Phased array radar joint space-time resource allocation method based on variable false alarm detection

Abstract

The application discloses a phased array radar joint space-time resource allocation method based on variable false alarm detection, first, according to a phased array radar signal receiver processing flow, a target echo signal and a motion state model are established, a signal space-time resource scheduling model is constructed through the established variable false alarm detection framework, a JBTA algorithm is used to solve an optimization problem to obtain signal space, time resource allocation conditions of each space domain in the next frame detection, and non-uniform search is carried out, finally, a point track of a real target is effectively detected, and a signal multi-domain resource allocation result is output. The method of the application sets different false alarm probabilities according to different distances by establishing a variable false alarm detection framework, reduces false targets, improves the detection performance of distant targets, simultaneously adds a signal multi-domain resource scheduling algorithm, proposes a joint beam and time resource scheduling method, allocates more resources to the space domain with greater threat degree, and increases the convergence speed and detection quality of multi-stage search.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar resource scheduling, and in particular relates to a phased array radar joint space-time resource allocation method based on variable false alarm detection. Background Art

[0002] Phased array radars, with their multi-beam combining and rapid scanning capabilities, possess powerful target search and tracking capabilities. Constant False Alarm Rate (CFAR) is a commonly used target search method for phased arrays. This method detects targets within the entire surveillance airspace by presetting the false alarm probability. However, this method cannot handle the simultaneous presence of both close-range and long-range targets. To detect long-range targets, a low threshold is required, but this results in a large number of false targets in the close-range airspace. Setting a high detection threshold, on the other hand, prevents detection of long-range targets. Therefore, to ensure the detection performance of long-range targets, it is important to develop a new detection framework for phased array radars. Furthermore, adaptively adjusting radar resource allocation based on real-time environmental information, allocating more search data to sub-airspaces with greater threat levels, can enable faster and more accurate detection of real targets, achieving simultaneous improvements in detection performance and resource utilization.

[0003] The research mainly focuses on the spatial and temporal resources of phased array radars. Spatial resource allocation includes beam pointing, beam selection, and node selection; temporal allocation controls dwell time, pulse repetition period, pulse width, and transmission timing. The paper "Shi C, Wang F, Sellathurai M, Zhou J and Salous S. Low Probability of Intercept-Based Optimal Power Allocation Scheme for an Integrated Multistatic Radar and Communication System. IEEE Sensors Journal, 2020, 14(1): 983-994" studies the optimal power allocation problem of multiple platforms under the traditional constant false alarm detection framework. By optimizing the transmission power allocation of each transmitter to radar signals and communication signals to minimize the total power consumption, the low intercept performance of the multi-station radar and communication system can be significantly improved. The paper "Yan J, Pu W, Dai J, et al. Resource Allocation for Search and Track Application in Phased Array Radar Based on Pareto Bi-Objective Optimization. IEEE Transactions on Vehicular Technology, 2019, 68(4): 3487-3499." addresses the time allocation problem of phased array radar search and tracking tasks. A dual-objective constrained resource allocation scheme is established and solved using the proposed minimax algorithm. One of these two methods is the study of single-domain signal resources under the traditional detection framework, while the other is the resource management of phased array radars in search and tracking tasks. Currently, there is little research on joint resource scheduling for single-station radars during the search phase, especially for long-range target search. Therefore, it is necessary to study the resource scheduling of single-station radars. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention proposes a phased array radar joint space-time resource allocation method based on variable false alarm detection.

[0005] The technical solution adopted by the present invention is: a phased array radar joint space-time resource allocation method based on variable false alarm detection, the specific steps are as follows:

[0006] Step S1: establishing a target echo signal and motion state model according to the phased array radar signal receiver processing flow;

[0007] Step S2: Establishing a false alarm detection framework;

[0008] Step S3: Based on the framework established in step S2, a signal space-time resource scheduling model is constructed;

[0009] Step S4: Use the JBTA algorithm to solve the optimization problem, obtain the allocation of signal space and time resources, perform non-uniform search, obtain the point trace of the real target, and output the signal multi-domain resource allocation result.

[0010] Furthermore, the step S1 is specifically as follows:

[0011] Assume the radar is located at (x R ,y R ), unknown targets are marked as {1,2,...,Q}, Q represents the number of targets, and the surveillance airspace is evenly divided into D sectors {d1,d2,...,d D}, each sector is illuminated by a beam. Assume that the transmitted signal is a linear frequency modulation signal, and the sector d in the kth frame i The transmitted signal x i,k (t) is:

[0012]

[0013] Where z represents the pulse sequence, N i,k Indicates sector d of the kth frame i The number of pulse repetition periods PRT, T r represents the pulse repetition period, f c represents the carrier frequency, t represents time, and s(t) represents the baseband linear frequency modulation signal, which can be expressed as:

[0014]

[0015] Among them, T p Indicates pulse width, μ=B / T p represents the frequency modulation slope, B represents the bandwidth, and rect(·) represents the rectangular function.

[0016] Set the initial position of the target q∈{1,2,…,Q} to (x L,q,0 ,y L,q,0 ), the speed is and located in sector d i .

[0017] Where Q represents the number of targets, x L,q,0 ,y L,q,0 , and Represents the initial distance and speed information of target q in the x direction and y direction respectively, and L represents the coordinate information. In the kth frame, sector di , the echo signal received from the target is expressed as follows after down-conversion:

[0018]

[0019] Among them, τ q,k represents the delay of target q in the kth frame, f d,q,k represents the Doppler shift of the target q, n(t) represents zero-mean white Gaussian noise, and its power is N0=k0T0B n F n ,k0,T0,B n , F n They represent the Boltzmann constant, radar system temperature, receiver bandwidth, and receiver noise coefficient respectively; α i,q,k It represents the attenuation of the signal amplitude caused by the propagation effect and the target reflection, and its amplitude is expressed as:

[0020]

[0021] Among them, P T Indicates the transmit power, G T , G R They represent the transmitting and receiving antenna gains, λ represents the signal wavelength, σ q,k represents the radar cross section RCS of target q in the kth frame, represents the distance between target q and the radar at the kth frame, x L,q,k and y L,q,k They represent the distance of target q in the x direction and y direction at the kth frame, L s Indicates system loss.

[0022] After pulse compression and coherent integration, the signal-to-noise ratio (SNR) of the kth frame is expressed as:

[0023]

[0024] Among them, P av Indicates the average transmission power, K0 = P av G T G R λ 2 T r / ((4π) 3 kT0F n L s ) represents a preset constant.

[0025] set up As the state equation of the target q at the kth frame, (·) T Represents the transpose operator of a vector or matrix.

[0026] In the kth frame, the dynamic model of the target q is expressed as:

[0027] x k,q =Fx k-1,q +n k,q (6)

[0028] Among them, F represents the state transfer matrix, n k,q represents the state noise with zero-mean Gaussian distribution.

[0029] Furthermore, the step S2 is specifically as follows:

[0030] Step S21: Divide the surveillance airspace into distance zones according to different distances;

[0031] Set different detection thresholds based on the different distances of the monitored airspace, with lower thresholds set for distant airspace and higher thresholds set for close airspace:

[0032]

[0033] Where R represents the distance to the radar, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame, P fa,k,s represents the specific false alarm probability of distance partition s, and divides the entire surveillance airspace into S distance partitions, R S-1 and R S Represents the two distance boundaries of the Sth distance partition.

[0034] Step S22: In the multi-stage search process, a low threshold is used for detection in the initial detection stage, and the detection threshold is gradually increased in subsequent detections. The detection threshold of each stage is expressed as:

[0035]

[0036] in, represents the change in false alarm probability between the kth frame and the k-1th frame (k>1).

[0037] Furthermore, the step S3 is specifically as follows:

[0038] Step S31, constructing an objective function;

[0039] Set the importance of each sector in the k-th frame stage to w k =[w 1,k ,w 2,k ,…,w D,k ] T .

[0040] Among them, w i,k (i=1,2,…D) represents sector di The importance at the kth stage.

[0041] Set N k =[N 1,k ,N 2,k ,...,N D,k ] H Indicates the number of PRTs residing in each sector, (·) H Represents the conjugation operation of a vector or matrix, N 1,k Indicates the number of PRTs residing in sector d1, N 2,k represents the number of PRTs residing in sector d2, N D,k Indicates sector d D Based on the false alarm detection framework, a joint spatial and temporal resource scheduling optimization model u(w k ,N k ):

[0042]

[0043] Among them, SNR i,k (N i,k ) represents sector d i The signal-to-noise ratio of the kth frame is determined by the SNR of each sub-spatial domain, and the determination standard of the SNR of each sub-spatial domain is set as:

[0044] (1) If sector d i There is no trace in the image, set SNR i,k (N i,k )=0;

[0045] (2) If sector d i There is a trace in the , set SNR i,k (N i,k ) is the signal-to-noise ratio of the trace;

[0046] (3) If sector d i There are multiple traces in the , set Q i,k Indicates sector d i The number of midpoint traces.

[0047] Step S32: construct constraint conditions;

[0048] The total search time constraint is expressed as:

[0049]

[0050] Among them, T total Indicates the total search time in one frame detection. In each frame detection, the maximum and minimum time constraints of each sector are:

[0051] T min,i,k ≤N i,k T r ≤T max (11)

[0052] Among them, T min,i,k Indicates sector d i The minimum time constraint at the kth frame, T max Indicates the maximum time constraint.

[0053] If sector d i If there are suspected points in , then the following conditions must be met:

[0054]

[0055] Among them, T uni Indicates the dwell time of each sector during uniform search, T min1 Indicates the minimum dwell time when there is no trace in the sector, T min2 Indicates the minimum dwell time when a point exists in the sector, a i,k Indicates the judgment factor of whether there is a point trace, specifically:

[0056]

[0057] In sectors where traces exist, constrain the signal-to-noise ratio:

[0058] SNR min,k ≤SNR m,k ≤SNR max,k (14)

[0059] Where m = 1, 2, ..., M, M represents the number of sectors with traces, SNR min,k and SNR max,k Represents the maximum and minimum values ​​of the signal-to-noise ratio of each sector, SNR m,k Indicates the signal-to-noise ratio of the mth target sector in the kth frame.

[0060] Step S33: Obtain an optimization model based on the constructed objective function and constraint conditions;

[0061] The optimization model is expressed as:

[0062]

[0063] Furthermore, in step S4, the JBTA algorithm solution process is specifically as follows:

[0064] Step S41: Set k=1 and initialize w k 、N k 、Pfa,k (R) and T uni , perform uniform search;

[0065] The importance of each sector in the kth frame w k Used to represent the k-th frame sector d i The spatial resource allocation result is the number of PRTs N that reside in each sector of the kth frame. k Used to represent the time resource allocation results of each sector in the kth frame, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame. When k=1, all the above values ​​are their initial values, and the monitoring airspace is uniformly searched based on the initial values.

[0066] Step S42: set k=k+1;

[0067] Step S43: Increase the detection threshold to reduce the false alarm probability of each partition.

[0068] Among them, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame, P fa,k-1 (R) represents the false alarm probability of each distance partition in the k-1th frame, represents the change in false alarm probability between the kth frame and the k-1th frame (k>1).

[0069] Step S44: Use the fuzzy analytic hierarchy process (FAHP) algorithm to allocate spatial resources and update w k ;

[0070] The specific process of the FAHP algorithm is as follows:

[0071] Step S441: Set the kth stage in sector d i Detect Q i,k point traces, for the target point trace p∈{1,2,…,Q i,k}, assess the threat level of the target point from the perspective of J (J ≥ 2) attributes, expressed as an attribute set b j ∈{b1,…b J}. For each attribute value b of target p j Take the measurement, record it as a pj , thus forming the attribute value matrix A i,k Then for the matrix A i,k Perform normalization processing to obtain the normalized matrix R i,k , R i,k The element r in pj It can be expressed as:

[0072]

[0073] Among them, a j Represents the matrix A i,k The vector consisting of the j-th column elements of .

[0074] Compare the attribute values ​​pairwise and make judgments. j With factor b i The relative importance is expressed as b ji After comparing all factors according to this rule, we can get the fuzzy judgment matrix Β=(b ji ) J×J , (i=1,2,…J,j=1,2,…J). Use 0.1~0.9 scaling method to calculate the element b ji Given a quantitative scale, the target attributes are compared pairwise to obtain the fuzzy judgment matrix B.

[0075] Step S442: Calculate the weight of the fuzzy complementary judgment matrix;

[0076] Set the weight vector of the fuzzy judgment matrix B to be α=[α1,α2,…,α J ] T , the jth element α in the vector α j It can be defined as:

[0077]

[0078] Among them, it is known At the same time The characteristic matrix of the judgment matrix is ​​M=(α ji ) J×J .

[0079] The compatibility index I(B,M) of B and M is:

[0080]

[0081] If I(B,M)≤T m , T m represents a pre-set parameter, then the judgment matrix is ​​considered to meet the consistency requirements.

[0082] Comprehensive consideration of the normalized matrix R i,k and weight vector α, we get sector d i Threat value of internal target point trace ξ i,k for:

[0083] ξ i,k =R i,k α (19)

[0084] Sector d i The quantitative threat value results of the internal target points are superimposed to obtain sector d i The threat value is ξi ' ,k Then, the threat value of each sector is compared with the pre-set threat level table to obtain the threat level of each sector:

[0085]

[0086] Among them, l0, l1, l2, l3 represent four threat levels respectively, β and γ represent level thresholds, 0<β<γ. This process is performed on each sector to obtain w k .

[0087] Considering the target's distance, speed and the number of targets in each sector, the threat level of each sector is obtained through the FAHP algorithm.

[0088] Step S45: Use CVX toolbox to schedule time resources and update N k ;

[0089] When getting w k Then, use formula (15) to schedule time resources and obtain the time resource allocation result.

[0090] Step S46: According to the optimized w k and N k Perform non-uniform search on the surveillance airspace to obtain detection results;

[0091] Step S47: determine whether the convergence condition is met;

[0092] If the trace information (number, position, and speed of target traces) obtained in two consecutive frame searches is consistent, it means that the real target has been successfully detected, the algorithm ends, and the signal multi-domain resource allocation result is output; otherwise, return to step S42.

[0093] Beneficial effects of the present invention: The method of the present invention first establishes a target echo signal and motion state model based on the processing flow of a phased array radar signal receiver, constructs a signal space-time resource scheduling model through the established variable false alarm detection framework, uses the JBTA algorithm to solve the optimization problem to obtain the signal space and time resource allocation of each airspace in the next frame detection, and performs non-uniform search, and finally effectively detects the point trace of the real target and outputs the signal multi-domain resource allocation result. The method of the present invention reduces false targets while improving the detection performance of long-range targets by establishing a variable false alarm detection framework and setting different false alarm probabilities according to different distances. At the same time, it adds a signal multi-domain resource scheduling algorithm and proposes a joint beam and time resource scheduling method to allocate more resources to airspaces with greater threat levels, thereby increasing the convergence speed and detection quality of multi-stage search. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 The present invention is a flow chart of a phased array radar joint space-time resource allocation method based on variable false alarm detection.

[0095] Figure 2 Schematic diagram of a false alarm framework in an embodiment of the present invention.

[0096] Figure 3 This is a flowchart of the JBTA algorithm solution in an embodiment of the present invention.

[0097] Figure 4 4 is a flow chart of the FAHP algorithm in an embodiment of the present invention.

[0098] Figure 5 This is a target deployment and movement direction diagram in an embodiment of the present invention.

[0099] Figure 6 This is a result diagram of the joint spatial and temporal distribution of simulation signals in an embodiment of the present invention.

[0100] Figure 7 This is a diagram showing the dot trace detection results of the low and high thresholds under the simulated constant false alarm (CFAR) in an embodiment of the present invention.

[0101] Figure 8 This is a comparison chart of the detection results of simulating JBTA and three other scheduling algorithms in an embodiment of the present invention. Specific implementation methods

[0102] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0103] like Figure 1 As shown in FIG, a flow chart of a phased array radar joint space-time resource allocation method based on variable false alarm detection of the present invention, the specific steps are as follows:

[0104] Step S1: establishing a target echo signal and motion state model according to the phased array radar signal receiver processing flow;

[0105] Step S2: establishing a false alarm detection framework;

[0106] Step S3: Based on the framework established in step S2, a signal space-time resource scheduling model is constructed;

[0107] Step S4: Use the JBTA algorithm to solve the optimization problem, obtain the allocation of signal space and time resources, perform non-uniform search, obtain the point trace of the real target, and output the signal multi-domain resource allocation result.

[0108] In this embodiment, step S1 is specifically as follows:

[0109] Assume the radar is located at (x R ,y R), unknown targets are marked as {1,2,...,Q}, Q represents the number of targets, and the surveillance airspace is evenly divided into D sectors {d1,d2,...,d D}, each sector is illuminated by a beam. Assume that the transmitted signal is a linear frequency modulation signal (LFM), and the sector d in the kth frame i The transmitted signal x i,k (t) is:

[0110]

[0111] Where z represents the pulse sequence, N i,k Indicates sector d of the kth frame i The number of pulse repetition time (PRT) that stays, T r represents the pulse repetition period, f c represents the carrier frequency, t represents time, and s(t) represents the baseband linear frequency modulation signal, which can be expressed as:

[0112]

[0113] Among them, T p Indicates pulse width, μ=B / T p represents the frequency modulation slope, B represents the bandwidth, and rect(·) represents the rectangular function.

[0114] Set the initial position of the target q∈{1,2,…,Q} to (x L,q,0 ,y L,q,0 ), the speed is and located in sector d i .

[0115] Where Q represents the number of targets, x L,q,0 ,y L,q,0 , and Represents the initial distance and speed information of target q in the x direction and y direction respectively, and L represents the coordinate information. In the kth frame, sector d i , the echo signal received from the target is expressed as follows after down-conversion:

[0116]

[0117] Among them, τ q,k represents the delay of target q in the kth frame, f d,q,k represents the Doppler shift of the target q, n(t) represents zero-mean white Gaussian noise, and its power is N0=k0T0B n F n ,k0,T0,B n , F nThey represent the Boltzmann constant, radar system temperature, receiver bandwidth, and receiver noise coefficient respectively; α i,q,k It represents the attenuation of the signal amplitude caused by the propagation effect and the target reflection, and its amplitude is expressed as:

[0118]

[0119] Among them, P T Indicates the transmit power, G T , G R They represent the transmitting and receiving antenna gains, λ represents the signal wavelength, σ q,k represents the radar cross section (RCS) of target q in the kth frame, represents the distance between target q and the radar at the kth frame, x L,q,k and y L,q,k They represent the distance of target q in the x direction and y direction at the kth frame, L s represents system loss; τ q,k Expressed as:

[0120]

[0121] Where c represents the propagation speed of electromagnetic waves; f d,q,k Expressed as:

[0122]

[0123] Among them, v q represents the target speed; the signal-to-noise ratio (SNR) of the kth frame is expressed as:

[0124]

[0125] Among them, P av Indicates the average transmission power, K0 = P av G T G R λ 2 T r / ((4π) 3 kT0F n L s ) represents a preset constant.

[0126] set up As the state equation of the target q at the kth frame, (·) T Represents the transpose operator of a vector or matrix.

[0127] In the kth frame, the dynamic model of the target q is expressed as:

[0128] x k,q =Fx k-1,q +n k,q (28)

[0129] Where F represents the state transfer matrix, which can be expressed as:

[0130]

[0131] in, represents the Kronecker product, T f represents the search frame period, I2 represents the two-dimensional unit matrix; n k,q represents the state noise of zero-mean Gaussian distribution, and its covariance is expressed as:

[0132]

[0133] Among them, σ t represents the process noise density.

[0134] In this embodiment, step S2 is specifically as follows:

[0135] Step S21: Divide the surveillance airspace into distance zones according to different distances;

[0136] like Figure 2 As shown in the figure, the false alarm detection framework diagram sets different detection thresholds according to the different distances of the monitored airspace, with a lower threshold set for long-range airspace and a higher threshold set for close-range airspace:

[0137]

[0138] Where R represents the distance to the radar, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame, P fa,k,s represents the specific false alarm probability of distance partition s, and divides the entire surveillance airspace into S distance partitions, R S-1 and R S Represents the two distance boundaries of the Sth distance partition.

[0139] Step S22: In the multi-stage search process, a low threshold is used for detection in the initial detection stage, and the detection threshold is gradually increased in subsequent detections. The detection threshold of each stage is expressed as:

[0140]

[0141] in, represents the change in false alarm probability between the kth frame and the k-1th frame (k>1).

[0142] In this embodiment, step S3 is specifically as follows:

[0143] Step S31, constructing an objective function;

[0144] Set the importance of each sector in the k-th frame stage to w k =[w 1,k ,w 2,k ,…,w D,k ] T .

[0145] Among them, w i,k (i=1,2,…D) represents sector d i The importance at the kth stage.

[0146] Set N k =[N 1,k ,N 2,k ,...,N D,k ] H Indicates the number of PRTs residing in each sector, (·) H Represents the conjugation operation of a vector or matrix, N 1,k Indicates the number of PRTs residing in sector d1, N 2,k represents the number of PRTs residing in sector d2, N D,k Indicates sector d D Based on the false alarm detection framework, a joint spatial and temporal resource scheduling optimization model u(w k ,N k ):

[0147]

[0148] Among them, SNR i,k (N i,k ) represents sector d i The signal-to-noise ratio of the kth frame is determined by the SNR of each sub-spatial domain according to the detection point traces in each spatial domain. The determination standard of the SNR of each sub-spatial domain is set as:

[0149] (1) If sector d i There is no trace in the image, set SNR i,k (N i,k )=0;

[0150] (2) If sector d i There is a trace in the , set SNR i,k (N i,k ) is the signal-to-noise ratio of the trace;

[0151] (3) If sector d i There are multiple traces in the , set Q i,k Indicates sector d i The number of midpoint traces.

[0152] Step S32: construct constraint conditions;

[0153] The total search time constraint is expressed as:

[0154]

[0155] Among them, T total Indicates the total search time in one frame detection. In each frame detection, the maximum and minimum time constraints of each sector are:

[0156] T min,i,k ≤N i,k T r ≤T max (35)

[0157] Among them, T min,i,k Indicates sector d i The minimum time constraint at the kth frame, T max Indicates the maximum time constraint.

[0158] If sector d i If there are suspected points in , then the following conditions must be met:

[0159]

[0160] Among them, T uni Indicates the dwell time of each sector during uniform search, T min1 Indicates the minimum dwell time when there is no trace in the sector, T min2 Indicates the minimum dwell time when a point exists in the sector, a i,k Indicates the judgment factor of whether there is a point trace, specifically:

[0161]

[0162] In sectors where traces exist, constrain the signal-to-noise ratio:

[0163] SNR min,k ≤SNR m,k ≤SNR max,k (38)

[0164] Where m = 1, 2, ..., M, M represents the number of sectors with traces, SNR min,k and SNR max,k Represents the maximum and minimum values ​​of the signal-to-noise ratio of each sector, SNR m,k Indicates the signal-to-noise ratio of the mth target sector in the kth frame.

[0165] Step S33: Obtain an optimization model based on the constructed objective function and constraint conditions;

[0166] The optimization model is expressed as:

[0167]

[0168] like Figure 3 As shown, in this embodiment, in step S4, the JBTA algorithm solution process is specifically as follows:

[0169] Step S41: Set k=1 and initialize w k 、N k 、P fa,k (R) and T uni , perform uniform search;

[0170] The importance of each sector in the kth frame w k Used to represent the k-th frame sector d i The spatial resource allocation result is the number of PRTs N that reside in each sector of the kth frame. k Used to represent the time resource allocation results of each sector in the kth frame, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame. When k=1, all the above values ​​are their initial values, and the monitoring airspace is uniformly searched based on the initial values.

[0171] Step S42: set k=k+1;

[0172] Step S43: Increase the detection threshold to reduce the false alarm probability of each partition.

[0173] Among them, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame, P fa,k-1 (R) represents the false alarm probability of each distance partition in the k-1th frame, represents the change in false alarm probability between the kth frame and the k-1th frame (k>1).

[0174] Step S44: Use the Fuzzy Analytical Hierarchy Process (FAHP) algorithm to allocate airspace resources and update w k ;

[0175] like Figure 4 As shown in Figure 2, the process of the FAHP algorithm is as follows:

[0176] Step S441: Set the kth stage in sector d i Detect Q i,kpoint traces, for the target point trace p∈{1,2,…,Q i,k}, assess the threat level of the target point from the perspective of J (J ≥ 2) attributes, expressed as an attribute set b j ∈{b1,…b J}. For each attribute value b of target p j Take the measurement, record it as a pj , thus forming the attribute value matrix A i,k Then for the matrix A i,k Perform normalization processing to obtain the normalized matrix R i,k , R i,k The element r in pj It can be expressed as:

[0177]

[0178] Among them, a j Represents the matrix A i,k The vector consisting of the j-th column elements of .

[0179] Compare the attribute values ​​pairwise and make judgments. j With factor b i The relative importance is expressed as b ji After comparing all factors according to this rule, we can get the fuzzy judgment matrix Β=(b ji ) J×J , (i=1,2,…J,j=1,2,…J). Use 0.1~0.9 scaling method to calculate the element b ji Given a quantitative scale, the target attributes are compared pairwise to obtain the fuzzy judgment matrix B:

[0180]

[0181] Step S442: Calculate the weight of the fuzzy complementary judgment matrix;

[0182] The consistency of the weight formula is tested by using the compatibility of the fuzzy judgment matrix. The weight vector of the fuzzy judgment matrix B is set to α=[α1,α2,…,α J ] T , the jth element α in the vector α j It can be defined as:

[0183]

[0184] Among them, it is known At the same time The characteristic matrix of the judgment matrix is ​​M=(α ji ) J×J .

[0185] The compatibility index I(B,M) of B and M is:

[0186]

[0187] If I(B,M)≤T m , T m represents a pre-set parameter, then the judgment matrix is ​​considered to meet the consistency requirements.

[0188] Comprehensive consideration of the normalized matrix R i,k and weight vector α, we get sector d i Threat value of internal target point trace ξ i,k for:

[0189] ξ i,k =R i,k α (44)

[0190] It can also be expressed as Represent the first target, the second target and the Qth target respectively i,k The threat value of the target.

[0191] Sector d i The quantitative threat value results of the internal target points are superimposed to obtain sector d i The threat value is ξ i ' ,k Then, the threat value of each sector is compared with the pre-set threat level table to obtain the threat level of each sector:

[0192]

[0193] Among them, l0, l1, l2, l3 represent four threat levels respectively, β and γ represent level thresholds, 0<β<γ. This process is performed on each sector to obtain w k .

[0194] This embodiment considers the distance, speed, and number of targets in each sector, and obtains the threat level value of each sector through the FAHP algorithm.

[0195] Step S45: Use CVX toolbox to schedule time resources and update N k ;

[0196] When getting w k Then, use formula (39) to schedule time resources and obtain the time resource allocation result.

[0197] Step S46: According to the optimized w k and N k Perform non-uniform search on the surveillance airspace to obtain detection results;

[0198] Step S47: determine whether the convergence condition is met;

[0199] If the trace information (number, position, and speed of target traces) obtained in two consecutive frame searches is consistent, it means that the real target has been successfully detected, the algorithm ends, and the signal multi-domain resource allocation result is output; otherwise, return to step S42.

[0200] The present invention also provides another embodiment to simulate and verify the method of the present invention:

[0201] In the phased array radar search mode, the radar transmits an LFM signal, which is reflected by the target and received by the receiver. The signal is processed based on the false alarm detection framework to obtain the trace information. Finally, the trace information is used to schedule the multi-domain resources of the signal. Assume that the number of phased array radar elements is 16, the distance between the elements is 0.25m, the signal wavelength is 0.5m, and the transmitted signal has 16 PRTs for one CPI. The time width of each PRT is T r =2ms, the duration of each PRT pulse is T p =200μs, sampling frequency f s =6MHz, the bandwidth of the LFM signal is 2MHz, and the antenna gain is 30dB. Assume that the initial positions of the real targets in the environment are (0,260)km, (50,160)km, (100,140)km, and their speeds are (0,-100)m / s, (50,50)m / s, (-60,-20)m / s, respectively. Figure 5 It is the deployment and movement direction map of the target.

[0202] like Figure 6 As shown in the figure, the result of the simulation signal time and power joint distribution in this embodiment is as follows: Figure 6 (a) Figure 6 (b) Figure 6 (c) shows the dot distribution diagram of the first, third and fifth frames of the phased array radar, respectively. Figure 6 (d) Figure 6 (e) Figure 6 (f) shows the dwell time distribution of the first, third and fifth frames of the phased array radar. Figure 6 In (a), there are three traces in sector 3. Based on their velocity information, this sector has the greatest threat level. Figure 6 (e) and Figure 6 In (f), the most time resources are allocated in sector 3. Figure 6 As can be seen from (a), (b), (c), and (d), the number of false targets decreases rapidly as the search progresses, and three real targets are successfully detected in the fifth frame. Figure 6The resource allocation in frame (f) confirms the detection. The resource allocation in frame 5 shows that the airspace containing the three targets presents the same threat level. However, due to the different distances between the targets, the long-range target in sector 9 requires more resources to ensure detection quality, while the close-range target in sector 12 requires fewer search resources. Using the JBTA algorithm can improve the detection convergence speed and quality.

[0203] Figure 7 The dot detection results of the low threshold and high threshold under constant false alarm detection are: Figure 7 (a) indicates the lower threshold (P fa =5×10 -3 ) CFAR test results, Figure 7 (b) indicates the high threshold (P fa =5×10 -5 ) CFAR detection results. From the results, we can see that when CFAR detection is used in the surveillance airspace, when the threshold value is low, a large number of false targets will appear. Moreover, due to the strong echo at close range, most of the false points will appear in the close range airspace, which will seriously affect the threat level assessment and detection quality. Figure 7 When the threshold value is high, the distant target cannot be effectively detected due to its weak echo, as shown in (a). Figure 7 (b) shown.

[0204] Figure 8 The following comparison chart shows the detection results of JBTA and three other scheduling algorithms. Three scheduling algorithms under the constant false alarm (CFAR) detection framework were compared with the JBTA algorithm, verifying the effectiveness and superiority of the JBTA algorithm. The FTP algorithm uses fixed spatial and temporal resources, while the OTA algorithm optimizes temporal resources. The simulation results show that the detection results using the resource scheduling algorithm outperform those using fixed search resources. Under the variable false alarm detection framework, the number of false traces after uniform search in the first frame is lower than that under the CFAR detection framework. Furthermore, the JBTA algorithm has the fastest convergence speed, successfully detecting and confirming the target in the fifth frame, improving the detection speed and effectiveness of long-range targets.

[0205] In summary, the method of the present invention establishes a variable false alarm detection framework and sets different false alarm probabilities according to different distances, thereby reducing false targets and improving the detection performance of long-range targets. At the same time, a signal multi-domain resource scheduling algorithm is added, and a joint beam and time allocation (JBTA) resource scheduling method is proposed, which allocates more resources to airspaces with greater threat levels, thereby increasing the convergence speed and detection quality of multi-stage search.

Claims

1. A phased array radar joint space-time resource allocation method based on variable false alarm detection, the specific steps are as follows: Step S1: establishing a target echo signal and motion state model according to the phased array radar signal receiver processing flow; Step S2: establishing a false alarm detection framework; Step S3: Based on the framework established in step S2, a signal space-time resource scheduling model is constructed; Step S4: Use the JBTA algorithm to solve the optimization problem, obtain the allocation of signal space and time resources, perform non-uniform search, obtain the point trace of the real target, and output the signal multi-domain resource allocation result; In step S4, the JBTA algorithm solution process is as follows: Step S41: Set k=1 and initialize w k 、N k 、P fa,k (R) and T uni , perform uniform search; T uni Indicates the dwell time of each sector during uniform search, and the importance of each sector in the kth frame w k Used to represent the k-th frame sector d i The spatial resource allocation result is the number of PRTs N that reside in each sector of the kth frame. k Used to represent the time resource allocation results of each sector in the kth frame, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame. When k=1, all the above values ​​are their initial values, and the surveillance airspace is uniformly searched based on the initial values; Step S42: set k=k+1; Step S43: Increase the detection threshold to reduce the false alarm probability of each partition. in, R represents the distance from the radar, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame, P fa,k-1 (R) represents the false alarm probability of each distance partition in the k-1th frame, represents the change in false alarm probability between the kth frame and the k-1th frame, and k>1; Step S44: Use the fuzzy analytic hierarchy process (FAHP) algorithm to allocate spatial resources and update w k ; Step S45: Use CVX toolbox to schedule time resources and update N k ; When getting w k Then, the signal space-time resource scheduling model constructed in step S3 is used to perform time resource scheduling to obtain the time resource allocation result; Step S46: According to the optimized w k and N k Perform non-uniform search on the surveillance airspace to obtain detection results; Step S47: determine whether the convergence condition is met; If the trace information obtained in two consecutive frames of search is consistent, it means that the real target has been successfully detected, the algorithm ends, and the signal multi-domain resource allocation result is output; Otherwise, return to step S42; The point trace information includes: the number, position and speed of the target point traces.

2. The phased array radar joint space-time resource allocation method based on variable false alarm detection according to claim 1, characterized in that: The step S1 is specifically as follows: Assume the radar is located at (x R ,y R ), unknown targets are marked as {1,2,...,Q}, Q represents the number of targets, and the surveillance airspace is evenly divided into D sectors {d1,d2,...,d D }, each sector is illuminated by a beam; the transmitted signal is set to a linear frequency modulation signal, and the sector d in the kth frame i The transmitted signal x i,k (t) is: Where z represents the pulse sequence, N i,k Indicates sector d of the kth frame i The number of pulse repetition periods PRT, T r represents the pulse repetition period, f c represents the carrier frequency, t represents time, and s(t) represents the baseband linear frequency modulation signal, which can be expressed as: Among them, T p Indicates pulse width, μ=B / T p represents the frequency modulation slope, B represents the bandwidth, and rect(·) represents the rectangular function; Set the initial position of the target q∈{1,2,…,Q} to (x L,q,0 ,y L,q,0 ), the speed is and located in sector d i ; Where Q represents the number of targets, x L,q,0 ,y L,q,0 , and Represents the initial distance and speed information of target q in the x direction and y direction respectively, L represents the coordinate information; in the kth frame, sector d i , the echo signal received from the target is expressed as follows after down-conversion: Among them, τ q,k represents the delay of target q in the kth frame, f d,q,k represents the Doppler shift of the target q, n(t) represents zero-mean white Gaussian noise, and its power is N0=k0T0B n F n ,k0,T0,B n , F n They represent the Boltzmann constant, radar system temperature, receiver bandwidth, and receiver noise coefficient respectively; α i,q,k It represents the attenuation of the signal amplitude caused by the propagation effect and the target reflection, and its amplitude is expressed as: Among them, P T Indicates the transmit power, G T , G R They represent the transmitting and receiving antenna gains, λ represents the signal wavelength, σ q,k represents the radar cross section RCS of target q in the kth frame, represents the distance between target q and the radar at the kth frame, x L,q,k and y L,q,k They represent the distance of target q in the x direction and y direction at the kth frame, L s Indicates system loss; After pulse compression and coherent integration, the signal-to-noise ratio (SNR) of the kth frame is expressed as: Among them, P av Indicates the average transmission power, K0 = P av G T G R λ 2 T r / ((4π) 3 kT0F n L s ) represents a preset constant; set up As the state equation of the target q at the kth frame, (·) T Represents the transpose operator of a vector or matrix; In the kth frame, the dynamic model of the target q is expressed as: x k,q =Fx k-1,q +n k,q (6) Among them, F represents the state transfer matrix, n k,q represents the state noise with zero-mean Gaussian distribution.

3. The phased array radar joint space-time resource allocation method based on variable false alarm detection according to claim 1, characterized in that: The step S2 is specifically as follows: Step S21: Divide the surveillance airspace into distance zones according to different distances; Set different detection thresholds based on the different distances of the monitored airspace, with lower thresholds set for distant airspace and higher thresholds set for close airspace: Where R represents the distance to the radar, P fa,k (R) represents the false alarm probability of each distance partition in the kth frame, P fa,k,s represents the specific false alarm probability of the distance partition s, and the entire surveillance airspace is divided into S distance partitions, R1 and R2 represent the two distance boundaries of the second distance partition, R S-1 and R S Represents the two distance boundaries of the Sth distance partition; Step S22: In the multi-stage search process, a low threshold is used for detection in the initial detection stage, and the detection threshold is gradually increased in subsequent detections. The detection threshold of each stage is expressed as: in, represents the change in false alarm probability between the kth frame and the k-1th frame, where k>

1.

4. The phased array radar joint space-time resource allocation method based on variable false alarm detection according to claim 1, characterized in that: The step S3 is specifically as follows: Step S31, constructing an objective function; Set the importance of each sector in the k-th frame stage to w k =[w 1,k ,w 2,k ,…,w D,k ] T ; Among them, w i,k Indicates sector d i The importance of the kth stage, i = 1, 2, ... D; Set N k =[N 1,k ,N 2,k ,...,N D,k ] H Indicates the number of PRTs residing in each sector, (·) H Represents the conjugation operation of a vector or matrix, N 1,k Indicates the number of PRTs residing in sector d1, N 2,k represents the number of PRTs residing in sector d2, N D,k Indicates sector d D Based on the false alarm detection framework, a joint spatial and temporal resource scheduling optimization model u(w k ,N k ): Among them, SNR i,k (N i,k ) represents sector d i The signal-to-noise ratio of the kth frame is determined by the SNR of each sub-spatial domain, and the determination standard of the SNR of each sub-spatial domain is set as: (1) If sector d i There is no trace in the image, set SNR i,k (N i,k )=0; (2) If sector d i There is a trace in the , set SNR i,k (N i,k ) is the signal-to-noise ratio of the trace; (3) If sector d i There are multiple traces in the , set Q i,k Indicates sector d i the number of midpoint traces; Step S32: construct constraint conditions; The total search time constraint is expressed as: Among them, T total Indicates the total search time in one frame detection; in each frame detection, the maximum and minimum time constraints of each sector are: T min,i,k ≤N i,k T r ≤T max (11) Among them, T min,i,k Indicates sector d i The minimum time constraint at the kth frame, T max Indicates the maximum time constraint; If sector d i If there are suspected points in , then the following conditions must be met: Among them, T uni Indicates the dwell time of each sector during uniform search, T min1 Indicates the minimum dwell time when there is no trace in the sector, T min2 Indicates the minimum dwell time when a point exists in the sector, a i,k Indicates the judgment factor of whether there is a trace, specifically: In sectors where traces exist, constrain the signal-to-noise ratio: SNR min,k ≤SNR m,k ≤SNR max,k (14) Where m = 1, 2, ..., M, M represents the number of sectors with traces, SNR min,k and SNR max,k Represents the maximum and minimum values ​​of the signal-to-noise ratio of each sector, SNR m,k Indicates the signal-to-noise ratio of the mth target sector in the kth frame; Step S33: Obtain an optimization model based on the constructed objective function and constraint conditions; The optimization model is expressed as: 。 5. The phased array radar joint space-time resource allocation method based on variable false alarm detection according to claim 1, characterized in that: In step S44, the process of the FAHP algorithm is as follows: Step S441: Set the kth stage in sector d i Detect Q i,k point traces, for the target point trace p∈{1,2,…,Q i,k }, assess the threat level of the target point from the perspective of J≥2 attributes, expressed as an attribute set b j ∈{b1,…b J }; For each attribute value b of target p j Take the measurement, record it as a pj , thus forming the attribute value matrix A i,k ; Then for the matrix A i,k Perform normalization processing to obtain the normalized matrix R i,k , R i,k The element r in pj It can be expressed as: Among them, a j Represents the matrix A i,k The vector consisting of the j-th column elements of ; Compare the attribute values ​​pairwise and make judgments. j With factor b i The relative importance is expressed as b ji After comparing all factors according to this rule, we can get the fuzzy judgment matrix Β=(b ji ) J×J ,i=1,2,…J,j=1,2,…J;using 0.1~0.9 scaling method to measure element b ji Given a quantitative scale, compare the target attributes pairwise to obtain the fuzzy judgment matrix B; Step S442: Calculate the weight of the fuzzy complementary judgment matrix; Set the weight vector of the fuzzy judgment matrix B to be α=[α1,α2,…,α J ] T , the jth element α in the vector α j It can be defined as: Among them, it is known At the same time, let α ji =α j / (α i +α j ), The characteristic matrix of the judgment matrix is ​​M=(α ji ) J×J ; The compatibility index I(B,M) of B and M is: If I(B,M)≤T m , T m If represents a pre-set parameter, the judgment matrix is ​​considered to meet the consistency requirements; Comprehensive consideration of the normalized matrix R i,k and weight vector α, we get sector d i Threat value of internal target point trace ξ i,k for: x i,k =R i,k a (19) Sector d i The quantitative threat value results of the internal target points are superimposed to obtain sector d i The threat value is ξ i ′,k; then, the threat value of each sector is compared with the pre-set threat level table to obtain the threat level of each sector: Among them, l0, l1, l2, l3 represent four threat levels respectively, β and γ represent level thresholds, 0<β<γ; perform this process on each sector to obtain w k ; Considering the target's distance, speed and the number of targets in each sector, the threat level of each sector is obtained through the FAHP algorithm.

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