Passive tracking method of underwater complex moving targets based on IMM-GMF

Abstract

The present invention relates to the technical field of passive tracking of moving targets, and provides a method for passive tracking of underwater complex moving targets based on IMM-GMF. The method comprises generating initial GM particles at time k, mixing interaction and prediction, updating and correcting the predicted GM particles, obtaining posterior GM particles at time k, and obtaining the target state estimation value at time k. In the step of generating the initial GM particles at time k, the posterior GM particles of N simple models at time k-1 are obtained as the initial GM particles of N model filters at time k. The Gaussian mixture model in the method represents the target state transition probability density with a complex motion form by the weighted sum of multiple Gaussian terms, and achieves filtering estimation by recursively inferring the GM particles composed of Gaussian term weights, means and covariances.

Description

Technical Field

[0001] The present disclosure relates to the technical field of passive tracking of moving targets, and in particular to a passive tracking method for underwater complex moving targets based on IMM-GMF. Background Art

[0002] Passive tracking has good concealment, easy to obtain azimuth measurement and high reliability, and is widely used in ocean monitoring and underwater exploration. Passive tracking based on pure bearings target motion analysis (TMA), also known as pure bearings target tracking (BOT), is an important technical means for underwater target tracking.

[0003] The passive tracking system is a highly nonlinear weakly observable system with serious nonlinear problems. Existing technologies often use extended Kalman filters (EKF) and unscented Kalman filters (UKF) to solve the nonlinear filtering problem of passive tracking. Although EKF and UKF can track moving targets with unchanged state models, their algorithm performance deteriorates seriously when the target maneuvers and the state model changes.

[0004] For the problem of tracking maneuvering targets with changing motion forms, the literature [Blom and Bar-Shalom, IEEE Transactions on Aerospace and Electronic Systems, 1989, 16(2), 296-300] proposed an interactive multi-model (IMM) parallel filtering algorithm with Markov transition coefficients based on the generalized pseudo-Bayesian algorithm. IMM is used to describe the motion state transition and the IMM filter is used to track the maneuvering target. Among similar methods, the IMM filter has better performance and has become the mainstream direction of maneuvering target tracking. However, due to the limitation of the number of models in the model set, IMM is difficult to express complex target motion forms.

[0005] In complex underwater environments, due to the influence of uncertain factors such as system errors and interference, there are still problems such as clutter and false alarms. For the problem of target tracking in a clutter background, people mainly use data association technology to solve it. The literature [Bar-Shalom Y and Jaffer AG, the 11th IEEE Conf. On Decision and Control, 1972,243-247] proposed the probabilistic data association algorithm (Probabilistic Data Association, PDA), and the literature [Bar-Shalom Y and Tse E, Automation, 1975, 11(9), 451-460] proposed the joint probabilistic data association algorithm (Joint Probabilistic Data Association, JPDA). Data association technology regards each valid echo in the tracking gate as a candidate echo, but the probability of each echo originating from the target is different, and the candidate echo is weighted according to the probability to correct the state prediction. Data association does not completely eliminate clutter, and the tracking accuracy is limited.

[0006] Passive maneuvering target tracking based on pure bearings TMA has achieved fruitful results and is widely used in underwater target tracking. However, there are still technical deficiencies in marine monitoring and underwater exploration applications, which are manifested as follows: the commonly used single-model EKF, UKF and other nonlinear filters are mainly used to track moving targets whose state models remain unchanged, and it is difficult to track maneuvering targets whose state models change. The IMM filter uses multiple parallel and interactive single models in the model set to represent the motion form of the maneuvering target, and synthesizes the results to estimate the state, which can track the maneuvering target. However, when the target has a complex motion form, it is limited by the number of single models in the model set, and the interactive multi-model is difficult to represent the complex target state, resulting in reduced IMM filter estimation accuracy or even divergence. In addition, the weight coefficient for model synthesis is the model probability calculated by the likelihood function update. In passive detection, the measurement is only a pure angle parameter, and its likelihood function is uncertain. The use of uncertain likelihood functions to update the weight coefficient often has a large error, resulting in a serious deterioration in the estimation performance of the IMM filter. The introduction of data association technology is intended to solve the problem of target tracking in a clutter background, rather than the problem of maneuvering target tracking. In addition, data association predicts the candidate echoes according to the probability weighted correction state, which essentially still contains clutter, affecting the tracking accuracy.

[0007] In view of the many problems existing in existing theories and methods, it is of great significance to conduct in-depth research on passive tracking of complex moving targets in clutter background. The application demand in ocean monitoring and underwater exploration is very urgent. Summary of the invention

[0008] In order to solve the technical problem of poor passive tracking effect of underwater maneuvering targets, the present disclosure provides a passive tracking method for underwater complex moving targets based on IMM-GMF.

[0009] The passive tracking method of underwater complex moving targets based on IMM-GMF provided by the present disclosure includes generating initial GM particles at time k, mixing interaction and prediction, updating and correcting the predicted GM particles, obtaining the posterior GM particles at time k, and obtaining the target state estimation value at time k. In the step of generating the initial GM particles at time k, obtain the posterior GM particles of N simple models at time k-1 As the initial GM particle of N model filters at time k, each simple model includes at least one posterior GM particle , and each simple model represents a form of motion, where 1≤n≤N, 1≤i≤ , is the number of posterior GM particles under model hypothesis n at time k-1. In the mixing interaction and prediction step, the initial GM particles at time k are mixed in each model filter to obtain the predicted GM particles predicted by each model filter according to its own model. , and obtain the predicted probability density function of the model hypothesis n at time k , is the number of predicted GM particles under model assumption n at time k. In the step of obtaining the a posteriori GM particles at time k, the measurement equation is constructed based on the position of the observation platform in the global coordinate system and the observation angle to obtain the azimuth measurement z at time k. k ; Measure z according to the orientation k and the measurement equations for predicting GM particles Update and obtain the updated GM particle at time k ; Update GM particles based on time k Get the posterior GM particle at time k ; Get the estimated value of the target state at time k : Using the weights of the posterior GM particles of all models at time k The mean Perform weighted averaging to obtain the estimated state of the complex moving target at time k .

[0010] Specifically, we construct a position measurement z in the local coordinate system representing the time k. k With target status The measurement equation of the corresponding relationship is In the formula, is the translation vector, is the rotation matrix of the state, is the coordinate system rotation matrix, and are the position and observation angle of the observation platform in the global coordinate system, v k is the observation noise, ( ) represents a block diagonal matrix. According to the orientation measurement z k And the measurement equation, calculate the gain matrix and the likelihood , and calculate the updated mean and covariance , and then obtain the updated probability density function of the model hypothesis n at time k :

[0011] ,in, are the azimuth measurements obtained from the observation platform at time k A collection of is to obtain the azimuth measurement z k The detection probability of the passive sensor is express is the probability of clutter, It is a position measurement and the likelihood value of the i-th predicted GM particle.

[0012] In some embodiments, the composite function derivation method is used in the process of updating the predicted GM particles. Specifically, the composite function is derived for the measurement equation to obtain the Jacobian matrix : .in, ; Based on the Jacobian matrix Calculate the gain matrix and likelihood , and calculate the updated mean and covariance ,

[0013] , , , .in, is the observation noise covariance.

[0014] In some other embodiments, an unscented transformation method is used in the process of updating the predicted GM particles. Sampling is performed to obtain sampling points; the predicted measurement is obtained based on the sampling points and the measurement equation and the innovation covariance matrix of the nonlinear measurement ; Use predictive measurement and the innovation covariance matrix Calculate the gain matrix and likelihood , and calculate the updated mean and covariance .

[0015] More specifically, for predicting GM particles Take samples and obtain Sigma points sampled ,in is the target state value The dimension of r=0,1,…,2 +1; change Sigma point Substitute into the measurement equation to obtain the Gama point in the local coordinate system of the observation platform :

[0016] The estimated azimuth measurement is obtained by calculating the following formula: and the innovation covariance matrix , , ,

[0017] in, , , , , is a constant;

[0018] According to the predicted measurement and the innovation covariance matrix , calculate the likelihood value , gain matrix , the updated mean , the updated covariance , , , , ,in, .

[0019] Optionally, when k=1, construct N primitive GM particles of a simple model As the initial GM particle of N model filters at time k, is the number of original GM particles under the model assumption n; the types of simple models include uniform straight line model, clockwise turning model and counterclockwise turning model, and the N simple models are at least two types.

[0020] Preferably, in the mixing interaction and prediction step, a first-order Markov chain is used to mix the initial GM particles at time k in each model filter to obtain the following mixed prediction probability density function: In the formula, is the Markov transition probability from model hypothesis m to model hypothesis n, and They are the state transfer matrix and the corresponding process noise covariance matrix under model assumption n, respectively.

[0021] Furthermore, the updated GM particle at time k Perform branch pruning or merging to obtain the posterior GM particles at time k . Preferably, the weight of the pruning k moment is The updated GM particles are too small, and the updated GM particles at time k are merged using the following formula:

[0022]

[0023] In the formula, , , is the threshold, |Z k | is the quantity measured in terms of orientation.

[0024] In particular, the tracking method of the present disclosure uses sound waves as the detection medium.

[0025] The present invention expresses the complex motion form of the target through the linear combination of GM particles; calculates the Jacobian matrix of the local angle measurement function (i.e., measurement function) with respect to the global state estimation through the composite function derivation method, solves the nonlinear problem of passive tracking and the problem of inconsistency between the angle measurement (i.e., azimuth measurement) and the state coordinates; suppresses clutter through GM particle pruning. The passive tracking method disclosed in the present invention has at least the following advantages:

[0026] 1) The Gaussian mixture model in this method represents the state transition probability density of the target with complex motion forms as the weighted sum of multiple Gaussian terms, and achieves filtering estimation by recursively inferring the GM particles composed of the weights, means and covariances of the Gaussian terms. The finite model in the IMM model set is used to describe the simple motion form of the target, while the diversified GM particles generated by the mixed interaction are used to represent the various states that the target may exist in, and all the updated GM particles in the IMM-GMF model are linearly combined to approximate the real motion form of the target. In this way, the complex motion form of the target is represented.

[0027] 2) This method suppresses clutter through GM particle pruning and eliminates the influence of clutter.

[0028] 3) In constructing the position measurement z representing time k k With target status When measuring the corresponding relationship between the two, the translation and rotation of the observation platform are fully considered, and the rotation matrix C is introduced. kBy converting the global coordinate system where the state estimation is located into the local coordinate system of the observation platform where the azimuth measurement is located, the inconsistency problem between the azimuth measurement and state estimation coordinate systems caused by platform translation and rotation is solved, and the accuracy of the filter estimation is improved.

[0029] 4) In the process of updating the predicted GM particles, the composite function derivation method or the traceless transformation method is used to solve the nonlinear problem and coordinate inconsistency problem. Among them, when the composite function derivation method is used, according to the composite function relationship that the orientation measurement in the local coordinate system is the target state in the global coordinate system, the composite function derivation method is used to calculate the Jacobian matrix of the local angle measurement function with respect to the global state estimate, and it is used as the linearized measurement matrix to realize the GM particle update, solving the highly nonlinear problem of passive tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0031] Figure 1 The block diagram of the passive tracking method for underwater complex moving targets disclosed in the present invention is shown;

[0032] Figure 2 A schematic diagram showing the process of the passive tracking method for underwater complex moving targets disclosed in the present invention is shown;

[0033] Figure 3 A schematic diagram of the process of updating the predicted GM particles using the composite function derivation method is shown;

[0034] Figure 4 A schematic diagram of the process of updating the predicted GM particles using the traceless transformation method is shown;

[0035] Figure 5 A schematic diagram of the target track and the observation platform track in the simulation example is shown;

[0036] Figure 6 A schematic diagram of azimuth angle measurement in a simulation example is shown;

[0037] Figure 7 A schematic diagram showing the track estimation of IMM-GMF and the track estimation of traditional IMM-PDA-EKF;

[0038] Figure 8 Shows Figure 7 Schematic diagram of the model probability estimation error of the two algorithms;

[0039] Fig. 9 Shows Figure 7 Position estimation errors of the two algorithms. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present disclosure to clearly and completely describe the technical solutions in the embodiments of the present disclosure. Obviously, the described embodiments are only part of the embodiments of the present disclosure, not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present disclosure.

[0041] The present disclosure provides a passive tracking method for underwater complex moving targets based on IMM-GMF (Interactive Multi-Model-Gaussian Mixture Filter), wherein IMM (Interactive Multi-Model) refers to interactive multi-model and GMF (Gaussian Mixture Filter) refers to Gaussian mixture filter. In the passive tracking method, a Gaussian mixture filter (GMF) is introduced as a model filter in the IMM filter tracking structure to form an IMM-GMF model.

[0042] In the passive tracking method, the observation platform is equipped with passive sensors (such as infrared sensors, radar sensors, acoustic wave sensors, etc.). The passive sensors are used to receive electromagnetic wave signals radiated or reflected by the moving target, or acoustic wave signals, etc., and obtain the position, speed and other information of the moving target by processing and analyzing these signals. In the passive tracking method disclosed in the present invention, the passive sensor is introduced by taking a hydrophone as an example. The hydrophone located on the observation platform can obtain an azimuth measurement z of a pure angle value. The azimuth measurement z represents the angle value in the local coordinate system of the observation platform. The azimuth measurement z is positive clockwise relative to the y-axis of the local coordinate system. In addition, the observation platform of the passive sensor should perform certain maneuvers to meet the observability of the target.

[0043] The passive tracking method disclosed in the present invention is used to track a moving target, and obtains the target state estimation value of the moving target in the global coordinate system by measuring the position z and updating the GM particles of the motion model. ,in =( , , , ),in , Respectively represent the estimated values ​​of the horizontal and vertical coordinates of the moving target, , Respectively represent the estimated speed of the moving target decomposed into the horizontal and vertical axes.

[0044] The moving target performs complex motion underwater, and its motion form is complex, and no single motion form can be simulated. When constructing the motion model of the moving target, the present disclosure uses a combination of multiple simple models to represent the motion form of the moving target. Each simple model represents a possible target motion form, and each simple model consists of one or more GM particles. Where n represents the nth simple model, 1≤n≤N, N represents the number of simple models; i represents the i-th GM particle in the simple model, 1≤i≤ , represents the number of GM particles of the nth simple model; is the weight of the Gaussian term; is the mean, is a vector; is the covariance, is a matrix.

[0045] The IMM disclosed in the present invention is composed of multiple simple model tracking filters in a model set, wherein each simple model tracking filter (model filter for short) is a GMF, and the initial GM particles at time k are mixed and updated in each model filter to achieve tracking of complex moving targets. The Gaussian mixture model in the GMF represents the target state transition probability density function with a complex motion form as a weighted sum of multiple Gaussian terms, and achieves filtering estimation by updating the GM particles composed of the Gaussian term weights, mean and covariance.

[0046] Specifically, each model filter converts the posterior GM particle at time k-1 into Mix them, and then predict them according to their own model to obtain the predicted GM particles at time k . Update the predicted GM particles to obtain the updated GM particles at time k , and then obtain the posterior GM particle The weight of the posterior GM particle at time k is used to perform a weighted average on its mean to obtain the target state estimate at time k: .

[0047] The passive tracking method disclosed in the present invention utilizes a finite model in the IMM model set to describe the simple motion form of the target, and uses a variety of GM particles generated by mixed interactions to fit the complex motion form of the target. The linear combination of GM particles can approximate the real motion of the target.

[0048] In the process of updating the predicted GM particles, it is necessary to obtain the azimuth measurement z from the observation platform. k . Direction measurement z k Located in the local coordinate system of the motion observation platform, and the target state estimate Located in the global coordinate system, and there is a nonlinear relationship between the orientation measurement and the target state. In target tracking, in order to ensure the observability of the moving target, the observation platform should perform certain maneuvers. Therefore, the observation platform itself may translate and rotate. The existing passive tracking only considers the translation of the moving observation platform, ignoring the rotation that leads to the inconsistency of the coordinate system of the orientation measurement and state estimation, which ultimately affects the filter estimation. In the passive tracking method disclosed in the present invention, the translation and rotation of the observation platform are fully considered, and the coordinate system rotation matrix c is introduced on the basis of the existing technology. k .

[0049] refer to Figures 1 to 4 , the passive tracking method disclosed in the present invention will be introduced in detail below. Figure 1 GM particles are represented by circles, and three simple models are shown, wherein the GM particles of each simple model are represented by circles of the same color. For example, the GM particles of the first simple model are red, the GM particles of the second simple model are blue, and the GM particles of the third simple model are white. Among them, the three simple models are specifically a uniform straight line model, a clockwise turning model, and a counterclockwise turning model. The passive tracking method includes three simple models, which is more conducive to tracking complex underwater moving targets. Optionally, in some embodiments, the passive tracking method may include only one or any two of the uniform straight line model, the clockwise turning model, and the counterclockwise turning model, for example, only the uniform straight line model, or only the uniform straight line model and the clockwise turning model, etc.

[0050] Figure 2 The flowchart of the passive tracking method of underwater complex moving targets is shown. In the passive tracking method disclosed in the present invention, when the number of models N=1, it becomes a Gaussian mixture filter. The passive tracking method disclosed in the present invention comprises: step S101, generating the initial GM particles at time k; step S102, each model filter performs mixed interaction on the initial GM particles, and predicts them according to its own model to obtain predicted GM particles Step S103, obtaining the azimuth measurement z of the moving target at time k k , according to the azimuth measurement z k Prediction of GM particles Update and obtain the updated GM particles of the moving target at time k , and then obtain the posterior GM particle ; Step S104, based on the posterior GM particles , output the target state estimate of the moving target at time k In step S103, the gain matrix of each GM particle is first calculated according to the measurement model h. , and then measure z according to the orientation k Wait to obtain the updated GM particles at time k.

[0051] Combination Figure 1 , Figure 3 , Figure 4 The passive tracking method disclosed in the present invention is introduced in detail.

[0052] In step S101, k≥1. When k is 1, that is, when k is the starting time, the original GM particle can be constructed. As the initial GM particle at time k, the original GM particle is used to represent the initial state of the target. Specifically, the model set of the moving target is , which contains N simple models, each of which represents a form of motion, that is, the original GM particles that construct N simple models As the initial GM particles of N model filters at time k. For example, two or three simple models are set. The types of simple models include uniform straight line model, clockwise turning model and counterclockwise turning model. Preferably, N is 3, and the N simple models are the three models mentioned above. Each simple model contains one or more original GM particles , ≥1, is the number of original GM particles under the original model n.

[0053] When k>1, obtain the posterior GM particles of N simple models at time k-1 As the initial GM particle of N model filters at time k, each simple model includes at least one posterior GM particle , and each simple model represents a form of motion, where 1≤n≤N, 1≤i≤ , is the number of posterior GM particles under the model assumption n at time k-1.

[0054] The posterior probability density function of the nth model hypothesis at time k-1 is expressed as the weighted sum of multiple Gaussian terms:

[0055] (1)

[0056] In formula (1), the weight of the Gaussian term is , mean and covariance Together they constitute the posterior GM particle of the moving target at time k-1, is the number of GM particles under model assumption n, and N is the number of models. When k = 1, the weight of the Gaussian term in equation (1) is , mean and covariance The original GM particles that together form the moving target .

[0057] See also Figure 1 , Figure 1 The figure shows that the number of models N is 3 and the number of posterior GM particles in the first model assumption at time k-1 is The second model assumes that the number of posterior GM particles is 3. =2, the posterior GM particle number assumed by the third model is 1. The posterior GM particles of the three simple models at time k-1 are used as the initial GM particles of the three model filters at time k.

[0058] In step S102, according to the first-order Markov chain, the initial GM particles at time k are mixed in each model filter to obtain the predicted GM particles predicted by each model filter according to its own model. , is the predicted number of GM particles under model assumption n at time k. And obtain the predicted probability density function of model assumption n at time k , see formula (2).

[0059] (2)

[0060] In the formula, is the Markov transition probability from model hypothesis m to model hypothesis n, and are the state transfer matrix and the corresponding process noise covariance matrix under model assumption n. When m=n, Larger; when m≠n, Smaller. The mixed prediction probability density function is uniformly recorded as:

[0061] (3)

[0062] In the formula, , and are the weight, mean and covariance of the i-th predicted GM particle, respectively. The number of predicted GM particles of each model filter is .

[0063] See also Figure 1 , the predicted GM particle numbers of the three models Both are 6.

[0064] The predicted GM particles generated by the hybrid interaction have rich and diverse characteristics, and the position measurement z kThe predicted GM particles are updated, and the posterior GM particles obtained at time k retain the richness and diversity of the predicted GM particles, and then represent the various states that may exist in the moving target. If large-weight GM particles are used to represent the target state, it may not conform to the real state of complex moving targets. The linear combination of all the posterior GM particles in the IMM-GMF model can approximate the real motion form of the target at time k, thereby representing the complex target motion form.

[0065] In step S103, it includes constructing a measurement equation. Specifically, constructing a position measurement z in the local coordinate system representing time k k With target status The measurement equation of the corresponding relationship between them.

[0066] In the local coordinate system of the observation platform, the azimuth is measured as z k ; The target state in the global coordinate system is The position of the observation platform in the global coordinate system is , the observation angle is , the observation angle is positive clockwise relative to the Y axis in the global coordinate system. In the local coordinate system of the observation platform, the target state is , see formula (4).

[0067] (4)

[0068] In the formula, is the translation vector; is the rotation matrix of the state, is the coordinate system rotation matrix, and blkdiag() is the block diagonal matrix.

[0069] In the local coordinate system of the motion observation platform, the measurement equation is shown in equation (5).

[0070] (5)

[0071] In formula (5), v k is the observation noise, which obeys a Gaussian distribution with zero mean.

[0072] In step S103, the azimuth measurement z of the observation platform at time k is obtained. k , according to the constructed measurement equation and azimuth measurement z k Calculate the gain matrix and the likelihood , and obtain the updated mean value accordingly and covariance , and then obtain the updated GM particle at time k .in, Indicates direction measurement and the likelihood value of the i-th predicted GM particle.

[0073] In the process of updating the predicted GM particles, the composite function derivation method or the traceless transformation method can be used to solve the nonlinear problem and the coordinate inconsistency problem. Both the composite function derivation method and the traceless transformation method can be used to update the GM particles. The composite function derivation method is used as an example to illustrate.

[0074] The observation function h in formula (5) is the target state in the global coordinate system According to the derivative rule of composite function, the Jacobian matrix of nonlinear observation function (measurement function) is:

[0075] (6)

[0076] in, .

[0077] See also Figure 3 According to formula (6), the measurement matrix of each predicted GM particle can be calculated. Using the Jacobian matrix as the angle measurement matrix (i.e., the measurement matrix) to update the predicted GM particles of the Gaussian mixture filter solves the nonlinear problem of passive tracking. The rotation matrix of the state introduced in the Jacobian matrix is The global coordinate system where the target state is estimated is converted into the local coordinate system of the observation platform where the orientation is measured.

[0078] According to formula (10), the gain matrix is ​​obtained According to the gain matrix , predicted mean, predicted covariance, etc., to obtain the updated mean and covariance , see equation (8) and equation (9). According to the azimuth measurement z k , predicted mean, predicted covariance and Jacobian matrix, etc., to obtain the likelihood value , see formula (7).

[0079] (7)

[0080] (8)

[0081] (9)

[0082] (10)

[0083] When the composite function derivation method is used in the process of updating the predicted GM particles, the nonlinear observation function is converted into a linearized measurement matrix. The Jacobian matrix of the local angle observation function with respect to the global state estimation is calculated using the composite function derivation method. The obtained measurement matrix is ​​the product of the Jacobian matrix of the local observation function with respect to the local state and the rotation matrix. The former solves the nonlinear problem, and the latter solves the problem of inconsistent coordinate systems of azimuth measurement and state estimation caused by platform rotation by converting the global coordinate system where the state estimation is located into the local coordinate system of the observation platform where the azimuth measurement is located.

[0084] The following describes the use of unscented transformation method to update the predicted GM particles. Figure 4 The unscented transformation method uses a statistical method to calculate the vectors and matrices required for filtering. The update steps are as follows: Step S103a, generate sampling points of particles; Step S103b, observe the sampling points; Step S103c, obtain the gain matrix , likelihood value , and obtain the updated mean value accordingly and covariance .

[0085] In step S103a, the parameters required for the unscented transformation are determined , , as well as ,in is the target state The dimension of Often takes a very small positive number (such as 0.01), Usually take 2, It is usually set to 0. The weight of the first-order moment in the unscented transformation is calculated based on these parameters and the weight of the second moment , where the calculation formula is shown in formula (11).

[0086] (11)

[0087] In formula (11), the superscript m represents the first-order moment, and the superscript c represents the second-order moment.

[0088] According to formula (12), the GM particles are predicted Take samples and get Sigma points sampled .

[0089] (12)

[0090] In step S103b, these sampling points are observed using formula (5) to calculate the Gama point , see formula (13). When these sampling points are observed using formula (5), due to the Sigma point of the sampling point It is not a real sampling through passive sensors, so the observation noise v in equation (5) is removed k Form formula (13).

[0091] (13)

[0092] In formula (13), h is the nonlinear observation function (measurement function) in formula (5), and are the rotation matrix and translation vector of the state of the observation platform. and the weight of the first-order moment Substituting into (14) we obtain the predicted measurement . and the weight of the second-order moment Substituting into equation (15) we obtain the new information covariance matrix .

[0093] (14)

[0094] (15)

[0095] In formula (15), is the observation noise covariance matrix.

[0096] In step S103c, according to the azimuth measurement z k , Predictive Measurement and the innovation covariance matrix , and obtain the likelihood value , see formula (16). See formula (19), according to the predicted measurement , the estimated value of the predicted target state at time k Sigma point , Gama point 、Innovation covariance matrix Etc., calculate the gain matrix . According to the direction measurement z k , Predictive Measurement 、Innovation covariance matrix Equal pair mean , covariance Update and obtain the updated mean , covariance Mean , covariance The formulas for are shown in equations (17) and (18).

[0097] (16)

[0098] (17)

[0099] (18)

[0100] (19)

[0101] Among them, in formula (18) and formula (19), .

[0102] In step 103, the azimuth measurement z at the current time (time k) is obtained. k . Direction measurement z k The number can be one or more, using the measurement set Represents all azimuth measurements z k . Direction measurement z k The measurement result is inaccurate because it is composed of the echo azimuth that may come from the target and the clutter azimuth that comes from the false alarm. Therefore, in order to improve the accuracy of the measurement result, the present disclosure introduces the missed detection probability, which can make up for the missed GM particles. Specifically, the updated probability density function is expressed by formula (20): By rearranging equation (20), we can obtain the updated GM particle at time k: .

[0103] (20)

[0104] In formula (20), is the detection probability, Specifically, they are fixed values ​​associated with passive sensors; express is the probability of clutter, and its value is usually the clutter density. It is a position measurement and the likelihood value of the i-th predicted GM particle, and By azimuth measurement Updated mean and covariance, is the gain matrix. , , , Substituting into formula (20) we can obtain the updated probability density function In formula (20), It is the product of the missed detection probability and the predicted probability density function. This term can make up for the missed GM particles and achieve the effect of compensating for missed detection.

[0105] The updated probability density function at the current moment is uniformly expressed as formula (21).

[0106] (twenty one)

[0107] In formula (21), , and are the weight, mean and covariance of the i-th updated GM particle, is the number of updated GM particles of the nth model filter at time k. The size of (|Z k |+1)× ,|Z k | is the direction measurement z k The number of (number).

[0108] In updating and compensating the predicted GM particles, the position measurement z obtained at the current moment is used k Calculate the likelihood value and the updated mean and the updated covariance , and use the likelihood value to update the weight of the GM particles; in the clutter background, the detection probability and clutter density are fully considered during the update, and the missed GM particles are introduced through the missed detection probability in order to correct the update result.

[0109] See also Figure 1 , the predicted GM particle number of the three model filters Both are 6, azimuth measurement z k The number of GM particles in the target state estimation of the three model filters is 2. is 18.

[0110] In some embodiments, due to false alarms and missed detections, there are posterior GM particles with too small weights or close distances after updating and correction. In order to suppress clutter and reduce the amount of calculation, the step S103 of the present disclosure also includes pruning or merging the updated GM particles after update and correction to obtain the posterior GM particles at time k. Preferably, the updated GM particles are pruned and merged.

[0111] Specifically, branch pruning is to remove the updated GM particles with too small weights. The updated GM particles with too small weights are the particles with noise updates. The noise is suppressed by GM particle branch pruning. For example, the weight of the updated GM particle If the value is less than or equal to 0.005, preferably equal to 0.001, the updated GM particle can be removed. Merging is to merge the updated GM particles with similar distances, which reduces the amount of calculation. The merging formula is

[0112] (twenty two)

[0113] In formula (22), , , is the threshold, |Z k | is the quantity measured in terms of orientation.

[0114] The probability density function after branch pruning and merging is expressed as formula (23).

[0115] (twenty three)

[0116] It should be pointed out that the number of particles after pruning and merging Less than or equal to the number of particles before the pruning merging . Alternatively, GM particles can be merged by other existing methods. For example, the updated GM particles are merged by the mean and covariance merging method. In the mean and covariance merging method, the inverse of the covariance of the updated GM particles to be merged is used as the weight, and the mean of the updated GM particles to be merged is weighted averaged as the merged mean; the inverse of the covariance of the updated GM particles to be merged is summed, and the inverse of the summation result is calculated as the merged covariance.

[0117] Step S104, based on the posterior GM particles , output the target state estimate of the moving target at time k Specifically, after executing branch pruning and merging, the weight of the final posterior GM particle is used to perform a weighted average on the mean of the posterior GM particle to obtain the target state estimate at time k: The estimation formula is shown in equation (24).

[0118] (twenty four)

[0119] The GM particles are linearly combined to approximate the complex motion form of the target. It should be noted that in some embodiments, the pruning and merging of the updated GM particles is not necessary, and the updated GM particles that are not pruned and merged can be directly used as the posterior GM particles to obtain the target state estimation value at time k through the posterior GM particles. .at this time, That is .

[0120] The posterior GM particle at time k can be used as the prior GM particle for the target state estimation at the next time (i.e., the initial GM particle for the target state estimation at the next time). After steps S101 to S104, the posterior GM particle and the target state estimation value at time k+1 are obtained. That is to say, , go to step S101 and perform state recursion at the next moment.

[0121] In a preferred embodiment, see Figure 1 The passive tracking method disclosed in the present invention includes steps S101 to S104. In step S101, when k=1, the model filter is initialized to construct the original GM particle at the initialization time. As the initial GM particle. In step S102, the initial GM particles are mixed, interacted and predicted. Specifically, each model filter mixes and interacts the initial GM particles at time k, and then predicts them according to its own model to obtain the predicted GM particles In step S103, GM particles are updated and modified, and GM particles are pruned and merged. Specifically, the position measurement z of the moving target at time k is obtained. k , according to the azimuth measurement z k Prediction of GM particles Update and obtain the updated GM particles of the moving target at time k , to update GM particles Perform branch pruning and merging to obtain posterior GM particles Among them, according to the azimuth measurement z k Prediction of GM particles When updating, the translation and rotation of the observation platform are considered, and the rotation matrix C of the state is introduced k In step S104, the state estimation is output and the state at the next moment is recursively deduced. Specifically, based on the posterior GM particle , output the target state estimate of the moving target at time k , let k = k + 1. In the process of recursively deriving the state at the next moment, in step S101, the posterior particle at moment k is used as the initial GM particle at moment k + 1.

[0122] When tracking complex moving targets, construct the original GM particles at the initialization time As the initial GM particles, GM particles representing the target state can be randomly generated as the initial value of the filter. The original GM particles include Gaussian item weights, mean and covariance. If the possible parameters of the current target state are known, the original GM particles can be generated as the initial value of the filter based on these prior information. Then the generated original GM particles are used as the initial GM particles for mixed interaction and prediction. Each GMF calculates the mixed weights of the initial GM particles according to the Markov transition probability interaction, and copies its mean and variance as the predicted mean and predicted variance after the mixed interaction. Mixed interaction can produce rich and diverse GM particles, and the linear combination of these particles can describe the possible complex motion state of the target. Each GMF obtains the predicted GM particles according to its own state transfer equation for all the initial GM particles. This step utilizes the prior knowledge of the target motion law.

[0123] Figures 5 to 8 A simulation example of the target passive tracking method disclosed in the present invention is shown. The initial value of the maneuvering target (moving target) is =[600m,900m,10m / s,-10m / s] T , performs uniform motion from 1 to 60 seconds, performs counterclockwise turning motion from 61 to 70 seconds, and performs uniform motion from 71 to 100 seconds. The process noise covariance of the moving target is = diagonal matrix (1,1,0.01,0.01). The speed of the observation platform (observation station) is 2m / s, and it always performs tail pursuit and always drives towards the received azimuth measurement mean. The observation noise covariance of the passive sensor is =1, the observation function is , the observation sector angle is -60° to 60°, the detection probability =98%. At each moment, the sensor is =0.01 / ° clutter.

[0124] IMM contains two models, namely the uniform motion model (n=1) and the counterclockwise turning motion model (n=2). The process noise covariance of the two models is (n=1,2), the Markov transition probability of each model is =0.02( ), =0.98. The pruning threshold of GMF is 0.001, and the merging threshold is = 2. The composite function derivation method is used in the process of updating the predicted GM particles.

[0125] Figure 5 The target track and observation station track are shown. Figure 6 The azimuth measurement is shown; Figure 7 The track estimation of IMM-GMF and the track estimation of traditional IMM-PDA-EKF are shown; Figure 8 The model probability estimation error of the two algorithms is shown, which is the absolute value of the difference between the estimated model probability and the true model probability; Fig. 9 is the position estimation error of the two algorithms.

[0126] exist Figure 5 In the process, the observation platform always performs tail pursuit motion, so that the target is always on the midline of the observation fan angle (the Y axis of the local coordinate system), so Figure 6 The average value of the azimuth measurement (azimuth measurement) in is almost 0. Figure 7 It can be seen that both algorithms can track maneuvering targets. Figure 8It can be seen that the model probability estimation of IMM-GMF is more accurate, so the accuracy of IMM-GMF is higher than that of traditional IMM-PDA-EKF. Fig. 9 It can be seen that the position error curve of IMM-GMF is lower than that of IMM-PDA-EKF. It should be noted that the error curves of both algorithms increase in the final stage of tracking. This is because the observation platform gradually moves radially toward the target, and this observation posture is not conducive to meeting the target observability.

[0127] After 200 Monte Carlo experiments, the average position error of the IMM-PDA-EKF algorithm is 68.7787m, while the average position error of the IMM-GMF algorithm is 51.3776m. The average position error of the IMM-GMF algorithm is 25.3% lower than that of the IMM-PDA-EKF algorithm, which fully proves the superiority of the IMM-GMF algorithm.

[0128] The above are only several embodiments of the present disclosure. Those skilled in the art may make various changes or modifications to the embodiments of the present disclosure based on the contents disclosed in the application documents without departing from the spirit and scope of the present disclosure.

Claims

1. A passive tracking method for underwater complex moving targets based on IMM-GMF, characterized in that: The steps include: Generate initial GM particles at time k: Get the posterior GM particles of N simple models at time k-1 As the initial GM particle of N model filters at time k, each simple model includes at least one posterior GM particle And each simple model represents a form of motion, where 1≤n≤N, 1≤i≤J k-1,n , J k-1,n is the number of posterior GM particles under the model assumption n at time k-1; Mixed interaction and prediction: The initial GM particles at time k are mixed in each model filter to obtain the predicted GM particles predicted by each model filter based on its own model And obtain the predicted probability density function p of the model hypothesis n at time k k|k-1 (x,n),J k|k-1,n is the predicted number of GM particles under model assumption n at time k; Update and correct the predicted GM particles to obtain the posterior GM particles at time k: Construct a position measurement z in the local coordinate system representing time k k With the target state x k The measurement equation of the corresponding relationship between k =h(C k (x k -t k ))+v k , get the position measurement z at time k k , in, is the translation vector, C k =blkdiag(c k ,c k ) is the rotation matrix of the state, is the coordinate system rotation matrix, and are the position and observation angle of the observation platform in the global coordinate system, v k To observe noise, blkdiag() represents a block diagonal matrix; Measure z based on the orientation k And the measurement equation, calculate the gain matrix and the likelihood And calculate the updated mean and covariance Then we get the updated probability density function of the model hypothesis n at time k This helps predict GM particles Update to obtain the updated GM particle at time k Among them, Z k are the azimuth measurements z obtained from the observation platform at time k k The collection of p D is to obtain the azimuth measurement z k The detection probability of the passive sensor, κ(z k ) represents z k is the probability of clutter, is the azimuth measurement z k and the likelihood value of the i-th predicted GM particle; Update GM particles based on k time Get the posterior GM particle at time k Get the target state estimate at time k Use the weights of the posterior GM particles of all models at time k The mean Perform weighted averaging to obtain the estimated state of the complex moving target at time k 2. The passive tracking method for underwater complex moving targets according to claim 1, characterized in that: In the process of updating the predicted GM particles, the composite function derivation method is used: Derivative the composite function of the measurement equation to obtain the Jacobian matrix in, Based on the Jacobian matrix Calculate the gain matrix and likelihood And calculate the updated mean and covariance Among them, R k is the observation noise covariance.

3. The passive tracking method for underwater complex moving targets according to claim 1, characterized in that: In the process of updating the predicted GM particles, the unscented transformation method is used: Conduct sampling and obtain sampling points; Obtain predicted measurements based on sampling points and measurement equations and the innovation covariance matrix of the nonlinear measurement Using Predictive Measurement and the innovation covariance matrix Calculate the gain matrix and likelihood And calculate the updated mean and covariance 4. The method for passively tracking underwater complex moving targets according to claim 3, characterized in that: Prediction of GM particles Sampling is performed to obtain 2n x +1 sampled Sigma point Where n x is the target state value x k The dimension of r = 0, 1, ..., 2n x +1; Sigma Point Substitute into the measurement equation to obtain the Gama point in the local coordinate system of the observation platform The estimated azimuth measurement is obtained by calculating the following formula and the innovation covariance matrix in, α, β, k, and λ are constants; According to the predicted measurement and the innovation covariance matrix Calculate the likelihood value Gain Matrix Updated mean Updated covariance in, 5. The method for passively tracking underwater complex moving targets according to any one of claims 1 to 4, characterized in that: When k=1, construct N primitive GM particles of simple model As the initial GM particle of N model filters at time k, J 0,n is the number of original GM particles under the model assumption n; The types of simple models include a uniform straight line model, a clockwise turning model, and a counterclockwise turning model, and the N simple models are of at least two types.

6. The method for passively tracking underwater complex moving targets according to any one of claims 1 to 4, characterized in that: In the mixed interaction and prediction step, a first-order Markov chain is used to mix the initial GM particles at time k in each model filter to obtain the following mixed prediction probability density function: In the formula, u mn is the Markov transition probability from model hypothesis m to model hypothesis n, F n and Q n They are the state transfer matrix and the corresponding process noise covariance matrix under model assumption n, respectively.

7. The passive tracking method for underwater complex moving targets according to claim 6, characterized in that: Update GM particle at time k Perform branch pruning or merging to obtain the posterior GM particles at time k 8. The method for passively tracking underwater complex moving targets according to claim 7, characterized in that: Weight of pruning at time k The updated GM particles are too small, and the updated GM particles at time k are merged using the following formula: In the formula, λ m is the threshold, |Z k | is the quantity measured in terms of orientation.

9. The method for passively tracking underwater complex moving targets according to any one of claims 1 to 4, characterized in that: The tracking method uses sound waves as the detection medium.

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