CN112308134B - Static fusion method based on Gaussian mixture probability hypothesis density filter - Google Patents
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Abstract
The invention discloses a static fusion method based on Gaussian mixture probability hypothesis density filter, which is characterized in that a multi-target tracking algorithm in a time dimension is migrated to a sensor dimension, a multi-source target static fusion problem can be regarded as a multi-target tracking problem with a time interval of 0, modeling of a state model and an observation model of a target is carried out on the basis, and then static fusion is carried out after a high-speed effective tracking algorithm, namely Gaussian Mixture Probability Hypothesis Density (GMPHD), is filtered according to the model, so that a fusion result with higher precision can be obtained, and the operation efficiency is greatly improved. The method is suitable for input measurement of various conditions, and can effectively improve the positioning accuracy and the operation efficiency of the fusion result.
Description
Technical Field
The invention belongs to the field of information processing, and particularly relates to a static fusion method of a filter.
Background
In performing underwater target tracking, it is often desirable to utilize multiple sensors to improve tracking performance by expanding and reinforcing the viewing space, i.e., a multi-base target tracking system. In order to integrate metrology data from all sources, multi-base data fusion is often required. The measurement data of different sensors obtained by single scanning are fused, and information is preprocessed and screened to obtain an equivalent measurement set with higher precision and fewer false alarms, so that the precision of follow-up target tracking is improved, and the process is called static fusion. The currently commonly used static fusion method comprises a Scan box method, a grid screening method, a Monte Carlo sampling static fusion method and the like. However, the existing method is simple to realize, but has low operation efficiency, the measured covariance is not fully utilized, and the fusion performance is poor under the condition of less sensors.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a static fusion method based on a Gaussian mixture probability hypothesis density filter, wherein a multi-target tracking algorithm in a time dimension is migrated to a sensor dimension, a multi-source target static fusion problem can be regarded as a multi-target tracking problem with a time interval of 0, a state model and an observation model of a target are modeled on the basis, and a high-speed effective tracking algorithm, namely Gaussian Mixture Probability Hypothesis Density (GMPHD), is subjected to static fusion after being modified according to the model, so that a fusion result with higher precision can be obtained, and the operation efficiency is greatly improved. The method is suitable for input measurement of various conditions, and can effectively improve the positioning accuracy and the operation efficiency of the fusion result.
The technical scheme adopted by the invention for solving the technical problems comprises the following steps:
step 1: assuming that N sensors which independently work are included in a multi-source target measurement information fusion scene, and establishing a Cartesian coordinate system by taking any one sensor as an origin; the sensor n returns m n measurements of the target to form a measurement set Z n,a is the a-th measurement of the target returned by sensor N, n=1, 2,..n is the serial number of the sensor, a=1, 2,..m n is the measurement serial number of the target;
assuming that the measurement of any pair of targets is two-dimensional vector z= (tau, theta), wherein tau is time delay, theta is azimuth, and the measurement errors of tau and theta are uncorrelated and obey Gaussian distribution, and the variances of the measurement errors are respectively And/>The two-dimensional Cartesian coordinate of z is z= [ x, y ] and the covariance matrix is/>
Step 2: the method for establishing the state model of the sensor for observing the static target comprises the following steps:
Xn+1＝FXn+wn (1)
Wherein X n and X n+1 are target states in the observation ranges of the nth and the (n+1) th sensors, the process noise w n is subjected to Gaussian distribution w n:N (0, Q), and the state transition matrix F and the process noise matrix Q are respectively a two-dimensional identity matrix I and a two-dimensional identity matrix 0;
the method for establishing the observation model for observing the static target by the sensor comprises the following steps:
Zn＝HXn+yn (2)
Wherein the observation matrix H is a two-dimensional identity matrix I, and the measurement noise y n obeys Gaussian distribution y n:N(0,Rn),Rn to be a measurement noise covariance matrix;
Step 3: acquiring Gaussian component parameters of the improved GMPHD filter;
Step 3-1: defining J n as the target number in the observation range of the nth sensor;
step 3-2: representing the target states within the nth sensor observation range as a finite set States of the 1 st to the J n th targets within the observation range of the nth sensor, respectively; the target states within the n-1 th sensor observation range are represented as a finite set X n-1, each target state X n-1∈Xn-1 continues to survive within the n-th sensor observation range with a probability of p S,n =1, and the transition probability density from the target state X n-1 to the target state X n is F n|n-1 (x|ζ) =n (X; fζ, Q), where ζ represents the previous target state and X represents the target state;
Step 3-3: assuming that no new target proliferated from the n-1 th sensor observation range exists in the n-th sensor observation range, the naturally occurring new target has an intensity of γ n(x),γn (x) which is a gaussian mixture model;
step 3-4: given a target state x n∈Xn, assuming that the probability of being detected by a sensor is P D,n(xn)＝PD, and the probability of being missed is 1-P D; under the condition that the target is detected, obtaining an observation value z n from x n, wherein the probability density is g n (z|ζ) =n (z; hζ, Σ), and z represents the observation value; a set of spurious measurements received by the sensor is defined as measurements for which k n(z),kn (z) obeys poisson distribution, independent of the target;
step 3-5: from the assumptions of steps 3-1 to 3-4, a Gaussian mixture model is obtained with the posterior intensity of the observed object in the n-1 th sensor observation range as follows:
where J n-1 denotes the number of targets in the observation range of the n-1 th sensor, Is the Gaussian mixture model parameter of the j-th target posterior intensity in the n-1-th sensor observation range: respectively weight, mean and covariance;
the predicted intensity of the observation target in the n-th sensor observation range is:
vn|n-1(x)＝vS,n|n-1(x)+γn(x) (4)
the posterior intensity of a target that survives continuously within the n-th sensor observation range with probability p S,n =1 is:
Wherein,
The predicted intensity within the nth sensor observation range is expressed by the following gaussian mixture model:
wherein J n|n-1 is the measured quantity from the new-born target and the still-alive target within the observation range of the nth sensor, Is the Gaussian mixture model parameter of the jth target predicted intensity in the observation range from the nth-1 sensor to the nth sensor: respectively weight, mean and covariance;
therefore, the posterior intensity of the observation target in the observation range of the nth sensor is
Wherein,
Wherein,Is the jth target process noise;
finally, obtaining a Gaussian mixture model component { w n,mn|n,Pn|n } of the updated target posterior intensity in the observation range of the nth sensor;
Step 4: and (3) performing pruning and merging treatment on the Gaussian component { w n,mn|n,Pn|n } obtained in the step (3):
Pruning shears: discarding Gaussian components with weights lower than a preset weight threshold T or reserving Gaussian components with a given number J max from large to small;
Combining: when the distance between the two Gaussian components is smaller than a preset threshold U, combining the two Gaussian components into one according to a minimum mean square error criterion;
and finally, extracting the mean value m of the Gaussian components with weights exceeding a given threshold value, and taking the obtained multi-target position estimation as a static fusion result.
Preferably, the t=10 -5,U＝100,Jmax =100;
The beneficial effects are that:
the static fusion method based on the Gaussian mixture probability hypothesis density filter is suitable for input measurement in various observation environments, and can effectively utilize covariance information of targets, so that fusion performance is improved under the condition of fewer sensors, and compared with a common static fusion method, the static fusion method based on the Gaussian mixture probability hypothesis density filter has remarkable advantages in positioning accuracy and operation efficiency after fusion.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
Fig. 2 is a graph of static fusion results of the method of the present invention, where (a) is a simulation scenario and (b) is a static fusion result.
Fig. 3 is a graph comparing the results of the method and the grid screening method according to the present invention, wherein (a) is a scene with a fixed azimuth measurement error (standard deviation) of 1 ° and (b) is a scene with a fixed distance measurement error (standard deviation) of 20 m.
Detailed Description
The invention will be further described with reference to the drawings and examples.
As shown in fig. 1, a static fusion method based on a gaussian mixture probability hypothesis density filter comprises the following steps:
step 1: assuming that N sensors which independently work are included in a multi-source target measurement information fusion scene, and establishing a Cartesian coordinate system by taking any one sensor as an origin; the sensor n returns m n measurements of the target to form a measurement set Z n,a is the a-th measurement of the target returned by sensor N, n=1, 2,..n is the serial number of the sensor, a=1, 2,..m n is the measurement serial number of the target;
assuming that the measurement of any pair of targets is two-dimensional vector z= (tau, theta), wherein tau is time delay, theta is azimuth, and the measurement errors of tau and theta are uncorrelated and obey Gaussian distribution, and the variances of the measurement errors are respectively And/>Linearizing z according to the geometric relation of the transmitting source, the target and the receiver to two-dimensional Cartesian coordinates, wherein the two-dimensional Cartesian coordinates of z are z= [ x, y ] and the covariance matrix is
Step 2: the method for establishing the state model of the sensor for observing the static target comprises the following steps:
Xn+1＝FXn+wn (1)
Wherein X n and X n+1 are target states in the observation ranges of the nth and the (n+1) th sensors, the process noise w n is subjected to Gaussian distribution w n:N (0, Q), and the state transition matrix F and the process noise matrix Q are respectively a two-dimensional identity matrix I and a two-dimensional identity matrix 0;
the method for establishing the observation model for observing the static target by the sensor comprises the following steps:
Zn＝HXn+yn (2)
Wherein the observation matrix H is a two-dimensional identity matrix I, and the measurement noise y n obeys Gaussian distribution y n:N(0,Rn),Rn to be a measurement noise covariance matrix;
Step 3: acquiring Gaussian component parameters of an improved GMPHD filter, wherein the targets are simultaneously estimated in number and two-dimensional positions of each target under a Cartesian coordinate system;
the GMPHD filter is an analytical solution of PHD recursion based on linear Gaussian target dynamics and Gaussian target birth model, approximates Probability Hypothesis Density (PHD) of multiple targets in the form of Gaussian sum, and obtains closed recursion of weights, means and covariance constituting Gaussian components;
Step 3-1: defining J n as the target number in the observation range of the nth sensor;
step 3-2: representing the target states within the nth sensor observation range as a finite set States of the 1 st to the J n th targets within the observation range of the nth sensor, respectively; the target states within the n-1 th sensor observation range are represented as a finite set X n-1, each target state X n-1∈Xn-1 continues to survive within the n-th sensor observation range with a probability of p S,n =1, and the transition probability density from the target state X n-1 to the target state X n is F n|n-1 (x|ζ) =n (X; fζ, Q), where ζ represents the previous target state and X represents the target state;
Step 3-3: assuming that a new target which is generated naturally exists in the observation range of the nth sensor, no new target which is proliferated from the observation range of the nth-1 sensor exists in the observation range of the nth sensor, and the strength of the new target which is generated naturally is gamma n(x),γn (x) which is a Gaussian mixture model;
Step 3-4: given a target state x n∈Xn, assuming that the probability of being detected by a sensor is P D,n(xn)＝PD, and the probability of being missed is 1-P D; under the condition that the target is detected, obtaining an observation value z n from x n, wherein the probability density is g n (z|ζ) =n (z; hζ, Σ), and z represents the observation value; in one scan, in addition to measurements from the target, the sensor receives a set of false measurements defined as k n(z),kn (z) following a poisson distribution, independent of the measurements of the target;
step 3-5: from the assumptions of steps 3-1 to 3-4, a Gaussian mixture model is obtained with the posterior intensity of the observed object in the n-1 th sensor observation range as follows:
where J n-1 denotes the number of targets in the observation range of the n-1 th sensor, Is the Gaussian mixture model parameter of the j-th target posterior intensity in the n-1-th sensor observation range: respectively weight, mean and covariance;
the predicted intensity of the observation target in the n-th sensor observation range is:
vn|n-1(x)＝vS,n|n-1(x)+γn(x) (4)
the posterior intensity of a target that survives continuously within the n-th sensor observation range with probability p S,n =1 is:
Wherein,
The predicted intensity within the nth sensor observation range is expressed by the following gaussian mixture model:
wherein J n|n-1 is the measured quantity from the new-born target and the still-alive target within the observation range of the nth sensor, Is the Gaussian mixture model parameter of the jth target predicted intensity in the observation range from the nth-1 sensor to the nth sensor: respectively weight, mean and covariance;
therefore, the posterior intensity of the observation target in the observation range of the nth sensor is
Wherein,
Wherein,Is the jth target process noise;
finally, obtaining a Gaussian mixture model component { w n,mn|n,Pn|n } of the updated target posterior intensity in the observation range of the nth sensor;
Step 4: and (3) performing pruning and merging treatment on the Gaussian component { w n,mn|n,Pn|n } obtained in the step (3):
Pruning shears: discarding Gaussian components with weights lower than 10 -5 or reserving 100 Gaussian components from large to small;
Combining: when the distance between the two Gaussian components is smaller than 100, the two Gaussian components are combined into one according to a minimum mean square error criterion;
and finally, extracting the mean value m of the Gaussian components with weights exceeding a given threshold value, and taking the obtained multi-target position estimation as a static fusion result.
The following assumptions about the measurement set apply: 1) The sensors work independently; 2) The measurements include a portion of the target-related measurements and spurious measurements (clutter). Wherein the target-dependent measurement has a multi-dimensional gaussian distribution of 0 mean; whereas the false measurement obeys a uniform distribution in the observation space, the number thereof obeys a poisson distribution, and has a parameter lambda (the expectation of the number of false measurements in the unit space); 3) Each sensor will have a different detection probability P D due to performance differences, i.e. the sensor does not guarantee that the target can be captured, which detection probability is known a priori.
Specific examples:
1. A fixed reference coordinate is assigned to the sensor nodes in space and to the target location, and a uniform reference direction is assigned to the azimuth measurement. Each sensor returns an azimuth measurement and a time delay measurement of the target, and there is a measurement error related to the performance of the sensor node. And measuring and converting by utilizing the geometric relation of the transmitting source, the target and the receiver, and converting the azimuth and time delay measurement into corresponding two-dimensional Cartesian coordinates.
2. The invention regards the multi-sensor static fusion problem as the object tracking problem in the dimension of the sensor, so that the time interval of each scanning in the scene is 0, the motion state of the object in the observation range of the sensor is static, no disappearance and proliferation of the object exist, but new objects possibly exist in the observation range of the sensor, mathematical modeling is carried out, and a corresponding object state model and an observation model are created.
3. In order to process the target measurement obtained in the step 1, a Gaussian mixture probability hypothesis density filtering algorithm is selected to track a 'static' target according to the target model in the step 2, and the 'static' target is used as a high-speed and effective multi-target tracking algorithm, and the GMPHD filtering algorithm has a good processing result and greatly improves the operation efficiency. And pruning and merging Gaussian components in GMPHD filtering results, and extracting the average value of Gaussian components with weights exceeding a threshold value, namely a final merging result.
4. The fusion result of the invention under a relatively visual environment is provided through computer simulation, the modeling method and the static fusion process of the invention are demonstrated, and the static fusion result of a common method under the same simulation environment is provided for comparison.
For a distributed underwater sensor network, there are 9 sensor nodes in space, of which 1 sensor node is the transmitting source and the positions (-5000 m ) and the other 8 sensor nodes are the receivers and the positions (-5000 m, -0) (-5000 m,5000 m), (0, -5000 m), (0, 0), (0, 5000 m), (5000 m, -5000 m), (5000 m, 0), (5000 m ) respectively. The sensor node measurement accuracy is higher, the azimuth estimation deviation standard deviation is set to be 1 degree, and the time delay estimation deviation standard deviation is set to be 0.01s. In the observation area, a single target moves along a straight line at a uniform speed, the appearance time of the target is 0s, the disappearance time is 3600s, clutter is in Rayleigh distribution, the detection threshold is 7dB, the sound speed is 1500m/s, and the sensor scans every 60 s. The scene simulation is shown in fig. 2 (a), wherein circles are sensor nodes, black dots are all measuring points detected by the sensor, and the black dots comprise target-derived and clutter-derived. GMPHD parameters set as: target survival probability P S,n =1, detection probability P D,n =0.9. The pruning shear parameter t=10 -5,U＝100,Jmax =100. The static fusion result by using the method is shown in fig. 2 (b), wherein circles are sensor nodes, black straight lines are real tracks, and points around the black straight lines are measurement points after fusion.
In order to characterize the advantages of the method, the root mean square error of 100 Monte Carlo tests is used for measuring the positioning accuracy of the position estimation after static fusion of the method and the grid screening method of the common method. The behavior of the two methods at different measurement errors is shown in fig. 3 (a) and fig. 3 (b). In fig. 3 (a), the fixed azimuth measurement error (standard deviation) is 1 °, the distance measurement error (standard deviation) is changed, and 100 monte carlo experiments are used each time to count the root mean square error; in fig. 3 (b), the fixed distance measurement error (standard deviation) was 20m, the azimuth error (standard deviation) was changed, and 100 monte carlo experiments were used each time to count the root mean square error. In addition, the running time of the GMPHD static fusion method and the grid screening static fusion method in the same simulation environment is respectively as follows: 9.071s and 69.756s. From the figure, the static fusion method based on GMPHD has definite advantages in fusion positioning accuracy, and the operation efficiency is greatly improved.
Claims (2)
1. The static fusion method based on the Gaussian mixture probability hypothesis density filter is characterized by comprising the following steps of:
step 1: assuming that N sensors which independently work are included in a multi-source target measurement information fusion scene, and establishing a Cartesian coordinate system by taking any one sensor as an origin; the sensor n returns m n measurements of the target to form a measurement set Z n,a is the a-th measurement of the target returned by sensor N, n=1, 2,..n is the serial number of the sensor, a=1, 2,..m n is the measurement serial number of the target;
assuming that the measurement of any pair of targets is two-dimensional vector z= (tau, theta), wherein tau is time delay, theta is azimuth, and the measurement errors of tau and theta are uncorrelated and obey Gaussian distribution, and the variances of the measurement errors are respectively And/>The two-dimensional Cartesian coordinate of z is z= [ x, y ] and the covariance matrix is/>
Step 2: the method for establishing the state model of the sensor for observing the static target comprises the following steps:
Xn+1＝FXn+wn (1)
Wherein X n and X n+1 are target states in the observation ranges of the nth and the (n+1) th sensors, the process noise w n is subjected to Gaussian distribution w n:N (0, Q), and the state transition matrix F and the process noise matrix Q are respectively a two-dimensional identity matrix I and a two-dimensional identity matrix 0;
the method for establishing the observation model for observing the static target by the sensor comprises the following steps:
Zn＝HXn+yn (2)
Wherein the observation matrix H is a two-dimensional identity matrix I, and the measurement noise y n obeys Gaussian distribution y n:N(0,Rn),Rn to be a measurement noise covariance matrix;
Step 3: acquiring Gaussian component parameters of the improved GMPHD filter;
Step 3-1: defining J n as the target number in the observation range of the nth sensor;
step 3-2: representing the target states within the nth sensor observation range as a finite set States of the 1 st to the J n th targets within the observation range of the nth sensor, respectively; the target states within the n-1 th sensor observation range are represented as a finite set X n-1, each target state X n-1∈Xn-1 continues to survive within the n-th sensor observation range with a probability of p S,n =1, and the transition probability density from the target state X n-1 to the target state X n is F n|n-1 (x|ζ) =n (X; fζ, Q), where ζ represents the previous target state and X represents the target state;
Step 3-3: assuming that no new target proliferated from the n-1 th sensor observation range exists in the n-th sensor observation range, the naturally occurring new target has an intensity of γ n(x),γn (x) which is a gaussian mixture model;
step 3-4: given a target state x n∈Xn, assuming that the probability of being detected by a sensor is P D,n(xn)＝PD, and the probability of being missed is 1-P D; under the condition that the target is detected, obtaining an observation value z n from x n, wherein the probability density is g n (z|ζ) =n (z; hζ, Σ), and z represents the observation value; a set of spurious measurements received by the sensor is defined as measurements for which k n(z),kn (z) obeys poisson distribution, independent of the target;
step 3-5: from the assumptions of steps 3-1 to 3-4, a Gaussian mixture model is obtained with the posterior intensity of the observed object in the n-1 th sensor observation range as follows:
where J n-1 denotes the number of targets in the observation range of the n-1 th sensor, Is the Gaussian mixture model parameter of the j-th target posterior intensity in the n-1-th sensor observation range: respectively weight, mean and covariance;
the predicted intensity of the observation target in the n-th sensor observation range is:
vn|n-1(x)＝vS,n|n-1(x)+γn(x) (4)
the posterior intensity of a target that survives continuously within the n-th sensor observation range with probability p S,n =1 is:
Wherein,
The predicted intensity within the nth sensor observation range is expressed by the following gaussian mixture model:
wherein J n|n-1 is the measured quantity from the new-born target and the still-alive target within the observation range of the nth sensor, Is the Gaussian mixture model parameter of the jth target predicted intensity in the observation range from the nth-1 sensor to the nth sensor: respectively weight, mean and covariance;
therefore, the posterior intensity of the observation target in the observation range of the nth sensor is
Wherein,
Wherein,Is the jth target process noise;
finally, obtaining a Gaussian mixture model component { w n,mn|n,Pn|n } of the updated target posterior intensity in the observation range of the nth sensor;
Step 4: and (3) performing pruning and merging treatment on the Gaussian component { w n,mn|n,Pn|n } obtained in the step (3):
Pruning shears: discarding Gaussian components with weights lower than a preset weight threshold or reserving a given number of Gaussian components from large to small according to weights;
combining: when the distance between the two Gaussian components is smaller than a preset threshold value, combining the two Gaussian components into one according to a minimum mean square error criterion;
and finally, extracting the mean value m of the Gaussian components with weights exceeding a given threshold value, and taking the obtained multi-target position estimation as a static fusion result.
2. A static fusion method based on gaussian mixture probability hypothesis density filters according to claim 1, wherein t= -5,U＝100,Jmax =100.
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