Joint optimization method of airborne radar flight path and power for multi-target tracking

Abstract

The present invention discloses a joint optimization method of airborne radar flight path and power for multi-target tracking, considering a freely movable airborne platform in two-dimensional space, equipped with a phased array radar with a simultaneous multi-beam working mode, to track multiple targets dispersedly deployed in space; secondly, construct BCRLB expressions characterizing the multi-target tracking accuracy respectively; finally, taking the given upper limit of the total radiated power of the airborne radar and the maneuvering direction of the airborne platform as constraints, taking the BCRLB prediction value of minimizing the multi-target tracking accuracy as the optimization target, establishing a joint optimization model of airborne radar flight path and power for multi-target tracking, and adaptively and dynamically optimizing the flight path of the airborne platform and the radiated power of the airborne radar. The present invention realizes the optimal airborne radar power allocation and the better airborne platform path planning, and effectively improves the multi-target tracking performance of the airborne radar.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a joint optimization method of airborne radar flight path and power for multi-target tracking. Background Art

[0002] Radar is known as the "eyes" of modern warfare because it can detect and track targets at all times and in all weather conditions. Airborne radar is an indispensable avionics system on modern aircraft. According to its purpose, it can be divided into interception radar, air reconnaissance and terrain display radar, navigation radar and airborne early warning radar, etc. It can effectively perform various tasks such as fire control, target tracking, airborne early warning and land surveillance. Airborne platforms equipped with phased array radars can simultaneously transmit multiple beams to independently perform different tasks in high-speed flight. This feature enables airborne platforms to quickly and adaptively adjust their flight paths and system RF radiation resources for different tasks, and complete different combat tasks more efficiently and excellently.

[0003] For multi-target tracking tasks, under the constraint of limited airborne radar radiation power resources, it is necessary to reasonably schedule and allocate the limited power resources to maximize the tracking accuracy of each target. In addition, since the target tracking errors obtained by different flight paths of the airborne platform are different, it is very urgent and necessary to plan the flight path of the airborne platform to improve the target tracking performance.

[0004] At present, there are a lot of research results on the optimization management of radar power resources under multi-target tracking tasks. However, most of them are designed for simulation scenarios of ground-based radar platforms, that is, the position of the radar platform is fixed, and the maneuverability of airborne radars and the impact of different flight paths on target tracking accuracy are not considered, which has certain limitations. In summary, there is no joint optimization method of airborne radar flight path and power for multi-target tracking in the existing technology. Summary of the invention

[0005] Purpose of the invention: The present invention provides a method for jointly optimizing the flight path and power of an airborne radar for multi-target tracking, which realizes the optimal airborne radar power allocation and better airborne platform path planning, and effectively improves the multi-target tracking performance of the airborne radar.

[0006] Technical solution: The invention discloses a method for joint optimization of airborne radar flight path and power for multi-target tracking, comprising the following steps:

[0007] (1) constructing an airborne platform that can move freely in two-dimensional space, wherein the airborne platform includes an airborne radar with a simultaneous multi-beam working mode to track multiple targets dispersed in space;

[0008] (2) Taking the airborne platform's motion speed, motion direction and airborne radar transmit power as independent variables, a predicted BCRLB matrix of the target state estimation error is constructed, and the trace of the diagonal of the BCRLB matrix is ​​taken as a measure of the target tracking accuracy;

[0009] (3) Taking the given upper limit of the total radiated power of the airborne radar and the maneuvering direction of the airborne platform as constraints and minimizing the BCRLB prediction value of the multi-target tracking accuracy as the optimization goal, a joint optimization model of the airborne radar flight path and power for multi-target tracking is established. The flight path of the airborne platform and the airborne radar radiated power are adaptively and dynamically optimized to improve the multi-target tracking performance.

[0010] Furthermore, the implementation process of step (1) is as follows:

[0011] For an airborne radar that performs a multi-target tracking task, its state includes position, speed, and direction, and the direction of motion is determined by the state control parameter, namely the heading angle; the state vector of the airborne radar at time k is in, and Respectively represent the position and velocity of the airborne radar; the motion model of the airborne radar is:

[0012]

[0013] In the formula, represents the state vector of the airborne radar at time k-1, represents the state control parameter of the airborne radar at time k-1, and F represents the state transfer function of the airborne radar; Formula (1) can be further described as follows:

[0014]

[0015] Where F1 and F2 represent the state transfer matrix, which is calculated as:

[0016]

[0017] Where T represents the sampling interval; v k-1 and θ k-1 They represent the speed and direction of the airborne radar at time k-1 respectively, and their relationship with the speed in the airborne radar state vector is as follows:

[0018]

[0019] Furthermore, the implementation process of step (2) is as follows: there are Q dispersed targets moving in a uniform linear motion on a two-dimensional plane, where the state vector of the qth (q = 1, 2, ..., Q) target at time k is in, and Respectively represent the position and velocity of the target; the motion model of the target q is:

[0020]

[0021] Where F is the target state transfer matrix; W q is a white Gaussian process noise with a mean of zero and a covariance of Q q for:

[0022]

[0023] In the formula, represents the process noise intensity of the target q;

[0024] The measurement equation of the airborne radar to the target q at time k is as follows:

[0025]

[0026] In the formula, is the measurement vector of the airborne radar to the target q at time k, h(·) represents the nonlinear measurement function, is zero-mean white Gaussian measurement noise; The calculation formula is as follows:

[0027]

[0028] In the formula, and They represent the actual distance and azimuth from the target q to the airborne radar at time k respectively; To measure noise The covariance of is expressed as:

[0029]

[0030] In the formula, and Respectively represent the measurement error variance of target distance and azimuth:

[0031]

[0032] Where β is the effective bandwidth of the airborne radar transmission signal, c = 3 × 10 8 m / s is the speed of light, is the echo signal-to-noise ratio of the airborne radar irradiating the target q at time k:

[0033]

[0034] In the formula, is the transmission power of the airborne radar to the target q at time k, Gt is the radar transmitting antenna gain, G r is the radar receiving antenna gain, σ q is the radar cross-section of target q relative to the airborne radar, λ is the wavelength of the radar transmitter, G RP is the radar receiver processing gain, k is the Boltzmann constant, T o is the noise temperature of the radar receiver, B r The bandwidth of the airborne radar receiver matched filter for target q, F r is the noise factor of the radar receiver, is the distance between the airborne radar and the target q at time k, T d is the dwell time of each radar on the target, T r is the pulse repetition period of the radar;

[0035] The predicted Bayesian information matrix of target q at time k It can be expressed as:

[0036]

[0037] In the formula, is the predicted state vector of the target q at time k, where represents the predicted position of the target q at time k, represents the predicted moving speed of target q at time k; and Represent the predicted Fisher information matrix of the prior information and the measured information at time k respectively:

[0038]

[0039] In the formula, Q q is the variance of the target q-process noise, is the prediction covariance matrix of the measurement noise, F is the target state transfer matrix, is a nonlinear measurement function The Jacobian matrix of is expressed as:

[0040]

[0041] In the formula, Represents the target state vector Find the first-order partial derivative, It represents the first-order partial derivative of the target's predicted distance from the airborne radar to the target's predicted position and predicted motion speed. It represents the first-order partial derivative of the target's predicted azimuth relative to the airborne radar with respect to the target's predicted position and predicted motion speed;

[0042] Substituting equation (14) into equation (13), we can obtain the predicted Bayesian information matrix of target q at time k:

[0043]

[0044] The predicted Fisher information matrix of the second measurement data is related to the radar's transmission power and motion path at time k; the predicted BCRLB matrix of the target motion state estimation error can be obtained by inverting equation (16):

[0045]

[0046] right The matrix trace is used as a measure of target tracking accuracy, and the following formula is used as the cost function of the joint optimization method of airborne radar flight path and power:

[0047]

[0048] Furthermore, the joint optimization model of airborne radar flight path and power for multi-target tracking in step (3) is:

[0049]

[0050] In the formula, θ k represents the direction of motion of the airborne radar at time k, Indicates the maximum turning angle of the airborne platform, v max and v min Respectively represent the maximum and minimum values ​​of the airborne platform speed, P max and P min Respectively represent the maximum and minimum values ​​of the radiation power of each beam, represents the total radiated power of the airborne radar system; the first constraint represents the maneuvering direction restriction of the airborne platform; the second constraint represents that the heading angle of the airborne platform is omnidirectional; the third constraint represents that the movement speed of the airborne platform at time k-1 is within the set threshold range; the last two constraints represent that the airborne radar radiation power resource meets the conditions, that is, the total radiation resource is fixed and the radiation power of each beam does not exceed the set upper and lower limits.

[0051] Beneficial effect: Compared with the prior art, the beneficial effect of the present invention is that by jointly optimizing parameters such as the flight path of the airborne platform and the radiation power of the airborne radar during multi-target tracking, the optimal airborne radar power allocation and better airborne platform path planning are achieved under the constraints of the maneuverability of the airborne platform and the upper limit of the total radiation power of the airborne radar, thereby effectively improving the multi-target tracking performance of the airborne radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flow chart of the present invention;

[0053] Figure 2 It is the motion trajectory of multiple targets and the motion trajectory of airborne radar;

[0054] Figure 3 It is the motion speed and motion direction diagram of the airborne platform at each moment;

[0055] Figure 4 Allocate radiated power resources for airborne radar;

[0056] Figure 5 Comparison chart of RMSE and BCRLB for three objectives;

[0057] Figure 6 Comparison chart of target total BCRLB in two scenarios. DETAILED DESCRIPTION

[0058] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0059] The present invention provides a method for jointly optimizing the flight path and power of an airborne radar for multi-target tracking. Figure 1 As shown, the specific steps include:

[0060] Step 1: Construct a freely movable airborne platform in two-dimensional space, wherein the airborne platform includes a phased array radar with a simultaneous multi-beam working mode to track multiple targets dispersed in space.

[0061] For an airborne radar that performs a multi-target tracking task, its state includes position, speed, and direction, and the direction of motion is determined by the state control parameter, namely the heading angle. The state vector of the airborne radar at time k is in, and Respectively represent the position and velocity of the airborne radar. The motion model of the airborne radar can be described as:

[0062]

[0063] In the formula, represents the state vector of the airborne radar at time k-1, represents the state control parameter of the airborne radar at time k-1, and F represents the state transfer function of the airborne radar. Formula (1) can be further described as follows:

[0064]

[0065] Where F1 and F2 represent the state transfer matrix, which can be calculated as:

[0066]

[0067] In the formula, T represents the sampling interval. In formula (2), v k-1 and θ k-1 They represent the speed and direction of the airborne radar at time k-1 respectively, and their relationship with the speed in the airborne radar state vector is:

[0068]

[0069] Step 2: Taking the airborne platform motion speed, motion direction and airborne radar transmit power as independent variables, construct the predicted BCRLB matrix of the target state estimation error, and take the trace of the diagonal of the BCRLB matrix as the measure of target tracking accuracy.

[0070] Assume that there are Q dispersed targets moving in a uniform linear motion on a two-dimensional plane, and the state vector of the qth (q=1,2,...,Q)th target at time k is in, and Represent the position and velocity of the target respectively. The motion model of the target q can be described as:

[0071]

[0072] In the formula, F represents the target state transfer matrix. Since the target moves in a uniform straight line, F can be expressed as:

[0073]

[0074] In formula (5), W q represents white Gaussian process noise with zero mean and covariance Q q It can be calculated by the following formula:

[0075]

[0076] In the formula, represents the process noise intensity of the target q.

[0077] The measurement equation of the airborne radar to the target q at time k is as follows:

[0078]

[0079] In the formula, is the measurement vector of the airborne radar to the target q at time k, h(·) represents the nonlinear measurement function, is white Gaussian measurement noise with zero mean. The calculation formula is as follows:

[0080]

[0081] In the formula, and They represent the actual distance and azimuth from target q to the airborne radar at time k. To measure noise The covariance of can be expressed as:

[0082]

[0083] In the formula, and Respectively represent the measurement error variance of target distance and azimuth, which can be calculated by the following formula:

[0084]

[0085] Where β is the effective bandwidth of the airborne radar transmission signal, c = 3 × 10 8 m / s is the speed of light, is the echo signal-to-noise ratio of the airborne radar to the target q at time k, which can be expressed as:

[0086]

[0087] In the formula, is the transmission power of the airborne radar to the target q at time k, G t is the radar transmitting antenna gain, G r is the radar receiving antenna gain, σ q is the radar cross-section of target q relative to the airborne radar, λ is the wavelength of the radar transmitter, G RP is the radar receiver processing gain, k is the Boltzmann constant, T o is the noise temperature of the radar receiver, B r The bandwidth of the airborne radar receiver matched filter for target q, F r is the noise factor of the radar receiver, is the distance between the airborne radar and the target q at time k, T d is the dwell time of each radar on the target, T r is the pulse repetition period of the radar.

[0088] The predicted Bayesian information matrix of target q at time k It can be expressed as:

[0089]

[0090] In the formula, is the predicted state vector of the target q at time k, where represents the predicted position of the target q at time k, represents the predicted moving speed of target q at time k; and The predicted Fisher information matrix represents the prior information and the measured information at time k, respectively, and can be calculated by the following formula:

[0091]

[0092] In the formula, Q q is the variance of the target q-process noise, is the prediction covariance matrix of the measurement noise, F is the target state transfer matrix, is a nonlinear measurement function The Jacobian matrix of can be expressed as:

[0093]

[0094] In the formula, Represents the target state vector Find the first-order partial derivative, It represents the first-order partial derivative of the target's predicted distance from the airborne radar to the target's predicted position and predicted motion speed. It represents the first-order partial derivative of the target's predicted azimuth relative to the airborne radar with respect to the target's predicted position and predicted motion speed.

[0095] Will indicate and Substitute the specific expression (14) into the Bayesian information matrix In the calculation formula (13), the predicted Bayesian information matrix of the target q at time k can be obtained as:

[0096]

[0097] From the above formula, we can see that The first item of the prior information of the predicted Fisher information matrix is ​​only related to the Bayesian information matrix of the target state at the previous moment and the target's motion model. It is related to the radar predicted echo signal-to-noise ratio at time k, and the predicted echo signal-to-noise ratio is a function of the radiation power and the radial distance from the target to the airborne radar. Therefore, The predicted Fisher information matrix of the second measurement data is related to the radar's transmission power and motion path at time k.

[0098] By inverting equation (16), we can obtain the predicted BCRLB matrix of the target motion state estimation error:

[0099]

[0100] right The matrix trace is used as a measure of target tracking accuracy, and the following formula can be used as the cost function of the joint optimization method of airborne radar flight path and power:

[0101]

[0102] Step 3: Taking the given upper limit of the total radiated power of the airborne radar and the maneuvering direction of the airborne platform as constraints, and minimizing the BCRLB prediction value of the multi-target tracking accuracy as the optimization goal, a joint optimization model of the airborne radar flight path and power for multi-target tracking is established, and the flight path of the airborne platform and the airborne radar radiated power are adaptively and dynamically optimized to improve the multi-target tracking performance.

[0103] Taking the given upper limit of the total radiated power of the airborne radar and the maneuvering direction of the airborne platform as constraints, and minimizing the BCRLB prediction value of the multi-target tracking accuracy as the optimization goal, a joint optimization model of the airborne radar flight path and power for multi-target tracking is established, as shown in the formula:

[0104]

[0105] In the formula, θ k represents the direction of motion of the airborne radar at time k, Indicates the maximum turning angle of the airborne platform, v max and v min Respectively represent the maximum and minimum values ​​of the airborne platform speed, P max and P min Respectively represent the maximum and minimum values ​​of the radiation power of each beam, In formula (19), the first constraint condition indicates the maneuvering direction limit of the airborne platform; the second constraint condition indicates that the heading angle of the airborne platform is omnidirectional; the third constraint condition indicates that the motion speed of the airborne platform at time k-1 is within the set threshold range; the last two constraints indicate that the airborne radar radiation power resource meets the conditions, that is, the total radiation resource is fixed and the radiation power of each beam does not exceed the set upper and lower limits.

[0106] The optimization model is solved by the interior point method. By solving the optimization model, the transmission power P that achieves the highest multi-target tracking accuracy under the constraints of satisfying the mobility of the airborne platform and the upper limit of the total radiation power of the radar is obtained. k , movement speed v k-1 and the direction of motion θ k-1 is the optimal solution of the model.

[0107] The operating parameters of the airborne radar are set as shown in Table 1:

[0108] Table 1 Simulation parameter settings

[0109] parameter Numeric parameter Numeric <![CDATA[T d ]]> 0.005s <![CDATA[G RP ]]> 28 <![CDATA[G t ]]> 32.5dB <![CDATA[T o ]]> 290K <![CDATA[σ q ]]> <![CDATA[1m 2 ]]> <![CDATA[F r ]]> 3dB λ 0.03m k <![CDATA[1.38×10 -23 J / K]]> <![CDATA[T r ]]> <![CDATA[5×10 -4 s]]> γ <![CDATA[1m 2 ]]>

[0110] Assume that there are Q = 3 targets scattered on a two-dimensional plane. The initial position of target 1 is (40, 20) km, and it flies at a constant speed of (-250, -200) m / s. The initial position of target 2 is (30, 30) km, and it flies at a constant speed of (-200, -200) m / s. The initial position of target 3 is (15, 45) km, and it flies at a constant speed of (-150, -350) m / s. The initial position of the airborne radar is at the origin, that is, [0, 0] km. Assume that the airborne radar sampling interval T = 1s, and the tracking process lasts for 50s. The total radiated power of the airborne radar is 12000W, and the maximum radiated power of each beam is P max =6000W, the minimum radiated power is P min = 200W. The upper and lower limits of the airborne platform's speed are 300m / s and 200m / s respectively. The maximum turning angle of the airborne platform is

[0111] The flow chart of the joint optimization method of airborne radar flight path and power for multi-target tracking is as follows: Figure 1 As shown in the figure, the multi-target motion trajectory and the airborne radar motion trajectory are as follows Figure 2 As shown in the figure, the speed and direction of the airborne platform at each moment are as follows: Figure 3 As shown in Figure 2, the distribution of airborne radar radiation power resources is as follows: Figure 4 As shown in the figure, it can be seen that the airborne platform always moves at the maximum speed.

[0112] The root mean square error (RMSE) of target tracking is defined as:

[0113]

[0114] Where N MC is the number of Monte Carlo experiments, is the estimated position of the target obtained in the nth Monte Carlo experiment. Here, let N MC =100. Figure 5 The comparison of RMSE and BCRLB of three objectives is given. Figure 5 It can be seen that the tracking accuracy of the target is gradually improved, and the proposed algorithm can effectively track all targets.

[0115] In order to verify the effectiveness of the present invention, a multi-target tracking simulation scenario is also set up with the airborne radar fixed at the origin position, and the multi-target tracking performance in the two scenarios is compared. The total BCRLB of all targets is as follows: Figure 6It can be seen that after the airborne radar flight path is adaptively planned and selected, the multi-target tracking accuracy is further improved, which illustrates the effectiveness of the present invention.

Claims

1. A joint optimization method of airborne radar flight path and power for multi-target tracking, characterized in that: The following steps are involved: (1) constructing an airborne platform that can move freely in two-dimensional space, wherein the airborne platform includes an airborne radar with a simultaneous multi-beam working mode to track multiple targets dispersed in space; (2) Taking the airborne platform's motion speed, motion direction and airborne radar transmit power as independent variables, a predicted BCRLB matrix of the target state estimation error is constructed, and the trace of the diagonal of the BCRLB matrix is ​​taken as a measure of the target tracking accuracy; (3) Taking the given upper limit of the total radiated power of the airborne radar and the maneuvering direction of the airborne platform as constraints, and taking the BCRLB prediction value that minimizes the multi-target tracking accuracy as the optimization goal, a joint optimization model of the airborne radar flight path and power for multi-target tracking is established, and the flight path of the airborne platform and the airborne radar radiated power are adaptively and dynamically optimized to improve the multi-target tracking performance; The joint optimization model of airborne radar flight path and power for multi-target tracking in step (3) is: Where, q = 1, 2, ..., Q, θ k represents the movement direction of the airborne radar at time k, represents the maximum turning angle of the airborne platform, v max and v min Respectively represent the maximum and minimum values ​​of the airborne platform speed, P max and P min Respectively represent the maximum and minimum values ​​of the radiation power of each beam, represents the total radiated power of the airborne radar system; the first constraint represents the maneuvering direction restriction of the airborne platform; the second constraint represents that the heading angle of the airborne platform is omnidirectional; the third constraint represents that the movement speed of the airborne platform at time k-1 is within the set threshold range; the last two constraints represent that the airborne radar radiation power resource meets the conditions, that is, the total radiation resource is fixed and the radiation power of each beam does not exceed the set upper and lower limits.

2. The method for joint optimization of airborne radar flight path and power for multi-target tracking according to claim 1 is characterized in that: The implementation process of step (1) is as follows: For an airborne radar that performs a multi-target tracking task, its state includes position, speed, and direction, and the direction of motion is determined by the state control parameter, namely the heading angle; the state vector of the airborne radar at time k is in, and Respectively represent the position and velocity of the airborne radar; the motion model of the airborne radar is: In the formula, represents the state vector of the airborne radar at time k-1, represents the state control parameter of the airborne radar at time k-1, and F represents the state transfer function of the airborne radar; Formula (1) can be further described as follows: Where F1 and F2 represent the state transfer matrix, which is calculated as: Where T represents the sampling interval; v k-1 and θ k-1 They represent the speed and direction of the airborne radar at time k-1 respectively, and their relationship with the speed in the airborne radar state vector is as follows:

3. The method for joint optimization of airborne radar flight path and power for multi-target tracking according to claim 1, characterized in that: The implementation process of step (2) is as follows: There are Q dispersed targets in a two-dimensional plane that are moving in a uniform linear motion. The state vector of the qth target at time k is in, and Respectively represent the position and velocity of the target; the motion model of the target q is: Where q = 1, 2, ..., Q, F is the target state transfer matrix; W q is a white Gaussian process noise with a mean of zero, and the variance of the target q process noise is Q q for: In the formula, represents the process noise intensity of the target q; The measurement equation of the airborne radar to the target q at time k is as follows: In the formula, is the measurement vector of the airborne radar to the target q at time k, h(·) represents the nonlinear measurement function, is zero-mean white Gaussian measurement noise; The calculation formula is as follows: In the formula, and They represent the actual distance and azimuth from the target q to the airborne radar at time k respectively; To measure noise The covariance of is expressed as: In the formula, and Respectively represent the measurement error variance of target distance and azimuth: Where β is the effective bandwidth of the airborne radar transmission signal, c = 3 × 10 8 m / s is the speed of light, is the echo signal-to-noise ratio of the airborne radar irradiating the target q at time k: In the formula, is the transmission power of the airborne radar to the target q at time k, G t is the radar transmitting antenna gain, G r is the radar receiving antenna gain, σ q is the radar cross-section of target q relative to the airborne radar, λ is the wavelength of the radar transmitter, G RP is the radar receiver processing gain, k is the Boltzmann constant, T o is the noise temperature of the radar receiver, B r The bandwidth of the airborne radar receiver matched filter for target q, F r is the noise factor of the radar receiver, is the distance between the airborne radar and the target q at time k, T d is the dwell time of each radar on the target, T r is the pulse repetition period of the radar; The predicted Bayesian information matrix of target q at time k It can be expressed as: In the formula, is the predicted state vector of the target q at time k, where represents the predicted position of the target q at time k, represents the predicted moving speed of target q at time k; and Represent the predicted Fisher information matrix of the prior information and the measured information at time k respectively: In the formula, Q q is the variance of the target q-process noise, is the prediction covariance matrix of the measurement noise, F is the target state transfer matrix, is a nonlinear measurement function The Jacobian matrix of is expressed as: In the formula, Represents the target state vector Find the first-order partial derivative, It represents the first-order partial derivative of the target's predicted distance from the airborne radar to the target's predicted position and predicted motion speed. It represents the first-order partial derivative of the target's predicted azimuth relative to the airborne radar with respect to the target's predicted position and predicted motion speed; Substituting equation (14) into equation (13), we can obtain the predicted Bayesian information matrix of target q at time k: The predicted Fisher information matrix of the second measurement data is related to the radar's transmission power and motion path at time k; the predicted BCRLB matrix of the target motion state estimation error can be obtained by inverting equation (16): right The matrix trace is used as a measure of target tracking accuracy, and the following formula is used as the cost function of the joint optimization method of airborne radar flight path and power:

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