIII equivalent weight function is adopted:
in the formula, Respectively representing the ith measurement residual value and a standardized residual thereof, omitting a time index t, wherein c 0 and c 1 are harmonic coefficients;
Step S52, taking the predicted value as an initial value of robust estimation iteration at any moment to obtain an initial value of residual error as follows:
Seventeenth formula;
Step S53, the measured values of different locomotive positions are processed separately, and for all the measured residual errors of the same locomotive position, the absolute value is taken and normalized at the measured residual error position corresponding to the predicted value, so as to further unify the error measurement standard:
Eighteen formulas;
wherein the superscript p represents the number of the locomotive, and the superscript (k) of the iteration number and the time subscript t are omitted, and the number of the iterations is the first time ;
Step S54, measuring the residual minimum value by the normalized sensorAs the selection basis of the harmonic coefficients c 0 and c 1:
Nineteenth formula;
Step S55, obtaining the equivalent weight omega i of each measurement value and eliminating the measurement value omega i < 0.1;
step S56, the robust estimation result is calculated through iteration:
formula twenty;
in the formula, the upper mark k represents the iteration number, and the following is similar when Stopping iteration to obtain the robust solution at the current moment,Is a minimum value;
Step S57 maintaining the initial weights, i.e Iterative operation is performed until convergence condition is satisfied, and the reserved measurement value has new equivalent weight;
Step S58, calculating the latest equivalent weight of each measurement by utilizing the methodAs the weight of the measured value in the subsequent filtering process, the arithmetic expression obtains the robust solution at the current moment。
The step S6 specifically comprises the following steps:
Step S61, the innovation vector is the actual measurement value Error vector between the measured prediction value, namely:
Formula twenty-one;
new theoretical covariance matrix And an actual covariance matrixThe method comprises the following steps of:
wherein N is the length of the sliding window;
step S62, constructing an adaptive factor alpha 1t as follows:
in the formula, Representing the trace of the matrix;
step S63, correcting and obtaining:
in the formula, The multiplication coefficient is determined by the value of Q t;
step S64 status disagreement value statistics To be used forReflecting as a referenceIs the degree of deviation of (2):
seventeenth formula;
Step S65 of Constructing an adaptive factor alpha 2t:
Wherein m and n are constants, Approaching 0, let M is taken to be close to the middle and late stagesEmpirical value of maximum;
step S66, further correcting and obtaining:
in the formula, From the following componentsThe value is determined and meets the following requirements;
And step S67, estimating the locomotive position and storing an estimation result.
The locomotive is an urban rail locomotive which is driven by electricity and is in a direct-current traction power supply mode.
In step S1, sensor measurement data is selected to determine a sector positioning result.
The invention establishes a city rail locomotive position estimation model taking into account electrical measurement information. Firstly, determining the number of running locomotives among adjacent traction according to locomotive section positioning results, constructing traction power supply system circuit equivalent models under different locomotive numbers, secondly, analyzing a multi-equation relation between the locomotive position and each electric measurement value in the traction power supply system based on a circuit theorem, acquiring a locomotive position calculation value and supplementing the position measurement, and then, designing an urban rail locomotive position estimation method based on robust adaptive Kalman filtering by considering the influence of measurement errors and modeling errors and combining with a locomotive running process to realize optimal estimation of the locomotive position.
According to the urban rail locomotive position estimation method, the problem of insufficient real-time measurement of the locomotive position can be effectively solved by combining the method for calculating the locomotive position by utilizing the electrical measurement value in combination with the circuit characteristic constraint, and the reliability of the robust estimation result is high. Meanwhile, under the condition of inaccurate measurement, the method can effectively improve the positioning accuracy of the locomotive, and the error is reduced from hundred meters to ten meters.
The main process of the method comprises a method for establishing correlation analysis and calculation between each piece of electric measurement information and the locomotive position in a traction power supply system, a method for establishing and solving a urban rail locomotive position estimation model based on robust adaptive Kalman filtering, meanwhile, related researches on urban rail locomotive position estimation are developed based on circuit constraint and locomotive running processes, and an urban rail locomotive position estimation method taking electrical measurement information into account is provided, so that the positioning accuracy of the urban rail locomotive is improved under limited measurement conditions, and the safe and efficient running of urban rail traffic is further ensured.
According to the urban rail locomotive position estimation method, locomotive position information contained in an electric measurement value of a traction power supply system is fully analyzed through system circuit topology and circuit theory, a multi-calculation equation of each locomotive position is established, and locomotive position calculation results are obtained and serve as measurement supplements. The position estimation model based on robust adaptive Kalman filtering is established, bad data possibly occurring in the measured value can be effectively eliminated, and parameters of the most critical prediction and measurement error covariance in the filtering model can be adaptively adjusted according to the running state of the locomotive, so that the optimal estimation of the locomotive position is realized, the applicability and the robustness of an algorithm are improved, and the positioning precision of the urban rail locomotive is further improved.
Drawings
The invention is described in further detail below with reference to the attached drawings and detailed description:
FIG. 1 is a schematic general flow diagram of an embodiment of the present invention;
FIG. 2 is a schematic diagram of an equivalent model of a traction power supply system circuit when a locomotive is arranged on both the upstream and downstream sides in the embodiment of the invention;
FIG. 3 is a schematic diagram of a locomotive position estimation error result obtained based on the locomotive position estimation method according to an embodiment of the present invention.
Detailed Description
In order to make the features and advantages of the present patent more comprehensible, embodiments accompanied with figures are described in detail below:
as shown in FIG. 1, when a urban rail locomotive position estimation model taking into account electrical measurement information is established, the method firstly determines the number of running locomotives between adjacent traction stations according to locomotive section positioning results, builds a traction power supply system circuit equivalent model under different locomotive numbers, analyzes a multi-equation relation between locomotive positions and electrical measurement values in a traction power supply system based on a circuit theorem to obtain locomotive position calculation values and supplement the position measurement, and then considers the influence of measurement errors and modeling errors to perform optimal estimation of locomotive positions by combining locomotive running processes according to the urban rail locomotive position estimation method based on robust adaptive Kalman filtering.
The method comprises the following steps;
step S1, acquiring the number of locomotives between adjacent traction stations based on locomotive section positioning results of trackside equipment based on a shaft counter and a transponder;
s2, constructing traction power supply system circuit equivalent models with different locomotive numbers in intervals by using intervals divided by adjacent traction;
S3, analyzing the correlation between the electric measurement value in the traction power supply system and the locomotive position in the section based on the circuit theory to obtain a locomotive position calculation formula;
S4, constructing a urban rail locomotive position estimation model based on Kalman filtering, and adding the locomotive position calculation value obtained in the step S3 into a measurement value;
S5, considering the influence of measurement errors, identifying and eliminating bad data in the measurement values based on the robust estimation idea, and reducing the influence of low-quality data;
And S6, taking modeling error influence into consideration, constructing a self-adaptive adjustment factor to act on the estimation model, realizing optimal estimation of the locomotive position, and outputting an estimation result.
Step S1 comprises the following steps;
S11, acquiring the section position information of an operating locomotive in a traction power supply system from an automatic locomotive monitoring system in real time;
And step S12, acquiring physical position information of each section and each traction station, and acquiring the number of running locomotives between adjacent traction stations according to the section positions of the locomotives.
The step S2 specifically comprises the following steps:
step S21, regarding both the traction station and the locomotive as power supply nodes, regarding contact networks and steel rails among all nodes as branches, wherein the resistances of all branches are as follows:
formula one;
Wherein R c and R r are branch resistances of the contact net and the rail respectively, R c and R r are resistance values of unit lengths of the contact net and the rail respectively, l is branch length, namely distance between adjacent nodes, and subscript i represents branch number;
And S22, neglecting longitudinal resistance and stray current between the steel rail and the ground, combining R c and R r between adjacent nodes, and further constructing chain circuit models of traction power supply systems under different locomotive numbers.
The step S3 specifically comprises the following steps:
Step S31, utilizing the electric quantity of the traction voltage U tss, the locomotive voltage U train and the feeder line current I, and establishing a multi-coupling relation between the locomotive position and each electric measurement value in the interval according to the circuit theorem, wherein the formula form is as follows:
a second formula;
wherein m is the distance from the locomotive to the traction position of the head end of the section, L is the distance between adjacent traction positions;
Step S32, when one locomotive is arranged in the section in the up-down direction, the position of the up-going locomotive relative to the front end traction station is as follows:
a formula III;
in the formula, U 1、U2、U3、U4 is the voltage of the head-tail traction station and the voltage of the up-down locomotive respectively, and I 1、I2、I3、I4 is the four feeder currents led out by the head-tail traction station;
Step S33, similar to the above case, the number of remaining locomotives in the interval is added or deleted, and the feeder current is unchanged.
The step S4 specifically comprises the following steps:
Step S41, taking a state variable x and a measurement z as follows:
Wherein m is the position vector of all locomotives, v is the speed vector of all locomotives, z m,mea is the position sensor measurement vector of all locomotives, and z v,mea is the speed measurement vector of all locomotives;
step S42, the state transition equation and the measurement equation are expressed as the following formulas:
Wherein, I and 0 are an identity matrix and a zero matrix respectively; The method comprises the steps of determining a time interval, wherein a is an acceleration measurement vector of all locomotives, F, B is a state transition matrix and a control matrix respectively, u is a control vector, H is a measurement matrix, corresponding elements of the matrix are 1 and the rest are 0 when only equivalent measurement is performed on locomotive state information which is the same as state quantity description, the corresponding elements are a sparse matrix, w and v respectively represent process noise and measurement noise and are Gaussian white noise which meets the conditions that the mean value is zero and the covariance is Q and R respectively, and subscript t represents time;
step S43, a position estimation model based on Kalman filtering comprises two steps of prediction and updating, wherein the two steps are expressed as follows:
in the formula, Respectively representing a predicted value vector, a predicted error covariance matrix and a state transition covariance matrix; And P represents an estimated value vector and an estimated error covariance matrix respectively, R represents a measurement error covariance matrix, and K represents a Kalman gain matrix.
The step S5 specifically comprises the following steps:
step S51, measuring residual error vector at any moment as V, measuring weight matrix as B, and equivalent weight matrix as The measurements are independent of each other, and have:
wherein n represents the number of measurement values, ω i represents an equivalent weight, which can be determined by an equivalent weight function, and IGGIII equivalent weight function is adopted:
in the formula, Respectively representing the ith measurement residual value and a standardized residual thereof, omitting a time index t, wherein c 0 and c 1 are harmonic coefficients;
Step S52, taking the predicted value as an initial value of robust estimation iteration at any moment to obtain an initial value of residual error as follows:
Seventeenth formula;
Step S53, the measured values of different locomotive positions are processed separately, and for all the measured residual errors of the same locomotive position, the absolute value is taken and normalized at the measured residual error position corresponding to the predicted value, so as to further unify the error measurement standard:
Eighteen formulas;
wherein the superscript p represents the number of the locomotive, and the superscript (k) of the iteration number and the time subscript t are omitted, and the number of the iterations is the first time ;
Step S54, measuring the residual minimum value by the normalized sensorAs the selection basis of the harmonic coefficients c 0 and c 1:
Nineteenth formula;
Step S55, obtaining the equivalent weight omega i of each measurement value and eliminating the measurement value omega i < 0.1;
step S56, the robust estimation result is calculated through iteration:
formula twenty;
in the formula, the upper mark k represents the iteration number, and the following is similar when Stopping iteration to obtain the robust solution at the current moment,Is a minimum value;
Step S57 maintaining the initial weights, i.e Iterative operation is performed until convergence condition is satisfied, and the reserved measurement value has new equivalent weight;
Step S58, calculating the latest equivalent weight of each measurement by utilizing the methodAs the weight of the measured value in the subsequent filtering process, the arithmetic expression obtains the robust solution at the current moment。
The step S6 specifically comprises the following steps:
Step S61, the innovation vector is the actual measurement value Error vector between the measured prediction value, namely:
Formula twenty-one;
new theoretical covariance matrix And an actual covariance matrixThe method comprises the following steps of:
wherein N is the length of the sliding window;
step S62, constructing an adaptive factor alpha 1t as follows:
in the formula, Representing the trace of the matrix;
step S63, correcting and obtaining:
in the formula, The multiplication coefficient is determined by the value of Q t;
step S64 status disagreement value statistics To be used forReflecting as a referenceIs the degree of deviation of (2):
seventeenth formula;
Step S65 of Constructing an adaptive factor alpha 2t:
Wherein m and n are constants, Approaching 0, let M is taken to be close to the middle and late stagesEmpirical value of maximum;
step S66, further correcting and obtaining:
in the formula, From the following componentsThe value is determined and meets the following requirements;
And step S67, estimating the locomotive position and storing an estimation result.
The locomotive is an urban rail locomotive which is driven by electricity and is in a direct-current traction power supply mode.
In step S1, sensor measurement data is selected to determine a sector positioning result.
Based on the above model and flow design, the present example implements the proposed urban rail locomotive position estimation method that accounts for electrical measurement information in a MATLAB environment. The modeling solving flow is shown in figure 1.
According to one embodiment of the invention, in order to further verify the effectiveness and accuracy of the urban rail locomotive position estimation method, simulation verification of a position estimation algorithm is performed based on Beijing subway 13A line data design simulation calculation, and the number of running locomotives in a total of 23 traction stations is 46.
The sensor measurements were selected as sector location results, approximately represented using random errors in the [ -0.2,0.2] km range, with simulated position estimation results shown in fig. 3 and table 1.
TABLE 1 average value of root mean square errors at different time points (unit: meters)
As can be seen from table 1 and fig. 3, in the proposed urban rail locomotive position estimation method, the method for calculating the locomotive position by using the electrical measurement value in combination with the circuit characteristic constraint can effectively solve the problem of insufficient real-time measurement of the locomotive position, and the reliability of the robust estimation result is higher. Meanwhile, under the condition of inaccurate measurement, the method can effectively improve the positioning accuracy of the locomotive, and the error is reduced from hundred meters to ten meters.
The main process of implementation of the method comprises a method for establishing correlation analysis and calculation formula between each piece of electric measurement information and the locomotive position in a traction power supply system, and a method for establishing and solving a urban rail locomotive position estimation model based on robust adaptive Kalman filtering.
The method for estimating the position of the urban rail locomotive is provided based on the related research of the position estimation of the urban rail locomotive and based on circuit constraint and locomotive operation processes, and the method for estimating the position of the urban rail locomotive is favorable for improving the positioning accuracy of the urban rail locomotive under limited measurement conditions, so that the safe and efficient operation of urban rail traffic is ensured.
The present invention is not limited to the above-mentioned best mode, any person can obtain other various methods for estimating the position of the urban rail locomotive according to the electric measurement information under the teaching of the present invention, and all equivalent changes and modifications according to the scope of the present invention shall be covered by the present invention.
Claims (9)
1. When the method establishes a urban rail locomotive position estimation model taking into account electrical measurement information, firstly determining the number of running locomotives between adjacent traction stations according to locomotive section positioning results, and constructing traction power supply system circuit equivalent models under different locomotive numbers; then, the influence of measurement errors and modeling errors is considered, and the locomotive operation process is combined to carry out optimal estimation of the locomotive position by a urban rail locomotive position estimation method based on robust adaptive Kalman filtering;
The method comprises the following steps;
step S1, acquiring the number of locomotives between adjacent traction stations based on locomotive section positioning results of trackside equipment based on a shaft counter and a transponder;
s2, constructing traction power supply system circuit equivalent models with different locomotive numbers in intervals by using intervals divided by adjacent traction;
S3, analyzing the correlation between the electric measurement value in the traction power supply system and the locomotive position in the section based on the circuit theory to obtain a locomotive position calculation formula;
S4, constructing a urban rail locomotive position estimation model based on Kalman filtering, and adding the locomotive position calculation value obtained in the step S3 into a measurement value;
S5, considering the influence of measurement errors, identifying and eliminating bad data in the measurement values based on the robust estimation idea, and reducing the influence of low-quality data;
And S6, taking modeling error influence into consideration, constructing a self-adaptive adjustment factor to act on the estimation model, realizing optimal estimation of the locomotive position, and outputting an estimation result.
2. The urban rail locomotive position estimation method taking into account electrical measurement information according to claim 1, wherein step S1 comprises the steps of;
S11, acquiring the section position information of an operating locomotive in a traction power supply system from an automatic locomotive monitoring system in real time;
And step S12, acquiring physical position information of each section and each traction station, and acquiring the number of running locomotives between adjacent traction stations according to the section positions of the locomotives.
3. The method for estimating a position of a urban rail locomotive according to claim 1, wherein the step S2 comprises the steps of:
step S21, regarding both the traction station and the locomotive as power supply nodes, regarding contact networks and steel rails among all nodes as branches, wherein the resistances of all branches are as follows:
Wherein R c and R r are branch resistances of the contact net and the rail respectively, R c and R r are resistance values of unit lengths of the contact net and the rail respectively, l is branch length, namely distance between adjacent nodes, and subscript i represents branch number;
And S22, neglecting longitudinal resistance and stray current between the steel rail and the ground, combining R c and R r between adjacent nodes, and further constructing chain circuit models of traction power supply systems under different locomotive numbers.
4. The method for estimating a position of a urban rail locomotive according to claim 2, wherein the step S3 comprises the steps of:
Step S31, utilizing the electric quantity of the traction voltage U tss, the locomotive voltage U train and the feeder line current I, and establishing a multi-coupling relation between the locomotive position and each electric measurement value in the interval according to the circuit theorem, wherein the formula form is as follows:
m=f (U tss,Utrain,I,rc,rr, L) formula two;
wherein m is the distance from the locomotive to the traction position of the head end of the section, L is the distance between adjacent traction positions;
Step S32, when one locomotive is arranged in the section in the up-down direction, the position of the up-going locomotive relative to the front end traction station is as follows:
Wherein r=r c+rr,U1、U2、U3、U4 is the voltage of the head-end traction station and the voltage of the up-and-down locomotive, and I 1、I2、I3、I4 is the four feeder currents led out by the head-end traction station;
Step S33, the condition that the number of other locomotives in the interval is equal to that in the step, the locomotive voltage value is required to be additionally added or deleted, and the feeder current is unchanged.
5. The method for estimating a position of a urban rail locomotive according to claim 4, wherein said step S4 comprises the steps of:
Step S41, taking a state variable x and a measurement z as follows:
x= [ m, v ] T formula four;
z= [ z m,mea,zm,cal,zv,mea]T formula five;
Wherein m is the position vector of all locomotives, v is the speed vector of all locomotives, z m,mea is the position sensor measurement vector of all locomotives, and z v,mea is the speed measurement vector of all locomotives;
step S42, the state transition equation and the measurement equation are expressed as the following formulas:
zt＝Htxt+vt Equation seven ;
Wherein I and 0 are respectively a unit matrix and a zero matrix, deltat is a time interval, a is an acceleration measurement vector of all locomotives, F, B is a state transition matrix and a control matrix respectively, u is a control vector, H is a measurement matrix, when only equivalent measurement is performed on locomotive state information which is the same as state quantity description, the corresponding element of the matrix is 1, the rest is 0, the matrix is a sparse matrix, w and v respectively represent process noise and measurement noise, are Gaussian white noise which meets the conditions that the mean value is zero and the covariance is Q and R respectively, and the subscript t represents time;
step S43, a position estimation model based on Kalman filtering comprises two steps of prediction and updating, wherein the two steps are expressed as follows:
p t -＝FPt-1FT+Qt formula nine;
P t＝(I-KtHt)Pt - formula twelve;
in the formula, P - and Q respectively represent a predicted value vector, a predicted error covariance matrix and a state transition covariance matrix; And P represents an estimated value vector and an estimated error covariance matrix respectively, R represents a measurement error covariance matrix, and K represents a Kalman gain matrix.
6. The method for estimating a position of a urban rail locomotive according to claim 5, wherein said step S5 comprises the steps of:
step S51, measuring residual error vector at any moment as V, measuring weight matrix as B, and equivalent weight matrix as The measurements are independent of each other, and have:
Wherein n represents the number of measurement values, ω i represents an equivalence weight, which is determined by an equivalence weight function, and IGGIII equivalence weight function is adopted:
Wherein V i and Respectively representing the ith measurement residual value and a standardized residual thereof, omitting a time index t, wherein c 0 and c 1 are harmonic coefficients;
Step S52, taking the predicted value as an initial value of robust estimation iteration at any moment to obtain an initial value of residual error as follows:
Step S53, the measured values of different locomotive positions are processed separately, and for all the measured residual errors of the same locomotive position, the absolute value is taken and normalized at the measured residual error position corresponding to the predicted value, so as to further unify the error measurement standard:
wherein the superscript p represents the number of the locomotive, and the superscript (k) of the iteration number and the time subscript t are omitted, and the number of the iterations is the first time
Step S54, measuring the residual minimum value by the normalized sensorAs the selection basis of the harmonic coefficients c 0 and c 1:
c ＝k*c0, nineteenth;
step 55, obtaining the equivalent weight omega i of each measurement value and eliminating the measurement value of omega i < 0.1;
step S56, the robust estimation result is calculated through iteration:
In the formula, the upper mark k represents the iteration number when Stopping iteration to obtain the robust solution at the current momentEpsilon is a minimum value;
Step S57 maintaining the initial weights, i.e Iterative operation is performed until convergence condition is satisfied, and the reserved measurement value has new equivalent weight
Step S58, calculating the latest equivalence weight of each measurement by using the formula fifteen and the formula sixteenAs the weight of the measured value in the subsequent filtering process, the arithmetic expression obtains the robust solution at the current moment
7. The method for estimating a position of a urban rail locomotive according to claim 5, wherein said step S6 comprises the steps of:
Step S61, the innovation vector is an error vector between the actual measured value z t and the measured predicted value, namely:
New theoretical covariance matrix C t and actual covariance matrix The method comprises the following steps of:
wherein N is the length of the sliding window;
step S62, constructing an adaptive factor alpha 1t as follows:
where tr (·) represents the trace of the matrix;
step S63, correction formula nine and formula ten are obtained:
Twenty-five of the formula P t -＝FPt-1FT+α1tQt;
Wherein, kappa 1 is a multiplication coefficient and is determined by Qt;
step S64 status disagreement value statistics To be used forReflecting as a referenceIs the degree of deviation of (2):
Step S65 of Constructing an adaptive factor alpha 2 t:
Wherein m and n are constants, ε approaches 0, let M is taken to approach middle and late stagesEmpirical value of maximum;
Step S66, the twenty-five and twenty-six formulas are further modified to obtain:
P t -＝(FPt-1FT+α1tQt)/α2t is twenty-nine;
Wherein, kappa 2 is determined by alpha 2t and satisfies P 1 -/α2t＞＞κ2R1;
and step S67, estimating the locomotive position and storing an estimation result.
8. The method for estimating a position of a urban rail locomotive based on electrical measurement information according to claim 1 wherein said locomotive is an electrically powered urban rail locomotive powered by DC traction.
9. The method for estimating a position of a urban rail vehicle according to claim 2, wherein the sensor measurement data is selected to determine the segment positioning result in step S1.
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