CN112162244B - Event trigger target tracking method under related noise and random packet loss environment - Google Patents

Event trigger target tracking method under related noise and random packet loss environment Download PDF

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CN112162244B
CN112162244B CN202010997121.3A CN202010997121A CN112162244B CN 112162244 B CN112162244 B CN 112162244B CN 202010997121 A CN202010997121 A CN 202010997121A CN 112162244 B CN112162244 B CN 112162244B
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CN112162244A (en
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姜露
吴鹏
王立
许继平
王小艺
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Beijing Technology and Business University
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Abstract

The invention discloses an event trigger target tracking method under a related noise and random packet loss environment, and belongs to the technical field of target tracking. The invention describes the observation of a sensor to a target in a radar system as a linear discrete time dynamic system, then carries out target tracking based on an improved Kalman filtering estimation method, introduces a transmission packet loss variable simulation random packet loss process in the target estimation, considers the limitation of system noise, network bandwidth and energy of the sensor measurement noise and the last moment and the current moment, and introduces event triggering parameter simulation measurement data to judge whether the measurement data are fused or not. The invention reduces redundant measurement transmission, improves the accuracy of target tracking estimation, saves network bandwidth and transmission energy consumption, has the characteristics of small operand, low energy consumption and the like, can be directly used for tracking estimation of a real target, is simple to implement, and has potential value in a plurality of application fields such as target tracking, integrated navigation, fault detection, control and the like.

Description

Event trigger target tracking method under related noise and random packet loss environment
Technical Field
The invention belongs to the technical field of radar target tracking in the aspect of information processing, and relates to a Kalman filtering estimation method triggered by an event under a noise correlation and random packet loss environment.
Background
Radar means "radio detection and ranging", i.e. the method of finding objects by radio and determining their spatial position. Thus, radar is also referred to as "radiolocation". The radar is generally divided into a radar front end and a radar terminal, wherein the radar front end comprises an antenna, a transmitter, a receiver and a signal preprocessor, pulse power with the intensity required by the radiation generated by the transmitter is fed to the antenna, the antenna obtains a larger observation distance by concentrating the radiation energy, the receiver amplifies a weak echo signal to a level sufficient for signal processing, and then the information such as the position, time, size and energy amplitude of an observation target is calculated through the signal processing; the radar terminal comprises a control unit, a display unit and a signal processing unit, realizes the control of the radar front end, receives and displays the radar image sent by the radar front end, receives the target point trace information sent by the radar front end, and tracks and displays the target.
Radar estimation tracks the target accurately, but there is inevitably some inherent noise, and the noise will definitely affect the received signal, so that the long-time radar is used to make the noise more and more diverse and complex, and the processing is more and more difficult. And meanwhile, the loss of tracking target information can be caused by instability of a communication link in the information transmission process. At present, the conventional filtering estimation method is not used for comprehensively considering the interference of noise correlation and packet loss problems to a system, which can lead to poor tracking effect.
The radar front end and the terminal perform bidirectional data transmission through the wireless sensor network, and the network bandwidth and the transmission capacity in the wireless sensor network are very limited, so that efficient bandwidth and energy utilization are very important. The event triggering mechanism can reduce the occupation of network transmission bandwidth and save the energy consumption of data transmission on the premise of ensuring the target tracking precision. And thus have received much attention.
Disclosure of Invention
The invention aims to provide a target tracking and positioning method based on wireless sensor data in a radar system, which considers the unreliability of a communication link in the transmission process, simulates the random packet loss process, considers the system noise of the sensor measurement noise and the last moment and the current moment and the limitation of network bandwidth and energy, and realizes the target tracking of the sensor by using a Kalman filtering estimation method triggered by the related noise and events in the random packet loss environment.
The invention provides an event trigger target tracking method under a related noise and random packet loss environment, which is used for target tracking of a radar system, wherein the observation of a sensor to a target in the radar system is described as a linear discrete time dynamic system, and then the target tracking is performed based on an improved Kalman filtering estimation method. The method comprises the following steps:
step 1, obtaining initial data of a tracked target, and setting the coincidence mean value of initial target states as
Figure BDA0002692965090000012
Variance is->
Figure BDA0002692965090000011
Is a gaussian distribution of (c); the target state includes the position and speed of the target; the system noise when the sensor observes the target is set to be zero in mean value and Q in covariance k White gaussian noise, Q k An initial value of Q 0 The method comprises the steps of carrying out a first treatment on the surface of the Setting the initial value of the estimated error covariance matrix between the sensor target state and the system noise as +.>
Figure BDA0002692965090000021
Let transmission packet loss variable lambda k Obeying a Bernoulli distribution with a parameter p;
step 2, at time k, the sensor is acquired at time (k-1, k]Observation data z of period k And observation transfer matrix C k The method comprises the steps of carrying out a first treatment on the surface of the k is a positive integer;
step 3, introducing a transmission packet loss variable lambda at the moment k k To simulate the packet loss process when lambda k When=1, the observed data arrives normally, when λ k When the value is=0, the observed data is lost, and probability distribution of packet loss and observation noise under normal conditions is obtained respectively;
step 4, calculating a target state prediction matrix at the current k moment according to the target state estimation value at the k-1 moment
Figure BDA0002692965090000022
Covariance matrix P of state prediction error k|k-1 ；
Step 5, at time k, using the observation data z obtained in step 2 k And 4, calculating a target state prediction matrix
Figure BDA0002692965090000023
Covariance matrix P of state prediction error k|k-1 Calculating event trigger parameter gamma of sensor k The method comprises the steps of carrying out a first treatment on the surface of the When gamma is k When=1, measurement data z k Is transmitted to a remote estimator when gamma k When=0, the measurement data z k Will not be transmitted to the remote estimator;
step 6, at time k, using the observation data z obtained in step 2 k And 3, obtaining a transmission packet loss variable lambda k Target state prediction matrix calculated in step 4
Figure BDA0002692965090000024
Covariance matrix P of state prediction error k|k-1 And the event triggering parameter gamma of the sensor calculated in step 5 k Calculating a target state estimation matrix at time k>
Figure BDA0002692965090000025
State estimation error covariance matrix P k|k System noise estimation matrix->
Figure BDA0002692965090000026
Systematic noise estimation error covariance matrix>
Figure BDA0002692965090000027
And an estimation error covariance matrix between state and system noise +.>
Figure BDA0002692965090000028
Step 7, assigning k+1 to k, repeating the steps 2 to 6, and outputting the target state estimation matrix at the k moment calculated in the step 6
Figure BDA0002692965090000029
State estimation error covariance matrix P k|k The result of tracking the target at any time k, k=1, 2, … can be obtained.
In the step 3, the packet loss variable lambda is transmitted at the observed value at the moment k k Observed noise v k The probability distribution is expressed as
Figure BDA00026929650900000210
Wherein N (0, R) k ) Represents a standard deviation of 0 and a variance of R k Normal distribution of R k An observation error variance matrix at the time k is represented; n (0, sigma) 2 I) Represents a standard deviation of 0 and a variance of sigma 2 Normal distribution of I, parameter σ→infinity, I represents the identity matrix.
In the step 4, at the transmission time k, a target state prediction matrix is calculated according to the target state estimation matrix at the time k-1
Figure BDA00026929650900000211
Sum-state prediction error covariance matrix P k|k-1 The following are provided:
Figure BDA00026929650900000212
wherein ,
Figure BDA00026929650900000213
P k-1|k-1 a target state estimation matrix and a state estimation error covariance matrix, which respectively represent k-1 time,/I>
Figure BDA00026929650900000214
A k-1 The system state transition matrix at the moment k-1 is represented, and the upper corner mark T represents transposition;
Figure BDA00026929650900000215
estimated value representing system noise at time k-1, < >>
Figure BDA00026929650900000216
An estimation error covariance matrix representing the system noise at time k-1 +.>
Figure BDA00026929650900000217
Figure BDA00026929650900000218
Representing the estimated error covariance matrix between the system state and the system noise at time k-1,
Figure BDA00026929650900000219
Figure BDA0002692965090000031
in the step 5, the event trigger parameter gamma of the sensor is calculated k The method of (1) is as follows:
firstly, calculating the difference between the observed data measured at the moment k and the predicted value of the observed data based on the state at the moment k-1 to obtain the innovation
Figure BDA0002692965090000032
New covariance matrix->
Figure BDA0002692965090000033
The gain matrix is: />
Figure BDA0002692965090000034
Figure BDA0002692965090000035
Figure BDA0002692965090000036
wherein ,
Figure BDA0002692965090000037
a covariance matrix representing the system noise at the previous time and the observed noise at the current k time. New covariance matrix->
Figure BDA0002692965090000038
Is a semi-positive definite matrix, calculating +.>
Figure BDA0002692965090000039
Characteristic value of +.>
Figure BDA00026929650900000310
m is z k And represents it as a form of a diagonal array:
Figure BDA00026929650900000311
unitary matrix U is calculated using k ：
Figure BDA00026929650900000312
Then, a matrix is set
Figure BDA00026929650900000313
Then a matrix of normalized and decorrelation is further obtained>
Figure BDA00026929650900000314
Finally, obtaining event triggering parameters of the sensor
Figure BDA00026929650900000315
Wherein I ∞ And representing the infinite norm of the matrix, wherein theta is the threshold value triggered by the event, and theta is more than or equal to 0.
In the step 6, the target state estimation matrix at the k moment and the state estimation error covariance matrix are respectively
Figure BDA00026929650900000316
And P k|k The calculation is as follows:
Figure BDA00026929650900000317
calculating a system noise estimation matrix at k moment, a system noise estimation error covariance matrix and a gain matrix of system noise
Figure BDA00026929650900000318
And an estimated error covariance matrix between state and system noise:
Figure BDA00026929650900000319
Figure BDA00026929650900000320
wherein ,γk Representing event trigger parameters, lambda k Representing a transmission packet loss variable S k A covariance matrix representing the system noise and the observation noise at the time k;
distribution of
Figure BDA00026929650900000321
Distribution->
Figure BDA00026929650900000322
Compared with the prior art, the invention has the advantages and positive effects that:
(1) Compared with the traditional time triggering, the invention reduces redundant measurement transmission, saves network bandwidth and transmission energy consumption on the premise of ensuring target estimation accuracy, has the characteristics of small operand, low energy consumption and the like, and can more effectively and fully utilize data under the condition of lowest energy consumption;
(2) The method considers the related noise, overcomes the complex environment that the system noise at the previous moment is related to the observation noise at the current moment, and improves the accuracy of target tracking estimation;
(3) The invention considers the problem of data packet loss caused by the unreliability of a communication link in the transmission process of the system, simulates the random packet loss process and improves the accuracy of target tracking estimation;
(4) The improved Kalman filtering estimation algorithm used in the method can obtain the optimal solution under the meaning of the minimum variance of the target observation error, and can effectively realize target tracking estimation;
(5) The method has strong anti-noise and anti-interference capability, and can improve the tracking and positioning precision of the system;
(6) The method can be directly used for tracking and estimating the real target, is simple to implement and easy to popularize, and has potential value in a plurality of application fields such as target tracking, integrated navigation, fault detection and control.
Drawings
Fig. 1 is a schematic flow chart of a target tracking method triggered by events in a random packet loss environment with correlated noise in the present invention;
FIG. 2 is a schematic representation of the relationship between average sensor communication rate and event trigger threshold in a simulated method of the present invention;
FIG. 3 is a graph of computer simulated root mean square error versus position and velocity for the method of the present invention at different thresholds;
FIG. 4 is a graph of the position and velocity root mean square error of a computer simulated method of the present invention versus a KF algorithm that considers packet loss but ignores noise;
fig. 5 is a graph of the computer simulated position and velocity root mean square error versus the KF algorithm that considers noise correlations but ignores packet losses.
Detailed Description
The invention will be described in further detail with reference to the drawings and examples.
The method is based on a linear discrete time dynamic system under the related noise and random packet loss environment, takes radar target tracking as a background, takes high-precision target information as a target, and researches the problem of Kalman filtering state estimation triggered by events.
In the embodiment of the invention, the hardware environment and software for realizing the method of the invention are configured as follows:
hardware environment: a computer; a correlator;
software configuration: windows 7/8//9/10; matlab or C language or C++, and the like.
A linear discrete time dynamic system in which a sensor observes an object can be described as
x k+1 ＝A k x k +ω k ，k＝0,1,2,…
z k ＝C k x k +v k
wherein ,
Figure BDA0002692965090000041
the system state vector at the moment k is an n-dimensional real number vector; r represents a real number; s is(s) k and />
Figure BDA0002692965090000051
The position and the speed of the tracked target at the moment k are respectively represented, and the system state is the target state; a is that k ∈R n×n The system state transition matrix at the moment k is an n multiplied by n real number matrix; omega k Is the process noise at time k, which is zero as the mean value and Q as the covariance k White gaussian noise of (1), initial Q k ＝Q 0 ；z k ∈R m The measured value of the sensor at the moment k is an m-dimensional real number vector; c (C) k ∈R m×n The measurement transfer matrix at the moment k is an m×n real number matrix. v k Is the observation noise at time k, v is set k Is zero mean and covariance is +.>
Figure BDA0002692965090000052
White noise of (1), and->
Figure BDA0002692965090000053
Figure BDA0002692965090000054
wherein δkl Is a crotamGram function. Measuring noise v k System noise omega from current time k And the system noise omega at the previous time k-1 And (5) correlation. v l Represents the observed noise at time l, R k An observation error variance matrix representing the k moment, S k A covariance matrix representing the system noise and the observation noise at the current k moment,/>
Figure BDA0002692965090000055
A covariance matrix representing the system noise at the previous time and the observed noise at the current time.
Initial state x 0 Is the mean value of
Figure BDA0002692965090000056
Variance is->
Figure BDA0002692965090000057
And omega k 、v k Independent of each other, k is a positive integer.
As shown in fig. 1, the event-triggered target tracking method under the related noise and random packet loss environment provided by the invention is divided into the following 8 steps for explanation.
Step 1, acquiring initial data of a sensor observation target, including acquiring a mean value of initial state vectors
Figure BDA0002692965090000058
Variance of
Figure BDA0002692965090000059
Initial system noise variance matrix Q 0 And the initial value of the estimated error covariance matrix between the target state and the system noise is as follows
Figure BDA00026929650900000510
wherein ,/>
Figure BDA00026929650900000511
For n-dimensional real vector, ">
Figure BDA00026929650900000512
Is an n-dimensional matrix, and->
Figure BDA00026929650900000513
Is a positive definite matrix, Q 0 ∈R n×n Is an n-dimensional matrix, ">
Figure BDA00026929650900000514
Is an n-dimensional matrix, and is provided with a transmission packet loss variable lambda k Obeying the bernoulli distribution with parameter p. Wherein (1)>
Figure BDA00026929650900000515
Representing the target state estimation error,/->
Figure BDA00026929650900000516
Representing the systematic noise estimation error.
Step 2, inputting a transmission packet loss variable lambda at time k, k=1, 2, … k Inputting event trigger threshold value theta and inputting system state matrix A k And a system noise variance matrix Q k The method comprises the steps of carrying out a first treatment on the surface of the Input (k-1, k)]Observations z from sensors obtained at a time k And an observation matrix C k Observed noise variance matrix R k Covariance matrix of system noise at last moment and observation noise at current moment
Figure BDA00026929650900000517
Covariance matrix S of system noise at current moment and observation noise at current moment k 。
The set values of the related parameters and the conditions to be satisfied involved in the method of the invention are as follows:
λ k : the transmission packet loss variable is used for describing whether the transmission packet loss is an amount, obeys Bernoulli distribution with the parameter p, and is more than 0 and less than 1;
θ: a threshold value for event triggering, which is used for describing an amount of a triggering critical value, wherein θ is more than or equal to 0;
z k : observed quantity of the sensor, the dimension of which is m, and the value range: m is less than or equal to n;
A k : a system state transition matrix for describing the amount of transitions between states. The value range is as follows: full order matrix of eigenvalues within a unit circle, if the dimension of the target state is n, then A k ∈R n×n ；
C k : an observation transfer matrix for describing the dimension of the observation data and the observation data, wherein the dimension is m, namely C k ∈R m×n ；
Q k : the system noise variance matrix is used for describing system modeling errors, and the dimension of the system noise variance matrix is n multiplied by n, and is a non-negative definite matrix in general;
R k : the observation error variance matrix is used for describing the observation error deviation, the dimension of the observation error variance matrix is m multiplied by m, and the value range of the observation error variance matrix is a non-negative definite matrix;
Figure BDA0002692965090000061
covariance of system noise at last moment and observation noise at current moment is used for describing correlation of system noise at last moment and observation noise at current moment, dimension of the covariance is n multiplied by m, and value range is non-negative definite matrix;
S k : covariance of system noise at current moment and observation noise at current moment is used for describing correlation of system noise at current moment and observation noise at current moment, dimension of the covariance is n multiplied by m, and value range is non-negative definite matrix;
i: representing the identity matrix;
I n : representing an n-dimensional identity matrix;
p (x|y): representing the probability of occurrence of x under the condition y;
n (μ, σ): the normal distribution with standard deviation μ and variance σ is shown.
Step 3, at the measurement transmission time k, k=1, 2, …, by transmitting the packet loss variable λ k The packet loss process is simulated, and the probability distribution of the observed noise is as follows:
Figure BDA0002692965090000062
wherein ,p(vk |λ k ) Variable lambda indicating packet loss at transmission at time k k Observed noise v k Probability distribution, parameter sigma → infinity. When lambda is k When=1, the observed value z k Can normally arrive; when lambda is k When=0, the observed value is lost.
Step 4, at a measurement transmission time k, k=1, 2,3,..
Figure BDA00026929650900000619
And a target state prediction error covariance matrix P k|k-1 ：
Figure BDA0002692965090000063
wherein ,
Figure BDA0002692965090000064
representing the target state at the current k time, P, predicted based on the system state at the previous time k|k-1 Error covariance matrix representing prediction,>
Figure BDA0002692965090000065
and Pk-1|k-1 Representing a target state estimation matrix and a state estimation error covariance matrix at time k-1, respectively, when k=1, ->
Figure BDA0002692965090000066
Figure BDA0002692965090000067
Estimated value representing system noise at time k-1, < >>
Figure BDA0002692965090000068
An estimation error covariance matrix representing the system noise at time k-1 +.>
Figure BDA0002692965090000069
Indicating time k-1The estimated error covariance matrix between the system state and the system noise, when k=1,
Figure BDA00026929650900000610
Figure BDA00026929650900000611
step 5, at time k, k=1, 2, …, using the observation data z input in step 2 k And the related parameters, and calculated in step 4
Figure BDA00026929650900000612
and Pk|k-1 Calculating an event trigger parameter gamma of the sensor using k ：
New information
Figure BDA00026929650900000613
And new covariance matrix ++>
Figure BDA00026929650900000614
And gain matrix K k The method comprises the following steps of:
Figure BDA00026929650900000615
Figure BDA00026929650900000616
Figure BDA00026929650900000617
wherein the new information
Figure BDA00026929650900000618
Representing the difference between the actual observations measured at time k and the observations predicted based on the state at time k-1.
Due to
Figure BDA0002692965090000071
Is a semi-positive definite matrix to obtain +.>
Figure BDA0002692965090000072
Characteristic value of +.>
Figure BDA0002692965090000073
m is z k And represents it as a diagonal matrix Λ k Form (f)
Figure BDA0002692965090000074
Unitary matrix U for establishing equation by the following calculation k ∈R m×m ：
Figure BDA0002692965090000075
Definition matrix H k ∈R m×m Is that
Figure BDA0002692965090000076
/>
Further obtaining a normalized and decorrelated matrix
Figure BDA0002692965090000077
Figure BDA0002692965090000078
Then according to the matrix
Figure BDA0002692965090000079
Determining event trigger parameters of the sensor:
Figure BDA00026929650900000710
wherein I ∞ Representing the infinite norm of the matrix, when gamma k When=1, the measured value z of the sensor k May be transmitted to a remote estimator, i.e. a fusion center; otherwise, when gamma k At=0, the fusion center does not receive the measurement.
Step 6, at time k, k=1, 2, …, using the observation data z input in step 2 k Calculating random packet loss parameters with related parameters in the step 3 and calculating in the step 4
Figure BDA00026929650900000711
and Pk|k-1 And step 5, calculating a state estimation matrix by using the following formula according to the Kalman filtering event triggering condition calculated in the step 5>
Figure BDA00026929650900000712
And corresponding estimation error covariance matrix P k|k ：
Figure BDA00026929650900000713
The white noise estimator is calculated as:
Figure BDA00026929650900000714
wherein ,
Figure BDA00026929650900000715
represents the estimated value of k time to system noise, < >>
Figure BDA00026929650900000716
Gain matrix representing system noise ++>
Figure BDA00026929650900000717
An estimation error covariance matrix, lambda, representing system noise k And the observation value transmission packet loss variable at the moment k is represented, and the upper corner mark T represents transposition.γ k Representing event-triggered parameters of the sensor.
A filtered error covariance matrix between system state and system noise:
Figure BDA00026929650900000718
Figure BDA00026929650900000719
a filtered error covariance matrix between the system state and the system noise representing the moment k,/>
Figure BDA00026929650900000720
Representing a filtered error covariance matrix between the system noise and the system state at time k.
Wherein, the distribution of beta (theta) and Q (theta) is as follows:
Figure BDA0002692965090000081
Figure BDA0002692965090000082
step 7, at time k, k=1, 2, …, output x k|k and Pk|k And obtaining an estimated value of the state of the sensor and an estimated error covariance matrix which are obtained at the moment k. X output from step 7 k|k 、P k|k I.e. calculated in step 6
Figure BDA0002692965090000083
and Pk|k As a result of the radar system tracking the target at the current k moment.
And 8, when the next k+1 moment is reached, assigning k+1 to k, and then repeating the steps 2-7 to track Kalman filtering of the target at the next moment to acquire a target state estimated value and an error covariance matrix.
The effectiveness of the method of the present invention will be tested by simulation experiments.
A single sensor radar tracking system can be described by the following formula:
Figure BDA0002692965090000084
z k ＝Cx k +v k ,k＝1,2,…,L
v k ＝η k +β 1 ξ k-1 +β 2 ξ k
where t=0.01 represents the sampling period. L=300 is the measured length of the estimated signal x. State vector
Figure BDA0002692965090000085
wherein sk Is to track the position of the target at the moment kT, < >>
Figure BDA0002692965090000086
Is the speed at kT time. Suppose that xi k E R is zero mean and covariance is +.>
Figure BDA0002692965090000087
Is a gaussian white noise of (c). Γ -shaped structure k ＝[T 1] T Is a noise transfer matrix. z k Is the measurement vector of the sensor, C= [ 10 ]]。v k Is the measurement noise, the measurement noise of the sensor and the system noise xi of the last moment and the current moment k-1 and ξk And (5) correlation. Correlation is formed by beta 1 and β2 Is determined by the value of (2). η (eta) k Is Gaussian noise and its mean is zero and covariance is +.>
Figure BDA0002692965090000088
And independent of xi k K=1, 2, …. Initial value is
Figure BDA0002692965090000089
ω 0 ＝[0 0] T ，/>
Figure BDA00026929650900000810
Systematic error variance matrix
Figure BDA00026929650900000811
It is the system noise omega k ＝Γ k ξ k Corresponding covariance matrix, measurement noise covariance +.>
Figure BDA00026929650900000812
ω k-1 and vk Covariance between +.>
Figure BDA00026929650900000813
But->
Figure BDA00026929650900000814
Is omega k and vk Covariance matrix between them.
To compare the impact of different thresholds on the estimated performance under event triggering conditions, 4 different thresholds were randomly set, θ=0, θ=0.5, θ=0.8, and θ=1.0, respectively. Wherein when θ=0, the event trigger degradation is a time trigger, i.e. the estimator can receive the measurements of the respective sensor at each instant.
The purpose of the experiment of the invention is that the sensor estimates the target, giving the state x k And compares the influence of neglecting the correlated noise and the packet loss on the estimation result under the condition of the correlated noise and the random packet loss.
Is provided with
Figure BDA00026929650900000815
and β1 ＝6，β 2 =6, and thus the measurement noise is correlated with the last time system noise and the current time system noise. The parameter p=0.1 of the transmission packet loss variable. The invention carries out 1000 Monte Carlo simulations and observes the effectiveness of the proposed algorithm. Simulation results are shown in fig. 2 to 5.
The average communication rate of the sensor of the improved Kalman filtering algorithm provided by the invention is defined as follows
Figure BDA0002692965090000091
Fig. 2 shows a relationship between the event trigger threshold θ and the average sensor communication rate γ. It can be seen that as the event trigger threshold increases, the communication rate of the sensor continues to decrease.
Fig. 3 shows statistical simulation curves of the position and velocity Root Mean Square Error (RMSE) of the Kalman filtering method under different trigger thresholds in the method of the present invention (KFO for short). As can be seen from fig. 3, the state estimation effect of the method according to the invention is always better at smaller trigger thresholds than at larger trigger thresholds. In the figure, a dotted line indicates θ=1.0, a solid line indicates θ=0.8, a dash-dot line indicates θ=0.5, and a dotted line indicates θ=0.
Fig. 4 shows statistical simulation curves of RMSE of the inventive method (KFO for short) taking into account noise correlations and packet losses and KF algorithm (KFN for short) taking into account packet losses but not noise correlations, including root mean square error of position and velocity, wherein an event trigger threshold θ=0.5 is set. In the figure, the solid line represents the method of the present invention, the dashed line represents the comparison method, and it can be seen that, at θ=0.5, the root mean square error curve of the KF algorithm in the method of the present invention is lower than the root mean square error curve of the KF algorithm (KFN) that considers packet loss but does not consider noise correlation, which indicates that the KF algorithm that considers noise correlation is effective, and ignoring noise correlation reduces the state estimation accuracy.
Fig. 5 shows a statistical simulation curve of RMSE of the inventive method taking into account noise correlation and packet loss and KF algorithm (KFD for short) taking into account noise correlation but not packet loss, including root mean square error of position and velocity, wherein an event trigger threshold θ=0.5 is set. In the figure, the solid line represents the method of the present invention, the dashed line represents the comparison method, and it can be seen that when θ=0.5, the root mean square error curve of the KF algorithm in the method of the present invention is lower than the root mean square error curve of the KF algorithm (KFD) which considers the noise correlation but does not consider the packet loss, which indicates that the KF algorithm which considers the packet loss is effective, and ignoring the packet loss reduces the state estimation accuracy.
Table 1 shows the time average velocity and location RMSE of KFO algorithm, KFN algorithm and KFD algorithm at different trigger thresholds.
TABLE 1 time-averaged RMSE at different thresholds θ for different cases
Figure BDA0002692965090000092
It can be seen that KFO is superior to the other two algorithms when θ takes the same value. Note that when θ=0 means that all raw sensor measurements are transmitted and the system degenerates into a time triggered system. Thus, the inventive method has the best estimation performance at θ=0. As θ increases, the accuracy of the estimation of the method of the present invention decreases. But under whatever conditions the method of the invention is optimal.
In summary, from the above simulation, the method of the present invention has a better simulation effect, and the Kalman filtering algorithm used to consider noise correlation and packet loss is superior to the Kalman filtering algorithm which ignores one of the two, so that the target tracking and positioning accuracy can be improved.

Claims (5)

1. An event triggering target tracking method under the environment of related noise and random packet loss is used for target tracking of a radar system, wherein the observation of a sensor on a target is described as a linear discrete time dynamic system, and the target state comprises the position and the speed of the target; characterized in that the method comprises the following steps:
step 1, obtaining initial data of a tracked target, and setting an initial state x of the target 0 The coincidence mean value is
Figure FDA0002692965080000011
Variance is->
Figure FDA0002692965080000012
Is a gaussian distribution of (c); let the mean value of system noise when the sensor observes the target be 0 and the covariance be Q k White gaussian noise, Q k An initial value of Q 0 The method comprises the steps of carrying out a first treatment on the surface of the Setting the initial value of the covariance matrix of the estimation error between the target state and the system noise as +.>
Figure FDA0002692965080000013
Let transmission packet loss variable lambda k Obeying a Bernoulli distribution with a parameter p;
step 2, at time k, the sensor is acquired at (k-1, k]Observation data z of time k And observation transfer matrix C k The method comprises the steps of carrying out a first treatment on the surface of the k is a positive integer;
step 3, transmitting packet loss variable lambda at k moment k Simulating the packet loss process when lambda k When=1, the observed data arrives normally, when λ k When the value is=0, the observed data is lost, and probability distribution of packet loss and observation noise under normal conditions is obtained respectively;
step 4, calculating a target state prediction matrix at the current k moment according to the target state estimation value at the k-1 moment
Figure FDA0002692965080000014
Covariance matrix P of state prediction error k|k-1 ；
Step 5, at time k, using the observation data z obtained in step 2 k And 4, calculating a target state prediction matrix
Figure FDA0002692965080000015
Covariance matrix P of state prediction error k|k-1 Calculating event trigger parameter gamma of sensor k The method comprises the steps of carrying out a first treatment on the surface of the When gamma is k When=1, measurement data z k Is transmitted to a remote estimator when gamma k When=0, the measurement data z k Will not be transmitted to the remote estimator;
step 6, at time k, using the observation data z obtained in step 2 k Random packet loss variable lambda obtained in step 3 k Target state prediction matrix calculated in step 4
Figure FDA0002692965080000016
And state ofPrediction error covariance matrix P k|k-1 And the event triggering parameter gamma of the sensor calculated in step 5 k Calculating a target state estimation matrix at time k>
Figure FDA0002692965080000017
State estimation error covariance matrix P k|k System noise estimation matrix->
Figure FDA0002692965080000018
Systematic noise estimation error covariance matrix>
Figure FDA0002692965080000019
And an estimation error covariance matrix between state and system noise +.>
Figure FDA00026929650800000110
Step 7, assigning k+1 to k, repeating the steps 2-6, and outputting the target state estimation matrix at the k moment calculated in the step 6
Figure FDA00026929650800000111
State estimation error covariance matrix P k|k And obtaining a result of tracking the target at any moment.
2. The method according to claim 1, wherein in the step 3, the packet loss variable λ is transmitted at the observed value at the time k k Observed noise v k The probability distribution is expressed as
Figure FDA00026929650800000112
Wherein N (0, R) k ) Represents a standard deviation of 0 and a variance of R k Normal distribution of R k An observation error variance matrix at the time k is represented; n (0, sigma) 2 I) Represents a standard deviation of 0 and a variance of sigma 2 Normal distribution of I, parameter σ→infinity, I represents the identity matrix.
3. The method according to claim 1, wherein in the step 4, the target state prediction matrix is calculated based on the target state estimation matrix at time k-1 at time k of transmission
Figure FDA00026929650800000113
Sum-state prediction error covariance matrix P k|k-1 The following are provided:
Figure FDA00026929650800000114
wherein ,
Figure FDA0002692965080000021
P k-1|k-1 a target state estimation matrix and a state estimation error covariance matrix, which respectively represent k-1 time,/I>
Figure FDA0002692965080000022
A k-1 The system state transition matrix at the moment k-1 is represented, and the upper corner mark T represents transposition; />
Figure FDA0002692965080000023
Estimated value of system noise representing time k-1,/->
Figure FDA0002692965080000024
An estimation error covariance matrix representing the system noise at time k-1 +.>
Figure FDA0002692965080000025
An estimated error covariance matrix between the system state and the system noise representing the moment k-1, +.>
Figure FDA0002692965080000026
Estimation error co-ordinates between system noise and system state representing time k-1Difference matrix, < >>
Figure FDA0002692965080000027
4. The method according to claim 1, wherein in step 5, the event trigger parameter γ of the sensor is calculated k The method of (1) is as follows:
first, the difference between the observed data measured at time k and the predicted value of the observed data based on the state at time k-1, i.e., the innovation, is calculated
Figure FDA0002692965080000028
Covariance matrix of innovation +.>
Figure FDA0002692965080000029
And gain matrix K k The following are respectively:
Figure FDA00026929650800000210
Figure FDA00026929650800000211
Figure FDA00026929650800000212
wherein ,
Figure FDA00026929650800000213
a covariance matrix representing system noise at the last moment and observation noise at the current k moment; new covariance matrix
Figure FDA00026929650800000214
Is a semi-positive definite matrix, calculating +.>
Figure FDA00026929650800000215
Characteristic value of +.>
Figure FDA00026929650800000216
m is z k And represents it as a form of a diagonal array:
Figure FDA00026929650800000217
unitary matrix U is calculated using k ：
Figure FDA00026929650800000218
Then, a matrix is set
Figure FDA00026929650800000219
Then a matrix of normalized and decorrelation is further obtained>
Figure FDA00026929650800000220
Finally, obtaining event triggering parameters of the sensor
Figure FDA00026929650800000221
Wherein I ∞ And representing the infinite norm of the matrix, wherein theta is the threshold value triggered by the event, and theta is more than or equal to 0.
5. The method according to claim 1, wherein in the step 6, the target state estimation matrix and the state estimation error covariance matrix at the k time are respectively
Figure FDA00026929650800000222
And P k|k The calculation is as follows:
Figure FDA00026929650800000223
calculating the noise estimation value of the system at the moment k
Figure FDA00026929650800000224
Error covariance matrix of system noise estimation and gain matrix of system noise
Figure FDA00026929650800000225
And an estimated error covariance matrix between system state and system noise:
Figure FDA00026929650800000226
/>
Figure FDA0002692965080000031
wherein ,γk Representing event trigger parameters, lambda k Representing a transmission packet loss variable S k A covariance matrix between system noise and observation noise at time k is represented;
distribution of
Figure FDA0002692965080000032
Distribution->
Figure FDA0002692965080000033
θ is the event-triggered threshold. />
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