Space-based ground multi-target positioning method based on multi-model PHD filtering

Abstract

The invention provides a space-based ground multi-target positioning method based on multi-model PHD filtering, which performs multi-model PHD filtering positioning on multiple ground targets by using space-based multi-platform optical observation information, adaptively determines a target motion model, and performs tracking positioning on the multiple targets at the same time. Firstly, a target motion model and an optical observation model are established; then constructing a PHD filtering algorithm framework, establishing a random finite set representation form of targets and observation, and realizing recursive estimation of multi-target posterior strength by constructing a state prediction and update mechanism; and on the basis of obtaining the multi-target posterior strength, estimating the number of the targets, and extracting the position of each target. According to the space-based ground multi-target positioning method based on multi-model PHD filtering, multiple ground targets can be tracked and positioned at the same time on the premise that data association is not needed, the utilization rate of space-based optical load observation data is greatly improved, and the calculation cost is reduced.

Description

Technical Field

[0001] The present invention relates to a ground multi-target positioning method applicable to space-based multi-platform optical observation, using multi-model probability hypothesis density (Probability Hypothesis Density, PHD). It involves using space-based multi-platform optical observation information to adaptively determine the target motion model and simultaneously track and locate multiple targets. It belongs to the field of space perception technology. Background Art

[0002] With the development of aerospace technology, the growing number of various targets, and the continuous competition for space superiority, the construction of space-based perception capabilities has become one of the goals of global competition, and the strategic position of space in the political, military, and economic fields has also been increasing. Target tracking and situational awareness capabilities have become the core capabilities of many activities. Whether we can seize air supremacy, space supremacy, and information supremacy is crucial for our country.

[0003] The aerospace situational awareness system is part of the national strategic information acquisition. With the development of aerospace technology, the real-time positioning and accurate forecasting technology of various targets will become an important component of the national security system and the infrastructure of information acquisition and target confrontation capabilities. In recent years, countries have included space-based space situational awareness systems in their aerospace development plans. Compared with ground-based situational awareness systems, space-based systems can overcome constraints such as lighting conditions, meteorological conditions, and geographical location, and have the potential for large-scale multi-target real-time detection, which can improve the comprehensiveness and real-time nature of perception capabilities.

[0005] Tracking and locating ground targets using large-scale low-orbit constellations has become a research hotspot in various countries. The present invention proposes a method for locating multiple ground targets using space-based multi-platform optical observation information. Most traditional multi-target positioning methods follow the steps of association-positioning. First, the observation data needs to be associated with the tracked targets respectively, and then the single targets after data association are tracked using single target positioning methods. These traditional multi-target tracking algorithms were developed earlier, and there are many mature algorithms at present, such as the nearest neighbor (NN) algorithm, the joint probabilistic data association (JPDA) algorithm, and the multiple hypothesis tracking (MHT) algorithm. These algorithms usually have problems such as being sensitive to target density and clutter intensity (NN) and large amount of association calculation (JPDA, MTT). They can only be used for simple multi-target association scenarios. In the current actual situation where the number of targets is huge and the interference sources are extensive, it is difficult to effectively complete the multi-target tracking task. The multi-model PHD filtering technology used in this project does not require the large computational costs of traditional association algorithms. This method has strong multi-target processing capabilities and is suitable for high-dimensional, nonlinear multi-target state estimation problems. It can adapt to changes in the number of targets and adaptively estimate the generation and disappearance of multiple targets. It can also provide more accurate target tracking results in complex situations such as target overlap and occlusion.

[0006] This space-based multi-target positioning method based on multi-model PHD filtering can directly track and locate multiple targets at the same time, and make the dynamic models of the targets converge synchronously, effectively solving the space-based multi-target positioning problem. Summary of the invention

[0007] In view of the current demand for simultaneous tracking and positioning of multiple ground targets and the development of large-scale low-orbit constellations, the present invention designs a ground multi-target positioning method suitable for space-based multi-platform optical observations and using PHD filtering. The advantages of the present invention are: using space-based multi-platform optical observations and multi-model PHD algorithms, it is possible to complete simultaneous tracking and positioning of multiple ground targets without data association, greatly improving the utilization rate of space-based optical payload observation data and reducing computing costs. At the same time, the multi-model filtering technology used enables the target dynamics model to converge synchronously during the positioning process, which can provide a basis for the judgment of target types and further enhance my country's space-based situational awareness capabilities.

[0008] The main technical solution of the present invention is: adopting the multi-model PHD filtering method, using the space-based multi-platform optical measurement data, to perform multi-model PHD filtering positioning on multiple ground targets, and at the same time determine the motion model of the target. Its main contents are as follows:

[0009] (1) Establishment of target motion model and optical observation model

[0010] In the geocentric fixed coordinate system, the state quantity x = [xyzv x v y v z a x a y a z ] T , each component of the state quantity is the position, velocity and acceleration components of the target under ECEF, and the static model, constant velocity model and constant acceleration model of different moving targets are constructed.

[0011] Use a space-based platform equipped with a visible light payload to image the target and extract its position information.

[0012] (2) Construction of multi-model PHD filtering algorithm

[0013] The PHD filtering algorithm framework is constructed, and the random finite set representation of targets and observations is established. By building a state prediction and update mechanism, the recursive estimation of the posterior strength of multiple targets is realized.

[0014] Establish a multi-model filtering technology framework, construct a multi-model Gaussian and implementation form, establish a model probability update mechanism, and combine it with PHD filtering.

[0015] (3) Target state extraction

[0016] Based on the obtained multi-target posterior strength, the number of targets is estimated and the position of each target is extracted. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is the workflow diagram of multi-model PHD filtering. DETAILED DESCRIPTION

[0018] The technical solution of the present invention will be fully described in detail below with reference to the accompanying drawings.

[0019] The specific steps include:

[0020] (1) Establishment of target motion model and optical observation model

[0021] In the geocentric fixed coordinate system, the state quantity x = [xyzv x v y v z a x a y a z ] T, each component of the state quantity is the position, velocity and acceleration components of the target under ECEF. The static model, constant velocity model and constant acceleration model of different moving targets are constructed. The static model can be constructed as:

[0022]

[0023] The constant velocity model can be constructed as:

[0024]

[0025] The constant acceleration model can be constructed as:

[0026]

[0027] Where w is Gaussian white noise.

[0028] The visible light payload is carried on the space-based platform to image the target and extract its orientation information. Assume that the position vectors of the observation camera and the observed target in the ECEF coordinate system are r i 、r j , then the azimuth measurement information obtained can be expressed by the azimuth angle α and the altitude angle β, and the measurement equation for visible light observation is obtained as follows:

[0029]

[0030] Among them, w α 、w β denote the measurement noise of two angle-only measurements, both of which are zero-mean white noise; and:

[0031]

[0032] The target is a light spot in the visible light imaging plane. In order to extract the precise position of the target, the centroid of the light spot needs to be extracted. The centroid of the light spot can be calculated based on the grayscale value of each pixel of the light spot as a weight. Assuming that the pixels of the image are m×n, and the grayscale value of each pixel is G(u,v), the calculated centroid (η,ξ) can be expressed as:

[0033]

[0034] Among them, w η 、w ξ Represents the centroid extraction error. The error probability distribution of the gray value G(u,v) is determined by the hardware conditions. According to the probability distribution of the camera error, the error probability distribution of the centroid position is estimated through Monte Carlo sampling.

[0035] (2) Construction of multi-model PHD filtering algorithm

[0036] Construct the PHD filter algorithm framework, establish the random finite set representation of targets and observations, and realize the recursive estimation of multi-target posterior strength by constructing the state prediction and update mechanism. Establish the multi-model filter technology framework, construct the multi-model Gaussian and implementation form, establish the model probability update mechanism, and combine it with PHD filtering. In the multi-target problem, since the respective sets of target states and measurements in time are not sorted, they can be represented as the following finite set form:

[0037]

[0038] where F(X) and F(Z) are the corresponding respective sets of all finite subsets.

[0039] For a given multi-target state at time k-1, each x k-1 ∈X k-1 At time k or p s,k (x k-1 ) with a probability of surviving, or with a probability of 1-p s,k (x k-1 ) has a probability of dying.

[0040] From the state x k-1 Transition to x k The probability density of is given by:

[0041] f k|k-1 (x k |x k-1 ).(8)

[0042] Therefore, for a given state x at time k-1 k-1 ∈X k-1 , its behavior at the next moment can be modeled as a random finite set form (RFS):

[0043] S k|k-1 (x k-1 )(9)

[0044] For a given multi-objective state X at time k-1 k-1 , the multi-objective state X at time k k Given by the survival goal, the spawning goal, and the natural generation goal:

[0045]

[0046] Among them, Γ k represents the naturally generated RFS at time k, B k|k-1 (ζ) represents the RFS derived from state ζ at time k.

[0047] The RFS measurement model considering detection uncertainty and clutter is described as follows: for a given target state x k ∈X k Either with p D,k (x k ) is detected with a probability of either 1-p D,k (x k ) is missed; in the case where the target is detected, the probability density of obtaining the observation value is given by g k (z k |x k ). Therefore, for each target state x at time k k ∈X k , will generate an RFS——Θ k (x k ).

[0048] Therefore, for a given multi-objective state X at time k k , the multi-target measurements received by the sensor are generated by combining the measurements produced by the target with the clutter:

[0049]

[0050] Based on the static multi-model estimator, it is assumed that the model at this moment is valid throughout the process and is one of the finite possible models in the model set:

[0051]

[0052] The prior probability that model j is correct is:

[0053] P{M f |Z 0}=μ f (0)f=1,...,r (13)

[0054] Where Z 0 is the prior information, and for the above formula, we have:

[0055]

[0056] Given the measurement data at time k, the correct posterior probability of model j is obtained by recursion using the Bayesian formula:

[0057]

[0058] The above formula is obtained from the given prior probability. Based on this, filters matching each model are established to produce state estimates under modal conditions and covariances under related modal conditions. After the filters are initialized, they will recursively operate according to their own estimates.

[0059] When using a static multi-model estimator, substituting the above multi-model problem, we will encounter model switching. The static multi-model estimator can be modified as follows: impose an artificial lower limit on the model probability, that is, properly normalize the remaining probability. However, this measure may increase the error of the unmatched filter to an unacceptable level. Therefore, in general, we can achieve correction by using the estimate of the filter corresponding to the best matching model among the other filters, that is, modify the model.

[0060] Since the PHD filter contains numerical integration operations, higher computational efficiency is required in practical engineering problems. Therefore, we use Gaussian mixture unscented Kalman filter (GMUKF) to implement the PHD filter more efficiently:

[0061] The GMUKF explanation prediction formula is as follows:

[0062]

[0063] The GMUKF explanation update formula is as follows:

[0064]

[0065] (3) Target state extraction

[0066] On the basis of obtaining the multi-target posterior intensity, the posterior intensity function is analyzed, the local maximum point is identified, and the peak value is extracted; the mean of the Gaussian function components with weights greater than 0.5 in the posterior intensity function is selected to describe the target state estimation (position, velocity, acceleration, etc.).

Claims

1. A method for multi-target positioning of space and ground based on multi-model PHD filtering, characterized by: Step 1: Establish target motion model and optical observation model In the geocentric fixed coordinate system, the components of the state quantity are taken as the position, velocity and acceleration components of the target in the geocentric fixed coordinate system, and the static model, constant velocity model and constant acceleration model of different moving targets are constructed. The visible light payload is carried by the space-based platform to image the target and extract its position information. Since the target is a light spot in the visible light imaging plane, the centroid of the light spot needs to be extracted to extract the precise position of the target. The centroid of the light spot can be calculated by weighting the gray value of each pixel of the light spot. Step 2: Multi-model PHD filtering algorithm construction Construct the PHD filtering algorithm framework, establish the random finite set representation of targets and observations, and realize the recursive estimation of the posterior strength of multiple targets by constructing the state prediction and update mechanism. Establish the multi-model filtering technology framework, construct the multi-model Gaussian and implementation form, establish the model probability update mechanism, and combine it with PHD filtering. Given the measurement data at time k, the correct posterior probability of model j is obtained by recursion using the Bayesian formula: The above formula is obtained from the given prior probability. Based on this, filters matching each model are established to produce state estimates under modal conditions and covariances under related modal conditions. After the filters are initialized, they will recursively operate according to their own estimates. When using a static multi-model estimator, when substituting into the above multi-model problem, we will encounter model switching. We can modify the static multi-model estimator as follows: impose an artificial lower limit on the model probability, that is, properly normalize the remaining probability. However, this measure may increase the error of the unmatched filter to an unacceptable level. Therefore, in general, the correction can be achieved by using the estimate of the filter corresponding to the best matching model among the other filters, that is, model modification. Since the PHD filter contains numerical integration operations, higher computational efficiency is required in practical engineering problems. Therefore, the Gaussian mixture unscented Kalman filter (GMUKF) is used to implement the PHD filter more efficiently: Step 3: Target state extraction On the basis of obtaining the multi-target posterior intensity, the posterior intensity function is analyzed, the local maximum point is identified, and the peak value is extracted; the mean of the Gaussian function components with weights greater than 0.5 in the posterior intensity function is selected to describe the target state estimation (position, velocity, acceleration, etc.).

Images