CN110675435B - Vehicle trajectory tracking method based on Kalman filtering and chi 2 detection smoothing processing - Google Patents
Vehicle trajectory tracking method based on Kalman filtering and chi 2 detection smoothing processing Download PDFInfo
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Abstract
The invention discloses a method based on Kalman filtering and chi 2 A vehicle track tracking method for detecting smoothing processing aims at finding a more effective vehicle tracking detection mode, and comprises the following steps: constructing a kinematic model and a measurement model of the running process of the target vehicle; obtaining the historical motion track of the target vehicle, substituting the kinematic model and the measurement model into a time updating equation and a state updating equation in a Kalman filter to iteratively update the motion state of the target vehicle, and predicting the motion state at the next moment; structure chi 2 And the fault detector is used for carrying out fault detection on the prediction result. The invention applies Chi to the problems of possible recognition error or loss and the like in the tracking of the prior art 2 The fault detector can effectively reduce the deviation of track prediction and improve the track identification accuracy.
Description
Technical Field
The invention relates to the field of automatic driving, in particular to a Kalman filtering and chi-based method 2 And detecting a vehicle track tracking method of smoothing processing.
Background
With the continuous development and progress of scientific technology, unmanned vehicles are taken as the main trend of modern vehicle development, and various research applications and experimental tests of various aspects are developed around various technologies and functions of large vehicle enterprises and universities. The track tracking control is a basis for realizing unmanned driving and also serves as an important technology for intelligent vehicle control, and long-time target tracking needs to be carried out on the vehicle to obtain the driving track of the vehicle in the current scene.
For a vehicle tracking detection mode through a video image, the obtained original vehicle track has the defects of unstable detection borrowing point frame, many jumps in the track, poor smoothness and the like, meanwhile, the noise problems of large-area shielding, illumination influence, background disorder, shade change and the like exist in the tracking process, the processing result obtained by applying the traditional tracking algorithm is not accurate, and the position information and the speed information of the target vehicle are difficult to obtain accurately.
Disclosure of Invention
In order to find a more effective vehicle tracking detection mode, the invention provides a method based on Kalman filtering and chi 2 Method for detecting smoothly processed vehicle trajectory tracking, Kalman filtering and chi 2 The vehicle track tracking method for detecting the smoothing processing comprises the following steps:
step S1, the obtained motion video image of the target vehicle is regarded as a two-dimensional plane coordinate system, and a kinematic model and a measurement model of the driving process of the target vehicle are constructed by taking the central point of the identification rectangular frame of the target vehicle as an analysis object:
step S2, obtaining the historical motion track of the target vehicle, substituting the kinematic model and the measurement model into a time updating equation and a state updating equation in a Kalman filter to iteratively update the motion state of the target vehicle, and predicting the motion state at the next moment;
step S3, constructing chi 2 Fault detector and constructing χ according to Kalman filter 2 A detection statistic of the fault detector; and comparing the detection statistic with a preset threshold, and when the detection statistic is greater than the threshold, selecting the prior state estimation value at the k moment as the posterior state estimation value at the k moment to participate in executing the step S2 so as to dynamically acquire the motion track of the target vehicle in real time, wherein k represents the moment and is an integer greater than 0.
Preferably, the kinematic model of the driving process of the target vehicle is:
X k+1 ＝AX k +BW k
in the formula, X k The real motion state of the target vehicle at the moment k;
A∈R 4×4 is expressed as acting on X k A state transition matrix of (c);
B∈R 4 representation of process noise W k A coefficient matrix of (a);
W k ∈R 4 denotes the compliance W at time k k N (0, Q) distributed process noise;
Q∈R 4×4 representing process noise covarianceA matrix;
the measurement model is as follows:
Z k ＝HX k +V k
in the formula, H is epsilon to R 2×4 A representation measurement model matrix that maps the true state space into an observation space;
V k ∈R 2 representing compliance V k N (0, R) distributed measurement noise;
R∈R 2×2 representing the measurement noise covariance matrix.
Preferably, said constructing said χ according to said kalman filtering algorithm 2 The detection statistics of the fault detector include the steps of:
substituting Kalman gain in a steady state of a Kalman filter into the state updating equation to obtain a state estimation value at the moment k;
obtaining a residual deviation L according to the state estimation value at the moment k and the measurement model k ；
According to the residual deviation L k Construct the detection statistic g k Wherein the detection statistic g k Comprises the following steps:
g k ＝L k T B k L k
B k ＝E(L k L k T )＝HPH T +R
in the formula, L k Obeying a Gaussian distribution, B k Is a residual deviation L k The covariance matrix of (a);
h represents a measurement model matrix;
p is an estimation error covariance matrix in the Kalman filter;
r is measurement noise V k The covariance matrix of (a);
g k and (3) the chi-square distribution of m degrees of freedom is obeyed, and the m is a natural number and is not far away from 0.
Preferably, the preset threshold value is confirmed by referring to a chi-square distribution table based on the detection statistic freedom value and a preset probability confidence range.
Preferably, the detection statistic freedom value is 1, and the preset probability confidence range is 95%.
Preferably, the step S2 is preceded by the steps of:
initializing the kinematic model and the measurement model according to preset conditions, wherein the preset conditions are process noise, measurement noise and a state initial value X 0 The following conditions are satisfied:
preferably, initializing the kinematic model and the measurement model according to preset conditions comprises the steps of:
confirming a sampling period, and initializing the kinematic model and the measurement model according to the sampling period and the preset condition.
Compared with the prior art, the Kalman filtering and Chi filtering based method is characterized in that 2 The vehicle track tracking method for detecting the smoothing processing has the following technical effects:
the invention is based on Kalman filtering and chi 2 The vehicle track tracking method for detecting smoothing processing applies chi to the problems of recognition error or loss and the like which may occur in the tracking process in the prior art 2 The fault detector can effectively reduce the deviation of track prediction and improve the track identification accuracy, and meanwhile, the X-shaped 2 The fault detector is a detector which is usually matched with Kalman filtering for use, and the complexity of detection calculation is low, so that the fault detector is convenient for industrial application.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 provides a Kalman filtering and chi-based algorithm according to an embodiment of the present invention 2 And detecting a flow schematic diagram of the vehicle track tracking method of the smoothing processing.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative only and should not be construed as limiting the invention.
Referring to fig. 1, an embodiment of the invention is based on kalman filtering and χ filtering 2 The vehicle track tracking method for detecting the smoothing processing comprises the following steps:
and step S1, regarding the acquired motion video image of the target vehicle as a two-dimensional plane coordinate system, and constructing a kinematic model and a measurement model of the running process of the target vehicle by taking the central point of the identification rectangular frame of the target vehicle as an analysis object.
In some embodiments, the target vehicle motion video image is preferably acquired by an in-vehicle vision system.
The specific address and the kinematic model of the target vehicle in the driving process are as follows:
X k+1 ＝AX k +BW k
in the formula, X k The real motion state of the target vehicle at the moment k;
A∈R 4×4 is expressed as acting on X k A state transition matrix of (c);
B∈R 4 representation of process noise W k A coefficient matrix of (a);
W k ∈R 4 denotes the compliance W at time k k N (0, Q) distributed process noise;
Q∈R 4×4 representing a process noise covariance matrix;
the measurement model is as follows:
Z k ＝HX k +V k
in the formula, H is epsilon to R 2×4 Representing a measurement model matrix that maps the true state space into observationsA space;
V k ∈R 2 representing compliance V k N (0, R) distributed measurement noise;
R∈R 2×2 representing the measurement noise covariance matrix.
Step S2, obtaining the historical motion track of the target vehicle, substituting the kinematic model and the measurement model into a time updating equation and a state updating equation in a Kalman filter to iteratively update the motion state of the target vehicle, and predicting the motion state at the next moment;
in some embodiments, step S2 is followed by the following steps:
initializing a kinematic model and a measurement model according to preset conditions, wherein the preset conditions are process noise, measurement noise and a state initial value X 0 The following conditions are satisfied:
preferably, the covariance matrix of the process noise can be estimated from the actual running process, and is referred to herein as:
E(W k W k T )＝Q
the covariance matrix of the measured noise can be generally obtained from data and actual measurements of the relevant measurement sensor, such as the camera manufacturer, and is referred to herein as:
E(V k V k T )＝R
the initial covariance of the system state is:
E(X 0 X 0 T )＝∑ 0|0 。
preferably, initializing the kinematic model and the measurement model according to preset conditions comprises the following steps: confirming a sampling period, and initializing a kinematic model and a measurement model according to the sampling period and preset conditions.
For example, assuming a sampling period Δ t during tracking, the kinematic model and measurement model parameter matrices are defined as follows:
the states of the kinematic model and the measurement model are defined as follows:
wherein, X k ∈R 4 Representing the real motion state of the target vehicle at the moment k;
x (k) and v x (k) Respectively representing the coordinate and the speed value of the target vehicle in the x-axis direction in the video image at the time of k;
y (k) and v y (k) Respectively representing the coordinate and the speed value of the target vehicle in the y-axis direction at the time of k;
a x (k) representing the acceleration of the target vehicle in the x-axis direction, a y (k) Representing the acceleration of the target vehicle in the y-axis direction;
Z k ∈R 2 representing the observation vector, i.e. the detected vehicle position in the camera or video, because only the center position of the moving vehicle can be detected and only the position of the center point of the identification rectangular frame of the target vehicle can be observed when the observation vector is established, the observation vector only comprises the coordinates of the center point of the position of the target vehicle and has no speed information, wherein x is z (k) And y z (k) And x-axis coordinate values and y-axis coordinate values corresponding to the center points of the rectangular frames of the target vehicle detected in the image sequence at the time k are respectively shown.
The kalman filter comprises two main processes: estimating and correcting, wherein the estimation process mainly comprises the steps of establishing prior estimation on the current state by using a time updating equation, and timely calculating the current state variable and the error covariance estimation value forwards so as to construct a prior estimation value for the next time state; the correction process is responsible for feedback, and an improved posterior estimation of the current state is established on the basis of the prior estimation value and the current measurement variable in the estimation process by using a measurement updating equation. The time update equation and the state update equation of the discrete kalman filter are given below.
The time update equation:
P k - ＝AP k-1 A T +Q
P k-1 (0)＝P 0
P 0 ＝diag(1,1,1,1)
the state update equation:
K k ＝P k - H T (HP k - H T +R) -1
P k ＝(I-K k H)P k -
in the formula (I), the compound is shown in the specification,
the prior estimation value of the Kalman filter for the motion state of the target vehicle at the moment k is represented;
P k - representing an n x n prior estimation error covariance matrix;
P k representing an n x n posteriori estimation error covariance matrix;
i represents an n × n-order identity matrix;
K k representing an n x m order matrix, called kalman gain or blending factor, functions to minimize the covariance of the a posteriori estimation errors.
In the embodiment of the present invention, the estimated predicted motion trajectory of the target vehicle can be obtained by substituting the kinematic model and the measurement model constructed in step S1 into the time update equation and the state update equation.
Step S3, constructing chi 2 Fault detector and constructing χ according to Kalman filter 2 A detection statistic of the fault detector; comparing the detection statistic with a preset threshold, and selecting the prior state estimation value of the k moment as the rear of the k moment when the detection statistic is larger than the thresholdThe state-of-experience estimation value participates in executing step S2 to dynamically acquire the motion trajectory of the target vehicle in real time, where k represents a time and is an integer greater than 0.
Specifically, χ is constructed according to a Kalman filtering algorithm 2 The detection statistics of the fault detector include the steps of:
substituting Kalman gain in a steady state of a Kalman filter into a state updating equation to obtain a state estimation value at the moment k;
obtaining residual deviation L according to state estimation value and measurement model at the moment k k ；
According to the residual deviation L k Construct the detection statistic g k Wherein the statistic g is detected k Comprises the following steps:
g k ＝L k T B k L k
B k ＝E(L k L k T )＝HPH T +R
in the formula, L k Obeying a Gaussian distribution, B k Is a residual deviation L k The covariance matrix of (a);
h represents a measurement model matrix;
p is an estimation error covariance matrix in the Kalman filter;
r is measurement noise V k The covariance matrix of (a);
g k and (3) the chi-square distribution of m degrees of freedom is obeyed, and the m is a natural number and is not far away from 0.
In some embodiments, the predetermined threshold is determined by consulting a chi-square distribution table based on the detection statistic freedom value and a predetermined probability confidence range.
For example, when the degree of freedom of the detection statistic is 1 and the preset probability confidence range is 95%, the corresponding preset threshold value of 3.84 can be obtained by referring to the chi-square distribution table. Thus, when g is k Less than a predetermined threshold, i.e. g k When the concentration is less than or equal to 3.84, χ 2 The fault detector will not activate an alarm, otherwise when g k When it is greater than the preset threshold value, χ 2 The fault detector gives an alarm that the residual deviation value is too large and exceeds the confidence range, and simultaneously the fault detector gives an alarm to the faultThe following adjustments are made in the state iteration process of kalman filtering:
i.e. discarding the measured value Z at time k k Directly selecting the prior state estimated value of k time
And the estimated value is used as the posterior state estimated value of the k moment and participates in the next prediction and iteration process. By continuously repeating the steps S2 and S3, the motion trail of the target vehicle can be dynamically obtained in real time,
it is worth noting that the chi-square detection in the steady state working state of the kalman filter is considered in the present invention, and the parameters in the steady state of the kalman filter are as follows:
K@PH T (HPH T +R) -1
in the formula, P k - The prior estimation error covariance matrix at the moment k is obtained, P is the estimation error covariance matrix when the Kalman filter reaches the steady state, and the prior estimation and the posterior estimation error covariance matrix P at the moment k - 、P k And when the covariance matrix of the estimation errors in the steady state of the Kalman filter is equal to P, substituting the covariance matrix of the estimation errors in the steady state of the Kalman filter into a formula state updating equation to obtain the Kalman gain K when the Kalman filter reaches the steady state.
Chi-square detection of residual deviation L of time k k Is defined as:
from the measurement model to the residual deviation L k Simultaneous residual error L k Another form of expression:
in the formula, X k Is the true value of the system state, V k To measure noise.
Compared with the prior art, the embodiment of the invention is based on Kalman filtering and chi 2 The vehicle track tracking method for detecting the smoothing processing has the following technical effects:
the embodiment of the invention is based on Kalman filtering and chi 2 The vehicle track tracking method for detecting smoothing processing applies chi to the problems of recognition error or loss and the like which may occur in the tracking process in the prior art 2 The fault detector can effectively reduce the deviation of track prediction and improve the track identification accuracy, and meanwhile, the X-shaped 2 The fault detector is a detector which is usually matched with Kalman filtering for use, and the complexity of detection calculation is low, so that the fault detector is convenient for industrial application.
The foregoing is only a partial embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (3)
1. Based on Kalman filtering and chi 2 Vehicle trajectory tracking method for detection smoothing, characterized in that it is based on Kalman filtering and chi 2 The vehicle track tracking method for detecting the smoothing processing comprises the following steps:
step S1, the obtained motion video image of the target vehicle is regarded as a two-dimensional plane coordinate system, and the central point of the identification rectangular frame of the target vehicle is used as an analysis object to construct a kinematic model and a measurement model of the target vehicle in the running process;
step S2, obtaining the historical motion track of the target vehicle, substituting the kinematic model and the measurement model into a time updating equation and a state updating equation in a Kalman filter to iteratively update the motion state of the target vehicle, and predicting the motion state at the next moment;
step S3, constructing chi 2 Fault detector and constructing χ according to Kalman filter 2 A detection statistic of the fault detector; comparing the detection statistic with a preset threshold, and when the detection statistic is greater than the threshold, selecting the prior state estimation value at the time k as the posterior state estimation value at the time k to participate in executing the step S2 so as to dynamically acquire the motion track of the target vehicle in real time, wherein the time k represents an integer greater than 0;
the kinematic model of the target vehicle in the running process is as follows:
X k+1 ＝AX k +BW k
in the formula, X k The real motion state of the target vehicle at the moment k;
A∈R 4×4 is expressed as acting on X k A state transition matrix of (c);
B∈R 4 representation of process noise W k A coefficient matrix of (a);
W k ∈R 4 denotes the compliance W at time k k N (0, Q) distributed process noise;
Q∈R 4×4 representing a process noise covariance matrix;
the measurement model is as follows:
Z k ＝HX k +V k
in the formula, H is epsilon to R 2×4 A representation measurement model matrix that maps the true state space into an observation space;
V k ∈R 2 representing compliance V k N (0, R) distributed measurement noise;
R∈R 2×2 representing a measurement noise covariance matrix;
constructing the χ according to the Kalman filtering algorithm 2 The detection statistics of the fault detector include the steps of:
substituting Kalman gain in a steady state of a Kalman filter into the state updating equation to obtain a state estimation value at the moment k;
obtaining a residual deviation L according to the state estimation value at the moment k and the measurement model k ；
According to the residual deviation L k Construct the detection statistic g k Wherein the detection statistic g k Comprises the following steps:
g k ＝L k T B k L k
B k ＝E(L k L k T )＝HPH T +R
in the formula, L k Obeying a Gaussian distribution, B k Is a residual deviation L k The covariance matrix of (a);
h represents a measurement model matrix;
p is an estimation error covariance matrix in the Kalman filter;
r is measurement noise V k The covariance matrix of (a);
g k the chi-square distribution of m degrees of freedom is obeyed, and the chi-square distribution is not far away from 0, wherein m is a natural number;
the preset threshold value is determined by looking up a chi-square distribution table based on the detection statistic freedom value and a preset probability confidence range;
the degree of freedom of the detection statistic is 1, and the preset probability confidence range is 95%.
2. The Kalman filtering and chi-based system of claim 1 2 The vehicle trajectory tracking method for detecting smoothing processing, characterized in that the step S2 is preceded by the steps of:
initializing the kinematic model and the measurement model according to preset conditions, wherein the preset conditions are process noise, measurement noise and a state initial value X 0 The following conditions are satisfied:
3. such as rightKalman filtering and chi-based according to claim 2 2 The vehicle track tracking method for detecting smoothing processing is characterized in that initializing the kinematic model and the measurement model according to preset conditions comprises the following steps:
confirming a sampling period, and initializing the kinematic model and the measurement model according to the sampling period and the preset condition.
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| CN111666891B (en) * | 2020-06-08 | 2023-09-26 | 北京百度网讯科技有限公司 | Method and device for estimating movement state of obstacle |
| CN112230801A (en) * | 2020-10-23 | 2021-01-15 | 上海磐启微电子有限公司 | Kalman smoothing processing method, memory and equipment applied to touch trajectory |
| CN112550294B (en) * | 2020-11-16 | 2021-12-24 | 东南大学 | Path tracking control method based on vehicle fault signal isolation |
| CN112433531A (en) * | 2021-01-27 | 2021-03-02 | 国汽智控(北京)科技有限公司 | Trajectory tracking method and device for automatic driving vehicle and computer equipment |
| CN113115230B (en) * | 2021-03-26 | 2023-08-18 | 北京工业大学 | Vehicle broadcast communication control method based on information physical system |
| CN113610263B (en) * | 2021-06-18 | 2023-06-09 | 广东能源集团科学技术研究院有限公司 | Power plant operation vehicle track estimation method and system |
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| CN114162134B (en) * | 2022-02-14 | 2022-05-06 | 西南交通大学 | Method, device and storage medium for predicting vehicle track on sea-crossing bridge |
| CN115376277A (en) * | 2022-08-05 | 2022-11-22 | 美的集团(上海)有限公司 | Health safety monitoring and early warning method, electronic equipment and storage medium |
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