A moving target tracking method, system, storage medium and electronic device

Abstract

The present invention belongs to the field of radar technology, and in particular, relates to a moving target tracking method, system, storage medium and electronic device. The method comprises: constructing a posterior Crommerow lower bound function of a moving target based on the equation of motion and all radar original measurements; performing a processing to minimize the lower bound of target tracking accuracy on the optimization function of the posterior Crommerow lower bound to obtain the power allocation result of each node airborne radar; calculating the noise statistics of any node airborne radar, and constructing an uncorrelated conversion function of any radar original measurement; obtaining an uncorrelated conversion filter corresponding to each node airborne radar based on the above content; and determining the state of the moving target at the current moment according to the number of sensors included in the uncorrelated conversion filter. The present invention can achieve the purpose of obtaining a more accurate target state estimation result while ensuring real-time processing by using a sequential nonlinear filtering method based on uncorrelated conversion networked radars.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and in particular relates to a moving target tracking method, system, storage medium and electronic equipment. Background Art

[0002] With the development of technology and the iteration of weapon systems, traditional radar systems in modern warfare are facing increasingly severe challenges. Advanced anti-radiation missile technology, continuously improving low-altitude penetration technology, rapidly developing target stealth technology, and ever-changing electronic jamming technology constitute the "four major threats" of modern radar. In this context, traditional radar systems are not only difficult to meet combat needs, but even their survivability is facing severe tests. The networked radar system adopts a multi-transmit-multi-receive form. Each part can obtain independent measurement information and transmit the received information to the fusion center for joint processing to achieve tasks such as detection, identification, positioning and tracking of targets. It has the advantages of strong survivability, multiple means of obtaining information, and high detection and tracking performance.

[0003] Increasing the number of radars in a networked radar system and improving the transmit power can effectively improve the detection, tracking and identification performance of targets. However, in practice, increasing the scale of the system means a sharp increase in data processing pressure on the fusion processing center. At the same time, the system information transmission capacity is limited by the communication transmission bandwidth, which also restricts the increase in the scale of the system. In addition, the transmit power is also restricted by factors such as equipment application scenarios and hardware (such as airborne surveillance radars, unmanned aerial vehicles, etc.), which further limits the number of radars in the networked radar system. Therefore, it is urgent to study the radar resource management method to obtain the highest possible precision measurement information by reasonably allocating radar resources; in addition, the networked radar system faces highly nonlinear measurement functions, which leads to limited target tracking accuracy. Therefore, it is necessary to adopt high-performance nonlinear filtering methods and corresponding sequential information fusion methods to ensure the real-time nature of information processing while giving full play to the efficient collaboration of radars, providing strong support for high-precision moving target tracking in complex scenes. In summary, multi-sensor resource management and high-precision nonlinear filtering are a key and difficult problem faced by satellite-machine collaborative moving target tracking. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a moving target tracking method, system, storage medium and electronic equipment.

[0005] The technical solution of the present invention to solve the above technical problem is as follows: A moving target tracking method, comprising:

[0006] Step 1, obtaining the motion equation of the moving target, the measurement noise statistic-radar power function of each node airborne radar in the satellite-aircraft collaborative tracking system, and the radar original measurement of each node airborne radar in the satellite-aircraft collaborative tracking system, and constructing the posterior Crommerow lower bound function of the moving target based on the motion equation and all radar original measurements, wherein the satellite-aircraft collaborative tracking system is composed of a geosynchronous orbit satellite and an airborne distributed multi-node airborne radar platform;

[0007] Step 2, deriving an optimization function of the posterior Cromerow lower bound function according to the measurement noise statistics-radar power function of multiple node airborne radars, performing a process of minimizing the lower bound of target tracking accuracy on the optimization function, and obtaining a power allocation result of each node airborne radar based on the processing result;

[0008] Step 3, calculating the noise statistic of any node airborne radar according to the power allocation result of any node airborne radar and its corresponding measurement noise statistic-radar power function, and constructing an uncorrelated conversion function of any radar original measurement according to any noise statistic and the radar original measurement of any node airborne radar;

[0009] Step 4, combining each uncorrelated transfer function with the linear minimum mean square error estimation filter framework to obtain the uncorrelated transfer filter corresponding to each node airborne radar;

[0010] Step 5: If the uncorrelated conversion filter includes a sensor, the radar raw measurement and the noise statistic corresponding to the radar raw measurement are input into the uncorrelated conversion filter corresponding to the node airborne radar to obtain the output result of the uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on the output result;

[0011] If the uncorrelated conversion filter contains multiple sensors, the original measurement of each radar is input into the uncorrelated conversion filter corresponding to each node airborne radar through sequential filtering to obtain the output result of each uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on multiple output results.

[0012] The beneficial effects of the present invention are as follows: the present invention performs power resource allocation for a networked radar system of a star-to-plane configuration, obtains an optimal allocation scheme based on the derived PCRLB metric, and can achieve optimal power allocation for each radar at each moment, which helps to improve target tracking performance in complex battlefield environments. The present invention uses an uncorrelated conversion filtering method to process the highly nonlinear radar measurement function faced by a networked radar system of a star-to-plane configuration, and proposes a targeted UC function in combination with a specific measurement form, which can effectively extract effective measurement information and improve the accuracy of target state estimation in complex scenarios. The present invention fully considers the real-time problem of information fusion processing brought about by multi-sensor measurement, and uses a sequential nonlinear filtering method based on uncorrelated conversion networked radars to better achieve a more accurate target state estimation result while ensuring real-time processing.

[0013] Based on the above technical solution, the present invention can also be improved as follows.

[0014] Furthermore, the expression of the posterior Crommerow lower bound function of the moving target is specifically:

[0015]

[0016] Among them, F k-1 represents the moving target state transfer matrix at time k-1, H k The Jacobian matrix represents the measurement function of the node airborne radar at time k. The Jacobian matrix is ​​obtained by taking the derivative of the original radar measurement around the estimated state. Q k-1 R represents the noise statistic of the moving target process at time k-1 k represents the noise statistic of the airborne radar measurement at the k-th time node, J k-1 represents the Fisher information matrix corresponding to the moving target at time k-1, J k represents the Fisher information matrix corresponding to the moving target at time k, F(P k ) represents the power allocation function of the satellite-aircraft cooperative tracking system at time k, P k =[p 1,k ,...,p i,k ,...,p N,k ], i=1,..., N represents the power allocation vector of the satellite-machine cooperative tracking system, p i,k represents the power of the i-th radar at time k; C PCRLB (·) represents the inverse of the Fisher information matrix, i.e., the posterior Cromer-Rao lower bound, x k|k-1 represents the target one-step prediction state at time k; J(x k|k-1 ) means that when the target state is x k|k-1 is the Fisher information matrix when , and Tr(·) represents the trace of the matrix.

[0017] Further, the expression of the measurement noise statistic-radar power function is:

[0018]

[0019] Among them, σ r,i represents the radial distance σ of the airborne radar of the i-th node f,i represents the Doppler noise of the airborne radar of the i-th node, B i,k represents the effective transmission bandwidth of the airborne radar of the i-th node, T i,k represents the effective transmission time width of the airborne radar of the i-th node, SNR i,k represents the signal-to-noise ratio (SNR) of the echo signal of the i-th radar at time k, that is,

[0020]

[0021] Among them, h i,k Indicates the radar cross section of a moving target, attenuation factor R i,k Represents the radial distance between the ith airborne radar and the moving target.

[0022] Further, the step 3 is specifically as follows:

[0023] Obtain the state prediction and corresponding state covariance of the moving target at any time, and construct an uncorrelated conversion function of any radar raw measurement based on the state prediction, the corresponding state covariance and the radar raw measurement of any node airborne radar. The expression of the uncorrelated conversion function is k Specifically:

[0024]

[0025] in, represents the original measurement of the i-th radar at time k, represents the one-step prediction of the original radar measurement at time k, f i,k represents the original Doppler measurement of the i-th radar at time k, R i,k represents the original radial distance of the i-th radar at time k, represents the one-step prediction of the original radial distance of the i-th radar at time k, represents the one-step prediction of the original Doppler measurement of the i-th radar at time k. The state of the target at time k can be expressed as: And the position of the i-th radar is expressed as: λ i represents the wavelength of the i-th radar; the radar raw measurement is specifically:

[0026]

[0027] in, represents the radial range noise of the i-th radar at time k, represents the Doppler noise of the i-th radar at time k.

[0028] Another technical solution of the present invention to solve the above technical problem is as follows: A moving target tracking system, comprising:

[0029] an acquisition module, for acquiring the motion equation of the moving target, the measurement noise statistic-radar power function of each node airborne radar in the satellite-aircraft collaborative tracking system, and the radar original measurement of each node airborne radar in the satellite-aircraft collaborative tracking system, and constructing the posterior Cromerow lower bound function of the moving target based on the motion equation and all radar original measurements, wherein the satellite-aircraft collaborative tracking system is composed of a geosynchronous orbit satellite and an airborne distributed multi-node airborne radar platform;

[0030] An optimization module is used to optimize the a posteriori Crommerow lower bound function according to the measurement noise statistics of multiple node airborne radars-radar power function to obtain an optimization function of the a posteriori Crommerow lower bound, perform a target tracking accuracy lower bound minimization process on the optimization function, and obtain a power allocation result of each node airborne radar based on the processing result;

[0031] A first construction module is used to calculate the noise statistic of any node airborne radar according to the power allocation result of any node airborne radar and its corresponding measurement noise statistic-radar power function, and to construct an uncorrelated conversion function of any radar original measurement according to any noise statistic and the radar original measurement of any node airborne radar;

[0032] The second building block is used to combine each uncorrelated transfer function with a linear minimum mean square error estimation filter framework to obtain an uncorrelated transfer filter corresponding to each node airborne radar;

[0033] A determination module, for inputting the radar raw measurement and the noise statistic corresponding to the radar raw measurement into the uncorrelated conversion filter corresponding to the node airborne radar if the uncorrelated conversion filter includes a sensor, obtaining an output result of the uncorrelated conversion filter, and determining the state of the moving target at the current moment based on the output result;

[0034] If the uncorrelated conversion filter contains multiple sensors, the original measurement of each radar is input into the uncorrelated conversion filter corresponding to each node airborne radar through sequential filtering to obtain the output result of each uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on multiple output results.

[0035] The beneficial effects of the present invention are as follows: the present invention performs power resource allocation for a networked radar system of a star-to-plane configuration, obtains an optimal allocation scheme based on the derived PCRLB metric, and can achieve optimal power allocation for each radar at each moment, which helps to improve target tracking performance in complex battlefield environments. The present invention uses an uncorrelated conversion filtering method to process the highly nonlinear radar measurement function faced by a networked radar system of a star-to-plane configuration, and proposes a targeted UC function in combination with a specific measurement form, which can effectively extract effective measurement information and improve the accuracy of target state estimation in complex scenarios. The present invention fully considers the real-time problem of information fusion processing brought about by multi-sensor measurement, and uses a sequential nonlinear filtering method based on uncorrelated conversion networked radars to better achieve a more accurate target state estimation result while ensuring real-time processing.

[0036] Furthermore, the expression of the posterior Crommerow lower bound function of the moving target is specifically:

[0037]

[0038] Among them, F k-1 represents the moving target state transfer matrix at time k-1, H k The Jacobian matrix represents the measurement function of the node airborne radar at time k. The Jacobian matrix is ​​obtained by taking the derivative of the original radar measurement around the estimated state. Q k-1 R represents the noise statistic of the moving target process at time k-1 k represents the noise statistic of the airborne radar measurement at the k-th time node, J k-1 represents the Fisher information matrix corresponding to the moving target at time k-1, J k represents the Fisher information matrix corresponding to the moving target at time k, F(P k ) represents the power allocation function of the satellite-aircraft cooperative tracking system at time k, P k =[p 1,k ,…,p i,k ,…,p N,k ], i=1,..., N represents the power allocation vector of the satellite-machine cooperative tracking system, p i,k represents the power of the i-th radar at time k; C PCRLB (·) represents the inverse of the Fisher information matrix, i.e., the posterior Cromer-Rao lower bound, x k|k-1 represents the target one-step prediction state at time k; J(x k|k-1 ) means that when the target state is x k|k-1 is the Fisher information matrix when , and Tr(·) represents the trace of the matrix.

[0039] Further, the expression of the measurement noise statistic-radar power function is:

[0040]

[0041] Among them, σ r,i represents the radial distance σ of the airborne radar of the i-th node f,i represents the Doppler noise of the airborne radar of the i-th node, B i,k represents the effective transmission bandwidth of the airborne radar of the i-th node, T i,k represents the effective transmission time width of the airborne radar of the i-th node, SNR i,k represents the signal-to-noise ratio (SNR) of the echo signal of the i-th radar at time k, that is,

[0042]

[0043] Among them, h i,k Indicates the radar cross section of a moving target, attenuation factor R i,k Represents the radial distance between the ith airborne radar and the moving target.

[0044] Furthermore, the first building block is specifically used for:

[0045] Obtain the state prediction and corresponding state covariance of the moving target at any time, and construct an uncorrelated conversion function of any radar raw measurement based on the state prediction, the corresponding state covariance and the radar raw measurement of any node airborne radar. The expression of the uncorrelated conversion function is k Specifically:

[0046]

[0047] in, represents the original measurement of the i-th radar at time k, represents the one-step prediction of the original radar measurement at time k, f i,k represents the original Doppler measurement of the i-th radar at time k, R i,k represents the original radial distance of the i-th radar at time k, represents the one-step prediction of the original radial distance of the i-th radar at time k, represents the one-step prediction of the original Doppler measurement of the i-th radar at time k. The state of the target at time k can be expressed as: And the position of the i-th radar is expressed as: λ i represents the wavelength of the i-th radar; the radar raw measurement is specifically:

[0048]

[0049] in, represents the radial range noise of the i-th radar at time k, represents the Doppler noise of the i-th radar at time k.

[0050] Another technical solution of the present invention to solve the above technical problem is as follows: a storage medium, in which instructions are stored. When a computer reads the instructions, the computer executes a moving target tracking method as described in any one of the above items.

[0051] The beneficial effects of the present invention are as follows: the present invention performs power resource allocation for a networked radar system of a star-to-plane configuration, obtains an optimal allocation scheme based on the derived PCRLB metric, and can achieve optimal power allocation for each radar at each moment, which helps to improve target tracking performance in complex battlefield environments. The present invention uses an uncorrelated conversion filtering method to process the highly nonlinear radar measurement function faced by a networked radar system of a star-to-plane configuration, and proposes a targeted UC function in combination with a specific measurement form, which can effectively extract effective measurement information and improve the accuracy of target state estimation in complex scenarios. The present invention fully considers the real-time problem of information fusion processing brought about by multi-sensor measurement, and uses a sequential nonlinear filtering method based on uncorrelated conversion networked radars to better achieve a more accurate target state estimation result while ensuring real-time processing.

[0052] Another technical solution of the present invention to solve the above technical problem is as follows: an electronic device comprises the above storage medium and a processor for executing instructions in the above storage medium.

[0053] The beneficial effects of the present invention are as follows: the present invention performs power resource allocation for a networked radar system of a star-to-plane configuration, obtains an optimal allocation scheme based on the derived PCRLB metric, and can achieve optimal power allocation for each radar at each moment, which helps to improve target tracking performance in complex battlefield environments. The present invention uses an uncorrelated conversion filtering method to process the highly nonlinear radar measurement function faced by a networked radar system of a star-to-plane configuration, and proposes a targeted UC function in combination with a specific measurement form, which can effectively extract effective measurement information and improve the accuracy of target state estimation in complex scenarios. The present invention fully considers the real-time problem of information fusion processing brought about by multi-sensor measurement, and uses a sequential nonlinear filtering method based on uncorrelated conversion networked radars to better achieve a more accurate target state estimation result while ensuring real-time processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A schematic diagram of a flow chart of a moving target tracking method embodiment of the present invention;

[0055] Figure 2 A structural framework diagram provided for an embodiment of a moving target tracking system of the present invention;

[0056] Figure 3 A simplified flow chart of a moving target tracking method embodiment of the present invention;

[0057] Figure 4 A schematic diagram of the geometric positions of a satellite, a receiver and a target in a simulation experiment provided in an embodiment of a moving target tracking method of the present invention;

[0058] Figure 5 A schematic diagram of radar position, target motion track and estimation results in a simulation experiment provided by an embodiment of a moving target tracking method of the present invention;

[0059] Figure 6 A schematic diagram of the allocation results of radar resources in a simulation experiment provided by an embodiment of a moving target tracking method of the present invention;

[0060] Figure 7 A PCRLB comparison result of different allocation methods in a simulation experiment provided in an embodiment of a moving target tracking method of the present invention;

[0061] Figure 8 The present invention provides a moving target tracking method embodiment of the present invention, which provides RMSE filtering accuracy comparison results after different resource allocations in a simulation experiment. DETAILED DESCRIPTION

[0062] The principles and features of the present invention are described below. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0063] like Figure 1 As shown, a moving target tracking method includes:

[0064] Step 1, obtaining the motion equation of the moving target, the measurement noise statistic-radar power function of each node airborne radar in the satellite-aircraft collaborative tracking system, and the radar original measurement of each node airborne radar in the satellite-aircraft collaborative tracking system, and constructing the posterior Crommerow lower bound function of the moving target based on the motion equation and all radar original measurements, wherein the satellite-aircraft collaborative tracking system is composed of a geosynchronous orbit satellite and an airborne distributed multi-node airborne radar platform;

[0065] Step 2, optimizing the a posteriori Crommerow lower bound function according to the measurement noise statistics-radar power function of multiple node airborne radars to obtain an optimization function of the a posteriori Crommerow lower bound, performing a process of minimizing the lower bound of target tracking accuracy on the optimization function, and obtaining a power allocation result of each node airborne radar based on the processing result;

[0066] Step 3, calculating the noise statistic of any node airborne radar according to the power allocation result of any node airborne radar and its corresponding measurement noise statistic-radar power function, and constructing an uncorrelated conversion function of any radar original measurement according to any noise statistic and the radar original measurement of any node airborne radar;

[0067] Step 4, combining each uncorrelated transfer function with the linear minimum mean square error estimation filter framework to obtain the uncorrelated transfer filter corresponding to each node airborne radar;

[0068] Step 5: If the uncorrelated conversion filter includes a sensor, the radar raw measurement and the noise statistic corresponding to the radar raw measurement are input into the uncorrelated conversion filter corresponding to the node airborne radar to obtain the output result of the uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on the output result;

[0069] If the uncorrelated conversion filter contains multiple sensors, the original measurement of each radar is input into the uncorrelated conversion filter corresponding to each node airborne radar through sequential filtering to obtain the output result of each uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on multiple output results.

[0070] In some possible implementations, the present invention allocates power resources for a networked radar system of a star-to-plane configuration, obtains an optimal allocation scheme based on the derived PCRLB metric, and can achieve optimal power allocation for each radar at each moment, which helps to improve target tracking performance in complex battlefield environments. The present invention uses an uncorrelated conversion filtering method to process the highly nonlinear radar measurement function faced by a networked radar system of a star-to-plane configuration, and proposes a targeted UC function in combination with a specific measurement form, which can effectively extract effective measurement information and improve the accuracy of target state estimation in complex scenarios. The present invention fully considers the real-time problem of information fusion processing brought about by multi-sensor measurement, and uses a sequential nonlinear filtering method based on uncorrelated conversion networked radars to better achieve a more accurate target state estimation result while ensuring real-time processing.

[0071] It should be noted that in the simulation, if the assumed scenario is relatively simple, the motion equation of the moving target is usually set to approximate uniform linear motion. This assumption will be used in the following simulation. If the scenario is complex, it will be represented by a more complex motion equation, such as a mixture of multiple motion equations such as uniform linear motion, uniform acceleration, and turning motion. For common targets such as aircraft and vehicles, a simple assumption can be made, that is, uniform linear motion. This model is known and can be used directly. Moving targets refer to targets detected and tracked by the satellite-machine collaborative tracking system, that is, moving targets in the air and on the ground, including aircraft, vehicles, etc. The sensor is an airborne radar, that is, each node airborne radar can obtain a set of radar raw measurements at each moment. The present invention can also add a process of further optimizing the preceding function according to the output results after the above steps. Specifically, please refer to the following steps:

[0072] Step 1: A satellite-aircraft collaborative tracking system is formed by a geosynchronous orbit (GEO) satellite and an airborne distributed multi-node airborne radar platform (such as Figure 2 As shown in the figure, the satellite and the multi-radar platform in the air are combined into a detection system), the system transmits signals through the GEO satellite, and the multi-node radar platform in the air receives the target echo signal. The transmitting station and the receiving station of the system are deployed separately, which belongs to a bistatic detection system. The bistatic radar equation can be used to analyze the functional relationship between the noise statistics of each node radar measurement and the radar power. The noise statistics and power functional relationship; the measurement noise statistics is a variable, and the radar power is also a variable. There is a definite functional relationship between the two.

[0073] In step 1, the relationship between the radar noise statistics and power function of each node is expressed as:

[0074]

[0075] Among them, σ r,i and σ f,i Denote the radial distance and Doppler noise respectively, B i,k represents the effective bandwidth of radar transmission, T i,k Indicates the effective time width of the radar, SNR i,k represents the signal-to-noise ratio (SNR) of the echo signal of the i-th radar at time k, that is,

[0076]

[0077] h i,k Indicates the radar cross section of the target, attenuation factor The radial distance R from the target to the receiving radar platform i,kIt is related to factors such as antenna gain. At this time, the distance between the target and the satellite is much greater than the distance between the target and the receiving radar platform, and can be approximately regarded as a constant (it can be omitted in the proportional relationship, and the attenuation factor can be regarded as only inversely proportional to the square of the distance between the target and the receiving radar platform).

[0078] Step 2, based on the motion equation of the moving target and the radar original measurement, the radar original measurement is the radar original measurement. The radar can directly obtain the measurement information. According to the different types of radars, the information including radial distance, azimuth, pitch angle and Doppler can be obtained. The specific posterior Crommerow lower bound (PCRLB) characterization of the moving target in the distributed multi-node satellite-machine cooperative tracking system at the current moment can be derived. PCRLB is used as the optimization criterion for measuring tracking accuracy. The specific PCRLB form and accuracy optimization function form are as follows: (First, the motion equation of the moving target and the radar original measurement are used to derive the PCRLB function form. The noise statistic R in the radar original measurement k It is related to power, so PCRLB can be formed into a functional relationship with power, that is, F(P k )), it should be noted that the function in step 1 is the relationship between noise and power. Here we continue to deduce and obtain the relationship between PCRLB and power, which can be expressed by the following formula: Pk in F(Pk) represents power, and CPCRLB represents the specific function form of PCRLB. The two are related by measuring the noise statistic R.

[0079]

[0080] Among them, F k-1 and H k They represent the dynamic transfer matrix and the Jacobian matrix of the measurement function (derivative of the original radar measurement around the estimated state), Q k-1 and R k They represent the process noise statistics and the measurement noise statistics (covariance), respectively, k is the Fisher information matrix, which is the inverse matrix of PCRLB. k ) represents the power allocation function of the distributed multi-node satellite-machine cooperative tracking system at time k, P k =[p 1,k ,...,p i,k ,...,p N,k ], i=1,...,N represents the power allocation vector of the distributed multi-node satellite-machine cooperative tracking system, p i,k represents the power of the i-th radar at time k; C PCRLB (·) represents the posterior Cromerow lower bound, x k|k-1 represents the target one-step prediction state at time k; J(x k|k-1 ) means that when the target state is x k|k-1is the Fisher information matrix when , and Tr(·) represents the trace of the matrix.

[0081] Step 3: First, use the noise statistic and power function relationship derived in step 1 to calculate the noise statistic R of each radar measurement at each moment. k , and use this information in the PCRLB optimization framework derived in step 2 to obtain the specific form of the PCRLB optimization function F(P k );

[0082] Step 4: Calculate the PCRLB optimization function F(P) based on the distributed network radar system constructed in step 3 using convex optimization theory. k ), by minimizing the lower bound of target tracking accuracy, the optimal power resource allocation result of each radar at the current moment is obtained (that is, the specific power allocation value of each radar, and there are several corresponding power allocation values ​​for several radars). The specific optimization model can be expressed as:

[0083]

[0084] in, Represents the minimization function and obtains the power allocation vector P k ; 1 T =[1,...,1] 1×N ;P total Represents the total power of all radars in the distributed network radar system; P imin Indicates the minimum transmission power of each radar; P imax Represents the maximum transmission power of each radar. It can be optimized and solved by using optimization methods such as the convex optimization toolbox CVX in Matlab to obtain the optimal power resource allocation results of different radars at each moment.

[0085] Step 5, using the optimal power resource allocation result of each radar obtained in step 4, combined with the noise statistics and power function relationship derived in step 1, calculate the specific noise statistics of each radar;

[0086] Step 6, after obtaining the noise statistics of each radar measurement using step 5, combine the original radar measurement at each moment (the specific representation of the original radar measurement includes radial distance, azimuth, pitch angle, etc.), based on the uncorrelated conversion principle (this principle has been proposed), construct an uncorrelated conversion function (UC, also called uncorrelated dimension expansion term) corresponding to the original radar measurement, and combine the UC with the linear minimum mean square error estimation (LMMSE) filtering framework (this framework is an existing classical filtering framework), and obtain an uncorrelated conversion filter (UCF), that is, bring the UC function into the LMMSE framework, and construct a UCF filtering framework, which is called UCF, and then estimate the high-precision estimation result (target position, speed and other information) of the moving target at each moment. The UCF filtering framework can also be called UCF filter, and the two are equivalent. This framework estimates the motion state of the moving target, that is, the target position and speed and other information, and needs to input the original measurement and noise statistics of each radar to estimate the target state;

[0087] In step 6, the uncorrelated conversion filter derivation process is as follows: (Note that the UC function is part of the UCF filter framework. The uncorrelated conversion function is constructed in combination with the original measurement in 2 below. The overall process from 1) to 3) is the UCF framework derivation)

[0088] 1) State prediction and measurement prediction

[0089] The target estimated state and the corresponding state covariance based on k-1 time and P k-1 (The above two data can be obtained from the previous moment k-2, and the initial moment can be obtained using prior information. This time we only discuss a certain filtering process) The state prediction is obtained by filtering one step prediction and the corresponding covariance P k|k-1 The first two moments (first two moments refer to expectation and variance) composed of the above state prediction and the corresponding covariance can be obtained by using fixed point sampling methods such as unscented transformation or Gauss-Hermitian quadrature criterion. Similarly, the above fixed point sampling method can be used to obtain the original radar measurement z at time k. k One-step prediction and the corresponding measurement covariance matrix Based on the above information, the fixed point adoption method can be used to obtain the and The cross-covariance

[0090] 2) Construct an uncorrelated transfer function UC by combining the original radar measurements

[0091] based on and And the irrelevant conversion theorem, the irrelevant conversion function can be constructed g(·) represents a function form. In this paper, combined with actual radar measurements (radial distance R i,k and Doppler f i,k ), construct a specific UC, and the specific form of the radar raw measurement is as follows:

[0092]

[0093] Among them, R i,k represents the radial distance between the target and the radar platform, f i,k represents Doppler information, and the state of the target at time k can be expressed as: And the position of the i-th radar is expressed as: λ i represents the wavelength of the i-th radar, represents the radial range noise of the i-th radar at time k, represents the Doppler noise of the i-th radar at time k.

[0094] Combining the specific function form of the above radar original measurement, an extended dimension term that satisfies the uncorrelated conversion characteristics is constructed, namely the UC function, which is expressed in the following specific form:

[0095]

[0096] in, represents the predicted radial distance value of the i-th radar at time k, represents the Doppler prediction value of the i-th radar at time k.

[0097] The uncorrelated dimension-expanding term constructed in the above formula is uncorrelated with the original radar measurement, that is, the UC form of the above formula can obtain more effective measurement information from the original radar measurement, thereby obtaining a more accurate estimation of the first second-order moment of the target state in the LMMSE filtering framework, thereby improving the target tracking performance.

[0098] 3) Target status update

[0099] Use an uncorrelated transformation function y k Dimensional measurement available The corresponding expanded dimension measurement one-step prediction state is obtained by using the numerical calculation method in step 1) (fixed point sampling method: traceless transformation or Gauss-Hermitian quadrature criterion) Cross-covariance and covariance Then, based on the LMMSE framework, the state estimation can be obtained And the corresponding MSE matrix P k :

[0100]

[0101]

[0102] The uncorrelated conversion filter UCF mentioned above can be used to accurately solve the strong nonlinear filtering problem. Compared with the original LMMSE framework, the UC form constructed based on the specific nonlinear problem can further extract more effective information from the original radar measurement and use it in the LMMSE filtering framework, thereby estimating more accurate first two-order moments with better estimation accuracy.

[0103] Step 7: The fusion center of the distributed networked radar system receives a large number of measurements at each moment. However, due to the existence of the irrelevant dimensional expansion term UC in the UCF, the computational complexity increases, making it difficult to ensure the real-time performance of the computation. In view of this, a networked radar sequential filtering method based on irrelevant conversion is proposed. By processing multiple radar raw measurements obtained at the same moment in steps, each measurement is filtered using UCF to ensure efficient and real-time estimation of the target state at each moment.

[0104] The core idea of ​​the sequential filtering method for networked radar based on uncorrelated transformation is to process the measurement data of each sensor in the distributed networked radar system in turn based on UCF. First, consider the spatiotemporal registration of the multi-sensor data that needs to be fused. On this basis, sequential filtering based on the UCF method is performed. This method can ensure the real-time data processing and avoid the timeliness problem caused by data explosion. At the same time, the measurement data is effectively utilized, thus ensuring the optimality of the estimation. The specific steps are as follows:

[0105] 1) First, assume that the noise measured by each sensor at the same time is uncorrelated;

[0106] 2) Given the target first second moment at time k-1 and P k-1 Get status prediction and the corresponding MSEP k|k-1 ;

[0107] 3) The radar raw measurements obtained by sensor 1 are filtered using the UCF filtering method proposed above. First, through a one-step prediction and etc., constructing an extended dimension term with characteristics unrelated to the original radar measurement This paper takes full account of the particularity of radar measurement and proposes a dimension-expanding structure function, giving a specific UC form, namely This form can ensure that as much effective information as possible is extracted from the original radar measurement; the above-mentioned expanded measurement information is then filtered through UCF to obtain the target state estimation for sensor 1 And the corresponding MSE matrix

[0108] 4) The first second-order moment of the target state obtained by sensor 1 is used as the state prediction and the corresponding MSE in the process of sequentially processing sensor 2, which can be expressed as:

[0109] 5) Using the idea of ​​uncorrelated transformation, we can obtain the dimension-expanded measurement in the sensor 2 process, that is, Based on UCF, nonlinear filtering is performed to obtain the corresponding first second-order moment of the target state. Similarly, after sequentially processing all sensors, the final fusion result is obtained, that is,

[0110] Step 8: Feedback the estimated current target state to the PCRLB framework, that is, by updating x in the PCRLB framework in step 2. k|k-1 That is, the accurate target estimation state obtained in step 7 can be used to further optimize the radar power resource allocation (still using convex optimization theory, which is a Markov process that progresses over time), improve the accuracy of allocation, and thus improve the accuracy of state estimation. (Accurate estimation can obtain an accurate PCRLB lower bound, and an accurate lower bound can be optimized to obtain a more accurate power allocation result, which is a cyclic progressive process).

[0111] Embodiment 1, step 1, constructing a satellite-aircraft collaborative tracking system consisting of a geosynchronous orbit (GEO) satellite and an airborne distributed multi-node airborne radar platform, and using a bistatic radar equation to analyze the relationship between the radar measurement noise statistic of each node and the radar power function; wherein the relationship between the radar measurement noise statistic of each node and the radar power function is expressed as:

[0112]

[0113] in, and represent the measurement noise of distance and Doppler frequency shift, and SNR i,k represents the SNR of the echo signal of the i-th radar at time k, that is,

[0114]

[0115] And h i,k Indicates the radar cross section of the target, attenuation factor The radial distance R from the target to the receiving radar i,k It is related to factors such as antenna gain. At this time, the distance between the target and the satellite is much greater than the distance between the target and the receiving radar, and can be approximately regarded as a constant (it can be omitted in the proportional relationship, and the attenuation factor can be regarded as only inversely proportional to the square of the distance between the target and the receiving radar).

[0116] Step 2: derive the posterior Crommerow lower bound (PCRLB) of the specific distributed multi-node satellite-machine collaborative tracking system for the moving target at the current moment, and use PCRLB as the optimization criterion for measuring tracking accuracy:

[0117] F(P k )=Tr(C PCRLB (x k|k-1 ))=Tr(J -1 (x k|k-1 ))

[0118] Among them, F(P k ) represents the power allocation function of the distributed multi-node satellite-machine cooperative tracking system at time k, P k =[p 1,k ,...,p i,k ,...,p N,k ], i=1,...,N represents the power allocation vector of the distributed multi-node satellite-machine cooperative tracking system, p i,k represents the power of the i-th radar at time k; C PCRLB (·) represents the posterior Cromerow lower bound, x k|k-1 represents the target one-step prediction state at time k; J(x k|k-1 ) means that when the target state is x k|k-1 is the Fisher information matrix when , and Tr(·) represents the trace of the matrix.

[0119] Step 3: At the initial moment, assuming that the power of each radar is evenly distributed, calculate the noise statistics of each radar measurement information at the initial moment, use this information in the PCRLB optimization framework to calculate the allocated power of each radar at the next moment;

[0120] Step 4: Calculate the multi-measurement fusion PCRLB based on the distributed network radar system using convex optimization theory. By minimizing the lower bound of target tracking accuracy, the optimal power resource allocation of each radar at the current moment is obtained. The specific optimization model can be expressed as:

[0121]

[0122] in, Represents the minimization function and obtains the power allocation vector P k ; 1 T =[1,...,1] 1×N ;P total It represents the total power of all radars in the distributed network radar system; P imin Indicates the minimum power of each radar; P imaxRepresents the maximum transmission power of each radar. It can be optimized and solved by using the convex optimization toolbox CVX in Matlab to obtain the power allocation results of different radars at each moment.

[0123] Step 5, using the allocated power of each radar obtained in step 4, the specific noise covariance statistics of each radar can be obtained according to the relationship between power and measurement noise function;

[0124] Step 6: After obtaining the specific measurement information of each radar, the corresponding uncorrelated conversion function (UC) is constructed in combination with the original radar measurement function at each moment, and the uncorrelated conversion filter (UCF) obtained by the linear minimum mean square error estimation (LMMSE) framework is used to estimate the high-precision estimation result of the moving target at each moment. The uncorrelated conversion function and the corresponding uncorrelated conversion filter are derived as follows:

[0125] 1) State prediction and measurement prediction

[0126] The target estimated state and the corresponding state covariance based on k-1 time and P k-1 Get status prediction and the corresponding covariance P k|k-1 The above second-order moment can be obtained by using fixed-point sampling methods such as unscented transformation or Gauss-Hermitian quadrature criterion. Similarly, the one-step prediction of the measurement can be obtained and the corresponding measurement covariance matrix Based on the above information, we can get and The cross-covariance

[0127] 2) Construct measurement dimension expansion term by combining the original radar measurement function

[0128] based on and etc., constructing unrelated conversion measures In this paper, a specific UC function is constructed by combining the specific radar measurement (radial distance and Doppler) function. The original measurement is as follows:

[0129]

[0130] Among them, the state of the target at time k can be expressed as: And the position of the i-th radar is expressed as: λ i represents the wavelength of the i-th radar.

[0131] Combining the above measurements, we construct an extended dimension measurement that satisfies the uncorrelated conversion characteristic, namely the UC function, which is expressed in the following form:

[0132]

[0133] The measurement dimension expansion term constructed by the above formula is not related to the original measurement, that is, the UC form of the above formula can obtain more effective measurement information from the original measurement, thereby obtaining a more accurate estimation of the first second-order moment of the target state in the LMMSE filtering framework, thereby improving the target tracking performance.

[0134] 3) Target status update

[0135] Use uncorrelated transformations to measure y k Dimensional measurement available Use the numerical calculation method in step 1) to obtain the corresponding dimension expansion measurement update state Cross-covariance and covariance Then, based on the LMMSE framework, the state estimation can be obtained And the corresponding MSE matrix P k :

[0136]

[0137]

[0138] The above-mentioned UCF filtering algorithm can be used to accurately solve the strong nonlinear filtering problem. Compared with the original LMMSE framework, the UC function form constructed based on the specific problem can further extract more effective information from the original measurement and use it in the LMMSE filtering framework to estimate more accurate first two-order moments with better estimation accuracy.

[0139] Step 7: In the multi-sensor information fusion of the networked radar, a large amount of measurement information is received at each moment. However, due to the existence of the dimension expansion term in the UCF filtering method, the computational complexity increases, and it is difficult to ensure the real-time performance of the calculation. A networked radar sequential filtering method based on uncorrelated conversion is proposed to obtain the target state at each moment in real time and efficiently. The core idea of ​​the networked radar sequential filtering method based on uncorrelated conversion is as follows:

[0140] The filtering method based on uncorrelated conversion is used to process the measurement data of each sensor in the multi-sensor system in turn. First, consider the spatiotemporal registration of the multi-sensor data that needs to be fused. On this basis, sequential filtering based on the UCF method is performed. This method can ensure the real-time data processing and avoid the timeliness problem caused by data explosion; at the same time, the measurement is fully utilized, thus ensuring the optimality of the estimation. The specific steps are as follows:

[0141] 1) First, assume that the noise measured by each sensor at the same time is uncorrelated;

[0142] 2) Given the target first second moment at time k-1 and P k-1 Get status prediction and the corresponding MSEP k|k-1 ;

[0143] 3) The measurement information obtained by sensor 1 is filtered using the UCF filtering method proposed above. First, through a one-step prediction and etc., constructing an extended dimension term with characteristics unrelated to the original measurement This paper takes full account of the particularity of radar measurement and proposes a dimension-expanding structure function, giving a specific UC form, namely This form can ensure that as much effective information as possible is extracted from the original measurement; the above-mentioned expanded measurement information is then filtered through the UCF framework to obtain the target state estimation for sensor 1 And the corresponding MSE matrix

[0144] 4) The first second-order moment of the target state obtained by sensor 1 is used as the predicted state and predicted state covariance in the process of sequentially processing sensor 2, which can be expressed as:

[0145] 5) Using the UC dimension expansion idea, we can obtain the dimension expansion measurement in the sensor 2 process, that is, Based on the UCF framework, nonlinear filtering is performed to obtain the corresponding first second-order moment of the target state. Similarly, after sequentially processing all sensors, the final fusion result is obtained, that is,

[0146] Step 8: Feedback the estimated target state at the current moment to the PCRLB framework, and use the accurate estimated state to further optimize the power allocation, improve the accuracy of the allocation, and thus improve the accuracy of the state estimation.

[0147] The advantages of the present invention can be further illustrated by the following simulation experiments.

[0148] 1) Simulation experiment environment:

[0149] Experimental environment: MATLAB R2015b, Intel(R) Core(TM) i5-9500 CPU 3.0GHz, Window 7 Ultimate Edition.

[0150] 2) Simulation experiment content and result analysis:

[0151] Assuming that the target moves in a straight line with an approximate uniform speed, given the initial position and velocity information of the target, four radar receiving stations distributed in different positions are used to obtain the target radial distance and Doppler information. The algorithms in the simulation include: the traditional unscented Kalman filter (UF) and the proposed uncorrelated conversion filter (UCF) method. Figure 4 This is a schematic diagram of the geometric positions of the satellite, receiver, and target in the simulation experiment. Figure 4 Schematic diagram of the geometric positions of the satellite, receiver and target in the simulation experiment; "Satellite transmitting station T" represents the signal transmission source, and the aircraft in the figure represents the moving target; the solid circles represent the four receiving stations, namely the node airborne radars; the arrow indicates that the target moves in a uniform straight line to the right, and "V" represents the speed of the moving target. Figure 5 are the radar positions and target motion tracks and estimation results in the simulation experiment. Figure 5 Schematic diagram showing the radar position, target motion track and estimation results in the simulation experiment; the four five-pointed stars represent the coordinates of the four node airborne radars in the scene; the middle horizontal line represents the motion track of the moving target, and the real track and the estimated track overlap, resulting in only one straight line being seen; it can be seen from the figure that for the target tracking problem with less noise, the error between the real track and the filtered track is small. In addition, as the sampling time goes by, the distance between the target and radar 1 increases, while the distance to radar 4 decreases. Figure 6 is the resource allocation result of each radar. Figure 6 Indicates the resource allocation results of each radar. Different line types correspond to different radar numbers. It can be seen that based on the resource management method of PCRLB, the power allocation is related to the distance between the target and the radar. When the target is close to radar 1, a larger power is allocated, and the allocated power continues to decrease as the target moves away; the target is farthest from radar 4, and a lower power is initially allocated. As the distance decreases, the power continues to increase; around 11s, the four sensors are basically at the same distance from the target, and the power allocation is the same. The simulation results are consistent with the actual analysis, which verifies the effectiveness of the algorithm. Figure 7 is the PCRLB comparison result of different allocation methods, Figure 7 The PCRLB comparison results of different allocation methods are shown. The upper line in the figure represents the power uniform allocation method; the lower line represents the power optimization allocation method. It can be seen that compared with the power uniform allocation, the resource management method based on PCRLB can obtain a better lower bound of tracking accuracy, indicating that this method can effectively improve the tracking accuracy. Figure 8 is the comparison result of filtering accuracy after different resource allocations. Figure 8The figure shows the comparison results of filtering accuracy after different resource allocations; the top line shows the tracking accuracy of the UF filtering method after average power allocation; the middle line shows the tracking accuracy of the UF filtering method after PCRLB power allocation, and the bottom line shows the tracking accuracy of the UCF method after PCRLB power allocation. It can be seen that the measurement errors obtained for radars with different resource management are different, which in turn affects the target tracking accuracy, indicating that resource management can further improve resource utilization and help improve tracking performance.

[0152] from Figure 5 It can be seen that for the target tracking problem with less noise, the error between the true trajectory and the filtered track is small. In addition, as the sampling time goes by, the distance between the target and radar 1 increases, while the distance between the target and radar 4 decreases.

[0153] from Figure 6 It can be seen that based on the resource management method of PCRLB, power allocation is related to the distance between the target and the radar. When the target is close to radar 1, a larger power is allocated, and the allocated power continues to decrease as the target moves away; the target is farthest from radar 4, and a lower power is initially allocated, and the power continues to increase as the distance decreases; around 11 seconds, the four sensors are basically at the same distance from the target, and the power allocation is the same. The simulation results are consistent with the actual analysis, which verifies the effectiveness of the algorithm.

[0154] from Figure 7 It can be seen that compared with the average power allocation, the resource management method based on PCRLB can obtain a better lower bound of tracking accuracy, which shows that the method of the present invention can effectively improve the tracking accuracy.

[0155] from Figure 8 It can be seen that for radars with different resource management, different measurement errors are obtained, which in turn affects the target tracking accuracy. This shows that resource management can further improve resource utilization and help improve tracking performance.

[0156] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention; thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these changes and variations.

[0157] Preferably, in any of the above embodiments, the expression of the posterior Crommerow lower bound function of the moving target is specifically:

[0158]

[0159] Among them, k represents the current moment, k-1 represents the previous moment, and F k-1 and H kThey represent the moving target state transfer matrix and the Jacobian matrix of the measurement function of the node airborne radar. The Jacobian matrix is ​​obtained by taking the derivative of the radar original measurement around the estimated state. Q k-1 and R k They represent the noise statistics of the moving target process and the noise statistics of the node connected to the radar measurement, respectively. k-1 Moving target state x k|k-1 The corresponding Fisher information matrix, J k It means that F(P k ) represents the power allocation function of the satellite-aircraft cooperative tracking system at time k, P k =[p 1,k ,...,p i,k ,...,p N,k ], i=1,..., N represents the power allocation vector of the satellite-machine cooperative tracking system, p i,k represents the power of the i-th radar at time k; C PCRLB (·) represents the posterior Cromerow lower bound, x k|k-1 represents the target one-step prediction state at time k; J(x k|k-1 ) means that when the target state is x k|k-1 is the Fisher information matrix when , and Tr(·) represents the trace of the matrix.

[0160] Preferably, in any of the above embodiments, the expression of the measurement noise statistic-radar power function is:

[0161]

[0162] Among them, σ r,i represents the radial distance σ of the airborne radar of the i-th node f,i represents the Doppler noise of the airborne radar of the i-th node, B i,k represents the effective transmission bandwidth of the airborne radar of the i-th node, T i,k represents the effective transmission time width of the airborne radar of the i-th node, SNR i,k represents the signal-to-noise ratio (SNR) of the echo signal of the i-th radar at time k, that is,

[0163]

[0164] Among them, h i,k Indicates the radar cross section of a moving target, attenuation factor R i,k Represents the radial distance between the ith airborne radar and the moving target.

[0165] Preferably, in any of the above embodiments, step 3 is specifically:

[0166] Obtain the state prediction and corresponding state covariance of the moving target at any time, and construct an uncorrelated conversion function of any radar raw measurement based on the state prediction, the corresponding state covariance and the radar raw measurement of any node airborne radar. The expression of the uncorrelated conversion function is k Specifically:

[0167]

[0168] in, represents the original measurement of the i-th radar at time k, represents the one-step prediction of the original radar measurement at time k, f i,k represents the original Doppler measurement of the i-th radar at time k, R i,k represents the original radial distance of the i-th radar at time k, represents the one-step prediction of the original radial distance of the i-th radar at time k, represents the one-step prediction of the original Doppler measurement of the i-th radar at time k. The state of the target at time k can be expressed as: And the position of the i-th radar is expressed as: λ i represents the wavelength of the i-th radar; the radar raw measurement is specifically:

[0169]

[0170] in, represents the radial range noise of the i-th radar at time k, represents the Doppler noise of the i-th radar at time k.

[0171] like Figure 2 As shown, a moving target tracking system comprises:

[0172] The acquisition module 100 is used to acquire the motion equation of the moving target, the measurement noise statistic-radar power function of each node airborne radar in the satellite-aircraft collaborative tracking system, and the radar original measurement of each node airborne radar in the satellite-aircraft collaborative tracking system, and construct the posterior Cromerow lower bound function of the moving target based on the motion equation and all radar original measurements, wherein the satellite-aircraft collaborative tracking system is composed of a geosynchronous orbit satellite and an airborne distributed multi-node airborne radar platform;

[0173] The optimization module 200 is used to optimize the a posteriori Cromer-Rao lower bound function according to the measurement noise statistics of multiple node airborne radars-radar power function to obtain an optimization function of the a posteriori Cromer-Rao lower bound, perform a target tracking accuracy lower bound minimization process on the optimization function, and obtain a power allocation result of each node airborne radar based on the processing result;

[0174] The first construction module 300 is used to calculate the noise statistic of any node airborne radar according to the power allocation result of any node airborne radar and its corresponding measurement noise statistic-radar power function, and to construct an uncorrelated conversion function of any radar original measurement according to any noise statistic and the radar original measurement of any node airborne radar;

[0175] The second building module 400 is used to combine each uncorrelated conversion function with a linear minimum mean square error estimation filter framework to obtain an uncorrelated conversion filter corresponding to each node airborne radar;

[0176] A determination module 500 is used to input the radar raw measurement and the noise statistic corresponding to the radar raw measurement into the uncorrelated conversion filter corresponding to the node airborne radar if the uncorrelated conversion filter includes a sensor, obtain the output result of the uncorrelated conversion filter, and determine the state of the moving target at the current moment based on the output result;

[0177] If the uncorrelated conversion filter contains multiple sensors, the original measurement of each radar is input into the uncorrelated conversion filter corresponding to each node airborne radar through sequential filtering to obtain the output result of each uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on multiple output results.

[0178] In some possible implementations, the present invention allocates power resources for a networked radar system of a star-to-plane configuration, obtains an optimal allocation scheme based on the derived PCRLB metric, and can achieve optimal power allocation for each radar at each moment, which helps to improve target tracking performance in complex battlefield environments. The present invention uses an uncorrelated conversion filtering method to process the highly nonlinear radar measurement function faced by a networked radar system of a star-to-plane configuration, and proposes a targeted UC function in combination with a specific measurement form, which can effectively extract effective measurement information and improve the accuracy of target state estimation in complex scenarios. The present invention fully considers the real-time problem of information fusion processing brought about by multi-sensor measurement, and uses a sequential nonlinear filtering method based on uncorrelated conversion networked radars to better achieve a more accurate target state estimation result while ensuring real-time processing.

[0179] Preferably, in any of the above embodiments, the expression of the posterior Crommerow lower bound function of the moving target is specifically:

[0180]

[0181] Among them, F k-1 represents the moving target state transfer matrix at time k-1, H kThe Jacobian matrix represents the measurement function of the node airborne radar at time k. The Jacobian matrix is ​​obtained by taking the derivative of the original radar measurement around the estimated state. Q k-1 R represents the noise statistic of the moving target process at time k-1 k represents the noise statistic of the airborne radar measurement at the k-th time node, J k-1 represents the Fisher information matrix corresponding to the moving target at time k-1, J k represents the Fisher information matrix corresponding to the moving target at time k, F(P k ) represents the power allocation function of the satellite-aircraft cooperative tracking system at time k, P k =[p 1,k ,...,p i,k ,...,p N,k ], i=1,..., N represents the power allocation vector of the satellite-machine cooperative tracking system, p i,k represents the power of the i-th radar at time k; C PCRLB (·) represents the inverse of the Fisher information matrix, i.e., the posterior Cromer-Rao lower bound, x k|k-1 represents the target one-step prediction state at time k; J( xk|k-1 ) means that when the target state is x k|k-1 is the Fisher information matrix when , and Tr(·) represents the trace of the matrix.

[0182] Preferably, in any of the above embodiments, the expression of the measurement noise statistic-radar power function is:

[0183]

[0184] Among them, σ r,i represents the radial distance σ of the airborne radar of the i-th node f,i represents the Doppler noise of the airborne radar of the i-th node, B i,k represents the effective transmission bandwidth of the airborne radar of the i-th node, T i,k represents the effective transmission time width of the airborne radar of the i-th node, SNR i,k represents the signal-to-noise ratio (SNR) of the echo signal of the i-th radar at time k, that is,

[0185]

[0186] Among them, h i,k Indicates the radar cross section of a moving target, attenuation factor R i,k Represents the radial distance between the ith airborne radar and the moving target.

[0187] Preferably, in any of the above embodiments, the first building module 300 is specifically used for:

[0188] Obtain the state prediction and corresponding state covariance of the moving target at any time, and construct an uncorrelated conversion function of any radar raw measurement based on the state prediction, the corresponding state covariance and the radar raw measurement of any node airborne radar. The expression of the uncorrelated conversion function is k Specifically:

[0189]

[0190]

[0191] in, represents the original measurement of the i-th radar at time k, represents the one-step prediction of the original radar measurement at time k, f i,k represents the original Doppler measurement of the i-th radar at time k, R i,k represents the original radial distance of the i-th radar at time k, represents the one-step prediction of the original radial distance of the i-th radar at time k, represents the one-step prediction of the original Doppler measurement of the i-th radar at time k. The state of the target at time k can be expressed as: And the position of the i-th radar is expressed as: λ i represents the wavelength of the i-th radar; the radar raw measurement is specifically:

[0192]

[0193] in, represents the radial range noise of the i-th radar at time k, represents the Doppler noise of the i-th radar at time k.

[0194] Another technical solution of the present invention to solve the above technical problem is as follows: a storage medium, in which instructions are stored. When a computer reads the instructions, the computer executes a moving target tracking method as described in any one of the above items.

[0195] In some possible implementations, the present invention allocates power resources for a networked radar system of a star-to-plane configuration, obtains an optimal allocation scheme based on the derived PCRLB metric, and can achieve optimal power allocation for each radar at each moment, which helps to improve target tracking performance in complex battlefield environments. The present invention uses an uncorrelated conversion filtering method to process the highly nonlinear radar measurement function faced by a networked radar system of a star-to-plane configuration, and proposes a targeted UC function in combination with a specific measurement form, which can effectively extract effective measurement information and improve the accuracy of target state estimation in complex scenarios. The present invention fully considers the real-time problem of information fusion processing brought about by multi-sensor measurement, and uses a sequential nonlinear filtering method based on uncorrelated conversion networked radars to better achieve a more accurate target state estimation result while ensuring real-time processing.

[0196] Another technical solution of the present invention to solve the above technical problem is as follows: an electronic device comprises the above storage medium and a processor for executing instructions in the above storage medium.

[0197] In some possible implementations, the present invention allocates power resources for a networked radar system of a star-to-plane configuration, obtains an optimal allocation scheme based on the derived PCRLB metric, and can achieve optimal power allocation for each radar at each moment, which helps to improve target tracking performance in complex battlefield environments. The present invention uses an uncorrelated conversion filtering method to process the highly nonlinear radar measurement function faced by a networked radar system of a star-to-plane configuration, and proposes a targeted UC function in combination with the specific measurement form, which can effectively extract effective measurement information and improve the accuracy of target state estimation in complex scenarios. The present invention fully considers the real-time problem of information fusion processing brought about by multi-sensor measurement, and uses a sequential nonlinear filtering method based on uncorrelated conversion networked radars to better achieve a more accurate target state estimation result while ensuring real-time processing.

[0198] The reader should understand that in the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples without contradiction.

[0199] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the method embodiments described above are only illustrative, for example, the division of steps is only a logical function division, and there may be other division methods in actual implementation, such as multiple steps can be combined or integrated into another step, or some features can be ignored or not executed.

[0200] If the above method is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0201] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A moving target tracking method, characterized in that: include: Step 1, obtaining the motion equation of the moving target, the measurement noise statistic-radar power function of each node airborne radar in the satellite-aircraft collaborative tracking system, and the radar original measurement of each node airborne radar in the satellite-aircraft collaborative tracking system, and constructing the posterior Crommerow lower bound function of the moving target based on the motion equation and all radar original measurements, wherein the satellite-aircraft collaborative tracking system is composed of a geosynchronous orbit satellite and an airborne distributed multi-node airborne radar platform; Step 2, deriving an optimization function of the posterior Cromerow lower bound function according to the measurement noise statistics-radar power function of multiple node airborne radars, performing a process of minimizing the lower bound of target tracking accuracy on the optimization function, and obtaining a power allocation result of each node airborne radar based on the processing result; Step 3, calculating the noise statistic of any node airborne radar according to the power allocation result of any node airborne radar and its corresponding measurement noise statistic-radar power function, and constructing an uncorrelated conversion function of any radar original measurement according to any noise statistic and the radar original measurement of any node airborne radar; Step 4, combining each uncorrelated transfer function with the linear minimum mean square error estimation filter framework to obtain the uncorrelated transfer filter corresponding to each node airborne radar; Step 5: If the uncorrelated conversion filter includes a sensor, the radar raw measurement and the noise statistic corresponding to the radar raw measurement are input into the uncorrelated conversion filter corresponding to the node airborne radar to obtain the output result of the uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on the output result; If the uncorrelated conversion filter contains multiple sensors, the original measurement of each radar is input into the uncorrelated conversion filter corresponding to each node airborne radar through sequential filtering to obtain the output result of each uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on multiple output results.

2. A moving target tracking method according to claim 1, characterized in that: The expression of the posterior Cromer-Rao lower bound function of the moving target is specifically: Among them, F k-1 represents the moving target state transfer matrix at time k-1, H k The Jacobian matrix represents the measurement function of the node airborne radar at time k. The Jacobian matrix is ​​obtained by taking the derivative of the original radar measurement around the estimated state. Q k-1 R represents the noise statistic of the moving target process at time k-1 k represents the noise statistic of the airborne radar measurement at the k-th time node, J k-1 represents the Fisher information matrix corresponding to the moving target at time k-1, J k represents the Fisher information matrix corresponding to the moving target at time k, F(P k ) represents the power allocation function of the satellite-aircraft cooperative tracking system at time k, P k =[p 1,k ,…,p i,k ,...,p N,k ], i=1,..., N represents the power allocation vector of the satellite-machine cooperative tracking system, p i,k represents the power of the i-th radar at time k; C PCRLB (·) represents the inverse of the Fisher information matrix, i.e., the posterior Cromer-Rao lower bound, x k|k-1 represents the target one-step prediction state at time k; J(x k|k-1 ) means that when the target state is x k|k-1 is the Fisher information matrix when , and Tr(·) represents the trace of the matrix.

3. A moving target tracking method according to claim 2, characterized in that: The expression of the measurement noise statistic-radar power function is: Among them, σ r,i represents the radial distance σ of the airborne radar of the i-th node f,i represents the Doppler noise of the airborne radar of the i-th node, B i,k represents the effective transmission bandwidth of the airborne radar of the i-th node, T i,k represents the effective transmission time width of the airborne radar of the i-th node, SNR i,k represents the signal-to-noise ratio (SNR) of the echo signal of the i-th radar at time k, that is, Among them, h i,k Indicates the radar cross section of a moving target, attenuation factor R i,k Represents the radial distance between the ith airborne radar and the moving target.

4. A moving target tracking method according to claim 2, characterized in that: The step 3 is specifically as follows: Obtain the state prediction and corresponding state covariance of the moving target at any time, and construct an uncorrelated conversion function of any radar raw measurement based on the state prediction, the corresponding state covariance and the radar raw measurement of any node airborne radar. The expression of the uncorrelated conversion function is k Specifically: in, represents the original measurement of the i-th radar at time k, represents the one-step prediction of the original radar measurement at time k, f i,k represents the original Doppler measurement of the i-th radar at time k, R i,k represents the original radial distance of the i-th radar at time k, represents the one-step prediction of the original radial distance of the i-th radar at time k, represents the one-step prediction of the original Doppler measurement of the i-th radar at time k. The state of the target at time k can be expressed as: And the position of the i-th radar is expressed as: λ i represents the wavelength of the i-th radar; the radar raw measurement is specifically: in, represents the radial range noise of the i-th radar at time k, represents the Doppler noise of the i-th radar at time k.

5. A moving target tracking system, characterized in that: include: an acquisition module, for acquiring the motion equation of the moving target, the measurement noise statistic-radar power function of each node airborne radar in the satellite-aircraft collaborative tracking system, and the radar original measurement of each node airborne radar in the satellite-aircraft collaborative tracking system, and constructing the posterior Cromerow lower bound function of the moving target based on the motion equation and all radar original measurements, wherein the satellite-aircraft collaborative tracking system is composed of a geosynchronous orbit satellite and an airborne distributed multi-node airborne radar platform; An optimization module is used to derive an optimization function of the posterior Cromerow lower bound function according to the measurement noise statistics of multiple node airborne radars-radar power function, perform a process of minimizing the lower bound of target tracking accuracy on the optimization function, and obtain a power allocation result of each node airborne radar based on the processing result; A first construction module is used to calculate the noise statistic of any node airborne radar according to the power allocation result of any node airborne radar and its corresponding measurement noise statistic-radar power function, and to construct an uncorrelated conversion function of any radar original measurement according to any noise statistic and the radar original measurement of any node airborne radar; The second building block is used to combine each uncorrelated transfer function with a linear minimum mean square error estimation filter framework to obtain an uncorrelated transfer filter corresponding to each node airborne radar; A determination module, for inputting the radar raw measurement and the noise statistic corresponding to the radar raw measurement into the uncorrelated conversion filter corresponding to the node airborne radar if the uncorrelated conversion filter includes a sensor, obtaining an output result of the uncorrelated conversion filter, and determining the state of the moving target at the current moment based on the output result; If the uncorrelated conversion filter contains multiple sensors, the original measurement of each radar is input into the uncorrelated conversion filter corresponding to each node airborne radar through sequential filtering to obtain the output result of each uncorrelated conversion filter, and the state of the moving target at the current moment is determined based on multiple output results.

6. A moving target tracking system according to claim 5, characterized in that: The expression of the posterior Cromer-Rao lower bound function of the moving target is specifically: Among them, F k-1 represents the moving target state transfer matrix at time k-1, H k The Jacobian matrix represents the measurement function of the node airborne radar at time k. The Jacobian matrix is ​​obtained by taking the derivative of the original radar measurement around the estimated state. Q k-1 R represents the noise statistic of the moving target process at time k-1 k represents the noise statistic of the airborne radar measurement at the k-th time node, J k-1 represents the Fisher information matrix corresponding to the moving target at time k-1, J k represents the Fisher information matrix corresponding to the moving target at time k, F(P k ) represents the power allocation function of the satellite-aircraft cooperative tracking system at time k, P k =[p 1,k ,...,p i,k ,...,p N,k ], i=1,..., N represents the power allocation vector of the satellite-machine cooperative tracking system, p i,k represents the power of the i-th radar at time k; C PCRLB (·) represents the inverse of the Fisher information matrix, i.e., the posterior Cromer-Rao lower bound, x k|k-1 represents the target one-step prediction state at time k; J(x k|k-1 ) means that when the target state is x k|k-1 is the Fisher information matrix when , and Tr(·) represents the trace of the matrix.

7. A moving target tracking system according to claim 6, characterized in that: The expression of the measurement noise statistic-radar power function is: Among them, σ r,i represents the radial distance σ of the airborne radar of the i-th node f,i represents the Doppler noise of the airborne radar of the i-th node, B i,k represents the effective transmission bandwidth of the airborne radar of the i-th node, T i,k represents the effective transmission time width of the airborne radar of the i-th node, SNR i,k represents the signal-to-noise ratio (SNR) of the echo signal of the i-th radar at time k, that is, Among them, h i,k Indicates the radar cross section of a moving target, attenuation factor R i,k Represents the radial distance between the ith airborne radar and the moving target.

8. A moving target tracking system according to claim 7, characterized in that: The first building block is specifically used for: Obtain the state prediction and corresponding state covariance of the moving target at any time, and construct an uncorrelated conversion function of any radar raw measurement based on the state prediction, the corresponding state covariance and the radar raw measurement of any node airborne radar. The expression of the uncorrelated conversion function is k Specifically: in, represents the original measurement of the i-th radar at time k, represents the one-step prediction of the original radar measurement at time k, f i,k represents the original Doppler measurement of the i-th radar at time k, R i,k represents the original radial distance of the i-th radar at time k, represents the one-step prediction of the original radial distance of the i-th radar at time k, represents the one-step prediction of the original Doppler measurement of the i-th radar at time k. The state of the target at time k can be expressed as: And the position of the i-th radar is expressed as: λ i represents the wavelength of the i-th radar; the radar raw measurement is specifically: in, represents the radial range noise of the i-th radar at time k, represents the Doppler noise of the i-th radar at time k.

9. A storage medium, characterized in that: The medium stores instructions, and when a computer reads the instructions, the computer executes a moving target tracking method as claimed in any one of claims 1 to 4.

10. An electronic device, characterized in that: The invention comprises the storage medium as claimed in claim 9 and a processor for executing instructions in the storage medium.

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