Three-dimensional reconstruction method based on random finite set track association

Abstract

The present invention discloses a three-dimensional reconstruction method based on random finite set track association, including: based on an improved GM-PHD filtering algorithm, the tracks of all target scattering centers are associated along the order and reverse order of an ISAR image sequence to obtain a sequential track and a reverse track; wherein the improved GM-PHD filtering algorithm introduces label information for each target scattering center on the basis of a traditional GM-PHD filtering algorithm; all track points in the sequential track and the reverse track are fused, and the missing track points in the sequential track and the reverse track are filled to obtain a complete track matrix; the complete track matrix is ​​calibrated, and the calibrated complete track matrix is ​​factorized to obtain a three-dimensional reconstructed position of each target scattering center. The present invention greatly reduces the difficulty of target scattering center track association and improves the accuracy of three-dimensional coordinate reconstruction.

Description

Technical Field

[0001] The invention belongs to the technical field of radar transmission signal processing, and in particular relates to a three-dimensional reconstruction method based on random finite set track association. Background Art

[0002] Three-dimensional imaging based on multi-view ISAR (Inverse Synthetic Aperture Radar, ISAR for short) images is a technology that realizes three-dimensional reconstruction of observed targets by fusing information from multi-view ISAR image sequences. Specifically, the track matrix of feature points is firstly formed by extracting and associating feature points in the ISAR image sequence, and then the track matrix is ​​decomposed by eigenvalues ​​using the factorization method, thereby solving the three-dimensional coordinates of the extracted feature points. How to correctly associate the projection positions of the scattering centers of each target has become one of the core issues in three-dimensional imaging based on ISAR image sequences. In this regard, some scholars have proposed a track association method based on target motion and observation modeling. This method models the track of the target scattering center with a specific motion form, derives the elliptical motion law of the target scattering center, and then obtains the correct association of the scattering center through Bayesian recursive filtering.

[0003] However, since the target motion model and ISAR observation model considered are too ideal, their feasibility is not high in practice. In addition, the data association algorithm in this type of method has high computational complexity and is difficult to meet the needs of fast processing. Summary of the invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a three-dimensional reconstruction method based on random finite set track association. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0005] The embodiment of the present invention provides a three-dimensional reconstruction method based on random finite set track association, comprising:

[0006] Based on the improved GM-PHD filtering algorithm, the tracks of all target scattering centers are associated along the sequential and reverse order of the ISAR image sequence to obtain sequential tracks and reverse order tracks. The improved GM-PHD filtering algorithm introduces label information for each target scattering center based on the traditional GM-PHD filtering algorithm.

[0007] Fusing the track points of the target scattering center in the sequential track and the reverse track, and filling the missing track points of the target scattering center in the sequential track and the reverse track to obtain a complete track matrix for each target scattering center;

[0008] The complete track matrix is ​​calibrated, and the calibrated complete track matrix is ​​factorized to obtain the three-dimensional reconstructed position of each target scattering center.

[0009] In one embodiment of the present invention, based on the improved GM-PHD filtering algorithm, the tracks of all target scattering centers are associated along the order and reverse order of the ISAR image sequence to obtain the order track and the reverse order track, including:

[0010] For each ISAR image in the sequential and reverse ISAR image sequences, the following steps are performed, including: calculating the PHD of the random finite set at the initial moment according to the measurement value at the initial moment, and assigning a label to each Gaussian component of the PHD of the random finite set at the initial moment; predicting the prior PHD of the random finite set at the current moment according to the PHD of the random finite set at the previous moment, and assigning a label to each Gaussian component of the prior PHD of the random finite set corresponding to the newly generated target scattering center in the prediction; updating the PHD of the random finite set at the current moment according to the measurement value at the current moment and the predicted prior PHD of the random finite set; pruning and merging the updated PHD of the random finite set; extracting several Gaussian components with the leading weights from the PHD of the random finite set after pruning and merging as the posterior PHD of the random finite set at the current moment, and obtaining the state estimation information of the target scattering center according to the mean value of the posterior PHD of the random finite set;

[0011] According to the state estimation information corresponding to each ISAR image in the sequential ISAR image sequence, the position information of each target scattering center is solved and associated to obtain a sequential track, and according to the state estimation information corresponding to each ISAR image in the reverse ISAR image sequence, the position information of each target scattering center is solved and associated to obtain a reverse track.

[0012] In one embodiment of the present invention, the PHD formula for calculating the random finite set at the initial time is expressed as:

[0013]

[0014] Among them, λ b,0 (x0) represents the PHD of a random finite set at the initial time, represents the number of target scattering centers at the initial moment, represents the weight of the hth target scattering center at the initial moment, represents the Gaussian distribution function, x0 represents the state information at the initial moment, and the value of x0 is the measured value at the initial moment. represents the mean value of the h-th target scattering center at the initial moment, represents the variance of the hth target scattering center at the initial moment;

[0015] Assigning labels to each Gaussian component of the PHD of a random finite set at the initial time is expressed as:

[0016]

[0017] Among them, L b,0 represents the set of all labels at the initial moment, Indicates that the initial time is The labels are assigned to the Gaussian components of the target scattering centers.

[0018] In one embodiment of the present invention, the a priori PHD formula for predicting the random finite set at the current moment based on the PHD of the random finite set at the previous moment is expressed as:

[0019]

[0020] Among them, D k|k-1 (x k ) represents the prior PHD of a random finite set predicted from time k-1 to time k, x k represents the state information at time k, represents the sum of the Gaussian components of the PHD of a random finite set of surviving target scattering centers from time k-1 to time k, λ b,k (x k ) represents the PHD of a random finite set of newly generated target scattering centers at time k, and the PHD of a random finite set of newly generated target scattering centers at time k is predicted based on the measured value at time k-1;

[0021] The label assignment for each Gaussian component of the PHD of a random finite set of newly generated target scattering centers at the current moment is expressed as:

[0022]

[0023] Among them, L b,k represents the set of new labels at time k, Indicates that time k is the first The labels are assigned to the Gaussian components of the target scattering centers.

[0024] In one embodiment of the present invention, the formula for updating the PHD of the random finite set at the current moment according to the measured value at the current moment and the predicted prior PHD of the random finite set is expressed as:

[0025]

[0026] Among them, D k|k (x k ) represents the PHD of a random finite set updated at time k, x k represents the state information at time k, represents the prior PHD of the random finite set corresponding to the measurement values ​​provided by the surviving target scattering center from time k-1 to time k, m k represents the number of measurements provided by the scattering center of the surviving target at time k, represents the number of surviving target scattering centers from time k-1 to time k, P D represents the survival probability of the target scattering center from time k-1 to time k, represents the weight of the i-th measurement value at time k corresponding to the h-th target scattering center, represents the mean value of the h-th target scattering center corresponding to the i-th measurement value at time k, represents the variance of the i-th measurement value at time k corresponding to the h-th target scattering center, represents the Gaussian distribution function, λ k|k (x k ) represents the PHD of the random finite set of measurements provided by the clutter at time k, represents the weight of the hth target scattering center from time k-1 to time k, represents the mean value of the h-th target scattering center from time k-1 to time k, It represents the variance of the h-th target scattering center from time k-1 to time k.

[0027] In one embodiment of the present invention, pruning and merging a random finite set of updated PHDs includes:

[0028] Pruning Gaussian components whose weights in the PHD of the updated random finite set are less than a preset weight, and merging multiple Gaussian components whose spatial distributions in the PHD of the updated random finite set are within a preset spatial range into one Gaussian component;

[0029] The sum of the weights of multiple Gaussian components within a preset spatial range is used as the weight of the combined Gaussian component.

[0030] In one embodiment of the present invention, for each target scattering center, the process of fusing the track points of the target scattering center in the sequential track and the reverse track includes:

[0031] Determine whether there is a track point of the target scattering center in the sequential track at the current moment:

[0032] If it exists, continue to determine whether there is a track point of the target scattering center in the reverse track at the current moment:

[0033] If it does not exist, the track point of the target scattering center in the sequential track at the current moment is used as the fused track point;

[0034] If it exists, then calculate the first track mean according to the track points of the target scattering center in the sequential track and the track points in the reverse track at the current moment, and use the track points corresponding to the first track mean as the fused track points;

[0035] If it does not exist, the track point of the target scattering center in the reverse track at the current moment will be used as the fused track point.

[0036] In one embodiment of the present invention, for each target scattering center, if there are missing track points for the target scattering center at the current moment, the process of filling the missing track points includes:

[0037] Determine whether there is a track point of the target scattering center in the sequential track at the previous moment:

[0038] If it exists, continue to determine whether there is a track point of the target scattering center in the reverse track at the next moment:

[0039] If it does not exist, the track point of the target scattering center in the sequential track at the previous moment is used as the filled track point;

[0040] If it exists, then calculate the second track mean according to the track point of the target scattering center in the sequential track at the previous moment and the track point of the target scattering center in the reverse track at the next moment, and use the track point corresponding to the second track mean as the filled track point;

[0041] If it does not exist, the track point of the target scattering center in the reverse track at the next moment will be used as the filled track point.

[0042] Beneficial effects of the present invention:

[0043] The present invention proposes a three-dimensional reconstruction method based on random finite set track association, comprising: based on an improved GM-PHD filtering algorithm, the tracks of all target scattering centers are respectively associated along the order and reverse order of an ISAR image sequence to obtain a sequential track and a reverse order track; wherein the improved GM-PHD filtering algorithm introduces label information for each target scattering center on the basis of a traditional GM-PHD filtering algorithm; the track points of the target scattering centers in the sequential track and the reverse order track are fused, and the missing track points of the target scattering centers in the sequential track and the reverse order track are filled to obtain a complete track matrix of each target scattering center; the complete track matrix is ​​calibrated, and the calibrated complete track matrix is ​​factorized to obtain a three-dimensional reconstructed position of each target scattering center. It can be seen that the present invention introduces label information in the track association process, so that the target scattering center is no longer constrained by the motion trajectory form. For example, better track association results can be obtained under both elliptical and non-elliptical trajectories, which greatly reduces the difficulty of target scattering center track association. Moreover, only some target scattering centers on the ISAR image sequence need to be observed for calculation, which greatly reduces the computational complexity of the data association algorithm, so that the method proposed in the present invention can be better applied to the motion model of highly maneuverable targets. Moreover, by introducing label information, the influence of clutter can be better filtered, and accurate track association can be achieved in the case of missed detection of the target scattering center, and it has a certain robustness against clutter and missed detection. Before factoring and estimating the position coordinates of the target scattering center, the present invention pre-fuse and fill the track points in the associated track, which can effectively improve the accuracy of three-dimensional coordinate reconstruction.

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of a three-dimensional reconstruction method based on random finite set track association provided by an embodiment of the present invention;

[0046] Figure 2 It is a schematic diagram of a process of obtaining a sequential track and a reverse track based on an improved GM-PHD filtering algorithm provided by an embodiment of the present invention;

[0047] Figure 3 is a schematic diagram of a target ISAR imaging model provided by an embodiment of the present invention;

[0048] Figure 4 is a schematic diagram of a random three-dimensional scattering center model of a space target provided by an embodiment of the present invention;

[0049] Figure 5 (a)~ Figure 5(f) is a schematic diagram of the track observation space and track association results of three-axis stabilized and non-three-axis stabilized space targets achieved by the method proposed in the present invention;

[0050] Figure 6 (a)~ Figure 6 (d) is a schematic diagram of the complete track and three-dimensional imaging results of the three-axis stabilized and non-three-axis stabilized targets achieved using the method proposed in the present invention. DETAILED DESCRIPTION

[0051] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0052] See also Figure 1 The embodiment of the present invention provides a three-dimensional reconstruction method based on random finite set track association, which specifically includes the following steps:

[0053] S10. Based on the improved GM-PHD filtering algorithm, the tracks of all target scattering centers are associated along the sequential and reverse order of the ISAR image sequence to obtain sequential tracks and reverse order tracks; wherein, the improved GM-PHD filtering algorithm introduces label information for each target scattering center on the basis of the traditional GM-PHD filtering algorithm.

[0054] In order to solve the problem that the practical application of the traditional track association method based on target motion and observation modeling is not feasible and the data association algorithm has high computational complexity and is difficult to meet the needs of fast processing, an embodiment of the present invention proposes an improved GM-PHD (Gaussian Mixture-Probability Hypothesis Density) filtering algorithm. The improved GM-PHD filtering algorithm introduces label information for each target scattering center on the basis of the traditional GM-PHD filtering algorithm, and models the target scattering center state and measurement as a random finite set. The label information is used to make track association possible in the track association process, thereby realizing accurate association of the scattering center tracks. Specifically, based on the improved GM-PHD filtering algorithm, the tracks of all target scattering centers are associated along the order and reverse order of the ISAR image sequence to obtain the order track and the reverse order track, see Figure 2 , including the following steps:

[0055] For each ISAR image in the sequential and reverse ISAR image sequences, the following steps are performed:

[0056] S101. Calculate the PHD of the random finite set at the initial moment according to the measurement value at the initial moment, and assign a label to each Gaussian component of the PHD of the random finite set at the initial moment.

[0057] The PHD formula for calculating the random finite set at the initial time in the embodiment of the present invention is expressed as:

[0058]

[0059] Among them, λ b,0 (x0) represents the PHD of a random finite set at the initial time, represents the number of target scattering centers at the initial moment, which is also the number of observed measurement values. represents the weight of the hth target scattering center at the initial moment, represents the Gaussian distribution function, x0 represents the state information at the initial moment, and the value of x0 is the measured value at the initial moment. represents the mean value of the h-th target scattering center at the initial moment, represents the variance of the h-th target scattering center at the initial moment; for the state information, the state information at the k-th moment is recorded as: f n (t) and r n (t) are the scattering centers p of any target on the target. n =[x n ,y n ,z n ] T The instantaneous Doppler and instantaneous distance in the radar imaging plane satisfy the following relationship:

[0060]

[0061] θ(t) represents the radar line of sight elevation angle, ω represents the equivalent rotation angular velocity of the ISAR target around the OZ axis of its own turntable model, represents the radar line of sight azimuth, and are the projection components of the target velocity in the instantaneous Doppler direction and the instantaneous distance direction, respectively. and are the projection components of the target motion acceleration in the instantaneous Doppler direction and the instantaneous distance direction respectively; in is the hth measurement value at the initial moment, and Z0 is the set of all measurement values ​​at the initial moment.

[0062] Assigning labels to each Gaussian component of the PHD of a random finite set at the initial time is expressed as:

[0063]

[0064] Among them, L b,0 represents the set of all labels at the initial moment, Indicates that the initial time is The labels are assigned to the Gaussian components of the target scattering centers.

[0065] S102, predicting the a priori PHD of the random finite set at the current moment according to the PHD of the random finite set at the previous moment, and assigning a label to each Gaussian component of the a priori PHD of the random finite set corresponding to the scattering center of the newly generated target in the prediction.

[0066] Since the random finite set of target scattering centers at time k includes the random finite set of surviving target scattering centers at time k-1 and the random finite set of new target scattering centers, that is, the predicted random finite set is also composed of these two parts, the prior PHD formula of the random finite set at the current moment predicted by the PHD of the random finite set at the previous moment in the embodiment of the present invention is expressed as:

[0067]

[0068] Among them, D k|k-1 (x k ) represents the prior PHD of a random finite set predicted from time k-1 to time k, x k represents the state information at time k, represents the sum of the Gaussian components of the PHD of a random finite set of surviving target scattering centers from time k-1 to time k, λ b,k (x k ) represents the PHD of a random finite set of newly generated target scattering centers at time k.

[0069] For the PHD of a random finite set of new target scattering centers, the parameters of the PHD of a random finite set of new target scattering centers at time k are predicted based on the measured values ​​at time k-1, where the parameters include weights, mean, variance and labels. The specific parameter prediction is:

[0070] for make

[0071]

[0072] End for

[0073] in, The PHD of a random finite set of newly generated target scattering centers at the current moment is calculated based on the measured values ​​of the target scattering centers at the k-1 moment.

[0074] The label assignment for each Gaussian component of the PHD of a random finite set of newly generated target scattering centers at the current moment is expressed as:

[0075]

[0076] Among them, L b,k represents the set of new labels at time k, Indicates that time k is the first The labels are assigned to the Gaussian components of the target scattering centers.

[0077] For the PHD of a random finite set of target scattering centers that survived at the last moment, the number of target scattering centers that survived at the last moment is recorded as because It is to find the sum of Gaussian distributions of multiple target scattering centers, which is also a Gaussian mixture distribution, and its parameter prediction is:

[0078] for make

[0079]

[0080] L k|k-1 =L k-1

[0081] End for

[0082] Among them, P S is the survival probability, F k is the state transfer matrix, Q k-1 is the covariance matrix of the motion model noise.

[0083]

[0084]

[0085] Where α represents the maneuvering frequency, which is the inverse of the maneuvering acceleration, Δt is the time interval between two adjacent ISAR observation frames, is the average acceleration, which can be replaced by the predicted acceleration, namely:

[0086]

[0087]

[0088]

[0089] S103. Update the PHD of the random finite set at the current moment according to the measured value at the current moment and the predicted a priori PHD of the random finite set.

[0090] In the embodiment of the present invention, the number of surviving target scattering centers from time k-1 to time k is recorded as If no target is detected, that is, the current measurement values ​​are all from clutter, then the PHD of the random finite set corresponding to the measurement values ​​provided by the clutter is denoted by λ k|k (x k), that is, the PHD of the random finite set of measurements provided by the clutter at time k:

[0091]

[0092] in, represents the number of surviving target scattering centers from time k-1 to time k, represents the weight of the hth target scattering center from time k-1 to time k, represents the mean value of the h-th target scattering center from time k-1 to time k, represents the variance of the hth target scattering center from time k-1 to time k, P D It represents the survival probability of the target scattering center from time k-1 to time k.

[0093] In addition, if a target is detected, that is, the current measurement value comes from the target and clutter, or the current measurement value all comes from the target, then the PHD of the random finite set corresponding to the measurement value provided by the target is recorded as That is, the prior PHD of the random finite set corresponding to the measurement value provided by the surviving target scattering center from time k-1 to time k is:

[0094]

[0095] Among them, m k represents the number of measurements provided by the scattering center of the surviving target at time k, represents the weight of the i-th measurement value at time k corresponding to the h-th target scattering center, represents the mean value of the h-th target scattering center corresponding to the i-th measurement value at time k, represents the variance of the i-th measurement value at time k corresponding to the h-th target scattering center. Further:

[0096]

[0097]

[0098] in, represents the i-th measurement value provided by the scattering center of the surviving target, x′, x represents the current state information, but different representations of different parts of the calculation. k represents the observation model matrix, R k represents the process (observation) noise covariance matrix, represents the i-th measurement value provided by the clutter at time k The corresponding PHD of a random finite set, D k|k-1(x) represents the prior PHD of the random finite set at the current moment of the prediction. The PHD of this part can be updated to:

[0099]

[0100] in, It means: the variable is x, the mean of the variable is μ, the covariance of the variable distribution is P, and the Gaussian distribution function, x is the state information of the target scattering center, is the probability density distribution of the measurement model of the i-th target scattering center, Represents the probability density distribution of the state information at time k-1.

[0101] Finally, in the embodiment of the present invention, the PHD formula of the random finite set at the current moment is updated according to the measured value at the current moment and the predicted prior PHD of the random finite set as follows:

[0102]

[0103] Among them, D k|k (x k ) represents the PHD of a random finite set updated at time k, x k Represents the state information at time k. The specific update process includes:

[0104] 1) Update each Gaussian component at time k-1 separately.

[0105] for make

[0106]

[0107] End for

[0108] 2) Update the status information of the target scattering center at the current moment according to the measured value.

[0109] Through the measurement model The Kalman filter can be used to Update to get Right now:

[0110] for make

[0111]

[0112]

[0113]

[0114]

[0115] End for

[0116] For the same predicted Gaussian component, the update process exists (m k +1) cases, which respectively represent the correction of the predicted Gaussian component when the observation is noise or the i-th measurement. Therefore, for the same predicted Gaussian component generated (m k +1) new Gaussian components, which should have the same label, namely:

[0117] for i=1:m k make

[0118] for make

[0119]

[0120]

[0121]

[0122]

[0123] End for

[0124] for make

[0125]

[0126] End for

[0127] End for

[0128] S104. Pruning and merging of PHDs of random finite sets of updates.

[0129] From S103, we can know that the number of target scattering centers corresponding to the PHD of the updated random finite set is recorded as It can be seen that most of the target scattering centers are repeated, so they need to be pruned and merged. The embodiment of the present invention provides a pruning and merging rule using the weights and spatial distribution positions of Gaussian components, specifically a method for pruning and merging the PHD of a random finite set of updates, including:

[0130] Prune the Gaussian components whose weights in the PHD of the updated random finite set are less than the preset weights, and / or prune the Gaussian components whose spatial distribution distances in the PHD of the updated random finite set are greater than the preset distance threshold, and merge multiple Gaussian components in the PHD of the updated random finite set whose spatial distributions are within the preset spatial range into one Gaussian component; wherein the sum of the weights of the multiple Gaussian components within the preset spatial range is used as the weight of the merged Gaussian component.

[0131] Here, the preset weight, preset spatial range, and preset distance threshold are all set according to actual needs.

[0132] S105. Extract several Gaussian components with the highest weights from the PHD of the pruned and merged random finite set as the posterior PHD of the random finite set at the current moment, and obtain the state estimation information of the target scattering center according to the mean of the posterior PHD of the random finite set.

[0133] The embodiment of the present invention extracts from the PHD of the random finite set after pruning and merging The Gaussian components with the highest weights are used as the posterior PHD of the random finite set, and the PHD of the effective random finite set after extraction is:

[0134]

[0135] Posterior PHD via random finite sets The mean The state estimation information x of the target scattering center can be obtained k .

[0136] In order to perform the next iterative solution, the embodiment of the present invention needs to update the PHD of the newly generated target scattering center:

[0137]

[0138] in, represents the number of new target scattering centers at time k+1, x k+1 represents the measurement value at time k+1, represents the mean of the scattering centers of the newly generated targets at time k+1, represents the variance of the scattering center of the newly generated target at time k+1, The hth measurement value at time k+1 is taken, that is, the posterior PHD of the random finite set at time k and the PHD of the random finite set calculated by the measurement value at time k+1 are simultaneously used as the PHD of the random finite set of the new target scattering center to ensure the robust detection and tracking of the target scattering center.

[0139] S106. Solve the position information of each target scattering center according to the state estimation information corresponding to each ISAR image in the sequential ISAR image sequence and associate them to obtain a sequential track, and solve the position information of each target scattering center according to the state estimation information corresponding to each ISAR image in the reverse ISAR image sequence and associate them to obtain a reverse track.

[0140] Through the above S101 to S105, the state estimation information corresponding to each ISAR image in the sequential ISAR image sequence and the state estimation information corresponding to each ISAR image in the reverse ISAR image sequence can be obtained. The position of the corresponding target scattering center in the sequential and reverse order can be solved through the state estimation information, and these position information are associated to obtain the sequential track and the reverse track.

[0141] It should be noted that the sequential track association is performed in the imaging order of the ISAR image sequence, while the reverse order is performed in the reverse order of the imaging order of the ISAR image sequence.

[0142] S20, fusing the track points of the target scattering center in the sequential track and the reverse track, and filling the missing track points of the target scattering center in the sequential track and the reverse track to obtain a complete track matrix for each target scattering center.

[0143] In the embodiment of the present invention, for each target scattering center, the process of fusing all track points in the sequential track and the reverse track includes:

[0144] Determine whether there is a track point of the target scattering center in the sequential track at the current moment: if so, continue to determine whether there is a track point of the target scattering center in the reverse track at the current moment: if not, use the track point of the target scattering center in the sequential track at the current moment as the fused track point; if so, calculate the first track mean based on the track point of the target scattering center in the sequential track and the track point in the reverse track at the current moment, and use the track point corresponding to the first track mean as the fused track point; if not, use the track point of the target scattering center in the reverse track at the current moment as the fused track point. Specifically:

[0145] Assume that the sequential and reverse tracks of the ith target scattering center obtained by S10 are:

[0146]

[0147] Where K represents the number of target scattering points in the sequential and reverse tracks, is the sequential track state of the i-th target scattering point at time k, is the reverse track state of the i-th target scattering point at time k, and and has a certain probability of being

[0148] The fusion process is as follows: If at time k, there is only a track point in the sequential track or a track point in the reverse track of the i-th target scattering center, that is then use this track point as the fused track point of the target scattering center at the current time; otherwise, calculate the first track mean value from the track points in the sequential track and the track points in the reverse track, and use the first track mean value as the fused track point at the current time. The entire fusion process is expressed as:

[0149]

[0150] wherein, is the track state of the i-th target scattering point after fusion at time k.

[0151] Furthermore, in the embodiments of the present invention, for each target scattering center, if there are missing track points of the target scattering center at the current time, the process of filling the missing track points includes:

[0152] Judge whether there is a track point of the target scattering center in the sequential track at the previous moment: If it exists, then continue to judge whether there is a track point of the target scattering center in the reverse track at the next moment: If not, then use the track point of the target scattering center in the sequential track at the previous moment as the filled track point; If it exists, then calculate the second track mean value according to the track point of the target scattering center in the sequential track at the previous moment and the track point of the target scattering center in the reverse track at the next moment, and use the track point corresponding to the second track mean value as the filled track point; If not, then use the track point of the target scattering center in the reverse track at the next moment as the filled track point. Specifically:

[0153] Through S10, the embodiments of the present invention can obtain the sequential and reverse state estimation information of each target scattering center at any time:

[0154]

[0155] Assume that the time when the i-th target scattering center lacks a track is k m (1 < k m < K), then the filling strategy for the missing track points is: If at time k m -1 there is state estimation information of the i-th target scattering center in the sequential track and at time k m +1 there is state estimation information of the i-th target scattering center in the reverse track then km The position information of the target scattering center at the moment can be obtained by and The mean of the one-step prediction is given by k m The track point and k of the target scattering center in the sequential track at time -1 m At time +1, the target scattering center calculates the second track mean at the track point in the reverse track. Since the parameter and The position information of the target scattering center is represented by the second track mean calculation formula:

[0156]

[0157]

[0158] The first track mean can also be calculated in a similar way to the second track mean. The above is just an illustration of the operation on two track points during the fusion process.

[0159] When k m State estimation information of the scattering center of the i-th target in the sequential track at time -1 or k m +1 time the state estimation information of the scattering center of the i-th target in the reverse track When it does not exist, k m The position information of the scattering center of the i-th target at the moment is respectively given by and In addition, when the number of missing track points is greater than 1, the position information of the missing target scattering center can be estimated by multi-step prediction, but the number of missing points usually does not exceed 3.

[0160] S30, calibrating the complete track matrix, and factorizing the calibrated complete track matrix to obtain a three-dimensional reconstructed position of a corresponding target scattering center.

[0161] Assume that the complete track matrix of the space target scattering center is:

[0162]

[0163] Where W' represents the complete track matrix, X represents the horizontal coordinate matrix of each target scattering center in the ISAR image sequence, Y represents the vertical coordinate matrix of each target scattering center in the ISAR image sequence, and x ki and ki are the horizontal and vertical coordinates of the scattering center of the i-th target in the k-th frame ISAR image, F represents the total number of observed sequences, and P represents the number of scattering center points.

[0164] Furthermore, the complete track matrix W' is calibrated to obtain the calibrated track matrix W.

[0165] In the embodiment of the present invention, the ordinate in the complete track matrix W' is multiplied by the distance resolution unit ρ r , multiply the horizontal coordinate by the azimuth resolution unit ρ a , and obtain the calibrated track matrix W. Among them,

[0166] The distance resolution unit is: γ=B / T p is the modulation frequency of the LFM (Linear Frequency Modulation) signal, T p is the pulse width, B is the bandwidth of the signal, C is the propagation speed of the electromagnetic wave, f s is the sampling frequency of the data, and N is the number of sampling points in the range direction of the ISAR image.

[0167] The orientation resolution unit is: λ is the wavelength of the transmitted signal, and θ is the angle accumulated by a single frame of ISAR imaging.

[0168] Furthermore, a registration operation is performed on the calibrated track matrix W.

[0169] Assume that the track matrix after calibration is:

[0170]

[0171] Where W represents the track matrix after calibration, U represents the horizontal coordinate matrix of the scattering center of each target in the ISAR image sequence after calibration, V represents the vertical coordinate matrix of the scattering center of each target in the ISAR image sequence after calibration, and u ki and v ki are the horizontal and vertical coordinates of the scattering center of the i-th target in the k-th frame ISAR image after calibration.

[0172] Next, preprocess each coordinate in the calibrated track matrix W:

[0173]

[0174]

[0175] The registered track matrix is ​​obtained through the above preprocessing:

[0176]

[0177] Furthermore, the registered track matrix Perform singular value decomposition.

[0178] According to the rank deficiency theory, the track matrix of the registration Through singular value decomposition:

[0179]

[0180] Among them, the diagonal matrix Σ=diag(σ1,σ2,σ3), and σ1>σ2>σ3. O1 and O2 are matrices composed of eigenvectors corresponding to eigenvalues ​​σ1, σ2, and σ3. Then there exists So that:

[0181]

[0182] Furthermore, constraints are introduced according to the orthogonality of the two-dimensional images to solve the singular value decomposition of the registered track matrix and obtain the three-dimensional coordinates of each target scattering center.

[0183] Since for any reversible matrix Q 3×3 , and Can satisfy That is, the above decomposition is not unique, so the following constraints are introduced:

[0184]

[0185]

[0186]

[0187] make The introduced constraints can be written in the following matrix form:

[0188] GI = C;

[0189]

[0190]

[0191]

[0192]

[0193] From this we can obtain:

[0194]

[0195] Based on I, the symmetric matrix L can be constructed. Under the condition that L satisfies the positive definite matrix, L is decomposed by Cholesky to obtain Q, thereby obtaining the three-dimensional coordinates of each target scattering center and the sensor motion parameters:

[0196]

[0197] Among them, S represents the three-dimensional coordinates of the scattering center, and M represents the sensor motion parameter.

[0198] In order to verify the effectiveness of the three-dimensional reconstruction method based on random finite set track association provided by the embodiment of the present invention, the following experiment is performed for verification.

[0199] (1) Simulation parameters

[0200] See also Figure 3 and Figure 4 , Figure 3 is a schematic diagram of a space target observation model provided by an embodiment of the present invention, Figure 4 is the spatial target point model provided by the embodiment of the present invention. The key parameters of the experiment are shown in Table 1.

[0201] Table 1 ISAR observation parameters and target motion parameters that generate elliptical and non-elliptical tracks

[0202]

[0203] In Table 1, [a,b]* indicates that the parameter changes linearly from a to b.

[0204] (2) Simulation experiment content and result analysis

[0205] The simulation model contains 10 randomly distributed three-dimensional target scattering centers. The simulated radar operates in the X-band with a bandwidth of 1 GHz. Through RD imaging, 92 frames of ISAR image sequences of the target in the three-axis stable state and the non-three-axis stable state are obtained. The signal-to-noise ratio of each frame is set to 10 dB. Some ISAR imaging results are shown in Figure 2. Figure 5 (a) and Figure 5 In the experiment, assuming that the extraction of the target scattering center has been completed, the following Figure 5 (c) and Figure 5 (d) shows the elliptical and non-elliptical tracks of the target scattering centers in the imaging plane. Considering the performance attenuation characteristics of the target scattering center extraction algorithm of the ISAR image sequence in practice, there are false alarms and missed detections in the extracted target scattering centers. At the same time, the detection probability of the target scattering center is set to 0.92 in the experiment, and the clutter density in the two-dimensional observation space is uniformly distributed to 3×10 -5 Each square pixel, and the area of ​​the two-dimensional observation space is 256×256 square pixels.

[0206] The proposed method can achieve accurate correlation between the elliptical track and the non-elliptical track of the point target scattering center. The results are as follows: Figure 5 (e) and Figure 5(f) is shown, where the curves of different colors represent the track correlation results of different target scattering centers. It can be seen that since the method proposed in the present invention introduces a motion model suitable for high-maneuverable targets, it is no longer constrained by the elliptical motion trajectory of the target scattering center, and can obtain good track correlation results under both elliptical and non-elliptical trajectories. In addition, the method proposed in the present invention can filter out clutter well, and can achieve accurate track correlation in the case of missed detection of the target scattering center, and has a certain robustness to clutter and missed detection.

[0207] At the same time, in order to quantitatively evaluate the performance of the method proposed in the present invention, the present invention defines the accuracy and error rate indicators of track association. Assume that the total number of target scattering centers on the target's real track is N total , the number of correctly associated target scattering centers is N true , the number of incorrectly associated target scattering centers is N false , then the track association accuracy can be defined as:

[0208]

[0209] The track association error rate is defined as:

[0210]

[0211] Among them, the correctly associated target scattering center means that the track point on the associated track is the real target scattering center and its track number is consistent with the real number. Otherwise, if the track point on the associated track is a false alarm point or does not belong to the corresponding real track, it is an incorrectly associated target scattering center.

[0212] Therefore, by counting the number of correctly associated target scattering centers and the number of incorrectly associated target scattering centers in the elliptical track association results and the non-elliptical track association results, the track association accuracy and error rate under different target motion forms can be calculated. The specific results are shown in Table 2, which further illustrate that the method proposed in the present invention has a high association accuracy for different tracks of three-axis stabilized and non-three-axis stabilized targets.

[0213] Table 2 Track correlation indicators for three-axis stabilized point targets and non-three-axis stabilized point targets

[0214]

[0215] In addition, through the fusion method of the present invention, the missing tracks of the scattering center can be filled, thereby forming a complete track matrix of the scattering center, and the three-dimensional imaging of the target can be achieved after accurate calibration. The complete tracks corresponding to the three-axis stabilized target and the non-three-axis stabilized target are as follows: Figure 6 (a) and Figure 6As shown in (b), it can be seen that the method proposed in the present invention can accurately estimate the missing track points. Based on this, the factorization method can be used to obtain the three-dimensional imaging results of the three-axis stabilized target and the non-three-axis stabilized target, as shown in Figure 2. Figure 6 (c) and Figure 6 As shown in (d), it can be seen that due to the accurate association and filling of the target scattering center tracks, the factorization method achieves accurate 3D reconstruction of all scattering centers of the target.

[0216] At the same time, in order to further evaluate the three-dimensional imaging quality of the method proposed in the present invention, the root mean square error (RMSE) evaluation index is defined:

[0217]

[0218] Where N represents the number of target scattering centers, represents the true three-dimensional coordinates of the nth target scattering center, represents the three-dimensional coordinates of the nth target scattering center obtained by the method proposed in the present invention. The root mean square error reflects the absolute error between the three-dimensional coordinates of the target scattering center reconstructed by three-dimensional imaging and the three-dimensional coordinates of the real target scattering center. The worse the three-dimensional imaging effect, the larger the RMSE; conversely, the smaller the RMSE.

[0219] The root mean square errors of the three-dimensional imaging results of the three-axis stabilized target and the non-three-axis stabilized target calculated by the root mean square error formula are 0.0278m and 0.0402m, respectively, which further illustrates the effectiveness and high precision of the method proposed in the present invention.

[0220] In summary, the three-dimensional reconstruction method based on random finite set track association proposed in an embodiment of the present invention includes: based on the improved GM-PHD filtering algorithm, the tracks of all target scattering centers are respectively associated along the sequential and reverse order of the ISAR image sequence to obtain sequential tracks and reverse order tracks; wherein the improved GM-PHD filtering algorithm introduces label information for each target scattering center on the basis of the traditional GM-PHD filtering algorithm; the track points of the target scattering centers in the sequential track and the reverse order track are fused, and the missing track points of the target scattering centers in the sequential track and the reverse order track are filled to obtain a complete track matrix of each target scattering center; the complete track matrix is ​​calibrated, and the calibrated complete track matrix is ​​factorized to obtain the three-dimensional reconstructed position of each target scattering center. It can be seen that the embodiment of the present invention introduces label information in the track association process, so that the target scattering center is no longer constrained by the motion trajectory form. For example, good track association results can be obtained under both elliptical and non-elliptical trajectories, which greatly reduces the difficulty of target scattering center track association. In addition, only some target scattering centers on the ISAR image sequence need to be observed for calculation, which greatly reduces the computational complexity of the data association algorithm, so that the method proposed in the present invention can be better applied to the motion model of highly maneuverable targets. Moreover, by introducing label information, the influence of clutter can be better filtered, and accurate track association can be achieved in the case of missed detection of the target scattering center, which has a certain robustness to clutter and missed detection. Before factoring and estimating the position coordinates of the target scattering center, the embodiment of the present invention pre-fuses and fills the track points in the associated track, which can effectively improve the accuracy of three-dimensional coordinate reconstruction.

[0221] In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0222] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art may understand and implement other variations of the disclosed embodiments by viewing the specification and its drawings. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "one" does not exclude multiple situations. Certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0223] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the scope of protection of the present invention.

Claims

1. A three-dimensional reconstruction method based on random finite set track association, characterized in that: The method comprises: Based on the improved GM-PHD filtering algorithm, the tracks of all target scattering centers are associated along the sequential and reverse order of the ISAR image sequence to obtain sequential tracks and reverse order tracks. The improved GM-PHD filtering algorithm introduces label information for each target scattering center based on the traditional GM-PHD filtering algorithm. The track points of the target scattering center in the sequential track and the reverse track are fused, and the missing track points of the target scattering center in the sequential track and the reverse track are filled to obtain a complete track matrix of each target scattering center; for each target scattering center, if there are missing track points of the target scattering center at the current moment, the process of filling the missing track points includes: judging whether there are track points of the target scattering center in the sequential track at the previous moment: if there are, then continue to judge whether there are track points of the target scattering center in the reverse track at the next moment: if not, then use the track points of the target scattering center in the sequential track at the previous moment as the filled track points; if there are, then calculate the second track mean according to the track points of the target scattering center in the sequential track at the previous moment and the track points of the target scattering center in the reverse track at the next moment, and use the track points corresponding to the second track mean as the filled track points; if not, then use the track points of the target scattering center in the reverse track at the next moment as the filled track points; The complete track matrix is ​​calibrated, and the calibrated complete track matrix is ​​factorized to obtain the three-dimensional reconstructed position of each target scattering center; wherein, Based on the improved GM-PHD filtering algorithm, the tracks of all target scattering centers are associated along the sequential and reverse order of the ISAR image sequence to obtain sequential tracks and reverse tracks, including: For each ISAR image in the sequential and reverse ISAR image sequences, the following steps are performed: calculating the PHD of the random finite set at the initial moment according to the measurement value at the initial moment, and assigning a label to each Gaussian component of the PHD of the random finite set at the initial moment; predicting the prior PHD of the random finite set at the current moment according to the PHD of the random finite set at the previous moment, and assigning a label to each Gaussian component of the prior PHD of the random finite set corresponding to the scattering center of the newly generated target in the prediction; updating the PHD of the random finite set at the current moment according to the measurement value at the current moment and the prior PHD of the predicted random finite set; pruning and merging the updated PHD of the random finite set; and In the PHD of the random finite set, several Gaussian components with the leading weights are extracted as the posterior PHD of the random finite set at the current moment, and the state estimation information of the target scattering center is obtained according to the mean of the posterior PHD of the random finite set; wherein, the state information used in the PHD calculation of the random finite set includes the instantaneous Doppler and instantaneous distance of any target scattering center on the target in the radar imaging plane, the projection components of the target motion velocity in the instantaneous Doppler direction and the instantaneous distance direction, and the projection components of the target motion acceleration in the instantaneous Doppler direction and the instantaneous distance direction; the state transfer matrix and the covariance matrix of the motion model noise used in the process of predicting the prior PHD of the random finite set at the current moment are both related to the target motion acceleration; According to the state estimation information corresponding to each ISAR image in the sequential ISAR image sequence, the position information of each target scattering center is solved and associated to obtain the sequential track, and according to the state estimation information corresponding to each ISAR image in the reverse ISAR image sequence, the position information of each target scattering center is solved and associated to obtain the reverse track; wherein, Pruning and merging the updated PHD of the random finite set, including: pruning the Gaussian components whose weights are less than the preset weights in the PHD of the updated random finite set, and merging multiple Gaussian components in the PHD of the updated random finite set that are spatially distributed within the preset spatial range into one Gaussian component; wherein the sum of the weights of the multiple Gaussian components within the preset spatial range is used as the weight of the merged Gaussian component; The state transfer matrix used is expressed as: Among them, F k represents the state transfer matrix, Δt is the time interval between two adjacent ISAR observation frames, and α represents the maneuvering frequency, which is the inverse of the maneuvering acceleration; The covariance matrix of the motion model noise used is expressed as: Among them, Q k represents the covariance matrix of the motion model noise, 2. The three-dimensional reconstruction method based on random finite set track association according to claim 1, characterized in that: The PHD formula for calculating a random finite set at the initial time is expressed as: Among them, λ b,0 (x0) represents the PHD of a random finite set at the initial time, represents the number of target scattering centers at the initial moment, represents the weight of the hth target scattering center at the initial moment, represents the Gaussian distribution function, x0 represents the state information at the initial moment, and the value of x0 is the measured value at the initial moment. represents the mean value of the h-th target scattering center at the initial moment, represents the variance of the hth target scattering center at the initial moment; Assigning labels to each Gaussian component of the PHD of a random finite set at the initial time is expressed as: Among them, L b,0 represents the set of all labels at the initial moment, Indicates that the initial time is The labels are assigned to the Gaussian components of the target scattering centers.

3. The three-dimensional reconstruction method based on random finite set track association according to claim 1, characterized in that: The prior PHD formula of the random finite set at the current moment is predicted based on the PHD of the random finite set at the previous moment: Among them, D k|k-1 (x k ) represents the prior PHD of a random finite set predicted from time k-1 to time k, x k represents the state information at time k, represents the sum of the Gaussian components of the PHD of a random finite set of surviving target scattering centers from time k-1 to time k, λ b,k (x k ) represents the PHD of the random finite set of new target scattering centers at time k, and the PHD of the random finite set of new target scattering centers at time k is predicted and calculated based on the measured value at time k-1; The label assignment for each Gaussian component of the PHD of a random finite set of newly generated target scattering centers at the current moment is expressed as: Among them, L b,k represents the set of new labels at time k, Indicates that time k is the first The labels are assigned to the Gaussian components of the target scattering centers.

4. The three-dimensional reconstruction method based on random finite set track association according to claim 1, characterized in that: The formula for updating the PHD of the random finite set at the current moment according to the measured value at the current moment and the predicted prior PHD of the random finite set is expressed as: Among them, D k|k (x k ) represents the PHD of a random finite set updated at time k, x k represents the state information at time k, represents the prior PHD of the random finite set corresponding to the measurement values ​​provided by the surviving target scattering center from time k-1 to time k, m k represents the number of measurements provided by the scattering center of the surviving target at time k, represents the number of surviving target scattering centers from time k-1 to time k, P D represents the survival probability of the target scattering center from time k-1 to time k, represents the weight of the i-th measurement value at time k corresponding to the h-th target scattering center, represents the mean value of the h-th target scattering center corresponding to the i-th measurement value at time k, represents the variance of the i-th measurement value at time k corresponding to the h-th target scattering center, represents the Gaussian distribution function, λ k|k (x k ) represents the PHD of the random finite set of measurements provided by the clutter at time k, represents the weight of the hth target scattering center from time k-1 to time k, represents the mean value of the h-th target scattering center from time k-1 to time k, It represents the variance of the h-th target scattering center from time k-1 to time k.

5. The three-dimensional reconstruction method based on random finite set track association according to claim 1, characterized in that: For each target scattering center, the process of fusing the track points of the target scattering center in the sequential track and the reverse track includes: Determine whether there is a track point of the target scattering center in the sequential track at the current moment: If it exists, continue to determine whether there is a track point of the target scattering center in the reverse track at the current moment: If it does not exist, the track point of the target scattering center in the sequential track at the current moment is used as the fused track point; If it exists, then calculate the first track mean according to the track points of the target scattering center in the sequential track and the track points in the reverse track at the current moment, and use the track points corresponding to the first track mean as the fused track points; If it does not exist, the track point of the target scattering center in the reverse track at the current moment will be used as the fused track point.

Images