Doppler information-assisted networked radar fusion detection method

Abstract

This invention discloses a Doppler information-assisted networked radar fusion detection method, primarily addressing the low performance problem of existing fusion detection technologies. The scheme involves: constructing a radar system consisting of a fusion detection center and multiple radar stations, and setting system parameters; the data fusion detection center receiving echo data and radar system parameters transmitted from each radar station; obtaining fusion detection results from the echo data of each radar station using a traditional fusion detection algorithm; reading the detected target angle and Doppler velocity from the fusion detection results, and constructing two sets of linear inequalities for each radar station regarding the target velocity component; randomly selecting one of the two sets of linear inequalities corresponding to each radar station and combining them into a new set of linear inequalities; sequentially determining whether the combined set of linear inequalities has a feasible region, and providing the target detection result based on the determination result. This invention improves the performance of fusion detection by introducing Doppler information and can be used for radar target detection.

Description

Technical Field

[0001] This invention relates to the field of radar technology, specifically a networked radar fusion detection method that can be used for target detection, tracking, and collaborative detection in networked radar systems. Background Technology

[0002] In the field of moving target detection, multi-station radars offer advantages over single-station radars in terms of spatial diversity, frequency diversity, and damage resistance. Therefore, how to fully utilize the observation information from each radar station to improve target detection performance has become a research hotspot in recent years. Common multi-station radar detection systems include distributed radar detection systems and centralized radar detection systems. Due to limitations in the communication capacity between radars, and the advantages of distributed radar detection systems such as low cost, high reliability, and strong survivability, they are superior to centralized radar detection systems in practical applications.

[0003] Distributed radar consists of a signal fusion center and multiple radar stations. Each sub-radar station sends its received and processed data to the fusion center for fusion, and a specific algorithm is used to provide the detection result after data fusion. Based on the different types of transmitted data, fusion detection methods can be divided into track-level fusion detection methods, decision-level fusion detection methods, and signal-level fusion detection methods. In terms of detection performance, signal-level fusion detection in multi-station radar is well-developed and mature, and outperforms the other two fusion methods. However, this current fusion detection method only relies on the amplitude information of the target echo and does not consider the application of easily obtainable Doppler information in the coherent system. If Doppler information is applied to traditional fusion detection, that is, if track-level fusion detection and signal-level detection are further combined, the resulting information increment will effectively improve detection performance. Based on this idea, scholars have proposed several Doppler information-assisted fusion detection algorithms.

[0004] Gao Chang et al. proposed a Doppler-assisted track formation algorithm in the journal Information Science 576(2021):345–354. This algorithm applies the coupling of Doppler information with spatial position observations to multi-frame fusion detection, performing fusion detection by judging whether the parameter information of the moving target observed by a single radar station satisfies kinematic constraints across multiple frames. However, this method is only applicable to multi-frame detection based on a single radar station and does not extend the algorithm to networked radar systems, thus failing to achieve the improvement in detection performance through the incremental target observation information from multiple radar stations.

[0005] In the *Journal of Radar*, 2019, 8(4):490–500, Wang Jinghe et al. proposed a multi-frame fusion detection algorithm based on a networked radar system. This algorithm incorporates an information vector composed of range, azimuth, elevation, and Doppler information into a dynamic programming-based pre-detection tracking algorithm. The fusion detection decision is made by judging whether the difference between the target spatial position estimated by the information vector and the target spatial position observed by the radar network meets a preset threshold. However, because this method utilizes information from both the range and angle dimensions for target spatial position estimation, it not only increases the computational load of the algorithm but also significantly increases the impact of radar observation angle errors on target spatial position estimation when the target is far away. This can even overwhelm the spatial position estimation bias caused by false alarms in the Doppler channel, leading to a decrease in detection performance. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the existing technologies by proposing a Doppler information-assisted networked radar fusion detection method to effectively improve the performance of fusion detection.

[0007] The technical solution of this invention is as follows: By introducing Doppler information into data fusion, and utilizing the physical constraints satisfied by the angle information and radial velocity of the target observed by different radar stations, a second detection decision is made on the traditional fusion detection results based solely on amplitude information. The improved fusion detection performance is achieved by utilizing the information increment from multiple radar station observations. The implementation steps include the following:

[0008] (1) Set up a radar system including a data fusion detection center and N radar stations, and set the common field of view of the radar network, the spatial location of each radar station, carrier frequency, bandwidth, waveform duration, coherent accumulation pulse number and pulse repetition period, as well as the maximum value of angle and velocity observation error Δθ. Mi ,Δv Mi i = 1, ..., N;

[0009] (2) The data fusion detection center obtains the fusion detection results of the data matrices of each radar station based on the echo data matrices transmitted from each radar station and the basic parameters of their respective radar systems, using a traditional fusion detection algorithm based on amplitude information, and reads the detected target angle θ from it. Oi And Doppler velocity v Oi ;

[0010] (3) Based on the target angle θ read Oi With Doppler velocity v Oi Construct each radar station about v x ,v y Two sets of linear inequalities:

[0011]

[0012]

[0013] Among them, v x ,v y Let v represent the components of the target velocity vector along the x and y axes, respectively. Di k represents the maximum unambiguous velocity determined by the radar's fundamental parameters. i ∈{-m,-m+1,…,m} represents the unknown velocity ambiguity number, and m≥0 is the maximum target velocity ambiguity number determined based on the basic radar parameters; Indicates in v x sin(θ Oi )-v y cos(θ Oi When )≥0, the target angle θ read by the i-th radar station Oi With Doppler velocity v Oi The set of inequalities that must be satisfied, where each element is the velocity fuzzy number k. i Given (2m+1) possible values ​​of v x ,v y A system of linear inequalities; Indicates in v x sin(θ Oi )-v y cos(θ Oi When θ < 0, the target angle θ read by the i-th radar station Oi With Doppler velocity v Oi The set of inequalities that must be satisfied;

[0014] (4) Choose any one of the elements from the two sets of linear inequalities corresponding to each radar station and combine them to form the following set of linear inequalities:

[0015]

[0016] in, Describe the set of inequalities corresponding to the i-th radar station. The ambiguity number at medium speed is k i The system of inequalities, q i ∈{1,2};

[0017] (5) Let q i Take {1, 2} in sequence, k i Take {-m, -m+1, ..., m} in sequence, and substitute these two parameters into the system of linear inequalities LI(q1, ..., q i ,…,q N ,k1,…,k i ,…,k NFrom this, we get 2(2m+1). N A system of linear inequalities;

[0018] (6) For 2(2m+1) N We iterate through a system of linear inequalities, construct a linear mathematical programming model using a two-phase algorithm from operations research, and solve the model using the linprog function in MATLAB to obtain the optimal value. Based on the obtained optimal value, we then determine whether the system of linear inequalities has a feasible region.

[0019] If the optimal value of one of the mathematical programming models is 0, it means that the system of linear inequalities has a feasible region, the traversal ends, and the data fusion detection center provides information on the actual existence of the target, obtaining the observation information of the radial distance, Doppler velocity and angle of the detected target;

[0020] If the optimal values ​​of these mathematical programming models are all non-zero, it means that the decision results of these linear inequalities are all infeasible regions, and the data fusion detection center will give the information that the target is a false alarm.

[0021] (7) Return to step (2), the data fusion center receives the echo data of each radar station at the next moment, and repeats steps (2) to (7) to perform the next round of fusion detection.

[0022] This invention incorporates Doppler information and utilizes the physical constraints satisfied by the angle information and radial velocity of targets observed by different radar stations to perform fault-tolerant processing on the detection results of traditional fusion detection, thereby improving the performance of fusion detection using Doppler information in radar networks. At the same time, because this invention utilizes the special property that the spatial position and radial velocity of targets observed by different radar systems in a networked radar system should satisfy certain physical constraints, it effectively reduces the false alarm probability and further improves the detection performance of the data fusion center. Attached Figure Description

[0023] To more clearly demonstrate the effectiveness and reliability of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0025] Figure 2 This refers to the radar network common field of view area set in this embodiment of the invention;

[0026] Figure 3 This is a schematic diagram of a radar system with different numbers of radar stations in an embodiment of the present invention;

[0027] Figure 4 Based on Figure 3 Comparison of the performance curves of the radar system simulation of the present invention and the traditional fusion detection method for target detection;

[0028] Figure 5 These are different deployment locations of radar stations in a three-radar-station system according to embodiments of the present invention;

[0029] Figure 6 Based on Figure 5 Comparison of detection performance curves of the present invention and the traditional fusion detection method under different deployments of three radar systems;

[0030] Figure 7 This is a schematic diagram showing the different positions of the target on the y-axis in a three-radar station system according to an embodiment of the present invention;

[0031] Figure 8 Based on Figure 7 A comparison of the detection performance curves of the present invention and the traditional fusion detection method at different target locations;

[0032] Figure 9 This is a schematic diagram of the boundary distribution of the target in the three-radar-station system under the common field of view of the radar network in an embodiment of the present invention;

[0033] Figure 10 Based on Figure 9 The simulation results show a comparison of the detection performance curves of the present invention and the traditional fusion detection method at different target locations. Detailed Implementation

[0034] The embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.

[0035] Reference Figure 1 The implementation steps for this example are as follows:

[0036] Step 1: Set up a radar network system consisting of a data fusion detection center and radar stations.

[0037] The data fusion detection center is used to receive data information from various radar stations, perform traditional fusion detection based on amplitude information, and perform fusion detection assisted by Doppler information.

[0038] The radar stations are set up in N numbers according to usage requirements. The basic parameters of the radar system, such as carrier frequency, bandwidth, waveform duration, coherent accumulation pulse count, and pulse repetition period, are set for each radar station according to the observation accuracy, as well as the maximum angle observation error Δθ. Mi Maximum error of velocity observation Δv Mi , i = 1, ..., N.

[0039] Step 2: Based on the echo data transmitted from each radar station and the basic parameters of their respective radar systems, the data fusion detection center uses a traditional fusion detection algorithm based on amplitude information to obtain the fusion detection results of the echo data from each radar station, and reads the detected target angle θ from it. Oi And Doppler velocity v Oi .

[0040] This example assumes the radar network is operating under the same Gaussian noise background, and the specific implementation is as follows:

[0041] (2.1) For N radar stations, the echo signal data received by the i-th radar station is denoted as... The test statistic for the echo signal is denoted as Z. i =X i / μ i , where X i Y represents the power observation value of the detection unit. i,j The value represents the power observation of the reference element, where n represents the number of reference elements, and μ represents the value of the reference element. i The noise power estimate for the i-th radar station is expressed as:

[0042] (2.2) Select the target fluctuation model Swerling I and obtain the expression for its optimal fusion detector:

[0043] (2.2.1) Based on the distribution function under the Swerling I model, the expression for the fusion center likelihood ratio Λ is obtained:

[0044]

[0045] in Let Z represent the test statistic, Z, and Z respectively. i Distribution functions for the case without a target (H0) and the case with a target (H1):

[0046]

[0047]

[0048] In the formula, u(·) represents the step function, and S i This represents the signal-to-noise ratio of the signal received by the i-th radar station;

[0049] (2.2.2) Taking the natural logarithm of the fusion center likelihood ratio Λ and simplifying it, we obtain the expression for the optimal fusion detector:

[0050]

[0051] (2.3) Set the false alarm rate P fa Based on T optDetermine the false alarm rate P using the Monte Carlo method fa The detection threshold T;

[0052] (2.4) The data fusion center receives the echo data transmitted from the radar network and substitutes this data into the optimal fusion detector in (2.2.2) to obtain the T corresponding to this set of echo data. opt The value is then compared with the detection threshold T determined in (2.3):

[0053] If T opt If T ≥ T, it indicates that the target exists, and the angle θ of the target observed by each radar station is obtained. Oi And Doppler velocity v Oi ;

[0054] Otherwise, the fusion center will determine that the target does not exist.

[0055] Step 3, based on the angle θ observed by each radar station Oi And Doppler velocity v Oi It possesses the characteristic of coupling, and constructs a set of linear inequalities that satisfy coupling constraints.

[0056] (3.1) Based on the velocity projection relationship and the target angle θ read from each radar station Oi With Doppler velocity v Oi The following equation is obtained:

[0057] v x cos(θ Oi +Δθ i )+v y sin(θ Oi +Δθ i ) = v Oi +Δv i +k i v Di

[0058] Where v x ,v y The components of the target velocity vector along the x and y axes are shown respectively, v Di k represents the maximum unambiguous velocity determined by the radar's fundamental parameters. i ∈{-m,-m+1,…,m} represents the unknown velocity ambiguity number, where m≥0 is the maximum target velocity ambiguity number determined based on the radar's basic parameters; Δθ i Δv i These represent the angle observation error and the velocity observation error, respectively.

[0059] (3.2) To A first-order Taylor expansion of the expression, omitting higher-order terms, yields:

[0060] v x cos(θ Oi )+v y sin(θ Oi ) = [v x sin(θ Oi )-v y cos(θ Oi )]Δθ i +v Oi +Δv i +k i v Di

[0061] Due to velocity observation error Δv i ∈[-Δv Mi ,Δv Mi and the angle observation error Δθ i ∈[-Δθ Mi ,Δθ Mi ] is a bounded random value, therefore when [v x sin(θ Oi )-v y cos(θ Oi When ] is a non-negative or negative value, The equations satisfy the following two sets of inequalities, thus yielding the equations for each radar station with respect to v. x ,v y Two sets of linear inequalities:

[0062]

[0063]

[0064] Where Δθ Mi ,Δv Mi This indicates the maximum value of the observation error for angle and velocity; Indicates in v x sin(θ Oi )-v y cos(θ Oi When )≥0, the target angle θ read by the i-th radar station Oi With Doppler velocity v Oi The set of inequalities that must be satisfied, where each element is the velocity fuzzy number k. i Given (2m+1) possible values ​​of v x ,v y A system of linear inequalities; Indicates in v x sin(θ Oi )-v y cos(θ Oi When θ < 0, the target angle θ read by the i-th radar station Oi With Doppler velocity v Oi The set of inequalities that must be satisfied.

[0065] Step 4: Select a set of inequalities from the set of inequalities corresponding to each radar station and combine them into a new set of linear inequalities.

[0066] (4.1) Choose any one of the elements from the two sets of linear inequalities corresponding to each radar station and combine them into the following set of linear inequalities:

[0067]

[0068] in, Describe the set of inequalities corresponding to the i-th radar station. The ambiguity number at medium speed is k i The system of inequalities, q i ∈{1,2};

[0069] (4.2) Let q i Take {1, 2} in sequence, k i Take {-m, -m+1, ..., m} in sequence, and substitute these two parameters into the system of linear inequalities LI(q1, ..., q i ,…,q N ,k1,…,k i ,…,k N From this, we get 2(2m+1). N A system of linear inequalities.

[0070] Step 5, for 2(2m+1) N A system of linear inequalities is traversed, and a linear mathematical programming model is constructed using a two-stage algorithm from operations research.

[0071] (5.1) The system of linear inequalities LI(q1,…,q) i ,…,q N ,k1,…,k i ,…,k N ) in v x ,v y They are represented as follows:

[0072]

[0073] in:

[0074] (5.2) will and Substituting these into the linear inequality system LI, and by negating both sides of the inequalities to convert "≥" to "≤", we obtain the following system of inequalities:

[0075]

[0076] Where a p1 v represents the p-th inequality in the original system of inequalities LI. x coefficient, a p2 v represents the p-th inequality in the original system of inequalities LI. y The coefficient, b p Let represent the constant value on the right side of the p-th inequality in the original system of inequalities LI, where p = 1, ..., 3N.

[0077] (5.3) In the system of linear inequalities <c>Add a nonnegative slack variable v to p This transforms it into the following system of equations:

[0078]

[0079] (5.4) In the system of equations <d>Add non-negative artificial variables Construct a new system of equations, using this system as constraints and the sum of artificial variables as the objective function, to create a linear mathematical programming model:

[0080]

[0081]

[0082] Step 6, based on 2(2m+1) N A system of linear inequalities can be constructed to form 2(2m+1). N Several linear programming models are used to perform target detection based on the optimal values ​​of these linear mathematical programming models.

[0083] The linprog function in MATLAB is used to iterate through and solve these linear mathematical programming models. Based on the obtained values, the existence of a feasible region is determined for each system of linear inequalities.

[0084] If the optimal value of one of the mathematical programming models is 0, it means that the system of linear inequalities has a feasible region, then the traversal ends, and the data fusion detection center provides information on the actual existence of the target, obtaining the observation information of the radial distance, Doppler velocity and angle of the detected target;

[0085] If the optimal values ​​of these mathematical programming models are all non-zero, it means that the decision results of these linear inequalities are all infeasible regions, and the data fusion detection center will give the information that the target is a false alarm.

[0086] The effectiveness of this invention is further illustrated by the following simulation comparison experiments:

[0087] I. Simulation conditions:

[0088] Assume that the echo signals from radar stations in the radar network have the same signal-to-noise ratio (SNR), with the total SNR ranging from 0 dB to 26 dB; the radar waveform used is a linear frequency modulated (LFM) wave.

[0089] The basic parameters of the radar waveform are shown in Table 1:

[0090] Table 1 Basic parameters of radar waveform

[0091]

[0092] The formulas for calculating the errors in angle and Doppler velocity measurements are as follows:

[0093]

[0094] Where λ represents wavelength and SNR represents signal-to-noise ratio. Let 3σ be the value. θ ,3σ v This represents the maximum value of the measurement error for angle and velocity.

[0095] Let the target's maximum flight speed be v. max =300m / s, flight direction is arbitrary angle, Swerling I is selected as the undulation model.

[0096] The target echo data is processed by CA-CFAR with a reference window length of n=8, no guard window, and a false alarm probability of P at the fixed fusion center. fa =10 -3 .

[0097] A schematic diagram of the radar network system is shown below.< / d> < / c> Figure 2 As shown, this illustrates the distribution of radar stations and targets. The square shaded area with a side length of 100 km represents the spatial range of targets jointly observed by the radar network.

[0098] II. Simulation Content

[0099] Simulation 1 sets up two-radar station systems, three-radar station systems, and four-radar station systems, that is, in Figure 2 Two radar stations are placed in the radar network system respectively, such as Figure 3 As shown in (a), three radar stations are placed as follows: Figure 3 As shown in (b), four radar stations are placed as follows: Figure 3 As shown in (c), the performance of the present invention and the traditional fusion detection method for target detection on different radar station systems was simulated under the above simulation conditions in these three systems, and the results are as follows: Figure 4 As shown.

[0100] from Figure 4 As can be seen from the comparison curves, when the number of radar stations in the radar system is greater than 2, the present invention effectively improves the detection performance of the fusion detection method compared with the prior art, and the improvement effect of the fusion detection of the present invention becomes more and more significant as the number of radar stations increases.

[0101] Simulation 2 involves setting different deployment locations for a three-radar station system. The three radar stations are connected to form an isosceles triangle, and the radar positions are set at different vertices of the triangle. For example, when the vertex angle of the triangle is 30°, the radar positions are as follows: Figure 5 As shown in (a), the radar position is as follows when the vertex angle of the triangle is 60°. Figure 5 As shown in (b), the radar position is as follows when the apex angle of the triangle is 90°. Figure 5 As shown in (c), the radar position is as follows when the vertex angle of the triangle is 120°. Figure 5 As shown in (d), using the above simulation conditions, the target detection performance of the present invention under these four deployment methods was simulated respectively, and compared with the target detection performance of the traditional fusion detection method. The results are as follows. Figure 6 As shown.

[0102] from Figure 6 As can be seen from the comparison curves, the detection performance of the present invention is higher than that of the traditional fusion detection method at different deployment locations. Moreover, the deployment location of the radar network will significantly affect the detection performance of the present invention. When the radar stations are symmetrical about the center point of the common field of view, the detection performance of the present invention will reach the best.

[0103] Simulation 3 sets different target positions for a three-radar station system, where the target distribution on the y-axis is as follows: Figure 7 As shown, the target distribution at the lower boundary of the shared viewing area is as follows: Figure 8 As shown, under the above simulation conditions, the performance of the present invention for target detection at different target locations is simulated under these two target distribution scenarios. The results are as follows: Figure 9 and Figure 10 As shown.

[0104] from Figure 9 , Figure 10 As can be seen from the comparison curves, the detection performance of the present invention is more significant when the target position is close to the center of the common viewing area.

[0105] The simulation experiments described above demonstrate that this invention introduces Doppler information increments for fault-tolerant processing in traditional fusion detection, effectively improving the detection performance of traditional fusion detection under the same radar application scenarios.

[0106] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A Doppler information aided networked radar fusion detection method, characterized in that, Comprising the following steps: (1) setting a radar system including one data fusion detection center and a radar station, and setting the common view area of the radar network, the spatial position of each radar station, the carrier frequency, the bandwidth, the waveform time width, the number of coherent accumulation pulses, and the pulse repetition period of the radar system basic parameters, and the maximum value of angle and velocity observation errors ; (2) The data fusion detection center obtains the fusion detection result of the data matrix of each radar station by using the traditional fusion detection algorithm based on amplitude information, based on the echo data matrix transmitted by each radar station and the basic parameters of each radar system, and reads the detected target angle from the fusion detection result and Doppler velocity ; (3) Target angle based on reading Doppler velocity Construct two sets of linear inequalities for each radar station with respect to the target ； ; where denote the components of the target velocity vector along the axes, denotes the maximum unambiguous velocity determined by the radar basic parameters, denotes the unknown velocity ambiguity number, is the maximum ambiguity number of the target velocity determined from the radar basic parameters; denotes the target angle read by the th radar station in the case that denotes the set of inequality systems that should be satisfied by the target angle and Doppler velocity in the case that denotes the set of linear inequality systems on in possible values; denotes the target angle read by the th radar station in the case that denotes the set of inequality systems that should be satisfied by the target angle (4) Arbitrarily select one inequality set from the elements of the two linear inequality set groups corresponding to each radar station to form the following linear inequality set: ； wherein, represents the inequality set corresponding to the th radar station with the velocity ambiguity number ;​ (5) Let Take , Take , and bring these two parameters into the linear inequality system , get linear inequality system; (6) For linear inequality system, a linear programming model is constructed by using two-stage algorithm in operational research, and the optimal value is obtained by solving the model using linprog function in MATLAB software. According to the optimal value, it is determined whether the linear inequality system has feasible region or not. If one of the optimal values of the mathematical programming model is , it indicates that the linear inequality system has a feasible region, the traversal is ended, the data fusion detection center gives the information that the target really exists, and the observation information of the radial distance, Doppler velocity and angle of the detected target is obtained. If the optimal values of these mathematical programming models are all not , it indicates that the decision results of these linear inequality systems are all no feasible region, and the data fusion detection center gives the information that the target is false alarm. (7) Return to step (2), the data fusion center receives the echo data of each radar station at the next time, and repeats steps (2) to (7) to perform the next round of fusion detection.

2. The method of claim 1, wherein, In step (2), the fusion detection result of the data matrix of each radar station is obtained by using the traditional fusion detection algorithm based on amplitude information, and the following is realized: (2a) for radar stations, the echo signal data received by the radar station is denoted by , the test statistic of the echo signal is denoted by , where represents the power observation value of the detection unit, represents the power observation value of the reference unit, represents the number of reference units, is the noise power estimation value of the radar station, expressed as: ; (2b) Select the target fluctuation model Swerling I to obtain the expression of the optimal fusion detector: (2b1) According to the distribution function under the Swerling I model, the expression of the fusion center likelihood ratio is obtained: ； where , denote the test statistics under the null hypothesis and the alternative hypothesis , respectively. ； wherein represents a step function, represents the signal-to-noise ratio of the signal received by the radar station; (2b2) The fusion center likelihood ratio Taking natural logarithm and simplifying, the optimal fusion detector expression is obtained: ； (2c) setting a false alarm probability , based on determining a detection threshold value that satisfies the false alarm probability ; (2d) The data fusion center receives the echo data transmitted by the radar network and substitutes these data into the optimal fusion detector of (2b2) to obtain its corresponding value, and compares this value with the detection threshold value determined in (2c) ​ If , it means that the target exists, and the angle and Doppler velocity observed by each radar station are obtained Otherwise, the fusion center gives the decision result as no target exists.

3. The method of claim 1, wherein, The target angle based on the reading in step (3) with the Doppler velocity Constructing the set of two linear inequality systems for each radar station with respect to is achieved as follows: (3a) The target angle read by each radar station with the Doppler velocity into the velocity projection equation below: ； wherein the components of the target velocity vector along the axes, denotes the maximum unambiguous velocity determined by the radar basic parameters, denotes the unknown velocity ambiguity number, is the maximum ambiguity number of the target velocity determined from the radar basic parameters; , denote the angle observation error and the velocity observation error, respectively;​ (3b) First-order Taylor expansion is performed on the formula, and high-order terms are omitted to obtain: In step (6), a linear mathematical programming model is constructed by using the two-stage algorithm in operational research, and the following is realized: ； Since the velocity observation errors and the angle observation errors are bounded random values, therefore when is non-negative and negative values, The equations satisfy the following two sets of inequalities, respectively, i.e. two sets of linear inequalities for each radar station about ​ ； ； wherein denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; denotes the maximum value of the angle and velocity observation error; 4. The method of claim 1, wherein, ​ (6a) the linear inequality set in is represented as follows, respectively: ； wherein: ; (6b) Substitute and into and, by negating both sides of the inequality, the sign in the inequality set is changed to , resulting in the following inequality set: ； wherein denotes the coefficients of the original inequality system in the th inequality of the original inequality system, denotes the coefficients of the original inequality system in the th inequality of the original inequality system, denotes the constant value on the right side of the th inequality of the original inequality system, ;​ (6c) in the linear inequality system <c>Adding slack variables to the middle Making it a system of equations:< / c> ； (6d) in the system of equations <d>Adding artificial variables Form a new equation set and take it as the constraint condition, and construct a linear mathematical programming model with the sum of artificial variables as the objective function:< / d> ； 。

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