CN102074112B - Time sequence multiple linear regression-based virtual speed sensor design method - Google Patents

Abstract

The invention discloses a time sequence multiple linear regression-based virtual speed sensor design method, which belongs to the technical field of traffic state acquisition and relates to data processing analysis and data fusion of a traffic flow sensor. The method comprises the following steps of: first, setting a virtual speed sensor between adjacent sensor nodes; then, mapping speed data on a time sequence to a space sequence and training a weight matrix which correlates to the speed of the virtual speed sensor and the speed data obtained by the traffic flow sensor by a least square method; and finally, estimating the speed of each virtual speed sensor through multiple linear regression by utilizing a weight coefficient and the speed data of the traffic flow sensor. The method can acquire the spatial distribution of the speed on a road section, can acquire more accurate traffic information and provides the basis for traffic management and control.

Description

Pseudo-velocity Sensor Design method based on the time series multiple linear regression

Technical field

The invention belongs to traffic behavior and obtain technical field, be specifically related to the Data Management Analysis of traffic flow sensor and a kind of pseudo-velocity Sensor Design method of data fusion based on the time series multiple linear regression.

Background technology

Transport information has the time-space domain characteristic, and traffic flow all has continuity in the time-space domain.Transport information is not only relevant with the current and historical traffic behavior in somewhere, and is simultaneously also relevant with the traffic behavior of upstream and downstream.To more reasonably confirm transport information, need confirm on the highway section continually varying traffic behavior on time and space.But owing to do not have measurement mechanism between the adjacent sensor node, the traffic data of sparse spatial sequence is difficult to directly obtain transport information accurately.

If the traffic behavior of locus, each sensor node place can be confirmed on the highway section, then when sensor abundant (trending towards infinite), can obtain traffic behavior accurately.Therefore we have defined virtual-sensor node (not actual traffic current detection functionality), if the traffic behavior of each locus, virtual-sensor node place can confirm that the traffic behavior that then can obtain the highway section distributes.

Traffic flow all has the characteristic of stream on time and space, so the continuity of the traffic behavior of the spatial sequence middle and lower reaches historical traffic behavior that is upper reaches is flowed.Therefore we utilize the speed data on the known sensor node time sequence, and the speed of the pseudo-velocity sensor node of diverse location on the spatial sequence is estimated.Utilize least square method to obtain the weight matrix with pseudo-velocity sensor node speed and traffic flow sensor velocity correlation, estimate the speed of pseudo-velocity sensor node, finally can obtain the space distribution of highway section speed through multiple linear regression.

Summary of the invention

In order to overcome the deficiency of the existing pick-up unit quantity of road, the present invention provides a kind of pseudo-velocity Sensor Design method based on the time series multiple linear regression, it is characterized in that, may further comprise the steps:

The step of (1) the pseudo-velocity sensor node being demarcated: adopt approach based on linear interpolation between adjacent traffic flow sensor, to set the pseudo-velocity sensor;

(2) according to the speed data of calibrated pseudo-velocity sensor node and traffic flow sensor, the step of training weight matrix: the seasonal effect in time series speed data is mapped to spatial sequence, the average velocity between the adjacent node is adopted to average is similar to, utilizes least square method that weight matrix is trained:

(3) estimate the step of pseudo-velocity sensor node speed: utilize data and the weight matrix of training on the sensor node time series, estimate the speed of pseudo-velocity sensor node through multiple linear regression.

Node in the said adjacent node comprises traffic flow sensor node and pseudo-velocity sensor node.

The said pseudo-velocity sensor node is demarcated is to suppose that the distance between traffic flow sensor node i and the i+1 is d _i, the distance setting between the adjacent node (node comprises traffic flow sensor and pseudo-velocity sensor) is a _i, then the number of the pseudo-velocity sensor node between traffic flow sensor node i and the i+1 is m _i=[d _i/ a _i].

In the said step (2) the seasonal effect in time series speed data being mapped to spatial sequence is: at t _NConstantly, (i, speed k) does defining virtual speed pickup node

Pseudo-velocity sensor node number between traffic flow sensor node i and the i+1 is m _i, then by

Wherein, n _iNumber for the speed data of the traffic flow sensor i of needs; w _KjBe weight coefficient,

w _Kj≤1; w _Kj>=0; t _NBe current time; Δ t is the time interval of traffic flow sensor acquisition data; v _i(t _N-q Δ t) (q=1,2...n _i) be traffic flow sensor i current time t _NThe q time preceding historical data.

Beneficial effect of the present invention:

The present invention is based on the method for time series multiple linear regression; Through between the neighboring sensors node, setting the pseudo-velocity sensor and weight matrix being trained based on least square method; Utilize the speed data of real sensor node time sequence; Obtain the speed of pseudo-velocity sensor node, realize design the pseudo-velocity sensor node.Through this result of design, can draw the space distribution of traffic behavior, can estimate transport information more accurately, for traveler provides real-time and effective information, help them to carry out routing better, realizing route is induced.

Description of drawings

Fig. 1 pseudo-velocity sensor node is demarcated synoptic diagram.

The time series speed data synoptic diagram of Fig. 2 sensor node i

Embodiment

The present invention provides a kind of pseudo-velocity Sensor Design method based on the time series multiple linear regression; Overcome the deficiency of the existing pick-up unit quantity of road; More reasonable aspect traffic flow theory, obtain the speed of pseudo-velocity sensor through the multiple linear regression on the time series, can obtain the space distribution of speed; Thereby estimate transport information more accurately, and foundation is provided for traffic administration and control.

Embodiment 1

A kind of pseudo-velocity Sensor Design method based on the time series multiple linear regression, contain following steps:

(1) the pseudo-velocity sensor node is demarcated.Suppose that the distance between traffic flow sensor node i and the i+1 is d _i(unit, rice), the distance setting between the adjacent node is a _i, then the number of the pseudo-velocity sensor node between traffic flow sensor node i and the i+1 is m _i=[d _i/ a _i]; Node in the said adjacent node comprises pseudo-velocity sensor node and traffic flow sensor node; Be labeled as (i, 1), (i, 2) respectively ... (i, m _i), as shown in Figure 1.

(2), train the step of weight matrix according to the speed data of calibrated pseudo-velocity sensor node and traffic flow sensor

Step 1: the seasonal effect in time series speed data is mapped to spatial sequence

Traffic flow all has the characteristic of stream on time and space, so the continuity of the traffic behavior of the spatial sequence middle and lower reaches historical traffic behavior that is upper reaches is flowed.Therefore can utilize the speed data on the known traffic flow sensor node time series, the speed of the pseudo-velocity sensor node of diverse location on the spatial sequence is estimated.

Traffic flow sensor node i (i=1,2 ... N) speed can directly be obtained, so pseudo-velocity sensor node (i, k) (k=1,2 ... M _i) speed can be by the seasonal effect in time series data of sensor node i through calculating.(i, speed k) does the pseudo-velocity sensor node

$v_{i,k}\left(t_N\right)=\underset{j=1}{\overset{n_i}{\mathrm{\Σ}}}{w}_{\mathrm{kj}}\×v_i(t_N-j\·\mathrm{\Δt})---\left(1\right)$

Wherein, n _iNumber for the speed data of the traffic flow sensor i of needs; w _KjBe weight coefficient,

w _Kj≤1; w _Kj>=0; t _NBe current time; Δ t is the time interval of traffic flow sensor acquisition data; v _i(t _N-q Δ t) (q=1,2 ... N _i) be traffic flow sensor i current time t _NThe q time preceding historical data.The signal of traffic flow sensor node i seasonal effect in time series speed data is as shown in Figure 2.

Weight coefficient w _KjCan constitute a weight matrix θ,

$\mathrm{\θ}={\left[\begin{array}{ccccccccccccc}{w}_{11}& w_{12}& ...& w_{1n_i}& w_{21}& w_{22}& ...& w_{{2n}_i}& ...& w_{m_{i}1}& w_{m_{i}2}& ...& w_{m_i{n}_i}\end{array}\right]}^T$

θ is relevant with the speed data of pseudo-velocity sensor node speed and traffic flow sensor.

On road conditions and the similar highway section of traffic flow situation, weight matrix is constant.Pseudo-velocity sensor node number between sensor node i and the sensor node i+1 is m _i, can get matrix by (1):

$\left[\begin{array}{cccc}{w}_{11}& w_{12}& ...& w_{1n_i}\\ w_{21}& w_{22}& ...& w_{{2n}_i}\\ ...& ...& ...& ...\\ w_{m_{i}1}& w_{m_{i}2}& ...& w_{m_i{n}_i}\end{array}\right]\left[\begin{array}{c}{v}_i(t_N-\mathrm{\Δt})\\ v_i(t_N-2\mathrm{\Δt})\\ ...\\ v_i(t_N-n_i\mathrm{\Δt})\end{array}\right]=\left[\begin{array}{c}{v}_{i,1}\left(t_N\right)\\ v_{i,2}\left(t_N\right)\\ ...\\ v_{i,m_i}\left(t_N\right)\end{array}\right]---\left(2\right)$

Step 2: adopt the method for averaging to be similar to the average velocity between the neighboring sensors

If enough pseudo-velocity sensors are arranged on the highway section, then the distance between the adjacent node (node comprises traffic flow sensor and pseudo-velocity sensor) will be very short.So, can adopt the method for averaging to be similar to for the average velocity between the adjacent traffic flow sensor, concerned as follows:

$\frac{d_i}{T_i\left(t_N\right)}=\frac{v_i\left(t_N\right)+v_{i+1}\left(t_N\right)+\underset{j=1}{\overset{m_i}{\mathrm{\Σ}}}{v}_{i,j}\left(t\right)}{m_i+2}---\left(3\right)$

Wherein, T _i(t _N) for the start time be t _NSensor node i and the real hourage between the sensor node i+1.

Step 3: utilize least square method that weight matrix is trained

Can get by (2) (3),

$\underset{j=1}{\overset{m_i}{\mathrm{\Σ}}}{v}_{i,j}=w_{11}\×v_i(t_N-\mathrm{\Δt})+w_{12}\×v_i(t_N-2\mathrm{\Δt})+...+w_{{1n}_i}\×v_i(t_N-n_i\mathrm{\Δt})$ ……(4)

$+w_{21}\×v_i(t_N-\mathrm{\Δt})+w_{22}\×v_i(t_N-2\mathrm{\Δt})+...+w_{{2n}_i}\×v_i(t_N-n_i\mathrm{\Δt})$

$+...$

$+w_{m_{i}1}\×v_i(t_N-\mathrm{\Δt})+w_{m_{i}2}\×v_i(t_N-2\mathrm{\Δt})+...+w_{m_i{n}_i}\×v_i(t_N-n_i\mathrm{\Δt})$

$=\frac{d_i}{T_i\left(t_N\right)}\×(m_i+2)-v_i\left(t_N\right)-v_{i+1}\left(t_N\right)$

Then following formula one has m _i* n _iIndividual known variables is utilized abundant data source, lists the overdetermination matrix equation that constitutes shape such as A θ=b, wherein,

$A={\left[\begin{array}{cccc}{v}_i(t_1-\mathrm{\Δt})& v_i(t_2-\mathrm{\Δt})& & v_i(t_l-\mathrm{\Δt})\\ v_i(t_1-2\mathrm{\Δt})& v_i(t_2-2\mathrm{\Δt})& & v_i(t_l-2\mathrm{\Δt})\\ ...& ...& & ...\\ v_i(t_1-n_i\mathrm{\Δt})& v_i(t_2-n_i\mathrm{\Δt})& & v_i(t_l-n_i\mathrm{\Δt})\\ v_i(t_1-\mathrm{\Δt})& v_i(t_2-\mathrm{\Δt})& & v_i(t_l-\mathrm{\Δt})\\ v_i(t_1-2\mathrm{\Δt})& v_i(t_2-2\mathrm{\Δt})& & v_i(t_l-2\mathrm{\Δt})\\ ...& ...& ...& ...\\ v_i(t_1-n_i\mathrm{\Δt})& v_i(t_2-n_i\mathrm{\Δt})& & v_i(t_l-n_i\mathrm{\Δt})\\ ...& ...& & ...\\ v_i(t_1-\mathrm{\Δt})& v_i(t_2-\mathrm{\Δt})& & v_i(t_l-\mathrm{\Δt})\\ v_i(t_1-2\mathrm{\Δt})& v_i(t_2-2\mathrm{\Δt})& & v_i(t_l-2\mathrm{\Δt})\\ ...& ...& & ...\\ v_i(t_1-n_i\mathrm{\Δt})& v_i(t_2-n_i\mathrm{\Δt})& & v_i(t_l-n_i\mathrm{\Δt})\end{array}\right]}^T---\left(5\right)$

$\mathrm{\θ}={\left[\begin{array}{ccccccccccccc}{w}_{11}& w_{12}& ...& w_{{1n}_i}& w_{21}& w_{22}& ...& w_{2n_i}& ...& w_{m_{i}1}& w_{m_{i}2}& ...& w_{m_i{n}_i}\end{array}\right]}^T$

$b=\left[\begin{array}{c}\frac{d_i}{T_i\left(t_1\right)}\×(m_i+2)-v_i\left(t_1\right)-v_{(i+1)}\left(t_1\right)\\ \frac{d_i}{T_i\left(t_2\right)}\×(m_i+2)-v_i\left(t_2\right)-v_{(i+1)}\left(t_2\right)\\ ...\\ \frac{d_i}{T_i\left(t_l\right)}\×(m_i+2)-v_i\left(t_l\right)-v_{(i+1)}\left(t_l\right)\end{array}\right]---\left(6\right)$

Wherein, l>=m _i* n _i

Adopt least square method to estimate weight matrix; Make quadratic sum

minimum of error, thereby draw the estimated value of weight matrix θ.

(3), estimate the step of pseudo-velocity sensor node speed according to weight matrix after the training and the speed data on the traffic flow sensor time sequence

Utilize data and the weight matrix of training on the sensor node time series, estimate the speed of the pseudo-velocity sensor node of different time through multiple linear regression.

Embodiment 2:

Adopt the Xizhimenwai Dajie to carry out case verification.The sensor placement in this highway section and between distance as shown in Figure 4.Wherein, 41003,41004 is microwave detector, and speed data is provided; 67,68,69 is detecting device hourage, and the journey time of each car process adjacent hourage of detecting device is provided.

Distance between 41003 to 41004 is 1.2020km; The number of setting the pseudo-velocity sensor node is [1202.0/100]=12; Distance between the adjacent node (comprising real sensor node and pseudo-velocity sensor node) is 1202.0/12=100.2m, and from 41003 to 41004 demarcate successively and are (41003,1), (41003; 2) ... (41003,12).

The pseudo-velocity number of sensors is 12; Need 12 historical speed data to calculate the speed of pseudo-velocity sensor; Then per two adjacent nodes have 12 parameters between (comprising real sensor node and pseudo-velocity sensor node), and one has 144 parameters and need confirm on 41003 to the 41004 whole highway sections.

The journey time of all vehicles in the same data collection cycle is on average obtained this collection period hourage of the zero hour.The hourage that 67 to 68 and 68 to the 69 different moment are corresponding, ratio through distance was converted into the hourage between this moment speed pickup 41003 to 41004, was designated as T respectively ₄₁₀₀₃(t ₁), T ₄₁₀₀₃(t ₂) ... T ₄₁₀₀₃(t ₁₄₄).With these hourages as real hourage.

Can get by (6), $b=\left[\begin{array}{c}\frac{d_3}{T_{41003}\left(t_1\right)}\×(m_{41003}+2)-v_{41003}\left(t_1\right)-v_{41004}\left(t_1\right)\\ \frac{d_3}{T_{41003}\left(t_2\right)}\×(m_{41003}+2)-v_{41003}\left(t_2\right)-v_{41004}\left(t_2\right)\\ ...\\ \frac{d_3}{T_{41003}\left(t_{144}\right)}\×(m_{41003}+2)-v_{41003}\left(t_{144}\right)-v_{41004}\left(t_{144}\right)\end{array}\right]$

Wherein, m ₃=12, v ₄₁₀₀₃(t _N), v ₄₁₀₀₄(t _N) (N=1,2 ... 144) be respectively t _NThe speed data of 41003 and 41004 detections constantly.Extract 2008.08.13 to the data of the 9:00-12:00 of 2008.08.15 and calculate matrix b.

A whenever definite b (i) (i=1,2 ... 144), all in the tabulation of 41003 historical speed from t _NThe zero hour get 12 speed datas forward, be designated as A (i, 1) respectively, A (i, 2) ... A (i, 12) obtains preceding 12 of A matrix and is listed as.Data collection cycle Δ t is 120s.Can be known that by Algorithm Analysis A should be one 144 * 144 matrix, per 12 row all are the repetitions of preceding 12 row.Thereby determine the A matrix.

Utilize least square method that parameter is trained, the parameter training model is following:

Min(Aθ-b) ²

$\left\{\begin{array}{c}{w}_{11}+w_{12}+...+w_{1\left(12\right)}=1\\ w_{21}+w_{22}+...+w_{2\left(12\right)}=1\\ ...\\ w_{1\left(12\right)}+w_{1\left(12\right)}+...+w_{\left(12\right)\left(12\right)}=1\\ w_{\mathrm{ij}\≤1}\\ w_{\mathrm{ij}\≥0}\end{array}\right.$

Thereby estimate parameter matrix θ.

Claims (3)

1. the pseudo-velocity Sensor Design method based on the time series multiple linear regression is characterized in that, may further comprise the steps:

The step of (1) the pseudo-velocity sensor node being demarcated: adopt approach based on linear interpolation between adjacent traffic flow sensor, to set the pseudo-velocity sensor;

(2) according to the speed data of calibrated pseudo-velocity sensor node and traffic flow sensor; The step of training weight matrix: the seasonal effect in time series speed data is mapped to spatial sequence, the average velocity between the adjacent node is adopted to average is similar to, utilizes least square method that weight matrix is trained: wherein, the seasonal effect in time series speed data is mapped to spatial sequence is: at t _NConstantly, (i, speed k) does defining virtual speed pickup node $v_{i,k}(t_N)={\displaystyle \underset{j=1}{\overset{{n_i}_{}}{\∑}}{w}_{kj}\×v_i(t_N-j\·\mathrm{\Δ}t)}$ Pseudo-velocity sensor node number between traffic flow sensor node i and the i+1 is m _i, then by $v_{i,k}(t_N)={\displaystyle \underset{j=1}{\overset{{n_i}_{}}{\∑}}{w}_{kj}\×v_i(t_{N}j\·\mathrm{\Δ}t)}$ Get matrix:

$\left[\begin{array}{cccc}{w}_{11}& w_{12}& \·\·\·& w_{1n_i}\\ w_{21}& w_{22}& \·\·\·& w_{2n_i}\\ \·\·\·& \·\·\·& \·\·\·& \·\·\·\\ w_{m_{i}1}& w_{m_{i}2}& \·\·\·& w_{m_i{n}_i}\end{array}\right]\left[\begin{array}{c}{v}_i(t_N-\mathrm{\Δt})\\ v_i(t_N-2\mathrm{\Δt})\\ \·\·\·\\ v_i(t_N-n_i\mathrm{\Δt})\end{array}\right]=\left[\begin{array}{c}{v}_{i,1}\left(t_N\right)\\ v_{i,2}\left(t_N\right)\\ \·\·\·\\ v_{i,m_i}\left(t_N\right)\end{array}\right],$

Wherein, n _iNumber for the speed data of the traffic flow sensor i of needs; K representes the pseudo-velocity sensor node; w _KjBe weight coefficient,

w _Kj≤1; w _Kj>=0; t _NBe current time; Δ t is the time interval of traffic flow sensor acquisition data; v _i(t _N-q Δ t) is traffic flow sensor i current time t _NThe q time preceding historical data, q=1,1,2 ... N _i

(3) estimate the step of pseudo-velocity sensor node speed: utilize data and the weight matrix of training on the sensor node time series, estimate the speed of pseudo-velocity sensor node through multiple linear regression.

2. the pseudo-velocity Sensor Design method based on the time series multiple linear regression according to claim 1 is characterized in that the node in the said adjacent node comprises traffic flow sensor node and pseudo-velocity sensor node.

3. the pseudo-velocity Sensor Design method based on the time series multiple linear regression according to claim 1 is characterized in that, the said pseudo-velocity sensor node is demarcated is to suppose that the distance between traffic flow sensor node i and the i+1 is d _i, the distance setting between the adjacent node is a _i, then the number of the pseudo-velocity sensor node between traffic flow sensor node i and the i+1 does

, said node comprises traffic flow sensor and pseudo-velocity sensor.

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