CN112748416B - Multi-node distributed GM-PHD fusion method for one-order propagation - Google Patents
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Abstract
The invention discloses a multi-node distributed GM-PHD fusion method of first-order propagation, which provides a multi-sensor distributed fusion algorithm framework and realizes a multi-node distributed GM-PHD fusion algorithm of first-order propagation under the condition that each moment of a sensor only carries out single communication with an adjacent sensor on the basis of a Gaussian mixture probability hypothesis density estimator (GM-PHD) in order to study fusion logic under a distributed structure. The invention has the advantages of clear configuration structure and strong robustness, and can be widely applied to the field of multi-target tracking.
Description
Technical Field
The invention relates to the field of multi-sensor fusion multi-target tracking based on multi-sensor limited coverage/limited link, in particular to a multi-sensor multi-target distributed fusion tracking method based on probability hypothesis density filtering, which is used for establishing the multi-sensor multi-target distributed tracking method, realizing the distributed fusion and tracking of multi-sensors on multi-targets and relieving the problem of high redundancy of fusion information under a distributed structure.
Background
Multi-objective tracking is to jointly estimate the number of unknown time-varying objectives and the multi-objective correspondence state by measuring. In multi-target tracking, there are adverse factors such as unknown number of targets, unknown detection probability, large measurement error, and even resistance interference, and multi-target tracking becomes a challenging problem. Most of the traditional multi-target tracking algorithms are based on data association, membership between targets and measurement needs to be established, and when the number of targets is large, the algorithms have NP difficult problems. Typical data association methods such as Nearest Neighbor (NN), probability data association (Probabilistic Data Association, PDA), joint probability data association (Joint Probabilistic Data Association, JPDA), etc. often assume that the number of targets is constant and known, and in reality this condition is difficult to satisfy. In recent years, limited set of statistical theory (Finite Sets Statistics, FISST) has received extensive attention from subjects in the field of object tracking as an engineering friendly bayesian theoretical tool. FISST forms a set of all single-target state spaces, and observations obtained from a single observation may also form a set. However, since the multi-objective state space and the observation space are infinitely dimensional, the optimal multi-objective bayesian filter is difficult to apply in practice. Aiming at the problem, mahler proposes to solve the problem of multi-target tracking by using a Random Finite Set (RFS) theory, and an algorithm converts complex operation of a multi-target state space into operation in a single-target state space, so that the problem of complex data association in multi-target tracking is effectively avoided, filtering precision is ensured, and meanwhile, the real-time performance of the algorithm is improved. In the field of Multi-Target Tracking (MTT), filtering algorithms based on the random finite set (Random Finite Set, RFS) theory are becoming a hot spot of research in recent years. The RFS method deals with the MTT problem from the limited set point of view, and represents the multi-objective state as a random set, where the elements and the number of elements in the set represent the state vector of the objective and the number of objectives that may occur, respectively. The MTT method based on RFS can effectively avoid the data association process of the traditional algorithm, has good engineering application prospect, is more and more valued by students at home and abroad, and mainly comprises a probability hypothesis density (Probability Hypothesis Density, PHD) algorithm and a potential probability hypothesis density (CPHD) algorithm. There are two implementations of PHD filters, one GMPHD filter based on a Gaussian Mixture (GM) model and another SMCPHD filter based on a Sequential Monte Carlo (SMC) model.
In the field of multi-sensor information fusion, research on a centralized type and a distributed type fusion structure is very mature, a great amount of research results exist at home and abroad, the two fusion structures are both in a central processing mode, and the basic principle of the processing mode is as follows: the fusion center designated by the command system is the only fusion processing unit in the data link network, the fusion center collects and processes local data and remote data, after comprehensive processing to form a unified situation, the unified situation is issued to other members in the data link network, and the main disadvantage of the central processing mode is that battlefield sensing capability of the whole data link network is lost when the fusion center unit works abnormally, so that instability of the system is increased. While another fusion structure: the distributed fusion structure is a centerless processing mode. In the centerless processing mode, each member node broadcasts the detected information in the network and simultaneously receives the target detection information issued by other nodes. Each node carries out comprehensive processing on local data detected by the node and remote data of other nodes received from a data network, and each node can form a comprehensive processing result of target information in the whole network range. In recent years, data link technology in the field of military communication shows a high-speed development trend, and is applied to more and more communication data links of an airborne platform, the communication transmission rate is faster and the communication bandwidth is larger and larger. This has led to an increasing enrichment of network structure related studies like decentralized such centerless.
Disclosure of Invention
For the influence of the limited coverage/limited link characteristics of the multi-sensor, the sensor cannot observe all existing targets (including false alarms) in the global prevention domain of the system by itself; the invention provides a multi-node distributed GM-PHD fusion method for first-order propagation, which can ensure the estimation accuracy of targets in a monitoring area and maintain a track under the condition of limited coverage/limited linkage of a sensor. In order to achieve the above purpose, the invention adopts the following technical scheme:
(1) Constructing a multi-sensor multi-target tracking scene, initializing a target motion model, and setting related parameters of target motion, including process noise of target motion and measurement noise of a sensor;
(2) Each sensor applies a gaussian mixture PHD filtering algorithm prediction part under a distributed structure.
(3) Each sensor applies a gaussian mixture PHD filtering algorithm update section under a decentralized architecture.
(4) The sensors perform information interaction among the sensors according to communication rules under the decentralized framework;
(5) The sensors respectively perform information fusion according to fusion rules under the decentralized frame;
(6) And (3) taking the final result of the step (5) as the input of the next moment, repeating the steps (2) to (6), and iterating all the moments to obtain the final estimation result.
The invention has the beneficial effects that: for the influence of multi-sensor detection ranges and communication limitations. Under the condition that each fusion period of the sensor is communicated with a neighbor sensor only once, the invention provides a set of complete multi-sensor distributed fusion rules, and a multi-node distributed GM-PHD fusion algorithm of first-order propagation is realized by combining a probability hypothesis estimation filter (PHD) under a limited set. The invention has the advantages of clear configuration structure and strong robustness, and can be widely applied to the field of multi-target tracking.
Drawings
FIG. 1 is a decentralized fusion single sensor approach framework;
FIG. 2 is a block diagram of a match fusion method;
FIG. 3 is a simulation result of a distributed target tracking sensor No. 1;
FIG. 4 is a simulation result of a distributed target tracking sensor No. 4;
Detailed Description
The following describes specific embodiments of the present invention in detail with reference to the technical schemes and drawings.
As shown in fig. 1, a multi-sensor distributed fusion method based on GM-PHD is specifically as follows:
(1) Constructing a multi-sensor multi-target tracking scene, initializing a target motion model, and setting related parameters of target motion, including process noise of target motion and measurement noise of a sensor; wherein the measurement of the sensor is from the target or from clutter;
establishing a motion model of a target: x is x k+1,i ＝f k,k+1 (x k,i )+w k,i
Where k represents a discrete time variable, i represents the sequence number of the target, i=1, 2, ··, N, x k,i Representing the state variable, w, of the ith target at time k k,i Representing a mean value of zero and a variance of Q k Gaussian white noise of (f) mapping f k|k+1 Representing the state transition of the ith target from time k to time k+1State transition equation of (2); state variable of the ith target at time k wherein ,(xi,k ,y i,k ) For the position component of the ith target in the monitored space at time k,a velocity component in the monitored space for the ith target at time k;
if the measurements of the sensor are from the target, the measurements of the sensor conform to the following sensor measurement model:
assuming s sensors, for any sensor j, its coordinates are (x j ,y j ) The detection range is r, and the P is not less than 0 for any target existing in the radius range of the sensor at the moment k d The detection probability is more than or equal to 1 and less than or equal to 0 and less than or equal to P d,j And is less than or equal to 1. Then sensor j is aligned with object x at time k k,i The observation equation is formed as follows,
wherein ,zk,j Is the observation vector, g k,j Is an observation function, v k,i,j Represents the observation error, d ij Representing the linear distance of the target from the observed sensor coordinates. It is generally assumed that the observed error obeys zero mean and the covariance matrix R j A known Gaussian random process, wherein process noise and measurement noise at each moment are mutually independent; the observation set of the sensor j at the moment k isCumulative observation set +.>
If the sensor measurements are from clutter, the sensor measurements conform to the following clutter model:
in the following description! Representing factorization, n k For the k-time monitoring of the number of clutter in the space domain, it is assumed that the number of clutter follows a poisson distribution with intensity λ, ρ (n) k ) For clutter number n k Probability function, y of l For the position state of the first clutter, ψ (x) is the volume of the monitored space, q (y) l ) Is the probability of the first clutter occurrence;
(2) Each sensor applies a gaussian mixture PHD filtering algorithm prediction part under a distributed structure.
The prediction process of the Gaussian mixture PHD filtering algorithm is specifically as follows:
1) Predicting a new-born target
in the formula ,represents the ith b The a priori weight of the individual target at time k-1,/->Represents the ith b Predictive weights of the targets at the time k; />Represents the ith b A priori state value of the individual target at time k-1,/->Represents the ith b Predicted state values of the targets at the moment k; />Represents the ith b A priori covariance of the individual targets at time k-1,/->Represents the ith b Prediction covariance of each target at k time, J γ,k Representing the predicted number of new targets;
2) Predicting existing targets
in the formula ,represents the ith s Weights of the individual targets at time k-1, p s Representing the survival probability of the target; />Show the ith s Predicting weights of the targets at the moment k; />Represents the ith s A priori state value of the individual target at time k-1,/->Represents the ith s Predicted state value of each target at k time，F k-1 A state transition matrix representing the target at time k-1; />Represents the ith s A priori covariance of the individual targets at time k-1,/->Represents the ith s Predictive covariance of the individual targets at time k; j (J) k-1 Representing the number of predicted existing targets, Q k-1 Representing the process noise covariance at time k-1, F' k-1 Represents F k-1 Is a transpose of (2);
assume that at time k-1, for sensor j, the coordinates areThe target Gaussian mixture particle group which has been obtained with the posterior can be classified as the particle +.>And particle outside the defense area-> wherein />Weight of the ith particle representing a posterior Gaussian mixture particle set in the jth sensor defense area at time k-1, +.>Mean value of ith particle of a posterior Gaussian mixture particle group in jth sensor defense area at moment k-1>Error covariance representing ith particle of posterior Gaussian mixture particle set in jth sensor defense area at k-1, J in,k-1 Represents the number of particles contained in the particle set in the sensor protection zone at time k-1, < ->The confidence of the ith particle representing the gaussian particle set in the guard area of the jth sensor,a label representing the ith particle of the gaussian particle set in the defense area of the jth sensor, and the parameter with the subscript out represents the particle set outside the defense area; different prediction logic is performed for the intra-defense and the extra-defense particles. The particles in the defense area are predicted in one step, the particle label and the particle confidence conf of the particles are prevented from being changed, the state before particle prediction is inherited, the particles outside the defense area are extrapolated in one step, the confidence of the particles outside the defense area is reduced after extrapolation treatment, and the particles are multiplied by a reduction coefficient alpha, so that the alpha can be flexibly adjusted according to actual conditions:
conf i j ＝α·conf i j ,i＝1,...,J out,k-1
after extrapolation, the particles need to judge the defense area again, and the judgment of the defense area is based on whether the linear distance between the current sensor position and the particle state position exceeds the detection range of the sensor.
And d represents the Euclidean straight line distance between the current particle and the sensor, and the particle set which is judged to be in the defense area is put into the defense area for subsequent GM-PHD measurement and update.
(3) Each sensor applies a gaussian mixture PHD filtering algorithm update section under a decentralized architecture.
The updating process of the Gaussian mixture PHD filtering algorithm is specifically as follows:
priori PHD intensity Density D k|k-1 The gaussian sum form of (c) is:
J k|k-1 ＝J γ,k +J k-1
wherein N (·; x, P) represents a Gaussian distribution with mean of x and covariance of P, J k|k-1 The number of prediction targets at the moment k is represented;
the posterior PHD intensity density D at time k k The gaussian sum form of (c) is:
in the formula
in the formula ,representing the probability of detection of a tracked object by a sensor j at time k, and κ k (z) represents clutter intensity in the monitored space.
The updating operation is only carried out on the particle sets in the defense area, the particle sets outside the defense area are kept unchanged, the updating mode is a GM-PHD updating mode, and the GM-PHD particle components in the defense area are updated by using the measurement of the sensor.
(4) The sensors perform information interaction among the sensors according to communication rules under the decentralized framework;
the sensor obtains Gaussian particle set in the defense area of k moment posterior through updatingThe resulting subset Gao Sili of the defense area is then combined with the subset of gaussian particles outside the defense area into a set:
wherein
J k ＝J in,k +J out,k
wherein Jin ,J out Respectively representing the particle number of the particle group in the sensor defense area and the particle number of the particle group outside the sensor defense area, J k Representing the total particle count of particle sets in and out of the sensor's defense area as the set inf to be transmitted by sensor j j When entering a communication stage, the sensor j communicates with the adjacent sensor, and sends a set to be sent of the sensor j and a set to be sent of other sensors.
(5) The sensors respectively perform information fusion according to fusion rules under the decentralized frame;
as shown in fig. 2, at time k, the sensor j has obtained a posterior gaussian mixture particle set of a sensor in communication relation with the sensor j, and the multi-sensor posterior gaussian mixture particle is matched and fused, and the matching algorithm specifically comprises the following steps:
1) Let the Gaussian mixture particle set of the current sensor j be the reference set
2) Setting a distance threshold lambda k The threshold may be set based on a priori information
3) Each particle in the GM-PHD particle set of all sensor posterior tests received by the sensor j is sequentially combined with M according to the sensor k|k Comparing the concentrated particles, calculating the minimum Euclidean distance, and if the minimum Euclidean distance meets the threshold value condition, comparing the particles with M k|k Corresponding particles in the set match, and if a matching particle has been matched by another particle of the current sensor, it is checked whether the other particle is matched, while the particle is incorporated into the particle set M k|k Otherwise, particlesI.e. the current non-matching particle, while incorporating the particle into the particle set M k|k 。
By means of a matching algorithm, the posterior gaussian particles of all sensors are finally merged into a reference particle set M k|k And for any set of matching particles, each sensor contributes at most one particle. For convenience of description, recordFor a set of matching particles from multiple sensors, +.>conf n ,label n The weight, state, covariance matrix, confidence and sensor label of the n-th particle after matching are represented respectively.
The fusion mode adopts covariance fusion for convenience in expressionTo represent the particle group to be fused, the specific fusion formula is as follows:
wherein ,representing the weight of the particles obtained after fusing a set of matching particles,/->As an intermediate variable, the number of which is,representing the state of the particles after fusion, +.>Representing the inverse of the covariance matrix of the fused particles.
Updating mode of confidence and label carried by particle after fusion: the confidence coefficient is the highest value of the confidence coefficient in the fusion particle, and the label is the current sensor number.
The global posterior Gaussian mixture particle set is obtained after fusion, the defense area is required to be re-judged, and the posterior Gaussian mixture particle set after the defense area is judged and dividedAnd (3) withFor filtering at the next instant and state extraction.
(5) And (3) taking the final result of the step (4) as the input of the next moment, repeating the steps (2) to (5), and iterating all the moments to obtain the final estimation result.
The fusion tracking result of the single sensor of the method is shown in fig. 3 and fig. 4.
Claims (2)
1. The multi-node distributed GM-PHD fusion method for the first-order propagation is characterized by comprising the following steps of:
step one: constructing a multi-sensor multi-target tracking scene, initializing a target motion model, and setting related parameters of target motion, including process noise of target motion and measurement noise of a sensor; wherein the measurement of the sensor is from the target or from clutter;
establishing a motion model of a target: x is x k+1,i ＝f k|k+1 (x k,i )+w k,i
Where k represents a discrete time variable, i represents the sequence number of the target, i=1, 2, …, N, x k,i Representing the state variable, w, of the ith target at time k k,i Representing a mean value of zero and a variance of Q k Gaussian white noise of (f) mapping f k|k+1 (x k,i ) A state transition equation representing state transition of the ith target from the k time to the k+1 time; state variable of the ith target at time k wherein ,(xk,i ,y k,i ) For the position component of the ith target in the monitored space at time k,a velocity component in the monitored space for the ith target at time k;
if the measurements of the sensor are from the target, the measurements of the sensor conform to the following sensor measurement model:
assuming s sensors, for any sensor j, its coordinates are (x j ,y j ) The detection range is r, and the detection probability of any target existing in the radius range of the sensor at the moment k is 0.ltoreq.P d,j Is less than or equal to 1; then sensor j is aligned with object x at time k k,i The observation equation is formed as follows,
wherein ,zk,j Is the observation vector, g k,j Is an observation function, v k,i,j Represents the observation error, d ij Representing the linear distance between the target and the coordinates of the observation sensor; assume that the observed error obeys zero mean and the covariance matrix R j A known Gaussian random process, wherein process noise and measurement noise at each moment are mutually independent; the observation set of the sensor j at the moment k isCumulative observation set +.>
If the sensor measurements are from clutter, the sensor measurements conform to the following clutter model:
in the following description! Representing factorization, n k For the k-time monitoring of the number of clutter in the space domain, it is assumed that the number of clutter follows a poisson distribution with intensity λ, ρ (n) k ) For clutter number n k Probability function, y of l For the position state of the first clutter, ψ (x) is the volume of the monitored space, q (y) l ) Is the probability of the first clutter occurrence;
step two: constructing a communication and fusion framework under a distributed structure;
assume that at time k-1, for sensor j, the coordinates areThe target Gaussian mixture particle group which has been obtained with the posterior can be classified as the particle +.>And particle outside the defense area-> wherein />Weight of the ith particle representing a posterior Gaussian mixture particle set in the jth sensor defense area at time k-1, +.>Mean value of ith particle of a posterior Gaussian mixture particle group in jth sensor defense area at moment k-1>Error covariance representing ith particle of posterior Gaussian mixture particle set in jth sensor defense area at k-1, J in,k-1 Represents the number of particles contained in the particle set in the sensor protection zone at time k-1, < ->The confidence of the ith particle representing the gaussian particle set in the guard area of the jth sensor,a label representing the ith particle of the gaussian particle set in the defense area of the jth sensor, and the parameter with the subscript out represents the particle set outside the defense area;
1) Prediction logic
Executing different prediction logic for the particles in the defense area and the particles outside the defense area; GM-PHD prediction is carried out on particles in the defense area, the label of the particles in the defense area is unchanged from the confidence level conf of the particles, the state before particle prediction is inherited, the particles outside the defense area are extrapolated by one step, the confidence level of the particles outside the defense area is reduced after extrapolation treatment, and the particles are multiplied by a reduction coefficient alpha:
after extrapolation, the particles need to judge the defense area again, and the judgment basis of the defense area is whether the linear distance between the current sensor position and the particle state position exceeds the detection range of the sensor;
d represents the Euclidean straight line distance between the current particle and the sensor, and the particle set which is judged to be in the defense area is put into the defense area to carry out subsequent GM-PHD measurement and update;
2) Update logic
The updating operation is only carried out on the particle sets in the defense area, the particle sets outside the defense area are kept unchanged, the updating mode is a GM-PHD updating mode, and the GM-PHD particle components in the defense area are updated by using the measurement of the sensor;
3) Communication logic
The sensor obtains Gaussian particle set in the defense area of k moment posterior through updatingThen the obtained subset Gao Sili in the defense area and the Gaussian particle set outside the defense area are +.>And is a set of:
J k ＝J in,k +J out,k
wherein Jin ,J out Respectively representing the particle number of the particle group in the sensor defense area and the particle number of the particle group outside the sensor defense area, J k Representing the total particle count of particle sets in and out of the sensor's defense area as the set inf to be transmitted by sensor j j When entering a communication stage, the sensor j communicates with an adjacent sensor, and sends a set to be sent of the sensor j and a set to be sent of other sensors;
4) Fusion logic
At the moment k, the sensor j obtains a posterior Gaussian mixture particle set of a sensor with a communication relation, and the posterior Gaussian mixture particle set of the multiple sensors is matched and fused, wherein the matching algorithm comprises the following specific steps:
1) Set current sensingGaussian mixture particle set of bin j is the benchmark set
2) Setting a distance threshold lambda k The threshold is set according to prior information;
3) Each particle in the GM-PHD particle set of all sensor posterior tests received by the sensor j is sequentially combined with M according to the sensor k|k Comparing the concentrated particles, calculating the minimum Euclidean distance, and if the minimum Euclidean distance meets the threshold value condition, comparing the particles with M k|k Corresponding particles in the set match, and if a matching particle has been matched by another particle of the current sensor, it is checked whether the other particle is matched, while the particle is incorporated into the particle set M k|k Otherwise, particlesNamely, the current non-matching particle is obtained, and the particle is deleted at the same time;
by means of a matching algorithm, the posterior gaussian particles of all sensors are finally merged into a reference particle set M k|k And for any set of matching particles, each sensor contributes at most one particle; recording deviceFor a set of matching particles from multiple sensors, +.>Respectively representing the weight, state, covariance matrix, confidence and sensor label of the n-th particle after matching;
the fusion mode adopts covariance fusion to realizeTo represent the particle group to be fused, the specific fusion formula is as follows:
wherein ,representing the weight of the particles obtained after fusing a set of matching particles,/->Is an intermediate variable, +.>Representing the state of the particles after fusion, +.>An inverse matrix representing the covariance matrix of the fused particles; updating mode of confidence and label carried by particle after fusion: the confidence coefficient is the highest value of the confidence coefficient in the fusion particles, and the label is the number of the current sensor;
the global posterior Gaussian mixture particle set is obtained after fusion, the defense area is required to be re-judged, and the posterior Gaussian mixture particle set after the defense area is judged and dividedAnd (3) withThe two particle sets are used for extracting the state at the current moment and transmitting the state to the next moment, and the next moment sensor uses the two particle sets to continue the processes of prediction, updating, communication and fusion, so that iteration is formed.
2. The first-order propagated multi-node decentralized GM-PHD fusion method of claim 1, wherein: updating or predicting through a GM-PHD filtering algorithm; the method comprises the following steps:
1) Predicting a new-born target
in the formula ,represents the ith b The a priori weight of the individual target at time k-1,/->Represents the ith b Predictive weights of the targets at the time k; />Represents the ith b A priori state value of the individual target at time k-1,/->Represents the ith b Predicted state values of the targets at the moment k; />Represents the ith b A priori covariance of the individual targets at time k-1,/->Represents the ith b Prediction covariance of each target at k time, J γ,k Representing the predicted number of new targets;
2) Predicting existing targets
in the formula ,represents the ith s Weights of the individual targets at time k-1, p s Representing the survival probability of the target; />Show the ith s Predicting weights of the targets at the moment k; />Represents the ith s A priori state value of the individual target at time k-1,/->Represents the ith s Predicted state values of each target at time k, F k-1 A state transition matrix representing the target at time k-1; />Represents the ith s A priori covariance of the individual targets at time k-1,/->Represents the ith s Predictive covariance of the individual targets at time k; j (J) k-1 Representing the number of predicted existing targets, Q k-1 Representing the process noise covariance at time k-1, F k ' -1 Represents F k-1 Is a transpose of (2);
3) Updating
Priori PHD intensity Density D k|k-1 The gaussian sum form of (c) is:
J k|k-1 ＝J γ,k +J k-1
wherein N (·; x, P) represents a Gaussian distribution with mean of x and covariance of P, J k|k-1 The number of prediction targets at the moment k is represented;
the posterior PHD intensity density D at time k k The gaussian sum form of (c) is:
in the formula
in the formula ,representing the probability of detection of a tracked object by a sensor j at time k, and κ k (z) represents clutter intensity in the monitored space;
4) Pruning shears, combining
The particles with too small weights of the posterior GM-PHD particles are eliminated, so that the calculation load is reduced, and the explosion of the calculated amount after multiple iterations is prevented;
5) Status output;
and outputting target estimation information.
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