Joint Optimization Method of Transmission Pattern and Path for Multi-Target Tracking in Airborne Centralized MIMO Radar

Abstract

This invention discloses a method for joint optimization of the transmission pattern and path of an airborne centralized MIMO radar for multi-target tracking, comprising: S1, forming a specific transmission pattern by optimizing the correlation array of the airborne radar's transmitted signal waveform, and establishing a motion model of the airborne platform; S2, constructing a prediction BCRLB matrix for target state estimation error using the correlation array of the airborne radar's transmitted signal waveform and the airborne platform's velocity and direction of motion as independent variables, and using its trajectory as a characterization index for target tracking accuracy; S3, establishing a joint optimization model for the airborne radar's multi-target tracking transmission pattern and path; S4, solving the joint optimization model using a three-step decomposition method based on particle swarm optimization, semidefinite programming, and cyclic minimum method. This invention can adaptively and dynamically optimize the airborne platform's flight path and the airborne radar's transmission pattern to improve multi-target tracking performance.

Description

Technical Field

[0001] This invention relates to radar signal processing technology, specifically to a method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar. Background Technology

[0002] Compared to traditional phased array radars, centralized MIMO radars allow each transmitting element to emit different waveforms, offering higher waveform diversity gain and degrees of freedom. Centralized MIMO radars can emit orthogonal waveforms to form a uniform amplitude omnidirectional transmission pattern, which can then be used to detect and track targets through adaptive receiver beamforming technology; alternatively, they can emit partially correlated waveforms to form specific transmission patterns. Therefore, the waveform correlation array of the transmitted signal from a centralized MIMO radar can be optimized to flexibly create patterns that meet specific mission requirements. Furthermore, by planning the motion path of an airborne centralized MIMO radar online and continuously optimizing its real-time observation position, the performance of multi-target detection and tracking missions can be effectively improved.

[0003] For multi-target tracking missions, given the limited maneuverability and radiated power resources of airborne centralized MIMO radars, it is necessary to plan the motion path of the airborne platform online and design a reasonable transmission pattern to maximize the overall tracking accuracy of multiple targets.

[0004] Currently, there is a wealth of research on radar power resource optimization management for multi-target tracking missions. However, most of these studies focus on simulation scenarios for ground-based radar platforms, assuming a fixed radar platform location, and do not consider the maneuverability of airborne radars or the impact of different flight paths on target tracking accuracy. Furthermore, these studies assume that the main lobe gain for each target is the same and fixed, failing to integrate resource allocation strategies with transmission pattern design, thus presenting certain limitations. In summary, there is currently no joint optimization method for transmission patterns and paths in airborne centralized MIMO radar multi-target tracking. Summary of the Invention

[0005] Purpose of the Invention: The purpose of this invention is to provide a method for joint optimization of the transmission pattern and path of airborne centralized MIMO radar for multi-target tracking. Under the given constraints such as the upper and lower limits of the total radiated power of the airborne radar transmitter and the maneuvering direction of the airborne platform, the method aims to minimize the BCRLB prediction value of the multi-target tracking accuracy. It adaptively optimizes parameters such as the flight path of the airborne platform and the radiated power of the airborne radar during the multi-target tracking process, thereby improving the multi-target tracking performance of the airborne radar.

[0006] Technical solution: The present invention provides a method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar, comprising the following steps:

[0007] S1. Consider an airborne platform in a two-dimensional plane equipped with a centralized MIMO radar that can move freely. It adopts a simultaneous multi-beam working mode to perform multi-target search and tracking tasks. The centralized MIMO radar has N transmitting array elements with an element spacing of half a wavelength. By optimizing the design of the transmitted signal waveform correlation array to form a specific transmission pattern, a motion model of the airborne platform is established.

[0008] S2. Establish the target motion model and the measurement equation of the airborne centralized MIMO radar for the target. Calculate the predicted Bayesian information matrix of the target based on the predicted Fisher information matrix corresponding to the prior information and the measurement information. Construct the predicted BCRLB matrix of the target state estimation error using the correlation array of the transmitted signal waveform of the airborne centralized MIMO radar and the speed and direction of the airborne platform as independent variables, and use its tracking as a characterization index of target tracking accuracy. Develop the cost function of the computer-aided radar flight path and transmission pattern joint optimization method.

[0009] S3. Given the performance limitations of the airborne platform and the upper and lower limits of the radiated power of the airborne centralized MIMO radar as constraints, and with the BCRLB prediction value of minimizing the multi-target tracking accuracy as the optimization objective, establish a joint optimization model of the transmission pattern and path for multi-target tracking of the airborne centralized MIMO radar.

[0010] S4. The joint optimization model is solved using a three-step decomposition method based on particle swarm optimization, semidefinite programming, and cyclic minimization, including: (a) First, for a pre-set emission pattern design parameter that meets the conditions, i.e., the pre-set emission waveform correlation array parameter. The joint optimization model in step S3 is rewritten to contain only path parameter C. k-1 (a) The motion control vector is obtained by solving the form of the wave-correlation array parameter R using the particle swarm optimization algorithm; (b) Based on the obtained motion control vector, the motion path of the airborne platform at that moment is determined, and the predicted position of the airborne centralized MIMO radar at the next moment is also fixed accordingly. Based on this, the joint optimization model is rewritten to include only the waveform correlation array parameter R. k The objective function is solved using a semidefinite programming algorithm. Finally, the steps (a) and (b) are iterated repeatedly using the cyclic minimization method until the difference between the objective function values ​​of the two iterations is less than the preset condition, thus obtaining the final multi-target tracking accuracy result and optimization result.

[0011] Furthermore, the transmission pattern of the centralized MIMO radar in step S1 is represented as follows:

[0012] φ k (θ)=a H (θ)R k a(θ)

[0013] in, S represents the correlation matrix of the transmitted signal waveform at time k; k This represents the transmit waveform matrix of the MIMO radar at time k. S represents the transmitted waveform matrix. k The conjugate transpose of θ, where a(θ) represents the launch steering vector.

[0014] Furthermore, the motion model of the airborne platform established in step S1 is represented as follows:

[0015]

[0016] in, This represents the state vector of the airborne platform at time k-1. This represents the state vector of the airborne platform at time k. The overall control function representing the motion of the airborne platform. Let v represent the motion control vector, where v k-1 and These represent the velocity and orientation angle of the airborne platform at time k-1, respectively.

[0017] Furthermore, the method for constructing the prediction BCRLB matrix of the target state estimation error in step S2 is as follows:

[0018] Suppose there are Q targets dispersed in a two-dimensional space, all moving at a constant velocity in a straight line. The state vector of the q-th target at time k is: Where q = 1, 2, ..., Q, and Let represent the position and velocity of target q at time k, respectively; then the motion model of target q can be described as follows:

[0019]

[0020] Where F represents the state transition matrix, This represents the state vector of the q-th target at time k-1. This represents noise in a zero-mean Gaussian process.

[0021] The measurement equation for target q by the airborne centralized MIMO radar at time k is expressed as:

[0022]

[0023] in, Let be the measurement vector of the airborne radar for target q at time k. Represents a nonlinear measurement function. This indicates zero-mean Gaussian measurement noise;

[0024] The Bayesian information matrix for predicting target q at time k Represented as:

[0025]

[0026] in, It is the predicted state vector of target q at time k. and Let x and y represent the predicted positions of target q in the x-axis and y-axis directions at time k, respectively. and Let x and y represent the predicted velocities of target q in the x-axis and y-axis directions, respectively, at time k. and Let the predicted Fisher information matrices at time k be the prior information and the measurement information, respectively, and be calculated as follows:

[0027]

[0028] in, Nonlinear measurement function Jacobian matrix, This represents the radar's predicted measurement noise covariance matrix for target q at time k;

[0029] The predicted Bayesian information matrix of target q at time k is then obtained as follows:

[0030]

[0031] The BCRLB matrix for predicting the target motion state estimation error is calculated as follows:

[0032]

[0033] right Matrix trace is used as a metric for target tracking accuracy.

[0034] Furthermore, the cost function of the joint optimization method for airborne radar flight path and transmission pattern in step S2 is:

[0035]

[0036] Among them, C k-1 R represents the motion control vector. k This represents the correlation array of the transmitted signal waveform. The predicted BCRLB matrix represents the error in estimating the target's motion state, and Tr represents the trace operation.

[0037] Furthermore, the joint optimization model of the airborne centralized MIMO radar multi-target tracking transmission pattern and path established in step S3 is as follows:

[0038]

[0039] Among them, C k-1 R represents the motion control vector. k P represents the correlation array of the transmitted signal waveform. k T P represents the total radiated power of an airborne centralized MIMO radar transmitter. max and P min These represent the maximum and minimum values ​​of the transmitter's transmit power, v and v', respectively. max and v min Let represent the maximum and minimum velocities of the airborne platform, respectively, and let Δv represent the maximum acceleration of the airborne platform. Indicates the maximum turning angle of the airborne platform, v k-1 and These represent the velocity and orientation angle of the airborne platform at time k-1, respectively; v k-2 and These represent the velocity and orientation angle of the airborne platform at time k-2, respectively.

[0040] Furthermore, in step S4, the joint optimization model is rewritten to contain only the path parameter C. k-1 The form is:

[0041]

[0042] Among them, C k-1 Represents the motion control vector, v max and v min Let represent the maximum and minimum velocities of the airborne platform, respectively, and let Δv represent the maximum acceleration of the airborne platform. Indicates the maximum turning angle of the airborne platform; v k-1 and These represent the velocity and orientation angle of the airborne platform at time k-1, respectively; v k-2 and Let represent the velocity and orientation angle of the airborne platform at time k-2, respectively; the rewritten joint optimization model is a non-convex nonlinear optimization model.

[0043] The joint optimization model is rewritten to include only the waveform correlation matrix parameter R. k The form is:

[0044]

[0045] Among them, P k T P represents the total radiated power of an airborne centralized MIMO radar transmitter. max and P minLet represent the maximum and minimum transmit power of the transmitter, respectively. Then, the rewritten joint optimization model is a semidefinite programming problem.

[0046] The airborne centralized MIMO radar multi-target tracking transmission pattern and path joint optimization system of the present invention includes:

[0047] The airborne platform construction module is used to construct a freely movable airborne platform in a two-dimensional plane, equipped with a centralized MIMO radar. The airborne platform adopts a simultaneous multi-beam working mode to perform multi-target search and tracking tasks. The centralized MIMO radar has N transmitting elements with an element spacing of half a wavelength.

[0048] The module for establishing the transmission pattern and motion model is used to form a specific transmission pattern by optimizing the design of the transmission signal waveform correlation array, and to establish the motion model of the airborne platform.

[0049] The BCRLB matrix construction module is used to establish the target motion model and the measurement equation of the airborne centralized MIMO radar for the target. Based on the predicted Fisher information matrix corresponding to the prior information and measurement information, the predicted Bayesian information matrix of the target is calculated. Using the correlation array of the transmitted signal waveform of the airborne centralized MIMO radar and the speed and direction of the airborne platform as independent variables, the predicted BCRLB matrix of the target state estimation error is constructed, and its tracing is used as a characterization index of the target tracking accuracy. The cost function of the computer-aided radar flight path and transmission pattern joint optimization method is also included.

[0050] The joint optimization model construction module is used to establish a joint optimization model of the transmission pattern and path for airborne centralized MIMO radar multi-target tracking, with given airborne platform performance limitations and upper and lower limits of radiated power of airborne centralized MIMO radar as constraints, and minimizing the BCRLB prediction value of multi-target tracking accuracy as the optimization objective.

[0051] The model solving module is used to solve the joint optimization model using a three-step decomposition method based on particle swarm optimization, semidefinite programming, and cyclic minimum method. The module includes: (a) First, for a pre-set emission pattern design parameter that meets the conditions, i.e., the pre-set emission waveform correlation array parameter. The joint optimization model in step S3 is rewritten to contain only path parameter C. k-1 (a) The motion control vector is obtained by solving the form of the wave-correlation array parameter R using the particle swarm optimization algorithm; (b) Based on the obtained motion control vector, the motion path of the airborne platform at that moment is determined, and the predicted position of the airborne centralized MIMO radar at the next moment is also fixed accordingly. Based on this, the joint optimization model is rewritten to include only the waveform correlation array parameter R. kThe objective function is solved using a semidefinite programming algorithm. Finally, the steps (a) and (b) are iterated repeatedly using the cyclic minimization method until the difference between the objective function values ​​of the two iterations is less than the preset condition, thus obtaining the final multi-target tracking accuracy result and optimization result.

[0052] An apparatus of the present invention includes a memory and a processor, wherein:

[0053] Memory is used to store computer programs that can run on a processor;

[0054] The processor is configured to, while running the computer program, execute the steps of the above-described method for joint optimization of transmission pattern and path for multi-target tracking of airborne centralized MIMO radar.

[0055] The present invention provides a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the above-described method for joint optimization of transmission pattern and path for multi-target tracking of airborne centralized MIMO radar.

[0056] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows:

[0057] This invention maximizes multi-target tracking accuracy by jointly optimizing parameters such as the airborne platform's flight path and the waveform correlation array of the airborne centralized MIMO radar during multi-target tracking, while satisfying constraints on the airborne platform's maneuverability and the upper and lower limits of the total radiated power of the airborne centralized MIMO radar transmitter. The method constructs a BCRLB matrix for target state estimation errors, with the airborne radar waveform correlation array and the airborne platform's velocity and direction of motion as independent variables. The traces of the BCRLB matrices corresponding to all targets are summed and used as an indicator of multi-target tracking accuracy. Based on this, with given airborne platform maneuverability limits and the upper and lower limits of the total radiated power of the airborne centralized MIMO radar transmitter as constraints, and minimizing the sum of the BCRLB predictions for overall multi-target tracking accuracy as the optimization objective, a model for joint optimization of the airborne radar flight path and transmission pattern is established. This adaptively plans the airborne platform's path and designs the corresponding transmission pattern to improve multi-target tracking performance. Attached Figure Description

[0058] Figure 1 This is a flowchart of the method of the present invention;

[0059] Figure 2 For the motion trajectories of multiple targets and the motion trajectory of airborne radar;

[0060] Figure 3 This is a graph showing the speed and direction of motion of the airborne platform at various moments.

[0061] Figure 4 Design results for the transmission pattern of an airborne centralized MIMO radar;

[0062] Figure 5 A comparison chart of the target total BCRLB. Detailed Implementation

[0063] The structure and working process of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0064] Based on actual combat scenarios, this invention proposes a joint optimization method for the transmission pattern and path of airborne centralized MIMO radar multi-target tracking. Under the constraints of given upper and lower limits of the total radiated power of the airborne radar transmitter and the maneuvering direction of the airborne platform, the optimization objective is to minimize the BCRLB prediction value of multi-target tracking accuracy. The method adaptively optimizes parameters such as the flight path of the airborne platform and the radiated power of the airborne radar during multi-target tracking, thereby improving the multi-target tracking performance of the airborne radar. First, assuming several targets are dispersed in a two-dimensional space, consider a freely moving airborne platform equipped with a centralized MIMO radar capable of flexibly designing its transmission pattern to track multiple targets dispersed in space. Second, construct a Bayesian Cramér-Rao Lower Bound (BCRLB) expression characterizing the multi-target tracking accuracy. Based on this, with given upper and lower limits of the total radiated power of the airborne radar transmitter and the maneuvering direction and speed of the airborne platform as constraints, and minimizing the BCRLB prediction value of the multi-target tracking accuracy as the optimization objective, establish a joint optimization model of the airborne centralized MIMO radar's multi-target tracking transmission pattern and path. Adaptively and dynamically optimize the airborne platform's flight path and the airborne radar's transmission pattern to improve multi-target tracking performance.

[0065] like Figure 1 As shown, the present invention provides a method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar, comprising the following steps:

[0066] S1. Consider an airborne platform equipped with a centralized MIMO radar that can move freely in a two-dimensional plane. It employs a simultaneous multi-beam operation mode to perform multi-target search and tracking tasks. This airborne centralized MIMO radar has N transmitting elements, with an element spacing of half a wavelength. The transmitted waveform of the nth transmitting element at time k is... L represents the code length of the transmitted waveform, and the transmitted waveform matrix can be defined as follows: in, For s n,kThe transpose of n = 1, 2, ..., N, then the signal x arriving at the far-field direction θ of the centralized MIMO radar at time k is... k (θ) can be expressed as:

[0067] x k (θ)=a H (θ)S k (1)

[0068] Where, a(θ)=[1,e jπsinθ ,…,e j(N-1)πsinθ ] T H represents the launch steering vector, and H represents the conjugate transpose. H (θ) represents the conjugate transpose of the transmit steering vector a(θ), and θ represents the far-field direction of the centralized MIMO radar.

[0069] The transmit pattern of a centralized MIMO radar can be defined as:

[0070] φ k (θ)=a H (θ)R k a(θ) (2)

[0071] in, This represents the correlation array of the transmitted signal waveform. S represents the transmitted waveform matrix. k The conjugate transpose of . Depending on the application scenario, a specific transmission pattern can be formed by optimizing the design of the waveform correlation array.

[0072] For an airborne centralized MIMO radar performing multi-target tracking tasks, its state includes position, velocity, and direction of motion. The state vector of the airborne platform at time k is... in, and Let represent the position and velocity of the airborne platform at time k, respectively. The motion model of the airborne platform can be described as:

[0073]

[0074] in, The overall control function representing the motion of the airborne platform. Let v represent the motion control vector, where v k-1 and Let the velocity and orientation angle of the airborne platform at time k-1 be represented respectively, and they have the following relationship:

[0075]

[0076] in, and Let T represent the position and velocity of the airborne platform at time k-1, respectively. s Indicates the sampling interval.

[0077] S2. Using the waveform correlation array of the airborne centralized MIMO radar and the velocity and direction of motion of the airborne platform as independent variables, construct the predicted BCRLB matrix of the target state estimation error, and use its tracing as a characterization index of target tracking accuracy. The specific calculation steps are as follows:

[0078] Suppose there are Q targets dispersed in a two-dimensional space, moving at a constant velocity in a straight line. The state vector of the q-th target (q = 1, 2, ..., Q) at time k is: in, and Let represent the position and velocity of the q-th target at time k, respectively. Then, the motion model of target q can be described as:

[0079]

[0080] in, Let F represent the state vector of the q-th target at time k-1, and let F represent the state transition matrix. Since the target moves at a constant velocity in a straight line, F can be expressed as:

[0081]

[0082] In formula (5) To represent the noise of a zero-mean Gaussian process, its covariance matrix is... It can be calculated as follows:

[0083]

[0084] Where κ represents the process noise intensity and I2 represents the identity matrix.

[0085] The measurement equation for target q by an airborne centralized MIMO radar at time k can be expressed as:

[0086]

[0087] in, Let be the measurement vector of the airborne centralized MIMO radar for target q at time k. Representing a nonlinear measurement function:

[0088]

[0089] in, and These represent distance and angle measurement information, respectively. In equation (8) The covariance matrix represents zero-mean Gaussian measurement noise. It can be represented as:

[0090]

[0091] in, and These represent the measurement errors and variances of the target distance and azimuth, respectively:

[0092]

[0093] In the formula, β k,q B represents the effective bandwidth of the transmitted signal of an airborne centralized MIMO radar. NN This indicates a 3dB width for the received beam. Let be the signal-to-noise ratio of the echo from the airborne radar to target q at time k:

[0094]

[0095] It can be seen that the signal-to-noise ratio of the airborne centralized MIMO radar echo is proportional to the negative fourth power of the transmit power and the range. Therefore:

[0096]

[0097] in, Let be the transmit power of the airborne centralized MIMO radar at time k for target q. This represents the matrix composed of the remaining parameters.

[0098] The Bayesian information matrix for predicting target q at time k It can be represented as:

[0099]

[0100] in, It is the predicted state vector of target q at time k. and These represent the predicted positions of target q in the x-axis and y-axis directions at time k, respectively. and Let x and y represent the predicted velocities of target q at time k, respectively, in the x-axis and y-axis directions. and The predicted Fisher information matrices, representing the prior information and measurement information at time k respectively, can be calculated using the following formula:

[0101]

[0102] in, This represents the radar's predicted measurement noise covariance matrix for target q at time k. Nonlinear measurement function The Jacobian matrix can be expressed as:

[0103]

[0104] in, Represents the target state vector Find the first-order partial derivative. and Let K and K represent the radar's predicted measurement information for target q at time k.

[0105] Substituting equation (15) into equation (14), we can obtain the predicted Bayesian information matrix of target q at time k as follows:

[0106]

[0107] Due to The signal-to-noise ratio (SNR) of the airborne MIMO radar echo at time k is related to the MIMO radar radiated power and the radial distance from the target to the airborne MIMO radar. Therefore, the Bayesian information matrix can be characterized as a function of the MIMO radar transmit power and the observation position at time k.

[0108] The prediction BCRLB matrix for the target motion state estimation error can be calculated as follows:

[0109]

[0110] right Matrix trace is used as a metric for target tracking accuracy, and the following formula can be used as the cost function of the joint optimization method for the airborne platform's flight path and launch pattern:

[0111]

[0112] Where Tr represents the trace operation.

[0113] S3. Establish a joint optimization model for the transmission pattern and path of multi-target tracking in airborne centralized MIMO radar:

[0114] Given the performance limitations of the airborne platform and the upper and lower limits of the radiated power of the airborne centralized MIMO radar as constraints, and with the goal of minimizing the BCRLB prediction value for multi-target tracking accuracy, a joint optimization model of the transmission pattern and path for multi-target tracking of the airborne centralized MIMO radar is established, as shown in the equation:

[0115]

[0116] Among them, P k T P represents the total radiated power of an airborne centralized MIMO radar transmitter. max and P minThese represent the maximum and minimum values ​​of the transmitter's transmit power, v and v', respectively. max and v min Let represent the maximum and minimum velocities of the airborne platform, respectively, and let Δv represent the maximum acceleration of the airborne platform. Indicates the maximum turning angle of the airborne platform, v k-2 and Let $\frac{k}{k-2}$ represent the velocity and orientation angle of the airborne platform at time $k-2$. The first constraint in equation (20) represents the radiated power limit of the airborne centralized MIMO radar transmitter; the second constraint represents $R$. k It is a Hermitian positive semi-definite matrix; the third constraint condition indicates that the airborne platform's speed at time k-1 is within the set threshold range; the last two constraints are the airborne platform's acceleration limit and turning angle limit, respectively.

[0117] S4. The optimization model (20) is solved by a three-step decomposition method based on particle swarm optimization, semidefinite programming and cyclic minimum method.

[0118] (a) First, for a pre-set transmission pattern design parameter that meets the conditions, i.e., the pre-set transmission waveform correlation array parameter. The optimization model (20) can be rewritten to contain only the path parameter C. k-1 In the form of:

[0119]

[0120] The rewritten optimization model (21) is a non-convex nonlinear optimization model, which can be solved using the particle swarm optimization algorithm to obtain the motion control vector C. k-1 .

[0121] (b) Secondly, after obtaining the motion control vector in step (a), the motion path of the airborne platform at that moment is also determined, and the predicted position of the airborne centralized MIMO radar at the next moment is also fixed accordingly. Based on this, model (20) can be rewritten to include only the waveform correlation array parameter R. k Format:

[0122]

[0123] The optimization problem described above can be transformed into a semidefinite programming problem, and then solved using a semidefinite programming algorithm.

[0124] (c) Finally, the steps (a) and (b) are iterated continuously using the minimum loop method until the difference between the objective function values ​​of the two iterations is less than the preset condition, thus obtaining the final multi-target tracking accuracy result and optimization result.

[0125] Simulation results:

[0126] Assume there are Q = 3 targets scattered on a two-dimensional plane. Target 1 has an initial position of (-10, 40) km and flies at a constant speed of (-150, -300) m / s. Target 2 has an initial position of (5, 55) km and flies at a constant speed of (800, 150) m / s. Target 3 has an initial position of (60, 50) km and flies at a constant speed of (550, -500) m / s. The airborne radar's initial position is at the origin, i.e., [0, 0] km. Assume the airborne centralized MIMO radar has a sampling interval T = 1 s and a tracking process duration of 30 s. The maximum radiated power of the airborne radar transmitter is P. max =1000W, minimum radiated power is P min =100W. The upper and lower limits of the airborne platform's movement speed are 500m / s and 300m / s, respectively. The maximum turning angle of the airborne platform is...

[0127] Multi-target motion trajectory and airborne centralized MIMO radar motion trajectory, such as Figure 2 As shown, the uniform distribution algorithm means that the radar distributes the radiated energy evenly to each target, optimizing only the motion path. The speed and direction of motion of the airborne platform at each moment are as follows: Figure 3 As shown in (a) and (b), it can be seen from the figure that the airborne platform always moves to the upper right at the maximum speed. Furthermore, the energy allocated to each target by the method proposed in this invention is different from that of the uniform allocation algorithm, resulting in different degrees of influence of each target on the overall tracking accuracy. Therefore, the movement path of the airborne centralized MIMO radar is also different. Figure 4 The results of several emission pattern design algorithms are presented, where the fixed radar algorithm indicates that the radar position is always fixed at the initial position, and only the emission pattern is optimized. As can be seen from the figure, the proposed algorithm concentrates more radiated energy on the farthest target 3, because it has the greatest impact on the overall target tracking accuracy. Furthermore, as the airborne radar moves, the azimuth angle of each target relative to the radar changes; therefore, the main lobe direction of the proposed algorithm differs from that of the fixed radar algorithm.

[0128] The root mean square error (RMSE) for target tracking is calculated as follows:

[0129]

[0130] In the formula, N MC For the number of Monte Carlo experiments, Let N be the estimated position of the target obtained in the nth Monte Carlo experiment. MC =100.

[0131] Figure 5A comparison between the overall target RMSE and BCRLB is given. From Figure 5 As can be seen, the algorithm proposed in this invention can achieve the highest target tracking accuracy, verifying the effectiveness of the algorithm proposed in this paper.

[0132] The airborne centralized MIMO radar multi-target tracking transmission pattern and path joint optimization system of the present invention includes:

[0133] The airborne platform construction module is used to construct a freely movable airborne platform in a two-dimensional plane, equipped with a centralized MIMO radar. The airborne platform adopts a simultaneous multi-beam working mode to perform multi-target search and tracking tasks. The centralized MIMO radar has N transmitting elements with an element spacing of half a wavelength.

[0134] The module for establishing the transmission pattern and motion model is used to form a specific transmission pattern by optimizing the design of the transmission signal waveform correlation array, and to establish the motion model of the airborne platform.

[0135] The BCRLB matrix construction module is used to establish the target motion model and the measurement equation of the airborne centralized MIMO radar for the target. Based on the predicted Fisher information matrix corresponding to the prior information and measurement information, the predicted Bayesian information matrix of the target is calculated. Using the correlation array of the transmitted signal waveform of the airborne centralized MIMO radar and the speed and direction of the airborne platform as independent variables, the predicted BCRLB matrix of the target state estimation error is constructed, and its tracing is used as a characterization index of the target tracking accuracy. The cost function of the computer-aided radar flight path and transmission pattern joint optimization method is also included.

[0136] The joint optimization model construction module is used to establish a joint optimization model of the transmission pattern and path for airborne centralized MIMO radar multi-target tracking, with given airborne platform performance limitations and upper and lower limits of radiated power of airborne centralized MIMO radar as constraints, and minimizing the BCRLB prediction value of multi-target tracking accuracy as the optimization objective.

[0137] The model solving module is used to solve the joint optimization model using a three-step decomposition method based on particle swarm optimization, semidefinite programming, and cyclic minimum method. The module includes: (a) First, for a pre-set emission pattern design parameter that meets the conditions, i.e., the pre-set emission waveform correlation array parameter. The joint optimization model in step S3 is rewritten to contain only path parameter C. k-1 (a) The motion control vector is obtained by solving the form of the wave-correlation array parameter R using the particle swarm optimization algorithm; (b) Based on the obtained motion control vector, the motion path of the airborne platform at that moment is determined, and the predicted position of the airborne centralized MIMO radar at the next moment is also fixed accordingly. Based on this, the joint optimization model is rewritten to include only the waveform correlation array parameter R.k The objective function is solved using a semidefinite programming algorithm. Finally, the steps (a) and (b) are iterated repeatedly using the cyclic minimization method until the difference between the objective function values ​​of the two iterations is less than the preset condition, thus obtaining the final multi-target tracking accuracy result and optimization result.

[0138] An apparatus of the present invention includes a memory and a processor, wherein:

[0139] Memory is used to store computer programs that can run on a processor;

[0140] The processor is configured to execute the steps of the above-described method for joint optimization of transmission pattern and path for multi-target tracking of airborne centralized MIMO radar when running the computer program, and to achieve the technical effects described in the above method.

[0141] The present invention provides a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the above-described airborne centralized MIMO radar multi-target tracking transmission pattern and path joint optimization method, and achieves the technical effects described above.

[0142] Working principle and process:

[0143] This invention considers a freely movable airborne platform in two-dimensional space, equipped with a centralized MIMO radar that flexibly designs the transmission pattern by optimizing the waveform correlation array. Assuming that several targets are dispersed on the two-dimensional plane, the airborne centralized MIMO radar tracks multiple targets dispersed in space. For scenarios involving airborne radar tracking multiple targets, firstly, using the airborne platform's velocity, direction of motion, and waveform correlation array parameters of the airborne centralized MIMO radar as independent variables, a predicted BCRLB matrix for target state estimation error is constructed. The traces of the diagonals are taken and summed as a measure of target tracking accuracy. Then, given constraints on the airborne platform's maneuverability (i.e., maneuver direction and acceleration limits, as well as maximum and minimum speed limits) and the upper and lower limits of the total radiated power of the airborne centralized MIMO radar transmitter, a joint optimization model of the transmission pattern and path for multi-target tracking using airborne centralized MIMO radar is established, with the optimization objective of minimizing the sum of the BCRLB predictions for overall multi-target tracking accuracy. Finally, a three-step solution strategy based on particle swarm optimization, native positive definite programming, and cyclic minimization is used to solve this optimization model. By solving this optimization model, the waveform correlation array R that achieves the highest multi-target tracking accuracy under the constraints of airborne platform maneuverability and the upper limit of the total radiated power of the centralized MIMO radar transmitter is obtained. k , velocity v k-1 and direction of motion θk-1 This is the optimal solution for the model.

Claims

1. A method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar, characterized in that, Includes the following steps: S1. Consider an airborne platform in a two-dimensional plane equipped with a centralized MIMO radar that can move freely. This platform employs a simultaneous multi-beam operating mode to perform multi-target search and tracking tasks. This centralized MIMO radar has... A transmitting array element with an element spacing of half a wavelength is used to form a specific transmission pattern by optimizing the design of the transmitted signal waveform correlation array, thereby establishing a motion model of the airborne platform. S2. Establish the target motion model and the measurement equation of the airborne centralized MIMO radar for the target. Calculate the predicted Bayesian information matrix of the target based on the predicted Fisher information matrix corresponding to the prior information and the measurement information. Construct the predicted BCRLB matrix of the target state estimation error using the correlation array of the transmitted signal waveform of the airborne centralized MIMO radar and the speed and direction of the airborne platform as independent variables, and use its tracking as a characterization index of target tracking accuracy. Develop the cost function of the computer-aided radar flight path and transmission pattern joint optimization method. S3. Given the performance limitations of the airborne platform and the upper and lower limits of the radiated power of the airborne centralized MIMO radar as constraints, and with the goal of minimizing the BCRLB prediction value of multi-target tracking accuracy, establish a joint optimization model for the transmission pattern and path of the airborne centralized MIMO radar multi-target tracking; the joint optimization model is expressed as: ； in, This indicates the trace operation. Represents the motion control vector. This represents the correlation array of the transmitted signal waveform. This indicates the total radiated power of the airborne centralized MIMO radar transmitter. and These represent the maximum and minimum values ​​of the transmitter's transmission power, respectively. and These represent the maximum and minimum speeds of the airborne platform, respectively. This indicates the maximum acceleration of the airborne platform. Indicates the maximum turning angle of the airborne platform. and They represent airborne platforms respectively. The speed and orientation angle of the motion at any given moment; and They represent airborne platforms respectively. The speed and orientation angle of the motion at any given moment; S4. The joint optimization model is solved using a three-step decomposition method based on particle swarm optimization, semidefinite programming, and cyclic minimization, including: (a) First, for a pre-set emission pattern design parameter that meets the conditions, i.e., the pre-set emission waveform correlation array parameter. The joint optimization model in step S3 is rewritten to contain only path parameters. (a) The motion control vector is obtained by solving the motion control vector using the particle swarm optimization algorithm; (b) Based on the obtained motion control vector, the motion path of the airborne platform at that moment is determined, and the predicted position of the airborne centralized MIMO radar at the next moment is also fixed accordingly. Based on this, the joint optimization model is rewritten to include only waveform correlation array parameters. The form is obtained by solving the problem using a semidefinite programming algorithm. Finally, the steps (a) and (b) are iterated continuously using the cyclic minimum method until the difference between the objective function values ​​of the two iterations is less than the preset condition, thus obtaining the final multi-target tracking accuracy result and optimization result.

2. The method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar according to claim 1, characterized in that, The transmission pattern of the centralized MIMO radar in step S1 is represented as follows: ； in, express The correlation matrix of the transmitted signal waveform at each moment; express Transmit waveform matrix of a real-time MIMO radar Represents the transmitted waveform matrix The conjugate transpose of . This represents the launch guidance vector.

3. The method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar according to claim 1, characterized in that, The motion model of the airborne platform established in step S1 is represented as follows: ； in, Indicates in The state vector of the airborne platform at any given moment. Indicates in The state vector of the airborne platform at any given moment. The overall control function representing the motion of the airborne platform. Denotes the motion control vector, where and They represent airborne platforms respectively. The speed and orientation angle of the motion at any given moment.

4. The method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar according to claim 1, characterized in that, The method for constructing the prediction BCRLB matrix of the target state estimation error in step S2 is as follows: Assuming there is in two-dimensional space A number of targets are dispersed and moving at a constant velocity in a straight line, wherein the first... One goal is The state vector at time t is ,in, , and Representing the target The position and velocity at a given moment; then the target The motion model is described as follows: ； in, Represents the state transition matrix. Indicates the first One goal is The state vector at time t, This represents noise in a zero-mean Gaussian process. Airborne centralized MIMO radar for target monitoring The measurement equation is expressed as: ； in, for Airborne radar is constantly monitoring the target. The measurement vector, Represents a nonlinear measurement function. This indicates zero-mean Gaussian measurement noise; Momentary Goal Predictive Bayesian Information Matrix Represented as: ； in, The goal exist The predicted state vector at time t. and Representing the target exist The predicted positions in the x-axis and y-axis directions at time 1. and Representing the target exist Predicted velocities in the x-axis and y-axis directions at time t. and They represent The predicted Fisher information matrix based on prior time information and measurement information is calculated as follows: ； in, Nonlinear measurement function Jacobian matrix, Indicates that the radar is in Always on the target The predicted value of the measurement noise covariance matrix; Then we get Momentary Goal The prediction Bayesian information matrix is ​​as follows: ； The BCRLB matrix for predicting the target motion state estimation error is calculated as follows: ； right Matrix trace is used as a metric for target tracking accuracy.

5. The method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar according to claim 1, characterized in that, The cost function of the joint optimization method for airborne radar flight path and transmission pattern in step S2 is: ； in, Represents the motion control vector. This represents the correlation array of the transmitted signal waveform. The predicted BCRLB matrix represents the error in estimating the target's motion state. This indicates the trace operation.

6. The method for joint optimization of transmission pattern and path for multi-target tracking in airborne centralized MIMO radar according to claim 1, characterized in that, In step S4, the joint optimization model is rewritten to contain only path parameters. The form is: ； in, This indicates that the rewritten joint optimization model of the motion control vector is a non-convex nonlinear optimization model; The joint optimization model is rewritten to include only waveform correlation matrix parameters. The form is: ； The rewritten joint optimization model is a semidefinite programming problem.

7. An airborne centralized MIMO radar multi-target tracking transmission pattern and path joint optimization system, characterized in that, include: The airborne platform construction module is used to build a freely movable airborne platform in a two-dimensional plane, equipped with a centralized MIMO radar. This airborne platform employs a simultaneous multi-beam operating mode to perform multi-target search and tracking tasks. The centralized MIMO radar has… Each transmitting array element has a spacing of half a wavelength between its elements. The module for establishing the transmission pattern and motion model is used to form a specific transmission pattern by optimizing the design of the transmission signal waveform correlation array, and to establish the motion model of the airborne platform. The BCRLB matrix construction module is used to establish the target motion model and the measurement equation of the airborne centralized MIMO radar for the target. Based on the predicted Fisher information matrix corresponding to the prior information and measurement information, the predicted Bayesian information matrix of the target is calculated. Using the correlation array of the transmitted signal waveform of the airborne centralized MIMO radar and the speed and direction of the airborne platform as independent variables, the predicted BCRLB matrix of the target state estimation error is constructed, and its tracing is used as a characterization index of the target tracking accuracy. The cost function of the computer-aided radar flight path and transmission pattern joint optimization method is also included. The joint optimization model construction module is used to establish a joint optimization model of the transmission pattern and path for multi-target tracking of airborne centralized MIMO radar, with given airborne platform performance limitations and upper and lower limits of radiated power of airborne centralized MIMO radar as constraints, and minimizing the BCRLB prediction value of multi-target tracking accuracy as the optimization objective. The joint optimization model is expressed as follows: ； in, This indicates the trace operation. Represents the motion control vector. This represents the correlation array of the transmitted signal waveform. This indicates the total radiated power of the airborne centralized MIMO radar transmitter. and These represent the maximum and minimum values ​​of the transmitter's transmission power, respectively. and These represent the maximum and minimum speeds of the airborne platform, respectively. This indicates the maximum acceleration of the airborne platform. Indicates the maximum turning angle of the airborne platform. and They represent airborne platforms respectively. The speed and orientation angle of the motion at any given moment; and They represent airborne platforms respectively. The speed and orientation angle of the motion at any given moment; The model solving module is used to solve the joint optimization model using a three-step decomposition method based on particle swarm optimization, semidefinite programming, and cyclic minimization. The module includes: (a) First, for a pre-set emission pattern design parameter that meets the conditions, i.e., the pre-set emission waveform correlation array parameter. The joint optimization model in step S3 is rewritten to contain only path parameters. (a) The motion control vector is obtained by solving the motion control vector using the particle swarm optimization algorithm; (b) Based on the obtained motion control vector, the motion path of the airborne platform at that moment is determined, and the predicted position of the airborne centralized MIMO radar at the next moment is also fixed accordingly. Based on this, the joint optimization model is rewritten to include only waveform correlation array parameters. The form is obtained by solving the problem using a semidefinite programming algorithm. Finally, the steps (a) and (b) are iterated continuously using the cyclic minimum method until the difference between the objective function values ​​of the two iterations is less than the preset condition, thus obtaining the final multi-target tracking accuracy result and optimization result.

8. A device, characterized in that, Includes memory and processor, wherein: Memory is used to store computer programs that can run on a processor; A processor, configured to, while running the computer program, perform the steps of the method for joint optimization of transmission pattern and path for multi-target tracking of airborne centralized MIMO radar as described in any one of claims 1-6.

9. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by at least one processor, implements the steps of the joint optimization method for multi-target tracking transmission pattern and path of airborne centralized MIMO radar as described in any one of claims 1-6.

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