CN110020475A - A kind of Markov particle filter method of forecasting traffic flow - Google Patents
A kind of Markov particle filter method of forecasting traffic flow Download PDFInfo
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Abstract
The present invention relates to a kind of Markov particle filter methods of forecasting traffic flow.The present invention combines Markov Chain with particle filter algorithm, replaces state space prediction model with Markov and determines initial weight, then carry out successive ignition update by particle filter algorithm, obtains prediction result.Make up that Markov is not applicable to nonlinear system, disadvantage of precision of prediction deficiency.And prediction result is subjected to error analysis, verify the applicability of this method.Present invention determine that phase identification, may be implemented short-term traffic flow forecast.Good theories integration and decision-making foundation can be provided for Traffic Control and Guidance.
Description
Technical field
The present invention designs a kind of prediction model, more particularly, to a kind of forecasting traffic flow mould of Markov particle filter
Type.
Background technique
In intelligent transportation system, short-time traffic flow forecast is to realize the key technology of advanced traffic control and traffic guidance
One of.Deficiency and magnitude of traffic flow randomness, fluctuation for current Markov model of traffic flux forecast in precision aspect
Property the characteristics of, propose Markov particle filter forecasting traffic flow model.
With rapid economic development, vehicles number constantly increases, and a series of traffic problems occurs, as traffic congestion,
Traffic pollution, traffic accident etc. affect daily life.In recent years, morning and evening peak period traffic jam oneself become life in
During inevitable problem, especially festivals or holidays, traffic jam issue is the principal element for influencing traffic capacity.In order to
Traffic administration and control are rationally carried out, needs that effective control strategy is taken to dredge the magnitude of traffic flow in current slot
It leads, with road improvement traffic congestion, reduces environmental pollution.Short-term traffic flow forecast becomes in an important research
Hold.
The information variable and applicable elements that single traffic flow forecasting method has its special, can only from respectively it is different
Angle carries out volume forecasting, so the traffic flow stronger for stochastic volatility of single prediction technique has certain limitation,
Prediction result also has certain one-sidedness.
Magnitude of traffic flow uncertainty is stronger, not only has the characteristics that Nonlinear Stochastic, can also be caused by the extraneous variation such as weather
The abnormal variation of flow.Markov model is the strong work of a metric states space and analysis time sequence data
Tool, but it can only obtain rough prediction result, not be suitable for nonlinear system.Particle filter technology for nonlinear system and
Non-Gaussian noise environment has the adaptability of height.Therefore, it combines Markov Chain with particle filter algorithm, uses Markov
It instead of state space prediction model and determines initial weight, then successive ignition update is carried out by particle filter algorithm, obtain pre-
Survey result.Make up that Markov is not applicable to nonlinear system, disadvantage of precision of prediction deficiency.And prediction result is subjected to error
Analysis, verifies the applicability of this method.
Summary of the invention
In consideration of it, the purpose of the present invention is to provide a kind of forecasting traffic flow prediction model of Markov particle filter,
The model determines phase identification, and short-term traffic flow forecast may be implemented.It can be provided for Traffic Control and Guidance good
Good theories integration and decision-making foundation.
In order to achieve the object of the present invention, used technical solution are as follows:
Before prediction, sample data need to be pre-processed, the sky data as caused by detector failures, using it is adjacent when
The method that segment data is averaging repairs it.
Correction formula is as follows:
xk--- --- --- ----is the k moment magnitude of traffic flow.
xk-1--- --- ----is the k-1 moment magnitude of traffic flow.
xk+1--- --- ----is the k+1 moment magnitude of traffic flow.
Since Markov model is the prediction to state transfer, so needing the magnitude of traffic flow to be belonged to different shapes
State.Its process is as follows:
Traffic flow modes are indicated with state set S, historical sample data constitutes traffic flow modes collection S={ s1,s2,...,
sn}。
Traffic flow status is determined using threshold method.Introduce parameter μ1、μ2。
μ1=xk-1(min):I:xk-1(max) (2)
μ2={ θ1, θ2..., θn} (3)
μ1--- --- ----indicates that traffic flow is divided into multiple states using I as interval.Generally take I=5.
μ2--- --- ----is used to save threshold value.
xk-1(min)--- -- indicates k-1 moment magnitude of traffic flow minimum value.
xk-1(max)--- -- indicates k-1 moment magnitude of traffic flow maximum value.
I---------- indicates that the magnitude of traffic flow divides interval.
θι--- --- ----is threshold value, represents state boundaries value, there are two boundary value, i=1,2 ..., n for a state.
si--- --- ----indicates that section is (θi-1,θi] state, i=1,2 ..., n.
State set determines.By volume of traffic xk-1Descending sequence calculates state numberWherein,
If h is not integer, then state s is addedh+1As the last one state.That is sh+1=xk-1(max)；State set is S={ s1,
s2,...,sh,sh+1}。
H---------- indicates state number.
sh+1--- --- --- -- indicates the h+1 state.
To construct Markov forecasting traffic flow model, it is first determined then the affiliated traffic behavior of the sample magnitude of traffic flow is asked
Do well transfer matrix, is predicted according to state-transition matrix future transportation state.Detailed process is as follows:
The determination of state transition probability.State-transition matrix shows the markov property of Markov, the i.e. state at k moment
It is only related with the traffic behavior at k-1 moment.State s of the traffic flow modes from the current k-1 momenti(k-1) it is transferred to subsequent time k
The state s at momentj(k) be it is uncertain, possibility is expressed as its state transition probability with probability:
mi--- --- --- -- indicates state siIn the number that different periods occur.
mij--- --- ----indicates by state siIt is transferred to state sjNumber.
p(si(k-1)→sj(k))、p(sj|si)、pij(k) --- --- --- -- indicates by state siIt is transferred to state sjIt is general
Rate.
The determination of state-transition matrix.According to determining state transition probability pij(k), state-transition matrix is then constituted, such as
Shown in lower:
--- --- --- -- indicates state-transition matrix to P (k).
Meet
pj(k) --- --- --- -- indicates that the k moment is in j shape probability of state.
Establish Markov particle filter prediction model.Method is as follows:
Establish state equation.
Establish observational equation.
u2(k-1) the state boundaries value at --- ----k-1 moment.
--- --- predicted value at --- --- k moment, i=1,2 ..., n.
--- --- observation at --- --- k moment, i=1,2 ..., n.
--- --- --- --- observation noise.
H------------- observes value coefficient, if it is unit matrix E.
Particle filter algorithm principle.Particle filter is the statistics based on sequential Monte Carlo method and recursion Bayesian Estimation
The nonlinear filtering algorithm of method emulation mode, its core concept are the stochastic regime particles by extracting from posterior probability
It indicates its probability distribution, is a kind of sequence importance sampling method.For real-time dynamic system, dynamic space model is as follows:
Determine state equation and observational equation
xk=f (xk-1)+uk-1 (9)
yk=h (xk)+vk (10)
xk--- --- --- the predicted value at --- -- k moment.
yk--- --- --- the observation at --- -- k moment.
uk-1--- --- --- --- process noise.
vk-1--- --- --- --- observation noise.
f(xk-1) --- --- --- ----is the system state equation at k-1 moment.
h(xk) --- --- --- ----is the systematic observation equation at k moment.
Prediction process:
If zk={ y1:i| i=1,2 ..., k be initial time to k moment in all observation value sets.
p(xk|zk-1)=∫ p (xk|xk-1)p(xk-1|zk-1)dxk-1 (11)
p(xk|xk-1) --- --- the state transition probability density of --- ----state equation is obtained by state equation (10).
p(yk|xk) --- --- --- the observation probability density of --- -- observational equation.
p(xk-1|zk-1) --- --- --- --- is Posterior probability distribution, is obtained by sample data.
p(xk|zk-1) --- --- --- ----is prior probability, according to state transition probability density p (xk|xk-1) gained.
State renewal process:
p(yk|zk-1)=∫ p (yk|xk)p(xk|zk-1)dxk (13)
Formula (12) and formula (13) are theoretical solution, be actually difficult to calculate out as a result, the basic principle is that
One group of random sample particle collection is generated, using particle collection to Posterior probability distribution function p (xk|zk) make approximation processing, thus
The predicted value at k moment, particle are obtained on the basis of observationIndicate i-th of possible magnitude of traffic flow,It can basisAnd shape
State equation obtains；Weight, i.e. weights of importance corresponding to the magnitude of traffic flow predicted for i-th,It needs in each iteration
Middle update simultaneously makees normalized.It may be expressed as:
δ-function, that is, Dirac delta function is meant that the function is equal to zero in the point value other than zero, and its
Integral in entire domain is equal to 1.
x0:k--- --- --- ----is 0 state set for arriving the k moment.
--- --- --- -- -- indicates direct proportion function to ∝.
--- --- --- ----is the corresponding normalization weight of i-th of particle of k moment.
--- --- --- ----is the corresponding weight of i-th of particle of k moment, and is met
Resampling process:
The basic intension of particle filter algorithm is iteration, is placed on the center of gravity calculated on the biggish particle of weight, Lai Tigao
The accuracy of prediction result, therefore resampling methods are used, thought is the duplication biggish particle of weight, and it is lesser to reject weight
Particle, but its phenomenon deficient there is also particle diversification.It is proposed random gravity treatment quadrat method, specific as follows:
Generate n random number { d equally distributed on [0,1]l, l=1,2 ..., n }, it is found by searching algorithm full
It is enough the integer m of formula (17).
Record sampleAnd as new sample particles.Finally, section [0,1] is pressedPoint
At n minizone, as random number dlFall in n-th of section (λn-1,λn] when, replicate corresponding sample
Detailed description of the invention
Two kinds of prediction techniques of Fig. 1 and actual traffic flow (whole day) comparison diagram
Two kinds of prediction techniques of Fig. 2 and actual traffic flow (morning peak) comparison diagram
Two methods of Fig. 3 (whole day) absolute error ER comparison diagram
Two methods of Fig. 4 (morning peak) absolute error ER comparison diagram
Two methods of Fig. 5 (whole day) relative error RER comparison diagram
Two methods of Fig. 6 (morning peak) relative error RER comparison diagram
Specific embodiment
For further instruction technical solution of the present invention, it is illustrated herein in conjunction with attached drawing and specific implement.
1, the reference standard value of each major parameter is determined:
Step1: it takes historical traffic flows as sample data by time interval of 5min, is handed over according to sample data
The division of through-current capacity state determines traffic flow modes collection S={ s1,s2,...,sn}。
Step2: parameter needed for determining, population n, h are state set number.
Step3: traffic flow forecasting is carried out according to Markov prediction model, calculates n Fe coatingsWith
If primary weight
--- --- the predicted value of i-th of particle of --- ----k moment.
--- --- the observation of i-th of particle of --- ----k moment.
Step4: more new particle weight.According to formulaCalculate weight corresponding to each particle
--- --- --- --- k moment predicts i-th of particleWhen, obtain observation ykProbability.
It is obtained by formula (16) weight normalization
Step5: judgement sample gravity treatment sample process.Judge whether particle sample carries out gravity treatment sample mistake using similar efficiencies method
Journey.Calculate effectively sampling scale Neff,
Nth--- --- --- ----is thresholding, threshold sets Nth=2n/3, n are the number of particle.
Neff--- --- --- ----is scale of effectively sampling.
When effectively sampling scale meets N less than the thresholding of settingeff≤NthWhen, weight is carried out according to random gravity treatment quadrat method
Sampling.Traffic flow is predicted again using new samples particle.
When effectively sampling scale meets N greater than the thresholding of settingeff> NthWhen, it carries out in next step.
Step6: predictive estimation value.Formula is as follows:
--- --- the predicted value of i-th of particle of --- ----k moment.
--- --- the weight after --- ----normalization.
xk--- --- the predicting traffic flow amount at --- ----k moment.
2, traffic flow sample determines:
(1) experimental data selects the traffic flow data of Changping District, Beijing intersection import direction detector acquisition,
Its acquisition interval is 5min.
(2) data set includes 21 day July in 2017 working day (Mon-Fri) whole day, 24 hours 6048 groups of traffic numbers
According to wherein 20 days (3~7,10~14,17~21,24~28 days) 5760 groups of traffic datas are determined and handed over as training sample for selection
Logical state set, predicts the 21st day (31 days) whole day flow.
(3) using 288 groups of data of the 21st day whole day as test sample, to whole day 24 hours and morning peak (7:00-8:55)
Period data is handled, and carries out error analysis with prediction result respectively.
(4) in experimentation, determine that the prediction result of interval I=5 is more excellent.
3, forecasting traffic flow interpretation of result:
(1) by the 21st day of Markov particle filter prediction result, traditional Prediction of Markov result and above-mentioned acquisition
Traffic flow test sample compares, and is analyzed with whole day flow and morning peak flow.As shown in Figure 1 and Figure 2.
(2) as seen from Figure 1, Markov particle filter prediction technique can be fitted actual conditions well, have
Variation tendency identical with actual traffic stream.The fluctuation that traditional Markov prediction model preferably describes the period becomes
Gesture, but prediction result is more rough, and which is greater than Markov particle filter model of traffic flux forecast.
4, forecasting traffic flow error analysis:
(1) in order to further illustrate the Stability and veracity of Markov particle filter model prediction result, its is pre-
It surveys result and the prediction result of traditional Markov prediction model compares and analyzes, using absolute error ER, relative error
As evaluation index, formula is as follows by RER, root-mean-square error RMSE, mean error ε:
The original value of x------------- traffic flow.
--- --- --- ----traffic flow forecasting value.
--- --- --- ----original traffic flow average value.
N------------- number of samples
To being when analyzed as follows Fig. 3, Fig. 4, Fig. 5, Fig. 6.
By that can be obtained in Fig. 3, Fig. 4, using 1h and 5min as the predicting interval, the absolute mistake of Markov particle filter prediction result
Poor fluctuation range is respectively within 0~60,2~10, and the fluctuating error range that traditional Prediction of Markov result is absolute
Then within 0~110,0~23.Therefore, absolute mistake of the Markov particle filter prediction model in the different predicting intervals
Difference is much smaller than the absolute error of traditional Markov prediction model.
It can be obtained by Fig. 5, Fig. 6, using 1h and 5min as the predicting interval, the relative error of Markov particle filter prediction result
Basic control 0.28,0.15 hereinafter, and the absolute error of traditional Prediction of Markov result then in 0.65,0.4 hereinafter, Ma Er
Section husband particle filter forecasting traffic flow model relative error is small and fluctuation is more gentle.
The root mean square deviation of two kinds of algorithms and error analysis are as shown in table 1, table 2.
The root mean square deviation of 1 two kinds of algorithms of table
The error analysis of 2 two kinds of algorithms of table
Root-mean-square error is very sensitive to the especially big or special small error amount of prediction data, can be well reflected method prediction
As a result precision.By table 1, the result shows that, whole day, the morning peak root-mean-square error of Markov particle filter prediction model are divided
Not Wei 32.94,5.24, the root-mean-square error of traditional Prediction of Markov method will be less than.
By table 2 the result shows that, using 1h and 5min as the predicting interval, the mean error of Markov particle filter prediction model
Respectively 6.04%, 6.41%, the mean error are less than the average mistake of traditional Prediction of Markov method and different time intervals
Difference difference is smaller.
Prediction result and traditional Markov model are subjected to precision of prediction and error comparative analysis, the results showed that, it proposes
It is stronger based on Markov particle filter forecasting traffic flow model applicability, and precision of prediction is high.
Invention is not limited to above-mentioned preferred forms, anyone can obtain other various shapes under the inspiration of the present invention
The product of formula, however, make any variation in its shape or structure, it is all that there is technology identical or similar to the present application
Scheme is within the scope of the present invention.
Claims (2)
1. a kind of Markov particle filter method of forecasting traffic flow, it is characterised in that:
Before prediction, sample data need to be pre-processed, the sky data as caused by detector failures, using adjacent time interval number
It is repaired according to the method for averaging；
Correction formula is as follows:
xk--- --- --- -- is the k moment magnitude of traffic flow；
xk-1--- --- ----is the k-1 moment magnitude of traffic flow；
xk+1--- --- ----is the k+1 moment magnitude of traffic flow；
Since Markov model is the prediction to state transfer, so needing the magnitude of traffic flow to be belonged to different states；Its
Process is as follows:
Traffic flow modes are indicated with state set S, historical sample data constitutes traffic flow modes collection S={ s1, s2..., sn}；
Traffic flow status is determined using threshold method；Introduce parameter μ1、μ2；
μ1=xk-1(min): I:xk-1(max) (2)
μ2={ θ1, θ2..., θn} (3)
μ1--- --- --- -- indicates that traffic flow is divided into multiple states using I as interval；Take I=5；
μ2--- --- --- -- is for saving threshold value；
xk-1(min)--- --- indicates k-1 moment magnitude of traffic flow minimum value；
xk-1(max)--- --- indicates k-1 moment magnitude of traffic flow maximum value；
I----------- indicates that the magnitude of traffic flow divides interval；
θl--- --- --- -- is threshold value, represents state boundaries value, there are two boundary value, i=1,2 ..., n for a state；
si--- --- --- -- indicates that section is (θi-1, θi] state, i=1,2 ..., n；
State set determines；By volume of traffic xk-1Descending sequence calculates state numberWherein, if h
It is not integer, then adds state sh+1As the last one state；That is sh+1=xk-1(max)；State set is S={ s1, s2..., sh,
sh+1}；
H---------- indicates state number；
sh+1--- --- -- indicates the h+1 state；
To construct Markov forecasting traffic flow model, it is first determined then the affiliated traffic behavior of the sample magnitude of traffic flow finds out shape
State transfer matrix predicts future transportation state according to state-transition matrix；Detailed process is as follows:
The determination of state transition probability；State-transition matrix shows the markov property of Markov, i.e., the state at k moment only with
The traffic behavior at k-1 moment is related；State s of the traffic flow modes from the current k-1 momenti(k-1) it is transferred to the subsequent time k moment
State sj(k) be it is uncertain, possibility is expressed as its state transition probability with probability:
mi--- --- --- --- indicates state siIn the number that different periods occur；
mij--- --- --- -- indicates by state siIt is transferred to state sjNumber；
p(si(k-1)→sj(k))、p(sj|si)、pij(k) --- --- --- -- indicates by state siIt is transferred to state sjProbability；
The determination of state-transition matrix；According to determining state transition probability pij(k), state-transition matrix, following institute are then constituted
Show:
--- --- --- -- indicates state-transition matrix to P (k)；
Meet
pj(k) --- --- --- -- indicates that the k moment is in j shape probability of state；
Establish Markov particle filter prediction model；Method is as follows:
Establish state equation；
Establish observational equation；
u2(k-1) --- --- the state boundaries value at --- ----k-1 moment；
--- --- predicted value at --- ----k moment, i=1,2 ..., n；
--- --- observation at --- ----k moment, i=1,2 ..., n；
--- --- --- ----observation noise；
H-------------- observes value coefficient, if it is unit matrix E；
Particle filter, dynamic space model are as follows:
Determine state equation and observational equation
xk=f (xk-1)+uk-1 (9)
yk=h (xk)+vk (10)
xk--- --- the predicted value at --- ----k moment；
yk--- --- the observation at --- ----k moment；
uk-1--- --- --- -- process noise；
vk-1--- --- --- -- observation noise；
f(xk-1) --- --- -- is the system state equation at k-1 moment；
h(xk) --- --- ----is the systematic observation equation at k moment；
Prediction process:
If zk={ y1:i| i=1,2 ..., k } be initial time to k moment in all observation value sets；
p(xk|zk-1)=∫ p (xk|xk-1)p(xk-1|zk-1)dxk-1 (11)
p(xk|xk-1) --- --- the state transition probability density of --- --- state equation is obtained by state equation (10)；
p(yk|xk) --- --- the observation probability density of --- ----observational equation；
p(xk-1|zk-1) --- --- --- -- is Posterior probability distribution, is obtained by sample data；
p(xk|zk-1) --- --- --- --- is prior probability, according to state transition probability density p (xk|xk-1) gained；
State renewal process:
p(yk|zk-1)=∫ p (yk|xk)p(xk|zk-1)dxk (13)
Formula (12) and formula (13) generate one group of random sample particle collection, using particle collection to Posterior probability distribution function p (xk|
zk) make approximation processing, to obtain the predicted value at k moment, particle on the basis of observationIndicate i-th of possible friendship
Through-current capacity,According toAnd state equation obtains；Weight, i.e. importance corresponding to the magnitude of traffic flow predicted for i-th
Weight,It needs to update in each iteration and makees normalized；It indicates are as follows:
δ-function, that is, Dirac delta function is meant that the function is equal to zero in the point value other than zero, and it is entire
Integral in domain is equal to 1；
x0:k--- --- --- --- is 0 state set for arriving the k moment；
--- --- --- ----indicates direct proportion function to ∝；
--- --- --- ----is the corresponding normalization weight of i-th of particle of k moment；
--- --- --- ----is the corresponding weight of i-th of particle of k moment, and is met
2. a kind of Markov particle filter method of forecasting traffic flow, main process are as follows:
Step1: it takes historical traffic flows as sample data by time interval of 5min, traffic flow is carried out according to sample data
The division of amount state determines traffic flow modes collection S={ s1, s2..., sn}。
Step2: parameter needed for determining, population n, h are state set number.
Step3: traffic flow forecasting is carried out according to Markov prediction model, calculates n Fe coatingsWithIf just
Beginning particle weight
--- --- the predicted value of i-th of particle of --- ----k moment.
--- --- the observation of i-th of particle of --- ----k moment.
Step4: more new particle weight.According to formulaCalculate weight corresponding to each particle
--- --- --- ----k moment predicts i-th of particleWhen, obtain observation ykProbability.Pass through formula
(16) weight normalization obtains
Step5: judgement sample gravity treatment sample process.Judge whether particle sample carries out gravity treatment sample process using similar efficiencies method.
Calculate effectively sampling scale Neff,
Nth--- --- --- ----is thresholding, threshold sets Nth=2n/3, n are the number of particle.
Neff--- --- --- --- is scale of effectively sampling.
When effectively sampling scale meets N less than the thresholding of settingeff≤NthWhen, gravity treatment is carried out according to random gravity treatment quadrat method
Sample.Traffic flow is predicted again using new samples particle.
When effectively sampling scale meets N greater than the thresholding of settingeff> NthWhen, it carries out in next step.
Wherein, resampling process is specific as follows:
Generate n random number { d equally distributed on [0,1]l, l=1,2 ..., n }, satisfaction is found with formula by searching algorithm
The integer m of sub (17)；
Record sampleAnd as new sample particles；Finally, section [0,1] is pressedPoint
At n minizone, as random number dlFall in n-th of section λn-1, λnWhen, replicate corresponding sample
Step6: predictive estimation value.Formula is as follows:
--- --- the predicted value of i-th of particle of --- ----k moment.
--- --- the weight after --- ----normalization.
--- --- the predicting traffic flow amount at --- ----k moment.
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| CN113408155A (en) * | 2021-08-03 | 2021-09-17 | 中国人民解放军海军航空大学青岛校区 | Wartime aviation material demand prediction method |
| CN114664089A (en) * | 2022-04-06 | 2022-06-24 | 杭州电子科技大学 | PI control method for traffic flow of urban road traffic system |
| CN115691137A (en) * | 2022-11-01 | 2023-02-03 | 北京航空航天大学 | Multi-modal data prediction method based on causal Markov model |
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| CN114664089A (en) * | 2022-04-06 | 2022-06-24 | 杭州电子科技大学 | PI control method for traffic flow of urban road traffic system |
| CN115691137A (en) * | 2022-11-01 | 2023-02-03 | 北京航空航天大学 | Multi-modal data prediction method based on causal Markov model |
| CN115691137B (en) * | 2022-11-01 | 2024-04-30 | 北京航空航天大学 | Multi-modal data prediction method based on causal Markov model |
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