CN113408586A - Out-of-order data fusion method based on bidirectional decorrelation - Google Patents
Out-of-order data fusion method based on bidirectional decorrelation Download PDFInfo
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Abstract
The invention discloses a disordering data fusion method based on bidirectional decorrelation, which is suitable for the field of multi-sensor target tracking and is used for fusing a disordering scene of measurement data of a center. Aiming at the problem that the target tracking performance of the fusion center track is lost due to a traditional discarding method, the method utilizes the historical state information of the fusion center track to update the out-of-order measurement information, solves the correlation between the updated result and the historical state information of the fusion center track in a bidirectional decorrelation mode, and finally utilizes the decorrelation result to update the current state of the fusion center track. The invention effectively improves the tracking performance of the fusion center track target.
Description
Technical Field
The invention belongs to the field of multi-sensor target tracking, and particularly relates to a fusion method for out-of-order measurement data of a fusion center. The discarding method is a traditional out-of-order data processing method, namely discarding out-of-order data of the fusion center, and certain target tracking performance loss exists. The invention is based on the out-of-order data fusion method of the two-way decorrelation, and can effectively improve the target tracking performance.
Background
In the field of multi-sensor target tracking, the fusion center receives the measurement data of each sensor and performs information fusion, so that higher target tracking performance than that of a single sensor can be realized. In fact, when data transmission is performed, the spatial distances between the sensors and the fusion center are different, communication delays of different degrees occur, and the delay increases with the increase of the transmission distance. The communication delay causes that the measurement data arrive at the fusion center out of order, and the target tracking performance of the track of the fusion center can be seriously deteriorated by directly carrying out fusion processing on the measurement data arriving at the fusion center. Therefore, how to process the out-of-order data of the fusion center is a technical difficulty of information fusion.
Aiming at the problem that measured data arrives at a fusion center out of order, the traditional discarding method directly discards out-of-order measured information of the fusion center in order to save computing resources of the fusion center and sacrifice part of target tracking performance of a flight path of the fusion center. The main idea is as follows: and comparing the observation time stamps of the measurement information uploaded to the fusion center by each sensor with the time range of the current fusion period and the latest time stamp of the flight path of the fusion center, judging whether the measurement information is out of order, directly discarding the measurement information if the out of order occurs, and fusing the measurement information in a sequential mode if the out of order does not occur.
According to the analysis, the traditional discarding method does not fully utilize the measurement information uploaded by each sensor, so that the tracking performance of the flight path in the fusion center has certain loss. In order to improve the tracking performance of the fusion center track as much as possible, a two-way decorrelation-based out-of-order data processing method is provided, and the target tracking performance of the fusion center track is improved.
Disclosure of Invention
The invention provides a disorder data processing method based on bidirectional decorrelation, which updates disorder measurement information by using historical state information of a fusion center track, solves the correlation between an updated result and the historical state information of the fusion center track in a bidirectional decorrelation mode, and finally updates the current state of the fusion center track by using the decorrelation result.
Compared with the existing discarding method, the method can greatly improve the tracking precision of the flight path of the fusion center by processing the out-of-order measurement data.
Drawings
FIG. 1 is a schematic diagram of the out-of-order arrival of multi-sensor measurement data at a fusion center;
FIG. 2 is a diagram of a simulation scenario;
FIG. 3 shows a comparison of the discard method and the two-way decorrelation method position RMSE;
detailed description of the preferred embodiments
The following detailed description of the embodiments of the invention is provided in connection with the accompanying drawings. And taking the track state of the fusion center as the k moment, and receiving the measurement information at the tau moment by the fusion center. Let τ < k, i.e., the measurement information is out-of-order observation information. Specific embodiments of the present invention are directed to such out-of-order information as follows:
on the premise that the current fusion center track state is known to be at the kth moment, the mixed state of the fusion center track at the kth moment is a probability density function and is expressed as
p(χk,xk|Zk)
Where χ represents a target present event, x represents a target dynamic state, subscript k represents time, ZkRepresenting all the sets of measurements received by the fusion center before time k, and p (-) representing the probability density function. When expanded according to the conditional probability density formula, then
p(χk,xk|Zk)＝P(χk|Zk)p(xk|χk,Zk)
Wherein P (·) represents probability, P (χ)k|Zk) Representing the probability of the presence of an object at time k, p (x)k|χk,Zk) Representing the probability density function of the target dynamic state at time k. Obey Gaussian distribution according to target dynamic state, then have
Wherein N (-) represents a Gaussian function,
representing the mean of the Gaussian distribution, i.e. the estimate of the target dynamic state at time k, Pk|kRepresenting the covariance of the Gaussian distribution, i.e. the target dynamic state at time kEstimated error covariance.
The above is the known information of the fusion center track k moment. Receiving out-of-order measurement information Z by the fusion centerτThe treatment scheme of the invention.
Step 1, the fusion center receives the measurement information ZτIf tau is less than k, finding the track state of the fusion center track relative to the previous moment b of the tau
p(χb,xb|Zb)
ZτRepresenting the set of measurements observed by the sensor at time instant τ. When the formula is expanded according to the conditional probability density function, the formula has
p(χb,xb|Zb)＝P(χb|Zb)p(xb|χb,Zb)
Wherein, P (χ)b|Zb) Indicates the probability of the existence of the target at the time b, p (x)b|χb,Zb) Representing a probability density function of the target dynamic state at the b-th moment and having
Wherein the content of the first and second substances,
representing an estimate of the target dynamic state at the b-th moment of the fusion center track, Pb|bAnd representing the estimation of the covariance of the target dynamic state error at the b-th moment of the fusion center track.
p(χτ,xτ|Zb)＝P(χτ|Zb)p(xτ|χτ,Zb)
Wherein, p (χ)τ,xτ|Zb) Representing a prediction of the mixing of the b-th to the t-th times of the fusion center track, P (χ)τ|Zb) Means for predicting the probability of the existence of the target from the b-th time to the t-th time, and has
P(χτ|Zb)＝p11P(χb|Zb)
Wherein p is11The transition probability, which indicates the existence of the target at the previous time to the existence of the target at this time, is usually set to 0.98. p (x)τ|χτ,Zb) Representing a prediction of a probability density function of a target dynamic state from the b-th time to the t-th time of a fusion center track, and having
Wherein the content of the first and second substances,
representing a prediction of the target dynamic state from the b-th to the t-th moment, Pτ|bRepresenting a prediction of the covariance of the errors of the target dynamic states from time b to time τ, and having
Wherein, Fτ|bRepresenting a state transition matrix of the target from the b-th moment to the t-th moment, the matrix being determined on the basis of a model of the movement of the target, Qτ|bAnd representing a covariance matrix of process noise from the b-th moment to the tau-th moment, wherein the process noise belongs to additive white Gaussian noise.
p(χτ,xτ|Zb,Zτ)
p(χτ,xτ|Zb,Zτ) And showing the mixed state of the integrated central track at the tau moment after updating. When expanded according to the conditional probability density formula, then
p(χτ,xτ|Zb,Zτ)＝P(χτ|Zb,Zτ)p(xτ|χτ,Zb,Zτ)
Wherein, P (χ)τ|Zb,Zτ) Representing the existence probability of the target at the Tth time of the fusion center track after updating, p (x)τ|χτ,Zb,Zτ) And representing the probability density function of the target dynamic state at the tau-th moment of the fusion center track after updating.
Obtaining P (x)τ|Zb,Zτ) And p (x)τ|χτ,Zb,Zτ) The update result of (2) requires the following 4 steps:
1) track threshold
Wherein z isτ,iRepresents ZτH denotes the observation matrix of the sensor and this matrix is determined by the sensor,
it has been found in step 2 that γ represents the track threshold size, is typically set at 13.816, and has
Sτ＝HPτ|bHT+R
Where R denotes the covariance matrix of the observation errors of the sensors and the matrix is determined by the sensors, Pτ|bAs already given in step 2. Finally, the threshold obtains a measurement set meeting the threshold condition as
2) Computing a set of measurements
Corresponding likelihood ratio
Wherein, PDIndicating the detection probability of the sensor, PGRepresenting the magnitude of the threshold probability, pτ,iRepresenting the clutter density, p, at the ith measurement position within the thresholdτ,iRepresents the likelihood value corresponding to the ith measurement in the threshold and has
3) Calculating association probability
4) Updating the hybrid state of the fusion center track at the Tth moment
At the time of tau, the target dynamic state is updated, then
Wherein the content of the first and second substances,
representing an estimate of the target dynamic state at the moment τ after the update, Pτ|τ,bError covariance representing target dynamic state at the time τ after update, and
wherein
Wherein I represents the identity matrix, dim represents the dimension of the target dynamic state, Kτ|bRepresenting a Kalman gain matrix, and having
Kτ|b＝Pτ|bHT(Sτ)-1
If the probability of the existence of the target at the time tau is updated, then
And 4, combining the mixed state of the fusion center track at the b-th moment in the step 1, and predicting the mixed state of the fusion center track at the k-th moment
p(χk,xk|Zb)＝P(χk|Zb)p(xk|χk,Zb)
Wherein, p (χ)k,xk|Zb) Represents the prediction of the mixing state of the fusion center track from the b th time to the k th time, P (x)τ|Zb) Means for predicting the probability of the existence of the target from the b-th time to the k-th time of the fusion center track, and has
Where int (·) denotes rounding up, and T denotes the sampling period. p (x)k|χk,Zb) Representing a prediction of a probability density function of a target dynamic state from the b-th time to the k-th time of a fusion center track, and having
Wherein the content of the first and second substances,
indicates the b-th timePrediction of the target dynamic State at time k, Pk|bRepresenting a prediction of the covariance of the target dynamic state errors from time b to time k, and having
Wherein, Fk|bRepresenting the target state transition matrix, Q, from time b to time kk|bRepresenting the noise covariance matrix during time b to time k.
And 5, combining the mixed state of the fusion center track at the tau-th moment after updating in the step 3, and predicting the mixed state of the fusion center track at the k-th moment
p(χk,xk|Zb,Zτ)＝P(χk|Zb,Zτ)p(xk|χk,Zb,Zτ)
Wherein, p (χ)k,xk|Zb,Zτ) Representing a prediction of the hybrid state of the fusion center track from the time τ to the time k, P (χ)k|Zb,Zτ) Means for predicting the probability of the existence of the target from the Tth time to the kth time of the fusion center track, and has
Wherein, P (χ)τ|Zb,Zτ) As already given in step 3. p (x)k|χk,Zb,Zτ) Representing a prediction of a probability density function of a target dynamic state from the time t to the time k of a fusion center track, and having
Wherein the content of the first and second substances,
is shown asPrediction of the target dynamic state from the time τ to the time k, Pk|τ,bRepresenting a prediction of the covariance of the target dynamic state error from time τ to time k, and having
Wherein, Fk|τRepresenting the target state transition matrix, Q, from time τ to time kk|τRepresenting the noise covariance matrix during time t to time k,
and Pτ|τ,bAs already given in step 3.
Step 6, combining the prediction results of the step 4 and the step 5 to carry out bidirectional decorrelation calculation
Decorrelation of the probability of existence of the track object is obtained
P(χk|Zτ)＝P(χk|Zb,Zτ)-P(χk|Zb)
Wherein, P (χ)k|Zb) And P (χ)k|Zb,Zτ) Obtained in step 4 and step 5, respectively.
Decorrelation of the dynamic state of the track target is obtained
Wherein
Wherein the content of the first and second substances,
Pk|b、
Pk|τ,bobtained in step 4 and step 5, respectively.
And 7, updating the flight path mixed state of the fusion center at the k-th moment by combining the bidirectional decorrelation result in the step 6
p(χk,xk|Zk,Zτ)
Wherein, p (χ)k,xk|Zk,Zτ) Representing utilization of out-of-order data ZτAnd updating the mixing state of the fusion center at the k-th moment. Expanded according to the conditional probability density, then there are
p(χk,xk|Zk,Zτ)＝P(χk|Zk,Zτ)p(xk|χk,Zk,Zτ)
Wherein, P (χ)k|Zk,Zτ) Representing utilization of out-of-order data ZτTarget existence probability p (x) at the k-th time after updateτ|χτ,Zb,Zτ) Representing utilization of out-of-order data ZτAnd updating the probability density function of the target dynamic state at the k-th moment.
Using out-of-order data ZτThe target existence probability at the k moment after updating is
P(χk|Zk,Zτ)＝P(χk|Zk)+P(χk|Zτ)-P(χk|Zk)P(χk|Zτ)
Using out-of-order data ZτThe target dynamic state at the k-th moment after the update is
Wherein
Namely, it is
When the fusion center receives the disordered data, the 7 steps are repeated, the current fusion center track state can be updated by utilizing the disordered data, and the fusion center track tracking precision is greatly improved.
As can be seen from fig. 1, the interval between two black dots on the fusion center time axis represents one fusion period, and two fusion periods are provided before and after in fig. 1. The arrow from the sensor to the fusion center indicates the transmission of the measurement data, the start position of the arrow indicates the timestamp generated by the sensor measurement, and the end position of the arrow indicates the timestamp of the arrival of the sensor measurement at the fusion center. In the second fusion period, the measurement information transmitted by the dashed arrow is not the measurement data generated by the sensor 2 during the second fusion period. Therefore, the measurement information transmitted by the sensor 2 in the dotted line is out-of-order measurement information in the second fusion period.
Simulation verification
This section is mainly to verify whether the performance of the method presented herein is improved over the conventional discarding method. The simulation scene setting meets the following requirements:
assuming that two sensors and one target exist in the monitoring area, the target makes a uniform linear motion in the monitoring area, and a schematic diagram of motion tracks of the sensors and the target is shown in fig. 2. The performance index of the simulation statistics is position Root Mean Square Error (RMSE), and in order to ensure the validity of the simulation result, the simulation statistics is carried out for 100 Monte Carlo simulation experiments.
As shown in fig. 3, the method provided herein can effectively improve the accuracy of target tracking compared to the conventional discarding method. As shown in table 1, the method proposed herein was found to be 4.75% better than the conventional discard method by averaging RMSE;
table 1.
Claims (1)
1. A out-of-order data fusion method based on bidirectional decorrelation is characterized by comprising the following steps:
on the premise that the current fusion center track state is known to be at the kth moment, and the mixed state of the fusion center track at the kth moment is a probability density function and is expressed as
p(χk,xk|Zk)
Where χ represents a target present event, x represents a target dynamic state, subscript k represents time, ZkRepresenting all measurement sets received by the fusion center before the moment k, and p (-) representing a probability density function; when expanded according to the conditional probability density formula, then
p(χk,xk|Zk)＝P(χk|Zk)p(xk|χk,Zk)
Wherein P (·) represents probability, P (χ)k|Zk) Representing the probability of the presence of an object at time k, p (x)k|χk,Zk) Representing a probability density function of a target dynamic state at the moment k; obey Gaussian distribution according to target dynamic state, then have
Wherein N (-) represents a Gaussian function,
representing the mean of the Gaussian distribution, i.e. the estimate of the target dynamic state at time k, Pk|kRepresenting the covariance of the Gaussian distribution, namely the error covariance of the target dynamic state estimation at the k moment;
the above is the known information of the fusion center track k moment; receiving out-of-order measurement information Z by the fusion centerτThe processing steps of the invention are as follows:
step 1, the fusion center receives the measurement information ZτIf tau is less than k, finding out the fusion center track corresponding toTrack state at a time b before the t-th time
p(χb,xb|Zb)
ZτRepresents the set of measurements observed by the sensor at time τ; when the formula is expanded according to the conditional probability density function, the formula has
p(χb,xb|Zb)＝P(χb|Zb)p(xb|χb,Zb)
Wherein, P (χ)b|Zb) Indicates the probability of the existence of the target at the time b, p (x)b|χb,Zb) Representing a probability density function of the target dynamic state at the b-th moment and having
Wherein the content of the first and second substances,
representing an estimate of the target dynamic state at the b-th moment of the fusion center track, Pb|bRepresenting the estimation of the target dynamic state error covariance at the b-th moment of the fusion center track;
step 2, combining the step 1 to obtain the mixed state of the fusion center track at the b-th moment, and predicting the mixed state of the fusion center track at the t-th moment
p(χτ,xτ|Zb)＝P(χτ|Zb)p(xτ|χτ,Zb)
Wherein, p (χ)τ,xτ|Zb) Representing a prediction of the mixing of the b-th to the t-th times of the fusion center track, P (χ)τ|Zb) Means for predicting the probability of the existence of the target from the b-th time to the t-th time, and has
P(χτ|Zb)＝p11P(χb|Zb)
Wherein p is11Indicating the probability of a transition from the last moment in time in which the target was present to the moment in time in which the target was still present, typicallySet to 0.98; p (x)τ|χτ,Zb) Representing a prediction of a probability density function of a target dynamic state from the b-th time to the t-th time of a fusion center track, and having
Wherein the content of the first and second substances,
representing a prediction of the target dynamic state from the b-th to the t-th moment, Pτ|bRepresenting a prediction of the covariance of the errors of the target dynamic states from time b to time τ, and having
Wherein, Fτ|bRepresenting a state transition matrix of the target from the b-th moment to the t-th moment, the matrix being determined on the basis of a model of the movement of the target, Qτ|bRepresenting a process noise covariance matrix from the b-th moment to the tau-th moment, wherein the process noise belongs to additive white Gaussian noise;
step 3, combining the prediction of the mixed state from the b-th time to the t-th time of the fusion center flight path in the step 2 and the disorder data Z received by the fusion center in the step 1τUpdating the mixed state of the integrated central track at the Tth moment
p(χτ,xτ|Zb,Zτ)
p(χτ,xτ|Zb,Zτ) Representing the mixed state of the integrated central track at the tau moment after updating; when expanded according to the conditional probability density formula, then
p(χτ,xτ|Zb,Zτ)＝P(χτ|Zb,Zτ)p(xτ|χτ,Zb,Zτ)
Wherein, P (χ)τ|Zb,Zτ) Representation updateTarget existence probability at the Tth moment of post-fusion central track, p (x)τ|χτ,Zb,Zτ) Representing the probability density function of the target dynamics state at the Tth moment of the fusion center track after updating;
obtaining P (x)τ|Zb,Zτ) And p (x)τ|χτ,Zb,Zτ) The update result of (2) requires the following 4 steps:
1) track threshold
Wherein z isτ,iRepresents ZτH denotes the observation matrix of the sensor and this matrix is determined by the sensor,
it has been found in step 2 that γ represents the track threshold size, is typically set at 13.816, and has
Sτ＝HPτ|bHT+R
Where R denotes the covariance matrix of the observation errors of the sensors and the matrix is determined by the sensors, Pτ|bAlready obtained in step 2;
finally, the threshold obtains a measurement set meeting the threshold condition as
2) Computing a set of measurements
Corresponding likelihood ratio
Wherein, PDIndicating the detection probability of the sensor, PGTo representMagnitude of threshold probability, ρτ,iRepresenting the clutter density, p, at the ith measurement position within the thresholdτ,iRepresents the likelihood value corresponding to the ith measurement in the threshold and has
3) Calculating association probability
4) Updating the hybrid state of the fusion center track at the Tth moment
At the time of tau, the target dynamic state is updated, then
Wherein the content of the first and second substances,
representing an estimate of the target dynamic state at the moment τ after the update, Pτ|τ,bError covariance representing target dynamic state at the time τ after update, and
wherein
Wherein I represents the identity matrix, dim represents the dimension of the target dynamic state, Kτ|bRepresenting a Kalman gain matrix, and having
Kτ|b＝Pτ|bHT(Sτ)-1
If the probability of the existence of the target at the time tau is updated, then
And 4, combining the mixed state of the fusion center track at the b-th moment in the step 1, and predicting the mixed state of the fusion center track at the k-th moment
p(χk,xk|Zb)＝P(χk|Zb)p(xk|χk,Zb)
Wherein, p (χ)k,xk|Zb) Represents the prediction of the mixing state of the fusion center track from the b th time to the k th time, P (x)τ|Zb) Means for predicting the probability of the existence of the target from the b-th time to the k-th time of the fusion center track, and has
Wherein int (·) represents rounding up, and T represents the sampling period; p (x)k|χk,Zb) Representing a prediction of a probability density function of a target dynamic state from the b-th time to the k-th time of a fusion center track, and having
Wherein the content of the first and second substances,
representing the prediction of the target dynamic state from time b to time k, Pk|bIndicates the b-th timePrediction of target dynamic state error covariance at time k, and
wherein, Fk|bRepresenting the target state transition matrix, Q, from time b to time kk|bRepresenting a noise covariance matrix from the b-th time to the k-th time;
and 5, combining the mixed state of the fusion center track at the tau-th moment after updating in the step 3, and predicting the mixed state of the fusion center track at the k-th moment
p(χk,xk|Zb,Zτ)＝P(χk|Zb,Zτ)p(xk|χk,Zb,Zτ)
Wherein, p (χ)k,xk|Zb,Zτ) Representing a prediction of the hybrid state of the fusion center track from the time τ to the time k, P (χ)k|Zb,Zτ) Means for predicting the probability of the existence of the target from the Tth time to the kth time of the fusion center track, and has
Wherein, P (χ)τ|Zb,Zτ) As already obtained in step 3; p (x)k|χk,Zb,Zτ) Representing a prediction of a probability density function of a target dynamic state from the time t to the time k of a fusion center track, and having
Wherein the content of the first and second substances,
representing the time from the t-th time to the k-th timePrediction of the Standard kinetic State, Pk|τ,bRepresenting a prediction of the covariance of the target dynamic state error from time τ to time k, and having
Wherein, Fk|τRepresenting the target state transition matrix, Q, from time τ to time kk|τRepresenting the noise covariance matrix during time t to time k,
and Pτ|τ,bAs already obtained in step 3;
step 6, combining the prediction results of the step 4 and the step 5 to carry out bidirectional decorrelation calculation
Decorrelation of the probability of existence of the track object is obtained
P(χk|Zτ)＝P(χk|Zb,Zτ)-P(χk|Zb)
Wherein, P (χ)k|Zb) And P (χ)k|Zb,Zτ) Respectively obtained in step 4 and step 5;
decorrelation of the dynamic state of the track target is obtained
Wherein
Wherein the content of the first and second substances,
Pk|b、
Pk|τ,brespectively obtained in step 4 and step 5;
and 7, updating the flight path mixed state of the fusion center at the k-th moment by combining the bidirectional decorrelation result in the step 6
p(χk,xk|Zk,Zτ)
Wherein, p (χ)k,xk|Zk,Zτ) Representing utilization of out-of-order data ZτUpdating the mixed state of the fusion center at the kth moment; expanded according to the conditional probability density, then there are
p(χk,xk|Zk,Zτ)＝P(χk|Zk,Zτ)p(xk|χk,Zk,Zτ)
Wherein, P (χ)k|Zk,Zτ) Representing utilization of out-of-order data ZτTarget existence probability p (x) at the k-th time after updateτ|χτ,Zb,Zτ) Representing utilization of out-of-order data ZτUpdating the probability density function of the target dynamic state at the kth moment;
using out-of-order data ZτThe target existence probability at the k moment after updating is
P(χk|Zk,Zτ)＝P(χk|Zk)+P(χk|Zτ)-P(χk|Zk)P(χk|Zτ)
Using out-of-order data ZτThe target dynamic state at the k-th moment after the update is
Wherein
Namely, it is
When the fusion center receives the disordered data, the 7 steps are repeated, the current fusion center track state can be updated by utilizing the disordered data, and the fusion center track tracking precision is greatly improved.
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