RCS information and Doppler information assisted adaptive PHD filtering method

Abstract

The invention relates to the technical field of space target monitoring, and discloses an RCS information and Doppler information-assisted adaptive PHD filtering method, which comprises the following steps of: 1, establishing a Gaussian mixture logarithmic normal distribution model; 2, on the basis of the Gaussian mixture logarithmic normal distribution model, improving the Gaussian component weight of the Gaussian mixture logarithmic normal distribution model, and establishing an adaptive PHD filter assisted by RCS information and Doppler information; according to the method, target RCS information and Doppler information are introduced into a multi-target filtering updating process, and target feature information is fully utilized to perform space multi-target tracking in a space-based scene; meanwhile, according to the method, the difference between the target and the clutter is enlarged by using the target RCS information and the Doppler information; the problems that an existing filtering method cannot provide target amplitude and RCS information, the accuracy cannot be effectively guaranteed, and different target tracks cannot be effectively distinguished are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of space target monitoring, and in particular relates to an adaptive PHD filtering method assisted by RCS information and Doppler information. Background Art

[0002] Obtaining effective information (position information, velocity information, electromagnetic information, etc.) of the space targets on orbit that are of particular concern to one's own side is a major challenge and difficulty in the field of space target monitoring. Generally, the space target monitoring task includes continuous monitoring of the targets of interest in the monitoring area, such as studying how the target orbit evolves over time, and then determining its own characteristics or status (such as: position information and velocity information in the reference coordinate system, etc.). Since the number of space targets in the monitoring area is time-varying and unknown, how to perform continuous high-precision tracking of the above targets is a typical multi-target tracking problem.

[0003] However, the inherent characteristics of space target monitoring tasks have brought a series of challenges to the multi-target tracking problem. Specifically, the monitoring area of ​​space-based radar is limited to a limited range due to the power aperture product constraint; in addition, how to continuously and accurately track space targets as they approach each other also brings inevitable problems to the filtering method; the limited monitoring area will lead to many problems such as target trajectory breakage and discontinuity, which also makes the low-orbit multi-target tracking problem of space-based radar more complicated and difficult. The above-mentioned multi-target tracking problem can be solved based on the random finite set framework. This type of method uses a finite set of random numbers as the processing object, and elevates the target processing from the single target level to the target set level. This theory provides an effective tool for solving the multi-target tracking problem. Finite set statistics theory (FISST) is a concise Bayesian filtering form that uses random finite set theory to solve the multi-target tracking problem. Vo and other scholars have successively proposed many effective methods such as probability density hypothesis filter and generalized probability density hypothesis filter. The core idea of ​​Bayesian filters is to update the first-order moment of the multi-target posterior probability and update the global posterior probability density. This method greatly reduces the computational complexity of the multi-target tracking problem. To alleviate the problem of inaccurate potential estimation in the standard PHD algorithm, Vo et al. proposed the CPHD filter, which obtains accurate potential estimation by transferring the potential function. Generally speaking, Gaussian mixture model and sequential Monte Carlo model are two classic implementation methods of the above Bayesian filter.

[0004] Among many multi-target tracking methods, PHD filters and CPHD filters are easy to implement due to their concise derivation form and low computational complexity. In the CPHD filter, although the PHD of the missed target can be correctly calculated, the PHD of the missed target is not correctly distributed to the corresponding target track, but evenly distributed to all tracks. This is because the independent and identically distributed assumption causes the filter to process all tracks together. This phenomenon is also called "spooky action". In addition, standard PHD filters and CPHD filters require prior models and parameters, such as clutter models, target birth models, and target detection probabilities. However, these models are usually time-varying and cannot be accurately obtained through actual tracking scenarios. These inaccurate model parameters will lead to deterioration of tracking accuracy. In particular, for RFS theory, it is difficult to derive an effective mathematical expression for its posterior probability density function. To this end, BTVo et al. proposed a multi-target potential balanced multi-Bernoulli filter (CBMeMBer), which can pass the posterior probability density of multiple targets. However, the tracking performance of this filter will deteriorate rapidly and fail in a low-clutter environment. In recent years, generalized labeled multi-Bernoulli and its simplified form labeled multi-Bernoulli filter have become the most advanced and tractable methods. Both of the above filters are developed based on a random finite set of labels. By setting different labels, LMB filters and GLMB filters can accurately identify the trajectories of different targets. The density of the GLMB filter has a conjugate posterior, which is closed under the Chapman-Kolmogorov equation of the standard multi-target likelihood. Therefore, the GLMB filter can be effectively implemented in practical applications. However, due to the moment approximation operation, it is difficult for the LMB filter to avoid missed detection.

[0005] In recent years, with the rapid development of stealth technology and supersonic technology, it has been difficult to meet the requirements of "seamless time domain and no blindness in airspace" for monitoring space targets by relying solely on ground-based radar equipment and ground-based optical equipment. Against this background, space-based radars have emerged. Compared with ground-based radars, space-based radars use satellites as platforms, which are not affected by the curvature of the earth and can detect targets in a larger range and at a longer distance. In addition, space-based radar detection is not restricted by national territory and can perform detection and monitoring tasks on space targets at any time and place. For stealth targets in the air, the radar scattering cross-section presented by the space-based radar beam irradiating downward from its upper half is much larger than the RCS presented by the ground-based radar irradiating from its lower part, front, and rear CCTV, making it easier to detect stealth targets.

[0006] It should be noted that the current traditional filters are all effective in utilizing some potentially useful information in the target echo, such as the target radar cross section, one-dimensional high-resolution range image, etc. Therefore, there are still some problems to be solved:

[0007] 1. The multi-target tracking method mentioned in the above prior art usually only uses the distance and direction information of the target. However, the multi-target tracking method cannot provide information such as the amplitude and RCS of the target when used.

[0008] 2. Although traditional RCS statistical distribution models, such as chi-square distribution, Weibull distribution and log-normal distribution, can describe the electromagnetic distribution characteristics of space targets, their accuracy cannot be effectively guaranteed.

[0009] 3. The multi-target tracking method mentioned in the above prior art cannot effectively complete the distinction between different target trajectories when space targets are close to each other, which is also the distinction between space-based radar tracking.

[0010] Therefore, in view of the above problems, the present invention proposes an adaptive PHD filtering method assisted by RCS information and Doppler information to solve the problems existing in the above prior art. Summary of the invention

[0011] 1. Technical issues to be resolved

[0012] In view of the shortcomings of the prior art, the present invention provides an adaptive PHD filtering method assisted by RCS information and Doppler information, which has the advantages of effectively improving target tracking performance, effectively improving the statistical accuracy of the RCS bimodal characteristics of space targets, and effectively improving the potential estimation accuracy and detection performance of multi-target filters. It solves the problems of the existing filtering methods, such as the inability to provide information such as the amplitude and RCS of the target, the inability to effectively guarantee the accuracy, and the inability to effectively distinguish between different target trajectories.

[0013] (II) Technical solution

[0014] In order to achieve the above-mentioned purpose of effectively improving the potential estimation accuracy and detection performance of the multi-target filter and enhancing the ability to distinguish spatially adjacent targets, the present invention provides the following technical solutions:

[0015] An adaptive PHD filtering method assisted by RCS information and Doppler information, comprising:

[0016] Step 1: Establish a mixed Gaussian lognormal distribution model and derive the observation geometry relationship between space targets and space-based radar

[0017] Step 1.1: Establish a target state model based on target RCS information and Doppler information;

[0018] Step 1.2: Based on the target state model of the target RCS information and Doppler information, establish the prediction and update algorithm model of the RDGI-PHD filter;

[0019] Step 1.3: Based on the prediction and update algorithm model of the RDGI-PHD filter, an improved RCS mixed statistical distribution model is established;

[0020] Step 1.4: Perform geometric transformation of space-based radar observations based on the improved RCS mixed statistical distribution model;

[0021] Step 2: Based on the mixed Gaussian log-normal distribution model, the Gaussian component weights of the mixed Gaussian log-normal distribution model are improved to establish an adaptive PHD filter assisted by RCS information and Doppler information.

[0022] In a preferred embodiment, the process of establishing the target state model based on the target RCS information and Doppler information includes:

[0023] The target monitoring area is three-dimensional, and the target measurement status is:

[0024] x k =[l x,k ,v x,k ,l y,k ,v y,k ,l z,k ,v z,k ] T (1)

[0025] In the formula, l x,k , l y,k and l z,k They represent the three-dimensional position information of the target at time k, v x,k , v y,k and v z,k Respectively represent the three-dimensional velocity information of the target;

[0026] By extending the target RCS information and Doppler information to the target measurement state, we can obtain:

[0027] z k =[z l,k ,z d,k ,z rcs,k ] (2)

[0028] In the formula, z l,k ,z d,k and z rcs,k They represent target position measurement, Doppler measurement and RCS measurement respectively.

[0029] In a preferred embodiment, the process of establishing the prediction and update algorithm model of the RDGI-PHD filter includes:

[0030] Step 1.2.1: Establish the prediction algorithm model of RDGI-PHD filter;

[0031] Step 1.2.2: Establish the update algorithm model of RDGI-PHD filter.

[0032] In a preferred embodiment, the prediction algorithm model of the RDGI-PHD filter is:

[0033]

[0034] In the formula, γ k (x k ) represents the RFS intensity at time k, p s,k (x k-1 ) represents the target survival probability, f k|k-1 (x k |x k-1 ) represents the Markov transition probability density, b k|k-1 (x k |x k-1 ) represents the target strength of splitting from the state at time k-1, D k-1|k-1 (x k-1 ) represents the PHD filter strength at time k-1, D k|k-1 (x k ) represents the PHD filter strength at time k.

[0035] In a preferred embodiment, the process of establishing the update algorithm model of the RDGI-PHD filter includes:

[0036] (1) After introducing RCS information and Doppler information into the standard PHD filter, the update expression of the RDGI-PHD filter is:

[0037] D k|k (x k )=L Z (x k )·D k|k-1 (x k ) (4)

[0038] Assuming that the target RCS information and Doppler information are independent of the target's position state, the target likelihood probability and clutter likelihood probability are:

[0039] g(z|x)=g((z l,k ,z d,k ,z a,k )|x)=g l (z l |x)g d (d)g rcs (rcs) (5)

[0040] c(z|x))=c z (z|x)cd (d)c rcs (rcs) (6)

[0041] In the formula, g l (z l |x), g rcs (rcs) and g d (d) represents the k-target position likelihood function, Doppler likelihood function and RCS likelihood function respectively; c z (z|x), c d (d) and c rcs (rcs) represent clutter position likelihood, clutter Doppler likelihood and RCS amplitude likelihood respectively;

[0042] (2) The Doppler likelihood function is:

[0043] g d (d) = N(z d,k ;h k (x k ),R d,k ) (7)

[0044]

[0045] In the formula, R d,k represents the noise room variance;

[0046] The RCS likelihood is obtained through Section III-D, and the RCS information and Doppler information are merged into the PHD update recursion. The PHD pseudo-likelihood probability is obtained using this auxiliary information:

[0047]

[0048] Where κ(z) = λ c Vc z (z|x) represents the clutter intensity function that obeys the Poisson distribution;

[0049] The Gaussian mixture form of the posterior density at time k-1 is:

[0050]

[0051] In the formula, represents the weight of the i-th Gaussian component at time k-1;

[0052] Substituting equation (9) into equation (4), we get the posterior strength at time k:

[0053]

[0054] Where, the normalized code Gaussian mixture weight is

[0055]

[0056] in

[0057] (3) For the standard GM-PHD filter and the RCS information-assisted GM-PHD filter, the posterior likelihood probabilities are

[0058]

[0059] Note that g rcs (rcs) and c rcs (rcs) represents the RCS likelihood function of the target and clutter respectively;

[0060] (4) Let the RCS likelihood of the measured value exceeding the detection threshold be and The normalized form is

[0061]

[0062] In the formula

[0063]

[0064] denote the detection probability and false alarm probability respectively;

[0065] (5) The RCS amplitude likelihood ratio under the detection threshold τ is defined as:

[0066]

[0067] Substituting formula (19) into formula (14), formula (19) is rewritten as:

[0068]

[0069] From the above formula, we can see that when the signal-to-noise ratio is 0, At this time, the RCS information assisted PHD filter is regarded as a standard PHD filter.

[0070] In a preferred embodiment, the improved RCS mixed statistical distribution model is:

[0071]

[0072] Where Θ=[λ1,...,λ M ; μ1,...,μ M ; s1,...,s M ], μ i and i represents the composition parameters of the proposed MLN model; I represents the number of components in the proposed MLN model.

[0073] In a preferred embodiment, the process of performing space-based radar observation geometry conversion based on the improved RCS mixed statistical distribution model includes:

[0074] Step 1.4.1: Based on the Earth Fixed (ECEF) coordinate system O e -X e Y e Z e and the target body coordinate system O t -X t Y t Z t The positions of the space target and the space-based radar in the ECEF coordinate system are obtained by transformation:

[0075]

[0076] In the formula, R x ,R y and R z They are respectively expressed as the rotation matrix around the x-axis, the rotation matrix around the y-axis and the rotation matrix around the z-axis, which can be expressed as follows:

[0077]

[0078] Step 1.4.1: The coordinate transformation matrix between the ECEF coordinate system and the target fixed coordinate system is

[0079] M ECEF-OF =[R z (Ω)R x (α)R z (ω+θ)] -1 (27)

[0080] Therefore, the positions of the space target and the space-based radar in the target body coordinate system are:

[0081]

[0082] Step 1.4.3: Finally, the radar sight angle in the target body coordinate system is calculated as:

[0083]

[0084] In the formula, [x Δ ,y Δ ,z Δ ] represents the position vector of the radar sight angle in the target body coordinate system, θ Δ and They represent the observation azimuth and elevation angle in the target body coordinate system respectively.

[0085] In a preferred embodiment, the process of improving the Gaussian component weights of the mixed Gaussian log-normal distribution model and establishing an adaptive PHD filter assisted by RCS information and Doppler information includes:

[0086] (1) First, filter out the index of the highest component in the target posterior probability density:

[0087]

[0088] In the formula, I represents the index set;

[0089] (2) Further, find the component order set that is closest to the component with the largest weight in the target posterior strength at time k:

[0090]

[0091] In the formula, σ s represents the variance of the measurement noise;

[0092] (3) If the Gaussian components satisfy equation (34) and the sum of the component weights does not exceed twice the state extraction threshold, a new set containing the following components is obtained:

[0093]

[0094] (4) When satisfied Except for the highest weight, all other sub-weights of the target are multiplied by a penalty factor, and the new weights are as follows:

[0095]

[0096] In the formula, represents the penalty factor, where 0≤α≤1 is a constant that determines the degree of penalty;

[0097] Substituting equation (37) into equation And renormalize the target new weight corresponding to each measurement to obtain the following renormalized weight

[0098]

[0099] In the formula, κ k (λ c )=λ c c rcs (rcs)c d (d);

[0100] (5) Finally, the new posterior probability density is:

[0101]

[0102] From formula (35), we can see that U mm It is an adaptive threshold that varies with component weights and measurement noise.

[0103] (III) Beneficial effects

[0104] Compared with the prior art, the present invention provides an adaptive PHD filtering method assisted by RCS information and Doppler information, which has the following beneficial effects:

[0105] 1. This method introduces the target RCS information and Doppler information into the multi-target filtering update process, and makes full use of the target feature information rather than just the position information and velocity information to track multiple targets in space in the space-based scenario; at the same time, considering that the time-varying target echo signal is strongly correlated while the clutter information is not correlated, this method can minimize the gap between the target and the clutter by making full use of the target RCS information and Doppler information, thereby distinguishing the two as early as possible in the filtering process and effectively improving the target tracking performance; in addition, due to the differences in the RCS characteristics of different types of targets, this method can distinguish spatially adjacent targets and further improve the tracking performance;

[0106] 2. This method proposes an improved RCS mixed statistical distribution model, which can more accurately describe the dynamic likelihood probability of space target RCS and effectively improve the statistical accuracy of the bimodal characteristics of space target RCS;

[0107] 3. Based on the mixed Gaussian log-normal distribution model, this method designs a method to improve the Gaussian component weights of the mixed Gaussian log-normal distribution model, which can effectively improve the potential estimation accuracy and detection performance of the multi-target filter; at the same time, this method also improves the ability of the multi-target filter to distinguish spatially neighboring targets; it achieves the purpose of effectively improving the potential estimation accuracy and detection performance of the multi-target filter and improving the ability to distinguish spatially neighboring targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 It is a flow chart of the PHD filtering method assisted by RCS information and Doppler information of the present invention;

[0109] Figure 2 This is a schematic diagram of the coordinate system conversion of the space-based radar of the present invention;

[0110] Figure 3 The single-station static RCS distribution result diagram of three space targets of the present invention;

[0111] Figure 4 This is a comparison diagram of the static RCS statistical distribution results of three space targets at two working frequencies using different methods;

[0112] Figure 5It is a scene diagram of the three-dimensional simulation experiment of the present invention;

[0113] Figure 6 A flow chart is established for the single-station static RCS database of the present invention;

[0114] Figure 7 It is a static RCS curve diagram of three typical space targets in the three-dimensional simulation experiment scene of the present invention;

[0115] Figure 8 The radar sight angle parameter curve diagrams of three typical space targets of the present invention;

[0116] Fig. 9 The following are the dynamic RCS sequence diagrams of three typical space targets of the present invention;

[0117] Fig.10 It is the average OSPA estimation error diagram of 100 Monte Carlos of the present invention;

[0118] Fig.11 This is a graph showing the target potential estimation results of 100 Monte Carlo simulations of the present invention.

[0119] Among them, Figure 3 In the figure, Figure (a) is a single-station static RCS distribution result diagram of a chi-square distribution space target, Figure (b) is a single-station static RCS distribution result diagram of a Weibull distribution space target, and Figure (c) is a single-station static RCS distribution result diagram of a log-normal distribution space target;

[0120] exist Figure 4 In the figure, Figure (a) is a curve diagram of target 1 at an operating frequency of 500 MHz; Figure (b) is a curve diagram of target 1 at an operating frequency of 1 GHz; Figure (c) is a curve diagram of target 2 at an operating frequency of 500 MHz; Figure (d) is a curve diagram of target 2 at an operating frequency of 1 GHz; Figure (e) is a curve diagram of target 3 at an operating frequency of 500 MHz; Figure (f) is a curve diagram of target 3 at an operating frequency of 1 GHz;

[0121] exist Figure 7 In the middle, the azimuth angle range is: 0-180 degrees, and the pitch angle is fixed at 90 degrees. DETAILED DESCRIPTION

[0122] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0123] Example 1: Please refer to Figure 1-Figure 2, the present invention provides a technical solution:

[0124] A PHD filtering method based on RCS information and Doppler information, including:

[0125] Step 1: Establish a mixed Gaussian lognormal distribution model and derive the observation geometry relationship between space targets and space-based radar

[0126] Step 1.1: Establish a target state model based on target RCS information and Doppler information

[0127] If the target monitoring area is three-dimensional, the target measurement state can be expressed as:

[0128] x k =[l x,k ,v x,k ,l y,k ,v y,k ,l z,k ,v z,k ] T (1)

[0129] In the formula, l x,k , l y,k and l z,k They represent the three-dimensional position information of the target at time k, v x,k , v y,k and v z,k Respectively represent the three-dimensional velocity information of the target;

[0130] By extending the target RCS information and Doppler information to the target measurement state, we can obtain:

[0131] z k =[z l,k ,z d,k ,z rcs,k ] (2)

[0132] In the formula, z l,k ,z d,k and z rcs,k They represent target position measurement, Doppler measurement, and RCS measurement respectively;

[0133] Step 1.2: Based on the target state model of target RCS information and Doppler information, establish the prediction and update algorithm model of RDGI-PHD filter

[0134] Step 1.2.1: Build the prediction algorithm model of RDGI-PHD filter

[0135] Since the filtering method proposed in this embodiment is consistent with the state vector form of the standard PHD filter, the prediction step is consistent with the iterative process of the standard filter, which can be expressed as:

[0136]

[0137] In the formula, γ k (x k ) represents the RFS intensity at time k, p s,k (x k-1 ) represents the target survival probability, f k|k-1 (x k |x k-1 ) represents the Markov transition probability density, b k|k-1 (x k |x k-1 ) represents the target strength of splitting from the state at time k-1, D k-1|k-1 (x k-1 ) represents the PHD filter strength at time k-1, D k|k-1 (x k ) represents the PHD filter strength at time k;

[0138] Step 1.2.2: Establish the update algorithm model of RDGI-PHD filter

[0139] (1) After introducing RCS information and Doppler information into the standard PHD filter, the update expression of the proposed RDGI-PHD filter is:

[0140] D k|k (x k )=L Z (x k )·D k|k-1 (x k ) (4)

[0141] Assuming that the target RCS information and Doppler information are independent of the target's position state, the target likelihood probability and clutter likelihood probability can be expressed as

[0142] g(z|x)=g((z l,k ,z d,k ,z a,k )|x)=g l (z l |x)g d (d)g rcs (rcs) (5)

[0143] c(z|x))=c z (z|x)c d (d)c rcs (rcs) (6)

[0144] In the formula, g l (z l |x), grcs (rcs) and g d (d) represents the k-target position likelihood function, Doppler likelihood function and RCS likelihood function respectively; c z (z|x), c d (d) and c rcs (rcs) represent clutter position likelihood, clutter Doppler likelihood and RCS amplitude likelihood respectively;

[0145] (2) The Doppler likelihood function can be expressed as

[0146] g d (d) = N(z d,k ;h k (x k ),R d,k ) (7)

[0147]

[0148] In the formula, R d,k represents the noise room variance;

[0149] The RCS likelihood can be obtained through Section III-D. The RCS information and Doppler information are incorporated into the PHD update recursion. Using these auxiliary information, the PHD pseudo-likelihood probability can be obtained as follows:

[0150]

[0151] Where κ(z) = λ c Vc z (z|x) represents the clutter intensity function that obeys the Poisson distribution;

[0152] The Gaussian mixture form of the posterior density at time k-1 can be expressed as follows:

[0153]

[0154] In the formula, represents the weight of the i-th Gaussian component at time k-1;

[0155] Substituting equation (9) into equation (4), we can get the posterior strength at time k:

[0156]

[0157] In the formula, the normalized code Gaussian mixture weight can be expressed as

[0158]

[0159] in

[0160] (3) This embodiment proves the consistency of the proposed information-assisted filter and the standard GM-PHD filter from a mathematical level. For ease of reading, this embodiment only provides the validity proof of the filter assisted by RCS information, and Doppler information can also be given in the same way. For the standard GM-PHD filter and the GM-PHD filter assisted by RCS information, the posterior likelihood probability can be expressed as

[0161]

[0162] Note that g rcs (rcs) and c rcs (rcs) represents the RCS likelihood function of the target and clutter respectively;

[0163] (4) Generally speaking, the typical detection process is to find the local maximum value among all the measured values ​​and then perform threshold processing on them. In this embodiment, the RCS likelihood of the measured value exceeding the detection threshold is defined as and The normalized form can be expressed as

[0164]

[0165] In the formula

[0166]

[0167] denote the detection probability and false alarm probability respectively;

[0168] (5) The RCS amplitude likelihood ratio under the detection threshold τ is defined as:

[0169]

[0170] Substituting formula (19) into formula (14), formula (19) can be rewritten as:

[0171]

[0172] From the above formula, we can see that when the signal-to-noise ratio is 0, At this time, the RCS information assisted PHD filter can be regarded as a standard PHD filter.

[0173] Step 1.3: Based on the prediction and update algorithm model of the RDGI-PHD filter, an improved RCS mixed statistical distribution model is established

[0174] Typical RCS distribution models, such as chi-square distribution and lognormal distribution, have concise expressions and few parameters. However, when targeting targets with drastic RCS fluctuations, such as stealth aircraft or military satellites, the fitting accuracy of these conventional RCS distribution models is not ideal. In addition, since the typical RCS statistical distribution model is unimodal, it can only roughly describe the characteristics of complex fluctuation distributions. Under certain conditions, such as for some satellites, the main peak with the largest weight is well described, while the fluctuation distribution with smaller weights is ignored. Inspired by the idea of ​​mixed lognormal distribution, the weight parameter is introduced to improve the fitting degree of the classic lognormal RCS distribution model. The proposed MLN RCS distribution model is obtained by adding sub-distribution models with different weights, which can be expressed as

[0175]

[0176] Where Θ=[λ1,...,λ M ; μ1,...,μ M ; s1,...,s M ], μ i and i represents the component parameters of the proposed MLN model; I represents the number of components in the proposed MLN model;

[0177] When I = 1, the above RCS statistical distribution model can be simplified to the traditional log-normal distribution model, so the improved RCS mixed statistical distribution model is established;

[0178] Step 1.4: Perform geometric transformation of space-based radar observations based on the improved RCS mixed statistical distribution model

[0179] In order to obtain the precise dynamic RCS of space targets based on space-based radar platforms, this step derives the observation geometry transformation to ensure accurate observation angle input.

[0180] Step 1.4.1: Figure 2 As shown, the Earth-centered, Earth-fixed (ECEF) coordinate system O e -X e Y e Z e The black line indicates the target body coordinate system O t -X t Y t Z t Indicated by the red line; the origin of the ECEF coordinate system is defined at the center of the earth, and it is a non-rotating right-handed Cartesian coordinate system; X e The axis points to the intersection of the equator and the prime meridian, Z e The axis passes through the Earth's North Pole; X t Axis parallel to the velocity direction, Zt The Y axis is along the satellite axis. t The axis is determined by the right-hand rule; N i (i=1,2) represents the ascending node, P i (i=1,2) indicates perigee;

[0181] The orbit of the space target can be determined by the six orbital elements in the given double-row orbital elements: specifically, the double-row orbital elements include the semi-major axis h, the orbital inclination α, the right ascension of the ascending node Ω, the eccentricity ω, and the perigee angle θ; then, based on the six orbital elements, the target center of mass position and the observation geometry transformation between the ECEF coordinate system and the OF coordinate system can be derived.

[0182] The positions of the space target and the space-based radar in the ECEF coordinate system are shown in (22) and (23):

[0183]

[0184] In the formula, R x ,R y and R z They are respectively expressed as the rotation matrix around the x-axis, the rotation matrix around the y-axis and the rotation matrix around the z-axis, which can be expressed as follows:

[0185]

[0186] Step 1.4.2: The coordinate transformation matrix between the ECEF coordinate system and the target fixed coordinate system can be expressed as

[0187] M ECEF-OF =[R z (Ω)R x (α)R z (ω+θ)] -1 (27)

[0188] Therefore, the positions of the space target and the space-based radar in the target body coordinate system can be expressed as:

[0189]

[0190] Step 1.4.3: Finally, the radar line of sight angle in the target body coordinate system can be calculated as:

[0191]

[0192]

[0193] In the formula, [x Δ ,y Δ ,z Δ ] represents the position vector of the radar sight angle in the target body coordinate system, θΔ and They represent the observation azimuth and elevation angle in the target body coordinate system respectively;

[0194] So far, through the above-mentioned observation geometry transformation process, this embodiment no longer considers the body motion of the space target;

[0195] Step 2: Based on the mixed Gaussian log-normal distribution model, the Gaussian component weights of the mixed Gaussian log-normal distribution model are improved to establish an adaptive PHD filter assisted by RCS information and Doppler information.

[0196] The target posterior probability density can be calculated by formula (11), so the probability density at different times can be represented by Gaussian components with different weights. In order to more effectively detect space targets under low detection probability or dense clutter background, this embodiment introduces labels κ for different space targets, so that there is a set

[0197]

[0198] in, represents the label of the kth target at time i;

[0199] Based on the random finite set framework, this embodiment provides a Gaussian component weight improvement strategy as follows:

[0200] (1) First, filter out the index of the highest component in the target posterior probability density as follows:

[0201]

[0202] In the formula, I represents the index set;

[0203] (2) Further, find the component order set that is closest to the component with the largest weight in the target posterior strength at time k, which can be expressed as

[0204]

[0205] In the formula, σ s represents the variance of the measurement noise;

[0206] (3) If the Gaussian components satisfy equation (34) and the sum of the component weights does not exceed twice the state extraction threshold, a new set containing the following components can be obtained:

[0207]

[0208] (4) When satisfied Except for the highest weight, all other sub-weights of the target are multiplied by a penalty factor, and the new weights are as follows:

[0209]

[0210] In the formula, represents the penalty factor, where 0≤α≤1 is a constant that determines the degree of penalty;

[0211] Substituting equation (37) into equation (12) and renormalizing the new target weight corresponding to each measurement, we can obtain the following renormalized weight:

[0212]

[0213] In the formula, κ k (λ c )=λ c c rcs (rcs)c d (d);

[0214] (5) Finally, the new posterior probability density can be expressed as:

[0215]

[0216] From formula (35), we can see that U mm is an adaptive threshold that varies with component weights and measurement noise;

[0217] Therefore, it can dynamically adjust during the merging process and better adapt to distinguishing neighboring spatial objects.

[0218] Example 2: Figure 3-Figure 11 As shown, in order to prove the effectiveness of the PHD filtering method based on RCS information and Doppler information assistance described in Example 1 of the present invention, a comparison of simulation experimental results is carried out in this embodiment.

[0219] 1. Target RCS fit comparison experiment

[0220] This example compares the RCS fitting results of the traditional methods (i.e., chi-square distribution, Weibull distribution, and lognormal distribution) and the MLN method proposed in Example 1.

[0221] First, the single-station RCS of three space targets is calculated using electromagnetic simulation software. The simulation results are as follows: Figure 3 .(a)~ Figure 3 .(c) shown.

[0222] Depend on Figure 3As shown in (a)-(c), the single-station static RCS of the three typical space targets all have large fluctuation characteristics, and the RCS curve distribution trends and amplitudes of the three targets are different. Specifically, the RCS amplitudes of the three targets in the belly direction are relatively high, and only the third target has a relatively high RCS amplitude in the nose cone direction. Analysis of the reason shows that the third target contains an antenna in the nose cone direction, which will cause strong mirror reflection, resulting in a higher amplitude. Based on the RCS data obtained above, the RCS fluctuation fitting results of the above three typical satellites in the two working frequency bands of 500GMz and 1GHz are obtained as shown below Figure 4 .As shown in (a)-(f).

[0223] According to the above curve fitting results, the MLN method proposed in Example 1 of the present invention has better fitting effects on the RCS data of three types of typical space targets at two radar operating frequencies than the chi-square distribution, Weibull distribution and lognormal distribution. Specifically, when there are two peaks in the probability density distribution curve of RCS, the proposed method can describe the bimodal characteristics more accurately than other methods. In addition, the RCS estimation result obtained by the MLN method proposed in Example 1 of the present invention is basically consistent with the RCS statistical data.

[0224] In order to further quantitatively compare the RCS fitting results, this example introduces the KS test as follows:

[0225] D=maxF(x)-G(x)(41)

[0226] Where F(x) and G(x) represent the cumulative distribution function of sample data and the cumulative distribution function of experimental data, respectively.

[0227] The KS test results are shown in Table 1. It can be seen that the result of the method proposed in Example 1 of the present invention is smaller than that of other methods, which verifies the effectiveness of the MLN RCS statistical distribution model.

[0228] L-In summary, the above simulation results verify that the filter proposed in Example 1 of the present invention has stronger robustness under complex RCS fluctuations, which is attributed to the fact that it consists of more adjustment parameters.

[0229] Table 1: KS test results

[0230]

[0231] 2. Target dynamic RCS sequence

[0232] First, this embodiment sets up the following three-dimensional simulation scene to obtain the dynamic RCS of three typical space targets. The simulation experiment scene is as follows: Figure 5 shown.

[0233] Figure 6The flowchart of establishing a single-station steady-state RCS database in Example 1 of the present invention is shown in Figure 1. Through computer-aided design (CAD) modeling, meshing, scattering characteristic calculation and post-data processing, the RCS data of all airspace targets is finally obtained. The single-station RCS of three typical space targets is obtained, such as Figure 7 In most practical applications, the LOS parameter sequence can be obtained by different methods. Embodiment 1 of the present invention uses TLE ephemeris to solve the satellite target, and uses the SGP4 model to calculate the position of the space target, and finally calculates the position of the target relative to the space-based radar, and finally obtains the radar line of sight angle data of the space target relative to the space-based radar, as shown in FIG. Figure 8 Table 2 gives the specific simulation parameters of the space-based radar and three satellite targets in the spacecraft orbit calculation software. Finally, by combining the full airspace RCS and LOS parameters, the target dynamic RCS sequence results can be obtained. Figure 5 It can be seen that the three space targets are within the effective monitoring range of the space-based radar.

[0234] Table 2: Simulation parameters of spacecraft orbit calculation software

[0235]

[0236] Depend on Fig. 9 It can be seen that by combining the LOS parameters obtained by the spacecraft orbit calculation software with the RCS data of a single station in the entire airspace, the dynamic RCS sequences of the above three space targets can be obtained. According to the experimental results, there is a great difference in the changing trend of the dynamic RCS curve with the detection time. Based on the proposed MLN model, the time-varying RCS likelihood of the target can be calculated and then added to the Gaussian mixture filter update process. Subsequent simulation experimental results will verify that RCS auxiliary information is conducive to improving the detection performance based on the Gaussian mixture filter.

[0237] 3. OSPA error comparison

[0238] The simulation experiment of this embodiment assumes that there are three space targets in the space-based radar monitoring area [0,100]km×[0,100]km×[0,100]km, and all targets obey the variable acceleration motion model. The motion state vector includes position, velocity, i.e., z k =[x,y,z,v x ,v y ,v z ] T In addition, the measurement vector includes the target position measurement and the target feature measurement, namely

[0239] In this embodiment, the observation duration of the simulation experiment is set to 100 seconds, and the survival probability of each target is 0.99 and they are independent of each other. The three space targets are all born at 0s, the second target and the third target disappear at 70s, and the other target exists throughout the tracking process. The truncation threshold T is used. th =10 -5 The pruning process of Gaussian weights that vary over time is implemented, and the maximum number of terms in the potential distribution function is 100. The detection probability of all filters is a fixed value P d =0.98, V = 8 × 10 6 m 3 represents the volume of the entire spatial surveillance area. The RFS of the clutter follows a Poisson distribution, and its intensity is 1.4×10 -5 m -3 (That is, there are 112 false alarms in the spatial monitoring area of ​​each frame). In addition, the probability density function of the clutter amplitude obeys the Rayleigh distribution, and the specific clutter likelihood probability can be calculated through the Rayleigh distribution model. The initial parameter setting state of the filter is shown in Table 3. The initial position and initial velocity of the space-based radar are (-5, 10, 400) km and (4600, 840, 15) m / s respectively.

[0240] Table 3: Target initial state

[0241]

[0242] Considering that OSPA has the comprehensive evaluation capability of taking into account both the number of targets and the target state estimation performance, the following of this embodiment will mainly use OSPA statistics to measure the performance of the multi-target tracking algorithm.

[0243] The specific OSPA expression is as follows:

[0244]

[0245] In the formula, represents the cutoff distance, where the cutoff parameter c>0. Adjusting c can change the degree of penalty for the target number estimation deviation. ||·|| represents the Euclidean distance. represents the combination of all permutations on {1,2,...,N}, p ​​represents the time-varying OSPA order, 1≤p≤∞, adjusting p can change the degree of penalty for target state estimation deviation, and under the condition of M>N, the OSPA distance has the following relationship:

[0246] In the simulation experiment, the OSPA order p is 2, and the truncation parameter c is 200m. The average OSPA result of 100 Monte Carlo experiments is as follows: Fig.10 shown.

[0247] from Fig.10 and Fig.11 It can be seen that among the four filtering methods, the GM-PHD filter has the highest positioning error and average OSPA estimation error. The Am-GM-PHD (amplitude-assisted GM-PHD) filter

[31] and the Do-GM-PHD (Doppler-assisted GM-PHD) filter

[32] have better positioning performance and potential estimation performance than the traditional GM-PHD filter, but the OSPA position error estimated by the Am-GM-PHD filter has a large fluctuation range with the tracking time. In contrast, the OSPA positioning error and OSPA potential estimation error of the RDGI-PHD filter proposed in Example 1 of the present invention are lower than those of the other three methods. In addition, Fig.11 It can be seen that the proposed filter has a better tracking effect on the target real data than the other three filters. The reason can be summarized as follows: the filter proposed in Example 1 of the present invention comprehensively utilizes the improved RCS likelihood and Doppler likelihood to assist the filter update process, and corrects the Gaussian mixture weights, thereby significantly improving the tracking performance of the filtering method. The simulation results show that in the low detection probability scenario, the RDGI-PHD filter has more obvious advantages over the GM-PHD filter, the Am-GM-PHD filter and the Do-GM-PHD filter.

[0248] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0249] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An adaptive PHD filtering method assisted by RCS information and Doppler information, characterized in that: include: Step 1: Establish a mixed Gaussian lognormal distribution model and derive the observation geometry relationship between space targets and space-based radar Step 1.1: Establish a target state model based on target RCS information and Doppler information; Step 1.2: Based on the target state model of the target RCS information and Doppler information, establish the prediction and update algorithm model of the RDGI-PHD filter; Step 1.3: Based on the prediction and update algorithm model of the RDGI-PHD filter, an improved RCS mixed statistical distribution model is established; Step 1.4: Perform geometric transformation of space-based radar observations based on the improved RCS mixed statistical distribution model; Step 2: Based on the mixed Gaussian log-normal distribution model, the Gaussian component weights of the mixed Gaussian log-normal distribution model are improved to establish an adaptive PHD filter assisted by RCS information and Doppler information.

2. The RCS information and Doppler information assisted adaptive PHD filtering method according to claim 1, characterized in that: The process of establishing the target state model based on the target RCS information and Doppler information includes: The target monitoring area is three-dimensional, and the target measurement status is: x k =[l x,k ,v x,k ,l y,k ,v y,k ,l z,k ,v z,k ] T (1) In the formula, l x,k , l y,k and l z,k They represent the three-dimensional position information of the target at time k, v x,k , v y,k and v z,k Respectively represent the three-dimensional velocity information of the target; By extending the target RCS information and Doppler information to the target measurement state, we can obtain: With k =[of l,k ,With d,k ,With rcs,k ] (2) In the formula, z l,k ,z d,k and z rcs,k They represent target position measurement, Doppler measurement and RCS measurement respectively.

3. The RCS information and Doppler information assisted adaptive PHD filtering method as claimed in claim 1, characterized in that: The process of establishing the prediction and update algorithm model of the RDGI-PHD filter includes Step 1.2.1: Establish the prediction algorithm model of RDGI-PHD filter; Step 1.2.2: Establish the update algorithm model of RDGI-PHD filter.

4. The RCS information and Doppler information assisted adaptive PHD filtering method as claimed in claim 3, characterized in that: The prediction algorithm model of the RDGI-PHD filter is: In the formula, γ k (x k ) represents the RFS intensity at time k, p s,k (x k-1 ) represents the target survival probability, f k|k-1 (x k |x k-1 ) represents the Markov transition probability density, b k|k-1 (x k |x k-1 ) represents the target strength of splitting from the state at time k-1, D k-1|k-1 (x k-1 ) represents the PHD filter strength at time k-1, D k|k-1 (x k ) represents the PHD filter strength at time k.

5. The RCS information and Doppler information assisted adaptive PHD filtering method as claimed in claim 3, characterized in that: The process of establishing the update algorithm model of the RDGI-PHD filter includes: (1) After introducing RCS information and Doppler information into the standard PHD filter, the update expression of the RDGI-PHD filter is: D k|k (x k )=L Z (x k )·D k|k-1 (x k ) (4) Assuming that the target RCS information and Doppler information are independent of the target's position state, the target likelihood probability and clutter likelihood probability are: g(z|x)=g((z l,k ,z d,k ,z a,k )|x)=g l (z l |x)g d (d)g rcs (rcs) (5) c(z|x))=c z (z|x)c d (d)c rcs (rcs) (6) In the formula, g l (z l |x), g rcs (rcs) and g d (d) represents the k-target position likelihood function, Doppler likelihood function and RCS likelihood function respectively; c z (z|x), c d (d) and c rcs (rcs) represent clutter position likelihood, clutter Doppler likelihood and RCS amplitude likelihood respectively; (2) The Doppler likelihood function is: g d (d)=N(z d,k ;h k (x k ),R d,k ) (7) In the formula, R d,k represents the noise room variance; The RCS likelihood is obtained through Section III-D, and the RCS information and Doppler information are merged into the PHD update recursion to obtain the PHD pseudo-likelihood probability: Where κ(z) = λ c Vc z (z|x) represents the clutter intensity function that obeys the Poisson distribution; The Gaussian mixture form of the posterior density at time k-1 is: In the formula, represents the weight of the i-th Gaussian component at time k-1; Substituting equation (9) into equation (4), we get the posterior strength at time k: Where, the normalized code Gaussian mixture weight is in (3) For the standard GM-PHD filter and the RCS information-assisted GM-PHD filter, the posterior likelihood probabilities are Note that g rcs (rcs) and c rcs (rcs) represents the RCS likelihood function of the target and clutter respectively; (4) Let the RCS likelihood of the measured value exceeding the detection threshold be and The normalized form is In the formula denote the detection probability and false alarm probability respectively; (5) The RCS amplitude likelihood ratio under the detection threshold τ is defined as: Substituting formula (19) into formula (14), formula (19) is rewritten as: From the above formula, we can see that when the signal-to-noise ratio is 0, At this time, the RCS information assisted PHD filter is regarded as a standard PHD filter.

6. The RCS information and Doppler information assisted adaptive PHD filtering method as claimed in claim 1, characterized in that: The improved RCS mixed statistical distribution model is: Where Θ=[λ1,...,λ M ; μ1,...,μ M ; s1,...,s M ], μ i and i represents the composition parameters of the proposed MLN model; I represents the number of components in the proposed MLN model.

7. The RCS information and Doppler information assisted adaptive PHD filtering method according to claim 1, characterized in that: The process of performing geometric transformation of space-based radar observation based on the improved RCS mixed statistical distribution model includes: Step 1.4.1: Based on the Earth Fixed (ECEF) coordinate system O e -X e Y e Z e and the target body coordinate system O t -X t Y t Z t The positions of the space target and the space-based radar in the ECEF coordinate system are obtained by transformation: In the formula, R x ,R y and R z They are respectively expressed as rotation matrices around the x-axis, rotation matrices around the y-axis, and rotation matrices around the z-axis, as shown below: Step 1.4.1: The coordinate transformation matrix between the ECEF coordinate system and the target fixed coordinate system is M ECEF-OF =[R z (Oh)R x (a)R z (ω+θ)] -1 (27) Therefore, the positions of the space target and the space-based radar in the target body coordinate system are: Step 1.4.3: Finally, the radar sight angle in the target body coordinate system is calculated as: In the formula, [x Δ ,y Δ ,z Δ ] represents the position vector of the radar sight angle in the target body coordinate system, θ Δ and They represent the observation azimuth and elevation angle in the target body coordinate system respectively.

8. The RCS information and Doppler information assisted adaptive PHD filtering method as claimed in claim 1, characterized in that: The process of improving the Gaussian component weight of the mixed Gaussian log-normal distribution model and establishing an adaptive PHD filter assisted by RCS information and Doppler information includes: (1) First, filter out the index of the highest component in the target posterior probability density: In the formula, I represents the index set; (2) Further, find the component order set that is closest to the component with the largest weight in the target posterior strength at time k: In the formula, σ s represents the variance of the measurement noise; (3) If the Gaussian components satisfy equation (34) and the sum of the component weights does not exceed twice the state extraction threshold, a new set containing the following components is obtained: (4) When satisfied Except for the highest weight, all other sub-weights of the target are multiplied by a penalty factor, and the new weights are as follows: In the formula, represents the penalty factor, where 0≤α≤1 is a constant that determines the degree of penalty; Substituting equation (37) into equation And renormalize the target new weight corresponding to each measurement to obtain the following renormalized weight In the formula, κ k (λ c ) = λ c c rcs (rcs)c d (d); (5) Finally, the new posterior probability density is: Among them, U mm It is an adaptive threshold that varies with component weights and measurement noise.

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