A method for cooperative resolving range and velocity ambiguities based on distributed radars

Abstract

The application discloses a method for solving distance ambiguity and velocity ambiguity based on distributed radars, the method for solving distance ambiguity comprises the following steps: measuring radar apparent distance, calculating maximum non-ambiguous distance to extend distance, calculating positioning equation of each radar relative to a reference radar, solving intersection points of the equation and screening, and calculating real distance of a target through the rest of the intersection points; the method for solving velocity ambiguity comprises the following steps: measuring radar apparent velocity, calculating maximum non-ambiguous velocity to extend velocity and obtain velocity combination, and obtaining target ambiguous velocity through information fusion; taking the target position as a starting point, obtaining a target radial velocity positioning graph; screening intersection points and setting real velocity of the target; and obtaining real velocity according to the number of ambiguous points of the real velocity point. The method utilizes the system and structure advantages of distributed radars, establishes a chi-square test algorithm based on Mahalanobis distance on the basis of radar cooperation, solves the problems of ranging ambiguity, velocity ambiguity and velocity-ranging ambiguity in radar detection under the premise of using only one pulse repetition frequency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar signal processing, and particularly relates to a method for solving distance ambiguity and velocity ambiguity in cooperation based on distributed radars. BACKGROUND

[0002] Solving ambiguity is an important research problem in the field of radars. The main task of radars is to receive echo signals reflected by targets and extract position information such as distance, velocity, and angle. In the past single-radar system, multiple pulse repetition frequencies are often used, and then the Chinese remainder theorem and one-dimensional set algorithm are used for solving ambiguity. Radar technology has made great progress in the past few decades and has become an indispensable part of modern science and engineering. With the development of stealth technology, single-radar systems gradually develop into multi-radar systems. Distributed radars are multi-radar systems composed of multiple independent radars developed in recent years. The system can solve problems such as single observation angle, low positioning accuracy, and low false alarm probability by using radar cooperation.

[0003] Single radars can also solve distance ambiguity and velocity ambiguity, and there are many mature ambiguity solving algorithms, but these algorithms need to use multiple pulse repetition frequencies, which causes waste of spectrum resources, has high radar signal processing complexity, and is not efficient. The distributed radar system is relatively single-radar system, and the target information obtained is more abundant because the radars are distributed in different positions, so the system advantages of distributed radars are considered to solve the ambiguity problem in radar detection. SUMMARY

[0004] The present application aims at overcoming the deficiencies of the prior art and providing a method for solving distance ambiguity and velocity ambiguity in cooperation based on distributed radars.

[0005] The purpose of the present application is achieved by the following technical solutions.

[0006] The present application provides a method for solving distance ambiguity and velocity ambiguity in cooperation based on distributed radars, which comprises a distance ambiguity solving step and a velocity ambiguity solving step.

[0007] The distance ambiguity solving step specifically comprises:

[0008] S1, measuring the radar to obtain an apparent distance, calculating the maximum unambiguous distance of the radar, and performing distance continuation according to the maximum unambiguous distance;

[0009] S2, solving the positioning equation of each radar relative to the reference radar based on reference node distance-angle plane cooperative positioning;

[0010] S3. Find the intersection point based on the positioning equation of each radar group;

[0011] S4. Based on Mahalanobis distance, chi-square distribution is used to detect and filter intersection points. The intersection point target is regarded as the target true distance of the reference node.

[0012] S5. Solve for the true target distance in its coordinate system using the remaining intersection points to obtain the distance from the target to each radar.

[0013] The steps for resolving velocity ambiguity specifically include:

[0014] a. Measure the radar to obtain the apparent velocity, calculate the radar's maximum unambiguous velocity, and perform velocity extension based on the maximum unambiguous velocity;

[0015] b. Obtain all possible velocity combinations for each radar, perform velocity information fusion, and obtain the target fuzzy velocity under each combination;

[0016] c. Starting from the target position, obtain the target radial velocity positioning diagram;

[0017] d. Based on the chi-square distribution of Mahalanobis distance, the intersection points are detected and screened. The intersection point targets are regarded as the true velocity of the reference node targets. Based on the ambiguity number of the true velocity points, the true velocity measured by each radar is calculated to obtain the true velocity of the target.

[0018] Further, step S1 includes: the coordinates of radar I in the distributed radar system are... Where I = A, B, C, D, and the coordinates of target P are... ; The apparent range is obtained by measuring radar I. ,pass Calculate the maximum unambiguous range of radar I ;in HPRF Let be the radar pulse repetition frequency, c be the speed of light, and be the true distance from radar I to target P. Radar I's apparent range Maximum unambiguous range of Radar I satisfy ,in INT represents the maximum detection range of radar I, and INT indicates rounding down.

[0019] Preferably, step S2 includes: setting radar A as the reference radar, forming a first radar-target system with radar B and target P, and establishing the target positioning equation using the law of cosines: ,in Let be the acute angle between the line connecting radar A and target P and the horizontal coordinate axis. is the distance between radar A and radar B; similarly, the target positioning equation of radar C and radar D with radar A is determined, and the total target positioning equation is: wherein is the ambiguity number of radar B, is the ambiguity number of radar C, is the ambiguity number of radar D, is the distance between radar A and radar C, is the distance between radar A and radar D; the function curve is obtained by traversing each ambiguity number.

[0020] Preferably, the method comprises: after obtaining all the curves, solving the intersection points of the two groups of target positioning equations of radar A and radar B and radar A and radar C, and solving the intersection points of the two groups of target positioning equations of radar A and radar B and radar A and radar D, so as to obtain the intersection point of the function curve of radar A and radar B and the function curve of radar A and radar C as , and the intersection point of the function curve of radar A and radar B and the function curve of radar A and radar D as .

[0021] Preferably, the step S4 comprises: is any point on the intersection point is any point on the intersection point is any point on the intersection point is any point on the intersection point and the square Mahalanobis distance of wherein is a covariance matrix, T represents transposition, and a hypothesis testing model is established , and represents the corresponding target distance is a real distance, represents the corresponding target distance is an ambiguous distance; the Gaussian distribution to which the measurement error conforms is ; according to the operation rule of the Gaussian distribution, wherein is the angle measurement accuracy, is the distance measurement accuracy, if is established, then the square Mahalanobis distance obeys distribution, that is, chi-square distribution; the extended distance correlation test is obtained as: ; wherein is a threshold, and satisfies , wherein is a degree of freedom, is a significance level, for the system, the degree of freedom is 2, and the number and accuracy of the selected data points are controlled through the significance level.

[0022] Preferably, the step a comprises: the coordinates of radar I in the distributed radar system are , where I=A, B, C, D, and the target P is the coordinate origin, forming a second radar-target system, is the maximum unambiguous velocity that radar I can measure, where is the signal wavelength, LPRF is the pulse repetition frequency; , is the maximum velocity that radar I can detect, INT represents the floor function, and the apparent velocity of radar I , the true velocity and the maximum unambiguous velocity satisfy: .

[0023] Preferably, the step b comprises: fusing the velocity information of the radars, selecting radar A and radar B as the first combination, and radar C and radar D as the second combination, and letting , , substituting the velocity continuation, we have: , , where is the ambiguity number of radar A, is the ambiguity number of radar B, is the ambiguity number of radar C, is the ambiguity number of radar D, and different ambiguous velocities are obtained by combining different ambiguity numbers.

[0024] Preferably, the step c comprises: starting from the target position, obtaining a scatter plot through all target velocities of the combination of radar A and radar B and all target velocities of the combination of radar C and radar D.

[0025] Preferably, the step d comprises: assuming that radar A and radar B form a radar A-B system, and the true velocity vector of the target of the radar A-B system is: , where is the acute angle between the line connecting radar A and the target P and the horizontal coordinate axis, is the acute angle between the line connecting radar B and the target P and the horizontal coordinate axis, and the partial derivative of the variable of this formula is obtained to obtain the conversion matrix: , and the error covariance of the true velocity vector of the target is: , where is a diagonal matrix, is the angle measurement accuracy of radar A, is the angle measurement accuracy of radar B, is the velocity measurement accuracy of radar A, is the velocity measurement accuracy of radar B, and T is the transpose. Similarly, we can obtain The covariance matrix is obtained according to the Gaussian distribution as follows: The square Mahalanobis distance is: Wherein Then, the target speed is screened out by a preset threshold value through chi-square test.

[0026] The beneficial effects of the present application are:

[0027] 1) On the basis of radar cooperation, a chi-square test algorithm based on Mahalanobis distance is established by using the system and structural advantages of distributed radar, and the problems of ranging ambiguity, velocity ambiguity and velocity-ranging ambiguity in radar detection are solved under the premise of using only one pulse repetition frequency.

[0028] 2) Single pulse repetition frequency de-ambiguity is realized, the cooperative information of radar data is used to improve the effect of target distance and velocity de-ambiguity by the joint work of multiple radar nodes, more accurate target positioning is realized, at the same time, the distributed radar is used for de-ambiguity, which avoids the traditional multi-pulse repetition frequency method, reduces the complexity of radar signal processing, increases the usage rate of spectrum resources, and improves the efficiency.

[0029] 3) The present application is applied to a distributed radar system, the data of multiple radar nodes are used for cooperative de-ambiguity to realize accurate positioning of the target, and the distributed radar system can effectively improve the coverage range and target detection capability of the radar system. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 A distributed radar cooperative distance ambiguity resolution method flow chart of the embodiment of the present application;

[0031] Figure 2 A first radar-target system model diagram of the embodiment of the present application;

[0032] Figure 3 A distributed radar cooperative velocity ambiguity resolution method flow chart of the embodiment of the present application;

[0033] Figure 4 A second radar-target system model diagram of the embodiment of the present application;

[0034] Figure 5 A radar A-B system model diagram of the embodiment of the present application. DETAILED DESCRIPTION

[0035] The technical solutions of the present application will be clearly and completely described below with examples. Obviously, the described examples are only some of the examples of the present application, but not all the examples. Based on the examples in the present application, all the other examples obtained by those skilled in the art without creative effort are within the scope of the present application.

[0036] Exemplarily, the present application provides a method for cooperatively resolving range ambiguity and velocity ambiguity based on distributed radars, which comprises resolving range ambiguity and resolving velocity ambiguity. The cooperative resolution of range ambiguity does not require the velocity information of the target, while the resolution of velocity ambiguity requires the range information. Therefore, when both range ambiguity and velocity ambiguity exist, the range ambiguity is resolved first, and then the velocity ambiguity is resolved. The distributed radars cooperatively resolve the range ambiguity to obtain the position of the target and the position of the radars relative to the target. In the resolution of range ambiguity, one of the radars is selected as the coordinate origin. In the resolution of velocity ambiguity, the target is selected as the coordinate origin for the convenience of describing the velocity vector. Therefore, the coordinate conversion is required to link the resolution of range ambiguity and the resolution of velocity ambiguity. The distributed radars cooperatively resolve the velocity ambiguity to obtain the radial velocity of the target. When the radars use high pulse repetition frequency (HPRF), only range ambiguity exists, and velocity ambiguity does not exist. Only the resolution of range ambiguity is required. When the radars use low pulse repetition frequency (LPRF), only velocity ambiguity exists, and range ambiguity does not exist. Only the resolution of velocity ambiguity is required. When the radars use medium pulse repetition frequency (MPRF), both range ambiguity and velocity ambiguity exist. The resolution of range ambiguity does not require velocity information, while the resolution of velocity ambiguity requires the known position of the radars relative to the target. Therefore, the resolution of range ambiguity is performed first, and then the resolution of velocity ambiguity is performed.

[0037] The flow chart of the method for cooperatively resolving range ambiguity by the distributed radars is shown in Figure 1 The steps for resolving range ambiguity specifically comprise:

[0038] S1, measuring the radars to obtain the apparent range, calculating the maximum unambiguous range of the radars, and extending the range based on the maximum unambiguous range;

[0039] S2, cooperatively positioning based on the reference node range-angle plane to obtain the positioning equation of each radar relative to the reference radar;

[0040] S3, finding the intersection point according to the positioning equation of each group of radars;

[0041] S4, screening the intersection point based on the chi-square distribution detection of Mahalanobis distance, and regarding the intersection point target as the real range of the reference node target;

[0042] S5, solving the real range of the target in the coordinate system of the remaining intersection points;

[0043] The flow chart of the method for cooperatively resolving velocity ambiguity by the distributed radars is shown in Figure 3As shown, the step of resolving velocity ambiguity specifically comprises:

[0044] a. Measuring the radar to obtain the apparent velocity, calculating the maximum unambiguous velocity of the radar, and performing velocity continuation according to the maximum unambiguous velocity;

[0045] b. Obtaining all possible velocity combinations of each radar, performing velocity information fusion to obtain the target ambiguous velocity under each combination;

[0046] c. Taking the target position as the starting point to obtain the target radial velocity positioning map;

[0047] d. Screening the intersection based on the chi-square distribution detection of Mahalanobis distance, regarding the intersection target as the reference node target real velocity; calculating the real velocity measured by each radar according to the ambiguity number of the real velocity point, and obtaining the real velocity of the target.

[0048] Specifically, the step S1 comprises: the coordinates of the radar I in the distributed radar system are , the coordinates of the target P are ; the position coordinates of the radar I are known, while the position coordinates of the target P are unknown; the radar I is measured to obtain the apparent distance , which is directly measured by the radar I, and the maximum unambiguous distance of the radar I is calculated by . , wherein HPRF is the pulse repetition frequency of the radar, c is the speed of light, the real distance of the radar I to the target P is , the apparent distance of the radar I is , and the maximum unambiguous distance of the radar I is , which satisfy , wherein is the maximum detection distance of the radar I, which is determined by the structure of the radar I itself, and INT represents the down rounding. To determine the real distance of the radar I, that is, to determine the value of the ambiguity number n. All possible distance values after distance continuation are obtained by traversing all possibilities of n.

[0049] The step S2 comprises: taking the radar A as the reference radar, and constructing a first radar-target system with the radar B and the target P, and the model diagram of the first radar-target system is as shown in Figure 2 , wherein is the distance between the radar A and the target P, is the distance between the radar B and the target P, is the distance between the radar A and the target P, is the distance between the radar D and the target P, and the target positioning equation is established by the cosine law: , wherein is the acute angle between the line connecting the radar A and the target P and the horizontal coordinate axis. is the distance between radar A and radar B; wherein There is ambiguity, but a specific numerical sequence can be obtained by distance continuation, and are unknown numbers, and other variables are known variables, so the two unknown numbers can determine a function curve, and the same reasoning is used to determine the target positioning equation constructed by radar C and radar D and radar A, and the total target positioning equation is: wherein is the ambiguity number of radar B, is the ambiguity number of radar C, is the ambiguity number of radar D, is the distance between radar A and radar C, is the distance between radar A and radar D; for each ambiguity number, each different ambiguity number determines a function curve. After obtaining all the curves, because each set of equation curves traverses the possible position (distance and angle) of the target, the true position point of the target must be on each set of curves. The intersection points of the two sets of target positioning equations formed by radar A and radar B and radar A and radar C are solved, and these intersection points should contain the true point. The intersection points of the two sets of target positioning equations formed by radar A and radar B and radar A and radar D are solved. Because the position parameters of the target are unique, if the target distance values measured by each radar are converted in a coordinate system, these values are relatively concentrated. The degree of concentration depends on the measurement error of each radar. However, even considering the measurement error, this correlation still exists. This correlation determines that the true distance-angle conversion of the same target in all node radars will be relatively concentrated when converted to the same real distance-angle coordinate plane. For ambiguous distances or other points, after conversion, they are relatively divergent. "Concentration" and "divergence" are actually a manifestation of similarity, so the chi-square distribution detection method based on Mahalanobis distance can be introduced to identify the target distance, and the intersection point of the function curve of radar A and radar B and the function curve of radar A and radar C is , and the intersection point of the function curve of radar A and radar B and the function curve of radar A and radar D is .

[0050] Specifically, the step S4 comprises: is any point on the intersection point is any point on the intersection point and The square Mahalanobis distance of and is wherein is the covariance matrix, T represents transposition, and a hypothesis test model is established , wherein represents The corresponding target distance is the true distance. express The corresponding target distance is the fuzzy distance; the measurement error follows a Gaussian distribution. The measurement error is an independently distributed random variable that approximately follows a zero-mean Gaussian distribution; according to the operational rules of the Gaussian distribution, ,in For angle measurement accuracy, For the sake of ranging accuracy, these two data points are usually given directly. If true, then the squared Mahalanobis distance is... obey The distribution, i.e., the chi-square distribution, yields the following extended distance correlation test: ;in As a threshold, satisfying ,in For degrees of freedom, The significance level is set to 2, and for this system, the degree of freedom is 2. The significance level controls the number and accuracy of the selected data points. After setting the significance level, the data point selection process is implemented programmatically. Ultimately, the point that best represents the true distance to the target can be obtained, thus achieving single-frequency distance ambiguity resolution.

[0051] For example, the algorithm process for resolving velocity ambiguity in distributed radar cooperatives is similar to that for resolving range ambiguity. However, when resolving velocity ambiguity, it is not necessary to establish a relational formula similar to the target localization equation. Instead, it directly utilizes the synthesis of velocity vectors, i.e., velocity information fusion, to achieve an effect similar to establishing a target equation and then finding the intersection point. Step a includes: the coordinates of radar I in the distributed radar system are... Where I = A, B, C, D, with target P as the origin, a second radar-target system is constructed. The model diagram of the second radar-target system is shown below. Figure 4 As shown, Let P be the distance between radar A and target P. Let P be the distance between radar B and target P. Let P be the distance between radar A and target P. Let D be the distance between radar D and target P. The distance between radar A and radar B. The distance between radar A and radar C. The distance between radar A and radar D. The true speed of radar A. This represents the actual speed of radar B. The true speed of radar C. The true speed of radar D. is the acute angle between the line connecting radar A and target P and the horizontal coordinate axis; unlike the system for solving range ambiguity, the target is taken as the reference point, i.e., the coordinate origin, and the advantage is that the end point coordinates of the velocity vector can represent the velocity vector, thus simplifying the vector composition problem into a coordinate calculation problem. In this model, only velocity ambiguity is considered, and thus the range is accurate, i.e., the positions of the radar and the target are known, is the maximum unambiguous velocity that can be measured by radar I, wherein is the signal wavelength, LPRF is the pulse repetition frequency; , is the maximum velocity that can be detected by radar I, which can be set according to actual conditions, and only needs to be greater than the actual velocity of the target, INT represents rounding down, and the range and velocity have symmetry, and the apparent velocity of radar I , the real velocity and the maximum unambiguous velocity satisfy: It should be noted that because the positions of the radars are known, the relationship between the velocity vector and the velocity magnitude is that the velocity vector is equal to the product of the velocity magnitude and the position vector of the radar.

[0052] Specifically, step b includes: fusing the velocity information of the radars, selecting radar A and radar B as the first combination, and radar C and radar D as the second combination, and letting , and substituting the velocity extension, we have: , , wherein is the ambiguity number of radar A, is the ambiguity number of radar B, is the ambiguity number of radar C, is the ambiguity number of radar D, and different ambiguous velocities are obtained by combining different ambiguity numbers. Step c includes: taking the target position as the starting point, drawing all target velocities of the combination of radar A and radar B and all target velocities of the combination of radar C and radar D, and obtaining a scatter plot, because the starting point coordinates of the velocity vector are (0, 0), the end point coordinates can represent the velocity vector, and thus the vector diagram is simplified into a scatter plot.

[0053] Specifically, similar to the solution of range ambiguity, the two groups of scatters obtained are similar to the intersection points of the two groups of target equations in the solution of range ambiguity, and thus the chi-square test algorithm based on Mahalanobis distance can be used for screening the real velocity points. The principle is similar to that of the solution of range ambiguity, and mainly includes deriving the covariance matrix. Step d includes: assuming that radar A and radar B form a radar A-B system, and the radar A-B system model is shown in Figure 5 , the coordinates of radar A are , and the coordinates of radar B are , is the distance between radar A and radar B, is the distance from radar A to target P, is the distance from radar B to target P, the actual velocity vector of the target of radar A-B system is: wherein is the acute angle between the line connecting radar A and target P and the horizontal coordinate axis, is the acute angle between the line connecting radar B and target P and the horizontal coordinate axis, the partial derivative of the variable of the formula is obtained to obtain the conversion matrix: , the error covariance of the actual velocity vector of the target is: wherein is a diagonal matrix, is the angle measurement accuracy of radar A, is the angle measurement accuracy of radar B, is the velocity measurement accuracy of radar A, is the velocity measurement accuracy of radar B, T is transposition, these values are directly given, and can be obtained similarly, the next step is similar to the distance ambiguity resolution, the covariance matrix of the vector difference of the two groups of points is obtained, and then the square Mahalanobis distance is further obtained, and chi-square test is performed. Because the two groups of radars are independent, the covariance is also independent, so the error covariance matrix is the covariance matrix of the velocity vector difference, according to the characteristics of Gaussian distribution, the covariance matrix is obtained according to Gaussian distribution: ; the square Mahalanobis distance is: wherein then the chi-square test is performed through a preset threshold to screen the target velocity.

[0054] The above only describes the preferred embodiments of the present application, and it should be understood that the present application is not limited to the forms disclosed herein, and should not be considered as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concepts described herein, by the above-mentioned teaching or related art or knowledge. The modifications and changes made by those skilled in the art without departing from the spirit and scope of the present application shall be within the protection scope of the appended claims of the present application.

Claims

1. A method for cooperative resolution of range and velocity ambiguities based on distributed radar, characterized in that, This includes steps for resolving distance ambiguity and steps for resolving velocity ambiguity; The steps for resolving distance ambiguity specifically include: S1. Measure the radar to obtain the apparent range, calculate the radar's maximum unambiguous range, and perform range extension based on the maximum unambiguous range; S2. Based on the reference node range-angle plane cooperative localization, the localization equation of each radar relative to the reference radar is obtained; S3. Find the intersection point based on the positioning equation of each radar group; S4. Based on Mahalanobis distance, chi-square distribution is used to detect and filter intersection points. The intersection point target is regarded as the target true distance of the reference node. S5. Solve for the true target distance in its coordinate system using the remaining intersection points to obtain the distance from the target to each radar. The steps for resolving velocity ambiguity specifically include: a. Measure the radar to obtain the apparent velocity, calculate the radar's maximum unambiguous velocity, and perform velocity extension based on the maximum unambiguous velocity; b. Obtain all possible velocity combinations for each radar, perform velocity information fusion, and obtain the target fuzzy velocity under each combination; c. Starting from the target position, obtain the target radial velocity positioning diagram; d. Based on the chi-square distribution of Mahalanobis distance, the intersection points are detected and screened. The intersection point targets are regarded as the true velocity of the reference node targets. Based on the ambiguity number of the true velocity points, the true velocity measured by each radar is calculated to obtain the true velocity of the target.

2. The method for cooperative resolution of range and velocity ambiguities based on distributed radar according to claim 1, characterized in that, Step S1 includes: the coordinates of radar I in the distributed radar system are... Where I = A, B, C, D, and the coordinates of target P are... ; The apparent range is obtained by measuring radar I. ,pass Calculate the maximum unambiguous range of radar I ;in HPRF Let be the radar pulse repetition frequency, c be the speed of light, and be the true distance from radar I to target P. Radar I's apparent range Maximum unambiguous range of Radar I satisfy ,in INT represents the maximum detection range of radar I, and INT indicates rounding down.

3. The method for cooperative resolution of range and velocity ambiguities based on distributed radar according to claim 2, characterized in that, Step S2 includes: assuming radar A is the reference radar, forming a first radar-target system with radar B and target P, and establishing the target localization equation using the law of cosines: ,in Let be the acute angle between the line connecting radar A and target P and the horizontal coordinate axis. Let the distance between radar A and radar B be denoted; similarly, determine the target positioning equations constructed by radar C and radar D with radar A, and obtain the overall target positioning equation as follows: ,in For radar B, Let C be the ambiguity number of radar. Let D be the ambiguity number of radar. The distance between radar A and radar C. Let be the distance between radar A and radar D; the function curve is obtained by iterating through each ambiguity number.

4. The method for cooperative resolution of range and velocity ambiguities based on distributed radar according to claim 3, characterized in that, include: After obtaining all the curves, the intersection points of the two sets of target location equations formed by radar A and radar B, and radar A and radar C, are solved. Similarly, the intersection points of the two sets of target location equations formed by radar A and radar B, and radar A and radar D, are obtained. The intersection points of the function curves of radar A and radar B with the function curves of radar A and radar D are: .

5. The method for cooperative resolution of range and velocity ambiguities based on distributed radar according to claim 4, characterized in that, Step S4 includes: Intersection any point on, Intersection any point on, and The square Mahalanobis distance is ,in Let T be the covariance matrix, and let T denote the transpose. Establish a hypothesis testing model. ,set up express The corresponding target distance is the true distance. express The corresponding target distance is the fuzzy distance; the measurement error follows a Gaussian distribution. According to the operational rules of the Gaussian distribution, ,in For angle measurement accuracy, For ranging accuracy, if If true, then the squared Mahalanobis distance is... obey The distribution, i.e., the chi-square distribution, yields the following extended distance correlation test: ;in As a threshold, satisfying ,in For degrees of freedom, The significance level is 2. For this system, the degree of freedom is 2. The significance level controls the number and accuracy of the selected data points.

6. The method for cooperative resolution of range and velocity ambiguities based on distributed radar according to claim 1, characterized in that, Step a includes: the coordinates of radar I in the distributed radar system are... Where I = A, B, C, D, with target P as the origin, forming the second radar-target system. It is the maximum unambiguous velocity that radar I can measure, of which For the signal wavelength, LPRF The pulse repetition frequency; , The maximum detectable speed of Radar I, where INT represents the floor function, and the apparent speed of Radar I is the floor function. Real speed and maximum unambiguous speed satisfy: .

7. The method for cooperative resolution of range and velocity ambiguities based on distributed radar according to claim 6, characterized in that, Step b includes: fusing velocity information from the radars, selecting radar A and radar B as a first combination, and radar C and radar D as a second combination, and letting... , Substituting the velocity extension, we have: , ,in Let A be the ambiguity number of radar A. For radar B, Let C be the ambiguity number of radar. Let be the ambiguity number of radar D. By combining different ambiguity numbers, different ambiguity velocities can be obtained.

8. The method for cooperative resolution of range and velocity ambiguities based on distributed radar according to claim 7, characterized in that, Step c includes: starting from the target position, obtaining a scatter plot by taking the velocity of all targets combined by radar A and radar B, and the velocity of all targets combined by radar C and radar D.

9. The method for cooperative resolution of range and velocity ambiguities based on distributed radar according to claim 8, characterized in that, Step d includes: Assuming radar A and radar B constitute a radar AB system, the actual velocity vector of the target in the radar AB system is: ,in Let be the acute angle between the line connecting radar A and target P and the horizontal coordinate axis. Let the acute angle between the line connecting radar B and target P and the horizontal coordinate axis be the angle between them. Taking the partial derivative of this equation with respect to the variables yields the transformation matrix: The actual velocity vector of the target is obtained. The error covariance is: ,in It is a diagonal matrix. For the angle measurement accuracy of radar A, For the angle measurement accuracy of radar B, For the velocity measurement accuracy of radar A, Let T be the velocity measurement accuracy of radar B, and T be the transpose. Similarly, we can obtain... The covariance matrix obtained from the Gaussian distribution is: The squared Mahalanobis distance is: ,in Then, a chi-square test is performed using a preset threshold to filter out the target speed.

Images