CN105372659A - Road traffic monitoring multi-target detection tracking method and tracking system - Google Patents

Abstract

The invention discloses a road traffic monitoring multi-target detection tracking method. The method includes the following steps that: a radar detects a plurality of moving targets; Kalman filtering and prediction are performed on feedback data of the detection of the plurality of moving targets by the radar, so that the motion states of the plurality of moving targets at the current time point can be obtained, and the motion states of the plurality of moving targets in future time points are predicted; and an interactive multi-model (IMM) algorithm with Markov switching coefficient is adopted to track the plurality of moving targets detected by the radar. According to the road traffic monitoring multi-target detection tracking method of the invention, based on Kalman filtering and the establishment of a road traffic monitoring model, the motion situations of a plurality of moving targets in a monitoring range can be monitored in real time without losing the targets.

Description

Road traffic monitoring multi-target detection tracking method and tracking system

Technical Field

The invention relates to a road traffic monitoring technology, in particular to a road traffic monitoring multi-target detection tracking method and a tracking system.

Background

With the rapid development of economy and road traffic in China and the increasing number of vehicles, the traffic monitoring is more and more valued by people. In multi-target tracking, a potential threat target is established and identified, so that theoretical support is provided for reducing the false alarm rate of a system and improving the reliability of the system; through comparison of vehicle-mounted distance detection technologies, a millimeter wave frequency modulation pulse Doppler radar is selected; the complex environment of road target tracking is deeply analyzed, and preliminary research is carried out on data association of radar data processing and the start and the stop of target tracking. Data association is one of key technologies of multi-target tracking and multi-sensor information fusion. The objective is to establish a relationship between the measurement and the track (target) to determine whether each measurement data originates from the same target, and the core problem of data association is how close the measurement is to the estimated value of the track (target), and the result of data association directly affects the estimation of the target state, so people pay more attention to the relationship. At present, methods (JPDA) such as a nearest neighbor method, a multi-hypothesis method, a probability data association method (PDA), a joint probability data association method and the like are applied more.

Disclosure of Invention

The invention provides a road traffic monitoring multi-target detection tracking method and a tracking system, which can monitor the motion conditions of a plurality of targets in a monitoring range in real time without losing the targets through the establishment of a Kalman filtering and road traffic monitoring model.

In order to achieve the purpose, the invention discloses a road traffic monitoring multi-target detection tracking method, which is characterized by comprising the following steps:

detecting a plurality of moving objects by a radar;

performing Kalman filtering and prediction on feedback data of a plurality of moving targets detected by a radar, acquiring the moving states of the plurality of moving targets at the current moment, and predicting the moving states of the plurality of moving targets at the future moment;

and tracking a plurality of moving targets detected by the radar by adopting an interactive multi-model method with Markov switching coefficients.

The moving target has two degrees of freedom in road traffic, which are respectively: rotation about the ground normal and translation along the road direction.

In the kalman filter, the state equation of the moving target is as shown in equation (27):

X(k+1)＝FX(k)+GW(k)(27)

in formula (27):

$F=\left[\begin{array}{cccccc}1& T& T^2/2& 0& 0& 0\\ 0& 1& T& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& T& T^2/2\\ 0& 0& 0& 0& 1& T\\ 0& 0& 0& 0& 0& 1\end{array}\right],X\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ x_3\left(k\right)\\ y_1\left(k\right)\\ y_2\left(k\right)\\ y_3\left(k\right)\end{array}\right],$

$G=\left[\begin{array}{cc}{T}^2/4& 0\\ T/2& 0\\ 1& 0\\ 0& T^2/4\\ 0& T/2\\ 0& 0\end{array}\right];$ W(k)＝[w₁(k)w₂(k)]，

wherein F is a state transition matrix; t is a sampling interval; the variable X (k) is a target state vector comprising the radial distance r, the relative velocityRelative accelerationAngle β, angular velocityAnd angular accelerationW (k) is the system noise vector; g is an action matrix of system noise; w is a₁(k)、w₂(k) Is a white noise sequence with a mean value of zero and uncorrelated and a variance ofThe covariance matrix of W (k) is as in formula (28):

$Q\left(k\right)=E\[W\left(k\right)W^T\left(k\right)\]=\left[\begin{array}{cc}{\mathrm{\σ}}_{\mathrm{\α}}^2& 0\\ 0& {\mathrm{\σ}}_{\mathrm{\β}}^2\end{array}\right]---\left(28\right).$

the basic equations of the one-step prediction of the kalman filter are as shown in equations (7), (8), (9):

$\hat{X}(k+1/k)=\mathrm{\Φ}(k+1/k)\hat{X}(k/k-1)+K_p\left(k\right)\[Y\left(k\right)\·H\left(k\right)\hat{X}(k/k-1)\]---\left(7\right)$

K_p(k)＝Φ(k+1/k)P(k/k-1)HT[H(k)P(k/k-1)HT(k)+R(k)]^-1(8)

P(k+1/k)＝[Φ(k+1/k)-K_p(k)H(k)]P(k/k-1)+G(k)Q(k)GT(k)(9)

k in the formulae (7), (8), (9)_p(k) To predict the gain matrix in one step, phi (k +1, k) (phi (k +1, k) ∈ R^n×n) Is a state transition matrix, Y (k) (Y (k)) ∈ R^m×1) Is a measurement vector, H (k) (H (k)) ∈ R^m×n) Is an observation matrix; equation (9) is the one-step prediction equation error.

The measurement model of the above interactive multi-model method with markov switching coefficients is:

Z(k)＝H(k)X(k)+V(k)(29)

wherein:

$Z\left(k\right)=\left[\begin{array}{c}{z}_1\left(k\right)\\ z_2\left(k\right)\\ z_3\left(k\right)\end{array}\right];H\left(k\right)=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\end{array}\right];V\left(k\right)=\left[\begin{array}{c}{v}_1\left(k\right)\\ v_2\left(k\right)\\ v_3\left(k\right)\end{array}\right];$

in the formula: z is a radical of₁(k)、z₂(k)、z₃(k) Respectively representing the distance, the relative speed and the azimuth angle of a target measured by a radar; h (k) is an observation matrix; v (k) is measurement noise; wherein v is₁(k)、v₂(k)、v₃(k) Is three mutually uncorrelated random white noise sequences with the equations ofAnd $E{\[v_3\left(k\right)\]}^2={\mathrm{\σ}}_3^2;$

the covariance matrix of v (k) is formula (30):

$R\left(k\right)=E{\[V\left(k\right)V^T\left(k\right)\]}^2=\left[\begin{array}{ccc}{\mathrm{\σ}}_1^2& 0& 0\\ 0& {\mathrm{\σ}}_2^2& 0\\ 0& 0& {\mathrm{\σ}}_3^2\end{array}\right]---\left(30\right)$

here, ,is the variance of the error of the distance measurement,is the variance of the error of the relative velocity (doppler) measurement,is the variance of the azimuth measurement error.

A tracking system suitable for the road traffic monitoring multi-target detection tracking method is characterized by comprising the following components:

the radar is used for detecting a plurality of moving targets and uploading feedback data;

the data processing system receives feedback data uploaded by the radar, performs Kalman filtering and prediction on the feedback data, acquires the motion states of a plurality of moving targets at the current moment, and predicts the motion states of a plurality of moving targets at the future moment; and controlling a plurality of moving targets of the radar to track by adopting an interactive multi-model method with Markov switching coefficients.

The radar is a millimeter wave frequency modulation pulse Doppler radar.

Compared with the tracking method of the road traffic moving target in the prior art, the road traffic monitoring multi-target detecting and tracking method and the tracking system have the advantages that the movement conditions of a plurality of moving targets in the monitoring range can be monitored in real time without losing the target through the establishment of the Kalman filtering and the road traffic monitoring model;

the radar is used as a monitoring and target tracking sensor, is particularly suitable for traffic monitoring in rainy days or severe weather environments, can accurately monitor the motion state of multiple targets so as to facilitate traffic enforcement of traffic polices, and has wide application prospect in the field of traffic monitoring.

Drawings

FIG. 1 is a flow chart of the operation of an interactive multimodal method;

FIG. 2 is a flow chart of the method of the road traffic monitoring multi-target detection tracking method of the invention.

Detailed Description

The following further describes specific embodiments of the present invention with reference to the drawings.

Data obtained by radar detection contains measurement errors and noise, so that the errors and the noise are reduced through data processing, namely tracking filtering, and the accuracy of the radar for environment perception is improved. The kalman filter estimates the current value of the signal under the linear unbiased minimum variance estimation criterion using only the previous estimate of the signal and the most recent observation, without necessarily requiring all past observations.

Kalman filtering computationally estimates the desired signal from measurements related to the extracted signal. Where the estimated signal is a random response caused by a white noise excitation, the system equations are known as the transfer structure between the excitation and the response, and the metrology equations are known as the functional relationship between the measurement and the estimated quantity. In the estimation process, known system equations, measurement equations, statistical characteristics of white noise excitation and statistical characteristics of measurement errors are utilized. The kalman filter is designed in the time domain, and the information used is also a quantity in the time domain. And the kalman filter is adapted to be multidimensional. Therefore, the application range of the Kalman filtering is very wide. It has the following characteristics:

1) the object of the Kalman filtering process is a random signal;

2) the processed signals have no useful and interference components, and the purpose of filtering is to estimate all the processed signals;

3) the white noise excitation and the measurement noise of the system are not the objects to be filtered, and the statistical characteristics of the white noise excitation and the measurement noise are just the information to be utilized in the estimation process.

Kalman filtering is generally classified into linear and nonlinear, each of which can be continuous and discrete, based on the nature of the system equations and metrology equations of the physical system. Nonlinear kalman filtering is also known as extended kalman filtering. In this case, the system equation is nonlinear, or both the system equation and the measurement equation are nonlinear. The system equations and the measurement equations established by the present patent are both non-linear and discrete.

Kalman filtering and prediction in motor vehicle target tracking:

the purpose of filtering and prediction is to estimate the motion state of the target at the current and future time instants, including position, velocity, angle, etc. The criterion for kalman filtering and prediction is that the root mean square error is minimal. Besides, it has many other advantages in maneuvering target tracking:

1) a sequence of kalman filtering and prediction gains based on the target maneuver and metrology noise models may be automatically selected. This means that by varying some critical parameters, the same filter can be adapted to different maneuvering targets and metrology environments;

2) the Kalman filtering and measurement gain sequence can automatically adapt to the change of the detection process, including the change of the sampling period and the condition of omission;

3) kalman filtering and prediction can conveniently measure the estimation accuracy through a covariance matrix. Such metrology tools may also be used in mobile multi-target tracking to track door formation and threshold size determination;

4) through the variation of residual vectors d (k) in Kalman filtering and prediction, whether the motion characteristics of the originally assumed target model and the actual target are consistent or not can be judged. Thus, d (k) can be used as a means of maneuver detection and maneuver identification. Meanwhile, the method can also be used for consistency analysis and the like.

(5) In the aspect of multi-maneuvering target tracking in a dense multi-echo environment, the influence of uncertainty related errors can be partially compensated through the use of Kalman filtering and prediction methods.

Basic kalman filter equations:

the state equation and the measurement equation of the target can be expressed by equation (1):

$\left\{\begin{array}{c}X(k+1)=\mathrm{\Φ}(k+1,k)X\left(k\right)+G\left(k\right)W\left(k\right)\\ Y\left(k\right)=H\left(k\right)X\left(k\right)+V\left(k\right)\end{array}\right.---\left(1\right)$

in formula (1):

X(k)(X(k)∈R^n×1) Is a target state vector, Y (k) ∈ R^m×1) Is a measurement vector of phi (k +1, k) (phi (k +1, k) ∈ R^n×n) Is a state transition matrix, G (k) (G (k)) ∈ R^n×n) Is the action matrix of the system noise, H (k) (H (k)) ∈ R^m×n) For observation of the matrix, W (k) (W (k)) ∈ R^n×1) Mean value E [ W (k)]0, covariance E [ W (k) W^T(j)]＝Q(k)_kjReferred to as system noise, V (k) (V (k) ∈ R^m×1) Mean value of E [ V (k)]0, covariance E [ V (k) V^T(j)]＝R(k)_kjWhite noise that is uncorrelated with W (k), i.e. E [ W (k) V^T(j)]0, is the measurement noise.

When in the initial state, X₀Independently of W (k), V (k), namely: e [ X ]₀W^T(k)]＝0，E[X₀V^T(k)]0. The corresponding kalman filter primitive equation is as follows:

state estimation, as in equation (2):

$\hat{X}(k/k)=\hat{X}(k/k-1)+K\left(k\right)\[Y\left(k\right)-H\left(k\right)\hat{X}(k/k-1)\]---\left(2\right)$

this state is further predicted, as in equation (3):

$\hat{X}(k/k-1)=\mathrm{\Φ}(k+1,k)\hat{X}(k-1/k-1)---\left(3\right)$

the filter gain is as shown in formula (4):

K(k)＝P(k/k-1)HT(k)[H(k)P(k/k-1)HT(k)+R(k)]^-1(4)

one step prediction of equation error, as in equation (5)

P(k/k-1)＝Φ(k+l,k)P(k-1/k-1)Φ^T(k+l,k)+G(k-1)Q(k-1)GT(k-1)(5)

The mean square error is estimated optimally, as shown in equation (6)

P(k/k)＝[I-K(k)H(k)]P(k/k-l)(6)

Where d (k) ═ y (k) -h (k) X (k/k-1) is defined as a residual vector whose covariance matrix is: s (k) ═ h (k) p (k/k-1) ht (k) + r (k).

In maneuvering target tracking, especially maneuvering multi-target tracking, filtering and prediction are extremely important. Basic equations of one-step prediction of Kalman filtering are shown as formulas (7), (8) and (9).

$\hat{X}(k+1/k)=\mathrm{\Φ}(k+1/k)\hat{X}(k/k-1)+K_p\left(k\right)\[Y\left(k\right)\·H\left(k\right)\hat{X}(k/k-1)\]---\left(7\right)$

K_p(k)＝Φ(k+1/k)P(k/k-1)HT[H(k)P(k/k-1)HT(k)+R(k)]^-1(8)

P(k+1/k)＝[Φ(k+1/k)-K_p(k)H(k)]P(k/k-1)+G(k)Q(k)GT(k)(9)

K in the formulae (7), (8), (9)_p(k) The gain array is predicted for one step.

Kalman filtering has two computation loops: a gain calculation loop and a filter calculation loop. Wherein the gain calculation loop is independent and the filter calculation loop depends on the gain calculation loop, there are two update processes in one cycle: a time update process and a measurement update process. When the predicted state estimation value at the time k-1 and the measured value at the time k are known, the optimal estimation value of the state vector at the time k can be obtained by using the one-step prediction mean square error at the time k-1, and the state estimation value and the measured value at the time k-1 can be predicted.

Moving objects, such as automobiles, often accelerate, decelerate, and turn while traveling on a road, resulting in changing states of motion. For the traffic monitoring radar, accurately tracking the states of a plurality of targets, such as vehicles, and estimating the motion state of each target in time are important tasks of the traffic monitoring radar. At present, most multi-target tracking methods are designed for tracking air targets with less clutter, and the environment of road vehicles, such as maneuvering state, background noise, environment clutter and the like of the targets, is greatly different from the environment of the air targets, and all the environments can influence the output of a monitoring radar. Therefore, the conventional tracking method for tracking multiple targets in the air is not suitable for tracking the road targets, and the road traffic monitoring and detecting system for multiple targets needs to take the actual conditions of the road targets into consideration and adopt a new or improved multiple target tracking method.

An interactive multi-model method (IMM method) with Markov switching coefficient is proposed based on the generalized Bayes method and taking Kalman filtering as a starting point, wherein a plurality of models work in parallel, and target state estimation is the result of interaction of a plurality of filters. The method does not need maneuvering detection, and simultaneously achieves the full-face self-adaptive capacity. Compared with a single model adaptive filter, the method has the following advantages:

1) the modeling can be refined by appropriately extending the model, since it employs multi-model descriptions for the parameter space;

2) in the filtering process, the adaptive variable structure is realized through the change of model probability. In addition, the adaptive structural capability can be enhanced by increasing or decreasing or changing the model in real time;

3) under the condition of satisfying the prior assumption, the method is the optimal estimation in the mean square error sense. Therefore, the reasonability of the hypothesis can be intensively researched, and a more reasonable hypothesis can be searched;

4) the method has an obvious parallel structure and is convenient for effective parallel implementation.

As shown in FIG. 1, the interactive multi-model method is implemented as follows:

assuming that there are r models at k moments, the target motion state mode is as follows:

X(k+1)＝Φ_jX(k)+G_jW_j(k),j＝1,…,r.(10)

wherein, W_j(k) Is mean zero and covariance matrix Q_jWhite noise sequence of (1). The transitions between these models are controlled by a Markov chain whose transition probability matrix is:the measurement model is formula (11):

Z(k)＝H_jX_j(k)+V_j(k)(11)

the steps of the interactive multi-model method can be summarized as follows:

input interaction, as in equations (12), (13):

${\hat{X}}^{oj}(k-1/k-1)=\underset{i=1}{\overset{r}{\Σ}}{\hat{X}}^i(k/k-1){\mathrm{\μ}}_{ij}(k-1/k-1),j=1,...,r---\left(12\right)$

$\begin{array}{c}{P}^{oj}\left(k-1/k-1\right)=\underset{i=1}{\overset{r}{\Σ}}{\mathrm{\μ}}_{ij}\left(k-1/k-1\right)\\ \left\{P^i\left(k-1/k-1\right)+\[{\hat{X}}^i\left(k/k-1\right)-{\hat{X}}^{oj}\left(k-1/k-1\right)\]{\[{\hat{X}}^i\left(k/k-1\right)-{\hat{X}}^{oj}\left(k-1/k-1\right)\]}^T\right\}\end{array}---\left(13\right)$

wherein, ${\mathrm{\μ}}_{ij}(k-1/k-1)=P\{M_j(k-1)/M_j\left(k\right),Z^{k-1}\}=p_{ij}{\mathrm{\μ}}_i(k-1)/{\stackrel{\‾}{c}}_j,$ p_ijthe transition probability of model i going to model j,in order to be a normalization constant, the method comprises the following steps of,

for model M_j(k) To do so byP^oj(k-1/k-1) and Z (k) as inputs for Kalman filtering.

The prediction equation, as in equation (14):

${\hat{X}}^j(k-1/k-1)={\mathrm{\Φ}}_j{\hat{X}}^{oj}(k-1/k-1)---\left(14\right)$

prediction error covariance, as in equation (15):

$P^j(k/k-1)={\mathrm{\Φ}}_j{P}^{oj}(k-1/k-1){\mathrm{\Φ}}_j^T+G_j{Q}_j{G}_j^T---\left(15\right)$

kalman gain, as in equation (16):

K_j(k)＝P^j(k/k-1)H^T[HP^j(k/k-1)H^T+R]^-1(16)

filtering, as in equation (17):

${\hat{X}}^j(k/k)={\hat{X}}^j(k/k-1)+K_j\left(k\right)\[Z\left(k\right)-H{\hat{X}}^j(k/k-1)\]---\left(17\right)$

filter covariance, as in equation (18):

P^j(k/k)＝[I-K_j(k)]P^j(k/k-1)(18)

model probability update, as in equation (19):

$\begin{array}{c}{\mathrm{\μ}}_j\left(k\right)=P\left\{Z\left(k\right)/M_j\left(k\right)/M_j\left(k\right),Z^{k-1}\right\}P\left\{M_j\left(k\right)/Z^{k-1}\right\}\\ =\frac{1}{c}{\mathrm{\Λ}}_j\left(k\right)\underset{i=1}{\overset{r}{\Σ}}{p}_{ij}{\mathrm{\μ}}_i\left(k-1\right)={\mathrm{\Λ}}_j\left(k\right){\stackrel{\‾}{c}}_j/c\end{array}---\left(19\right)$

wherein c is a normalization constant, andand Λ_j(k) To observe the likelihood function of the matrix z (k), ${\mathrm{\Λ}}_j\left(k\right)=P\left\{Z\left(k\right)/M_i\left(k\right),Z^{k-1}\right\}=\frac{1}{{\left(2\mathrm{\π}\right)}^{n/2}{\left|S_j\left(k\right)\right|}^{1/2}}\exp \left\{-\frac{1}{2}{v_j}^T{s_j}^{-1}\left(k\right)v_j\right\},$ wherein, $v_j\left(k\right)=Z\left(k\right)-H{\hat{X}}^j(k/k-1),$ S_j(k)＝HP^j(k/k-1)H^T+R。

output interaction, as in equations (20), (21):

$\hat{X}(k/k)=\underset{j=1}{\overset{r}{\Σ}}{\hat{X}}^j(k/k){\mathrm{\μ}}_j\left(k\right)---\left(20\right)$

$P(k/k)=\underset{j=1}{\overset{r}{\Σ}}{\mathrm{\μ}}_j\left(k\right)\{P^j(k/k)+\[{\hat{X}}^j(k/k)-\hat{X}(k/k)\]{\[{\hat{X}}^j(k/k)-\hat{X}(k/k)\]}^T\}---\left(21\right)$

based on the above method, an embodiment of a road traffic monitoring multi-target detection tracking method is specifically described below.

Firstly, determining a road target motion model in the embodiment, namely a state equation of a tracking target:

the two degrees of freedom of the movement of the target are considered in this embodiment, based on the dynamics of the vehicle movement, including ① the rotation of the target about the ground normal with the direction of the target moving non-parallel to the direction of the road, ② the translation along the direction of the roadThe distance r between the target and the radar is the relative speed of movementIs calculated. Angular velocity of lateral movement of target relative to radarAnd angle β determines the location of the target on the road at the next time, which is important for system predictionMeasuring the distance, relative speed and angle of the target, wherein the signal to be estimated is the distance r and relative speed of the target at the next momentAnd angle β.

As shown in fig. 2, the road traffic monitoring multi-target detection tracking method specifically includes the following steps:

and S1, periodically detecting by the radar, monitoring a plurality of moving targets in road traffic, and uploading the received feedback data.

And S2, filtering and predicting the feedback data received by the radar through Kalman filtering, and estimating the motion states of the target at the current and future moments, including the distance, the speed and the angle between the target and the radar.

In this embodiment, the distance, speed and angle of the moving target at the time k (when the radar scans for a certain time) are respectively defined as r (k),β (k), the distance, speed and azimuth at time k +1 (at the next scan of the radar) are r (k +1),β (k + 1). if the time T of two adjacent scans of the radar is small enough, it can be approximated as:

$r(k+1)=r\left(k\right)+T\stackrel{\·}{r}\left(k\right)+\frac{1}{2}{T}^2\stackrel{\·\·}{r}\left(k\right)---\left(22\right)$

$\stackrel{\·}{r}(k+1)=\stackrel{\·}{r}\left(k\right)+T\stackrel{\·\·}{r}\left(k\right)---\left(23\right)$

$\mathrm{\β}(k+1)=\mathrm{\β}\left(k\right)+\stackrel{\·}{\mathrm{\β}}\left(k\right)---\left(24\right)$

in formulae (22), (23), and (24):andrespectively the radial acceleration and the azimuthal variation velocity of the target at time k.

The method is characterized in that the radial acceleration and the azimuth angle variation acceleration of a moving object are assumed to be changed randomly due to the influence of random factors such as environment variation, road conditions and irregular variation of a road adhesion coefficient:

$\stackrel{\·\·}{r}(k+1)=\stackrel{\·\·}{r}\left(k\right)+u_1\left(k\right)---\left(25\right)$

$\stackrel{\·\·}{\mathrm{\β}}(k+1)=\stackrel{\·\·}{\mathrm{\β}}\left(k\right)+u_2\left(k\right)---\left(26\right)$

in the formulae (25) and (26), u₁(k) Mean is zero and variance isThe random white noise sequence of (1). u. of₂(k) The increment of the radial acceleration and the change speed of the azimuth angle from the k moment to the k +1 moment is₁(k) Is an uncorrelated random white noise sequence.

The equation of state of the motion of the moving object at this time can be described as formula (27):

X(k+1)＝FX(k)+GW(k)(27)

in formula (27):

$F=\left[\begin{array}{cccccc}1& T& T^2/2& 0& 0& 0\\ 0& 1& T& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& T& T^2/2\\ 0& 0& 0& 0& 1& T\\ 0& 0& 0& 0& 0& 1\end{array}\right],X\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ x_3\left(k\right)\\ y_1\left(k\right)\\ y_2\left(k\right)\\ y_3\left(k\right)\end{array}\right],$

$G=\left[\begin{array}{cc}{T}^2/4& 0\\ T/2& 0\\ 1& 0\\ 0& T^2/4\\ 0& T/2\\ 0& 0\end{array}\right];$ W(k)＝[w₁(k)w₂(k)]，

wherein F is the state transition matrix, T is the sampling interval, and the variable X (k) is the target state vector comprising the radial distance, relative velocity, relative acceleration, angle, angular velocity, and angular acceleration, denoted r, and k, respectively,β、Andw (k) is the system noise vector, w₁(k)、w₂(k) Is a white noise sequence with a mean value of zero and uncorrelated and a variance ofThe covariance matrix of W (k) is as in formula (28):

$Q\left(k\right)=E\[W\left(k\right)W^T\left(k\right)\]=\left[\begin{array}{cc}{\mathrm{\σ}}_{\mathrm{\α}}^2& 0\\ 0& {\mathrm{\σ}}_{\mathrm{\β}}^2\end{array}\right]---\left(28\right).$

s3, taking Kalman filtering as a starting point, providing an interactive multi-model method with Markov switching coefficients as a road traffic multi-target tracking method, and operating a radar to track the multi-target in the road traffic by the interactive multi-model method with the Markov switching coefficients.

In this embodiment, the radar is a millimeter wave pulse doppler radar (ARS100 millimeter wave radar), and the measurement equation of the distance, the relative speed, and the azimuth angle of the moving target can be written as formula (29):

Z(k)＝H(k)X(k)+V(k)(29)

wherein:

$Z\left(k\right)=\left[\begin{array}{c}{z}_1\left(k\right)\\ z_2\left(k\right)\\ z_3\left(k\right)\end{array}\right];H\left(k\right)=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\end{array}\right];V\left(k\right)=\left[\begin{array}{c}{v}_1\left(k\right)\\ v_2\left(k\right)\\ v_3\left(k\right)\end{array}\right];$

in the formula: z is a radical of₁(k)、z₂(k)、z₃(k) Respectively representing the distance, the relative speed and the azimuth angle of a target measured by a radar; h (k) is an observation matrix; v (k) is measurement noise; wherein v is₁(k)、v₂(k)、v₃(k) Is three mutually uncorrelated random white noise sequences with the equations ofAnd $E{\[v_3\left(k\right)\]}^2={\mathrm{\σ}}_3^2.$

the covariance matrix of v (k) is formula (30):

$R\left(k\right)=E{\[V\left(k\right)V^T\left(k\right)\]}^2=\left[\begin{array}{ccc}{\mathrm{\σ}}_1^2& 0& 0\\ 0& {\mathrm{\σ}}_2^2& 0\\ 0& 0& {\mathrm{\σ}}_3^2\end{array}\right]---\left(30\right)$

here:is the variance of the error of the distance measurement,is the variance of the error of the relative velocity (doppler) measurement,is the variance of the azimuth measurement error.

The invention also discloses a tracking system suitable for the road traffic monitoring multi-target detection tracking method, which comprises the following steps:

the radar is a millimeter wave frequency modulation pulse Doppler radar and is used for detecting a plurality of moving targets and uploading feedback data;

the data processing system receives feedback data uploaded by the radar, performs Kalman filtering and prediction on the feedback data, acquires the motion states of a plurality of moving targets at the current moment, and predicts the motion states of a plurality of moving targets at the future moment; and controlling a plurality of moving targets of the radar to track by adopting an interactive multi-model method with Markov switching coefficients.

At present, road traffic monitoring mainly depends on means such as video transmission to judge the motion condition of a target vehicle so as to facilitate traffic enforcement for traffic police, but the effect cannot be achieved in rainy days or severe weather environments. The invention adopts the radar as a monitoring and target tracking sensor, is particularly suitable for traffic monitoring in severe weather environment, and can accurately monitor the motion state of multiple targets.

While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (7)

1. A road traffic monitoring multi-target detection tracking method is characterized by comprising the following steps:

detecting a plurality of moving objects by a radar;

performing Kalman filtering and prediction on feedback data of a plurality of moving targets detected by a radar, acquiring the moving states of the plurality of moving targets at the current moment, and predicting the moving states of the plurality of moving targets at the future moment;

and tracking a plurality of moving targets detected by the radar by adopting an interactive multi-model method with Markov switching coefficients.

2. The road traffic monitoring multi-target detection and tracking method according to claim 1, wherein the moving target has two degrees of freedom in road traffic, which are respectively: rotation about the ground normal and translation along the road direction.

3. The road traffic monitoring multi-target detection tracking method according to claim 1 or 2, characterized in that in the kalman filter, the state equation of the moving target is as follows (27):

X(k+1)＝FX(k)+GW(k)(27)

in formula (27):

$F=\left[\begin{array}{cccccc}1& T& T^2/2& 0& 0& 0\\ 0& 1& T& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& T& T^2/2\\ 0& 0& 0& 0& 1& T\\ 0& 0& 0& 0& 0& 1\end{array}\right],$ $X\left(k\right)=\left[\begin{array}{c}{x}_1\left(k\right)\\ x_2\left(k\right)\\ x_3\left(k\right)\\ y_1\left(k\right)\\ y_2\left(k\right)\\ y_3\left(k\right)\end{array}\right],$

$G=\left[\begin{array}{cc}{T}^2/4& 0\\ T/2& 0\\ 1& 0\\ 0& T^2/4\\ 0& T/2\\ 0& 0\end{array}\right];$ W(k)＝[w₁(k)w₂(k)]，

wherein F is a state transition matrix; t is a sampling interval; the variable X (k) is a target state vector comprising the radial distance r, the relative velocityRelative accelerationAngle β, angular velocityAnd angular accelerationW (k) is the system noise vector; g is an action matrix of system noise; w is a₁(k)、w₂(k) Is a white noise sequence with a mean value of zero and uncorrelated and a variance of The covariance matrix of W (k) is as in formula (28):

$Q\left(k\right)=E\[W\left(k\right)W^T\left(k\right)\]=\left[\begin{array}{cc}{\mathrm{\σ}}_{\mathrm{\α}}^2& 0\\ 0& {\mathrm{\σ}}_{\mathrm{\β}}^2\end{array}\right]---\left(28\right).$

4. the road traffic monitoring multi-target detection tracking method according to claim 3, characterized in that basic equations of one-step prediction of the Kalman filtering are as shown in formulas (7), (8) and (9):

K_p(k)＝Φ(k+1/k)P(k/k-1)HT[H(k)P(k/k-1)HT(k)+R(k)]^-1(8)

P(k+1/k)＝[Φ(k+1/k)-K_p(k)H(k)]P(k/k-1)+G(k)Q(k)GT(k)(9)

k in the formulae (7), (8), (9)_p(k) To predict the gain matrix in one step, phi (k +1, k) (phi (k +1, k) ∈ R^n×n) Is a state transition matrix, Y (k) (Y (k)) ∈ R^m×1) Is a measurement vector, H (k) (H (k)) ∈ R^m×n) Is an observation matrix; equation (9) is the one-step prediction equation error.

5. The road traffic monitoring multi-target detection tracking method according to claim 1 or 2, characterized in that the measurement model of the interactive multi-model method with markov switching coefficients is:

Z(k)＝H(k)X(k)+V(k)(29)

wherein:

$Z\left(k\right)=\left[\begin{array}{c}{z}_1\left(k\right)\\ z_2\left(k\right)\\ z_3\left(k\right)\end{array}\right];$ $H\left(k\right)=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\end{array}\right];$ $V\left(k\right)=\left[\begin{array}{c}{v}_1\left(k\right)\\ v_2\left(k\right)\\ v_3\left(k\right)\end{array}\right];$

in the formula: z is a radical of₁(k)、z₂(k)、z₃(k) Respectively representing the distance, the relative speed and the azimuth angle of a target measured by a radar; h (k) is an observation matrix; v (k) is measurement noise; wherein v is₁(k)、v₂(k)、v₃(k) Is three mutually uncorrelated random white noise sequences with the equations of $E{\[v_2\left(k\right)\]}^2={\mathrm{\σ}}_2^2$ And $E{\[v_3\left(k\right)\]}^2={\mathrm{\σ}}_3^2;$

the covariance matrix of v (k) is formula (30):

$R\left(k\right)=E{\[V\left(k\right)V^T\left(k\right)\]}^2=\left[\begin{array}{ccc}{\mathrm{\σ}}_1^2& 0& 0\\ 0& {\mathrm{\σ}}_2^2& 0\\ 0& 0& {\mathrm{\σ}}_3^2\end{array}\right]---\left(30\right)$

here, ,is the variance of the error of the distance measurement,is the variance of the error of the relative velocity (doppler) measurement,is the variance of the azimuth measurement error.

6. A tracking system adapted to the road traffic monitoring multi-target detection tracking method according to any one of claims 1 to 5, the tracking system comprising:

the radar is used for detecting a plurality of moving targets and uploading feedback data;

the data processing system receives feedback data uploaded by the radar, performs Kalman filtering and prediction on the feedback data, acquires the motion states of a plurality of moving targets at the current moment, and predicts the motion states of a plurality of moving targets at the future moment; and controlling a plurality of moving targets of the radar to track by adopting an interactive multi-model method with Markov switching coefficients.

7. The tracking system of claim 6, wherein the radar is a millimeter wave frequency modulated pulse doppler radar.