Radiation source orientation system orientation matrix and orientation array optimization method

Abstract

The present application relates to radiation source direction technology. The present application discloses a kind of radiation source direction system direction matrix optimization method, comprising the following steps: establishing radiation source direction matrix;Obtain the non-zero singular value of direction matrix;According to the minimum non-zero singular value σ min And the number of elements m of direction matrix, determine the optimal direction matrix of radiation source direction system.According to another aspect of the present application, a kind of radiation source direction system direction array optimization method is disclosed, the noise energy affecting radiation source direction system is classified, and the optimal direction array is determined according to the non-zero singular value of direction matrix for different noise energy distribution characteristics.The present application is for the performance optimization method of existing direction method, and lays the foundation for the optimal design of the polyhedral array of direction system.Using the optimal direction matrix and array provided by the present application, the direction accuracy of radiation source direction system can be effectively improved, and the anti-interference ability of direction system is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radiation source orientation, in particular to a radiation source orientation system performance optimization method, and more particularly to a radiation source orientation system orientation matrix and orientation array optimization method. BACKGROUND

[0002] Radiation sources, including optical radiation sources, electromagnetic wave radiation sources, radioactive radiation sources, etc., can all radiate energy outward. Radiation source orientation technology is a technology for observing the direction of a spatial radiation source.

[0003] Radiation source orientation technology mainly calculates the spatial direction of a radiation source through the received radiation energy of observation points with known spatial positions, such as array elements arranged on a polyhedron. The technologies disclosed in Chinese Patent Publication Nos. CN101907457A, CN102798374A, and CN108181606A are all such radiation source orientation technologies.

[0004] Passive radiation source orientation technology has an important position and role in military and civilian application fields such as navigation, spaceflight, and electronic warfare. The technology realizes orientation based on the basic characteristic radiation energy of a radiation source, and theoretically satisfies passive orientation of all radiation sources, thus having great advantages in application range.

[0005] The technology for orienting a radiation source using radiation energy only requires that the ratio of the radiation energy detected and output by an array element to the energy radiated by the radiation source on the array element detection surface be constant, and the measurement of radiation energy is relatively simple, thus also having advantages in system implementation.

[0006] Radiation source orientation based on polyhedral array element energy is a basic method for orienting a radiation source using radiation energy. It obtains the spatial angles of a radiation source, i.e., the azimuth angle and the zenith angle, by solving an orientation equation including a radiation source vector. In orientation applications, orientation noise caused by internal and environmental interference of a system is inevitable, and the direct calculation of a radiation source vector through a radiation source orientation equation usually has no solution, which makes the method for directly solving the orientation equation to orient a radiation source usually unimplementable. Therefore, a method for estimating a radiation source vector through a radiation source orientation equation by using the least square method is first proposed. To improve the orientation accuracy of a radiation source and compensate for orientation noise caused by internal interference of a system, an algorithm and a method for optimizing the design of a polyhedral structure are subsequently proposed. However, there are few reports on in-depth research on the performance of the least square orientation, and in particular, there is no relevant research achievement on the performance evaluation of a radiation source orientation system, the orientation matrix of a radiation source orientation system, and the optimization method of an orientation array, which seriously hinders the optimization and improvement of the performance of a radiation source orientation. SUMMARY

[0007] The main purpose of the present application is to provide a radiation source orientation system orientation matrix and orientation array optimization method, which provides a basis for optimizing the design of the performance of the radiation source orientation system.

[0008] In order to achieve the above-mentioned purpose, according to one aspect of the embodiment of the present application, a radiation source orientation system orientation matrix optimization method is provided, characterized in that it comprises the following steps:

[0009] establishing a radiation source orientation matrix;

[0010] obtaining the non-zero singular values of the orientation matrix;

[0011] determining the optimal orientation matrix of the radiation source orientation system according to the minimum non-zero singular value σ min of the orientation matrix and the number m of elements constituting the orientation matrix.

[0012] Further, when the interference energy is bounded, among all the orientation matrices of the radiation source orientation system, the orientation matrix with the maximum minimum non-zero singular value σ min is the optimal orientation matrix.

[0013] Further, when the interference energy is unbounded but the average interference energy is bounded, among all the orientation matrices of the radiation source orientation system, the matrix with the minimum value is the optimal orientation matrix.

[0014] Further, when both bounded interference energy and unbounded interference energy but bounded average interference energy exist, the orientation matrix that simultaneously satisfies the minimum interference coefficient κ and the minimum average interference coefficient κ a is the optimal orientation matrix.

[0015] wherein k = 1 / σ min , m is the number of elements constituting the orientation matrix, m ≥ 3; and ε is the directional noise vector.

[0016] According to another aspect of the embodiment of the present application, a radiation source orientation system orientation array optimization method is provided, characterized in that the interference energy affecting the radiation source orientation system is classified, and the optimal orientation array is determined according to the non-zero singular values of the orientation matrix for different interference energy distribution characteristics.

[0017] Further, when the interference energy is bounded, all the elements of the optimal orientation array are irradiated by the radiation source in a given detection field of view, and the minimum non-zero singular value σ min of the orientation matrix formed by all the elements of the optimal orientation array satisfies the following relationship:

[0018]

[0019] ​Wherein, m is the number of elements of the directional matrix, m≥3.

[0020] Further, when the interference energy is unbounded but the average interference energy is bounded, in all directional matrices of the optimal directional array irradiated by the elements, there is at least one directional matrix whose minimum nonzero singular value σ min Satisfying the relationship:

[0021]

[0022] Wherein, m is the number of elements of the directional matrix, m≥3.

[0023] Further, when both the bounded interference energy and the unbounded interference energy but the average interference energy is bounded exist, in the given detection field of view, all elements of the optimal directional array are irradiated by the radiation source, and the minimum nonzero singular value σ min Satisfying the relationship:

[0024]

[0025] Wherein, m is the number of elements of the directional matrix, m≥3.

[0026] The beneficial effect of the present application is to provide a performance optimization method for the existing directional method, and to lay a foundation for the optimal design of the polyhedral array of the directional system. The optimal directional matrix and array provided by the present application can effectively improve the directional accuracy of the radiation source directional system and improve the anti-interference ability of the directional system.

[0027] The present application will be further described below in conjunction with the drawings and specific embodiments. Additional aspects and advantages of the present application will be partially given in the following description, partially will become apparent from the following description, or will be understood by practicing the present application. BRIEF DESCRIPTION OF DRAWINGS

[0028] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application, and are incorporated in and constitute a part of this specification. The illustrations are provided to explain the present application and are not intended to limit the present application in an inappropriate manner. In the drawings:

[0029] Figure 1 It is a schematic diagram of the zenith angle and azimuth angle of the vector;

[0030] Figure 2 It is a schematic diagram of the geometric relationship between the radiation source vector and the element mounting surface in the radiation source directional coordinate system;

[0031] Figure 3 It is a schematic diagram of the geometric model of the radiation source directional error. DETAILED DESCRIPTION

[0032] It should be noted that, unless otherwise specified, the specific embodiments, examples, and features described in this application can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and the following description.

[0033] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of specific embodiments and examples. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. All other embodiments and examples obtained by those skilled in the art based on the specific embodiments and examples of the present invention without creative effort should fall within the scope of protection of the present invention.

[0034] The radiation source orientation correlation technology involved in this invention is described below.

[0035] 1. Radiation source orientation

[0036] It is assumed that the rays from the radiation source to the observation point are parallel, or that the distance from the radiation source to the observation point is far enough that the rays from the radiation source to the observation point are approximately parallel, such as sunlight shining on the ground.

[0037] To describe the spatial orientation of a radiation source and its radiant energy at the observation point, we construct a vector pointing towards the radiation source, with a magnitude equal to the irradiance (radiant energy per unit area of ​​the irradiated object's surface) of the radiation source incident perpendicularly on the plane, and define it as the radiation source vector.

[0038] In addition, to describe the direction of a vector in a Cartesian coordinate system, we define two angles for the vector: azimuth and zenith angle. For example... Figure 1 As shown, the azimuth angle of a vector is the angle from which the y-axis rotates clockwise (or from north to east on Earth) to the projection of the vector onto the xoy coordinate plane, and the zenith angle of the vector is the angle between the z-axis and the vector.

[0039] A radiation source orientation coordinate system is established with the observation point as the origin O. The geometric relationship between the radiation source vector and the mounting surface of the array elements on the polyhedron in this coordinate system is as follows: Figure 2 As shown. Figure 2 In the diagram, the azimuth angle of the radiation source vector r is α. s The zenith angle is γ s ; Illuminated array element p on the polyhedron i The unit normal vector n of the mounting surface (i∈{1,2,…,m},m≥3) i The azimuth angle is α i The zenith angle is γ i ; Radiation source vector r and unit normal vector n i The included angle is

[0040] According to the cosine law of radiation, the irradiance of any surface varies with the cosine of the angle between the direction of radiation energy propagation and the normal of the surface, we have Figure 2 The irradiance of the array element p i by the radiation source is (|r| is the irradiance of the array element p by the radiation source vertically incident on the array element). Since Therefore, the irradiance of the radiation source on the plane is equal to the inner product of the radiation source vector and the unit normal vector of the irradiated plane.

[0041] Generally, there is a conversion factor between the irradiance of the radiation source on the array element mounting surface and its measured value, such as the output conversion efficiency of a solar cell panel to solar radiation energy. Let the conversion factor between the irradiance of the radiation source on the array element mounting surface p i and its measured value s i be η i , then s i can be expressed as:

[0042]

[0043] According to equation 2-1, we can obtain a matrix equation with the radiation source vector as the unknown vector through the m irradiated array elements on the polyhedron:

[0044]

[0045] In equation 2-2, (n1 n2 … n m ) T is composed of the unit normal vectors of the m irradiated array elements. In the spatial position and orientation coordinate system of the radiation source, n i = (sinα i sinγ i cosα i sinγ i cosγ i ) T ,

[0046] r = |r| (sinα s sinγ s cosα s sinγ s cosγ s ) T , |r| is equal to the irradiance of the array element by the radiation source vertically incident on the array element.

[0047] Assuming (n1 n2 … n m ) TIf the rank is 3, meaning the normals to the mounting surfaces of the m illuminated array elements are non-coplanar, then matrix equation 2-2 has a unique solution. Let the coefficient matrix of matrix equation 2-2 be (n1 n2 … n m ) T For H, we have:

[0048]

[0049] Substituting equation 2-3 into equation 2-2, we get

[0050]

[0051] Under ideal conditions, using the same type of measuring device, array element p i The conversion coefficient η between the irradiance on the mounting surface and its measured value i It is equal to the constant η (η>0). Therefore, equation 2-4 can be simplified to:

[0052]

[0053] Since η > 0, ηr is in the same direction as the radiation source vector r, so the direction of the radiation source vector can be determined by solving for vector ηr. Furthermore, the irradiance of the radiation source on the mounting surface of the irradiated array element is measurable. Since the unit normal vector of the mounting surface of the array element on the polyhedron is known, the coefficient matrix H is also known. Therefore, the direction of the radiation source vector can be obtained by solving the linear equation system 2-5. Thus, let s = (s1 s2 … s m ) T From equation 2-5, the orientation equation of the radiation source can be obtained as follows:

[0054] Hηr=s (2-6)

[0055] Since the rank of the coefficient matrix H is 3, the radiation source vector has a unique solution:

[0056]

[0057] Since the radiation source vector *r* points towards the radiation source, the spatial orientation of the radiation source can be determined by solving the radiation source orientation equation. According to the linear least squares method, the radiation source vector calculated by Equation 2-7 is actually the least squares solution of the radiation source vector. Therefore, Equation 2-7 is also the least squares estimate of the radiation source vector. Thus, we can simply refer to the above method for orienting the radiation source as the least squares orientation of the radiation source, and the coefficient matrix *H* of the orientation equation can be simply referred to as the least squares orientation matrix. This invention mainly involves the performance estimation of this orientation method and the performance optimization based on it.

[0058] In the equation of the orientation of the radiation source, the least square orientation matrix H is composed of the unit normal vectors of the mounting surfaces of the illuminated elements whose normals are not coplanar. Therefore, when the number of the illuminated elements on the polyhedral array is greater than 3 and their mounting surfaces satisfy the condition that their normals are not coplanar, the least square orientation matrix H obtained by the array will not be unique.

[0059] 2. Orientation error

[0060] In practical applications, there are internal disturbances in the orientation system caused by the internal noise of the irradiance measuring device and the position deviation of the elements on the polyhedron, and external disturbances caused by the multipath propagation and the interfering radiation sources usually existing in the external environment. Due to the influence of these disturbances, there is noise in the measured value of the irradiance on the mounting surface of the element irradiated by the radiation source. For convenience of description, we define the noise in the measured value of the irradiance on the mounting surface of the element caused by the internal and external disturbances of the orientation system as orientation noise. At the same time, in the constant term of the equation of the orientation of the radiation source (i.e. the vector s in equation 2-7), the disturbance vector composed of the orientation noise is defined as the orientation noise vector ε.

[0061] In the orientation application, due to the existence of the orientation noise vector ε, there is usually a deviation between the least square solution of the radiation source vector and the true value of the radiation source vector r. Let the least square solution of the radiation source vector be r', and the difference between the radiation source vector and its least square solution be the estimation error Δr of the radiation source vector. Through the geometric relationship between the radiation source vector and its least square solution, we can define their included angle as the orientation error θ of the radiation source.

[0062] Assuming that the radiation source vector and its estimation error satisfy the condition |Δr| < |r|. The geometric relationship between the orientation error of the radiation source, the radiation source vector, the least square solution of the radiation source vector and its estimation error is shown in Figure 3 .

[0063] From Figure 3 it can be seen that the orientation error θ varies with the estimation error Δr. Keeping |Δr| unchanged, when the error Δr is perpendicular to the least square solution of the radiation source vector r', the orientation error θ reaches the maximum value θ max ; but when the error Δr is in the same direction as the radiation source vector r or in the opposite direction, the orientation error is 0. When |Δr| < |r| is satisfied, according to the geometric relationship of Figure 3 , the orientation error of the radiation source can be expressed as:

[0064] θ ≤ θ max = arcsin(|Δr| / |r|) (3-4)

[0065] Upper bound of orientation error

[0066] Substitute the directional noise vector ε into the least square estimation of the radiation source vector 2-7, the error estimation of the radiation source vector is obtained as:

[0067]

[0068] Since the directional matrix H is a column full rank matrix of m x 3, it is known that the column space of the directional matrix is a closed subspace of the m-dimensional real vector space R m . Thus, according to the orthogonal decomposition theorem of the vector, it is known that the m-dimensional directional noise vector ε has a unique decomposition vector v and u in the column space of the directional matrix, such that ε = v + u, where v is the projection vector of ε in the column space, and u is the projection vector of ε in the orthogonal complement space of the column space. Since the column space of the directional matrix H is orthogonal to the vector u, it is known that H T u = 0. Substitute ε = v + u into equation 3-5, and it is known that:

[0069]

[0070] It is known from the comparison of equations 3-5 and 3-6 that in the least square direction of the radiation source, the interference radiation source direction is actually only the projection of the directional noise vector in the column space of the directional matrix, rather than the projection in the orthogonal complement space of the column space.

[0071] According to the properties of the norm, ‖Tx‖2≤‖T‖2‖x‖2, where T is a linear operator and x is a real vector. Since the 2-norm of the real vector x is equal to its vector modulus, it is known from equation 3-6 that:

[0072]

[0073] Divide both sides of inequality 3-7 by |r|, and it is known that:

[0074]

[0075] Substitute equation 3-8 into equation 3-4, and it is known that:

[0076]

[0077] According to the establishment condition of equation 3-4: |Δr| < |r|, it is known that θ max <π / 2, and thus it is known that inequality 3-9 is established by satisfying Generally, |v| is much smaller than η|r|, and for smaller ‖(H T H) -1 H T ‖2, it is easy to satisfy. Thus, for smaller ‖(H T H) -1 H TThe minimum directional error upper bound of the least square direction of the radiation source can be described by inequality 3-9.

[0078] According to the property of singular value, the non-zero singular value of matrix H is the positive square root of the non-zero eigenvalue of matrix (H T H) T . Similarly, the non-zero singular value of matrix (H T H) -1 H T is the positive square root of the non-zero eigenvalue of matrix (H T H) -1 H T ((H T H) -1 H T ) T . However, (H T H) -1 H T ((H T H) -1 H T ) T = (H T H) -1 , the eigenvalue of (H T H) -1 is reciprocal to the eigenvalue of matrix H T H. Therefore, the non-zero singular value of matrix (H T H) -1 H T is reciprocal to the non-zero singular value of matrix H.

[0079] Let the minimum non-zero singular value of matrix H be σ min . Since the spectral norm of a matrix is equal to its maximum non-zero singular value, ||(H T H) -1 H T ||2 = 1 / σ min . Generally, v is unknown, so |v| 2 / |ε| 2 = μ. Substituting 1 / σ min and μ into inequality 3-9, the error relationship of the least square direction of the radiation source is:

[0080]

[0081]

[0082] where η |r| is the irradiance of the radiation source vertically incident on the plane, which is determined by the radiation source energy of the radiation source; σ min is the singular value of the directional matrix H; |ε| 2 ​is the square of the modulus of the projection vector of the directional noise vector ε on the column space of the directional matrix H, and we call it the energy of the directional noise; μ is the square of the modulus of the projection vector of the directional noise vector ε on the column space of the directional matrix H 2 and the square of the modulus of ε 2 , which is determined by the directional noise vector ε and the directional matrix H. Therefore, the directional error of the radiation source is related to three factors: the directional noise, the directional matrix, and the radiation energy of the radiation source.

[0083] The upper bound of the directional error of the radiation source (that is, the least upper bound of the directional error) is defined as θ sup According to formula 3-10, its expression is:

[0084]

[0085] In practical applications, the ratio μ is usually unknown. According to the Pythagorean theorem, the directional noise vector ε and its orthogonal component v satisfy the inequality |v| 2 ≤ |ε| 2 Therefore, the value of μ cannot be greater than 1, that is, μ ≤ 1. When the directional noise vector is completely projected on the column space of the directional matrix H, μ is the maximum value 1, and θ sup takes the maximum value. Therefore, the θ sup when the directional noise vector is completely projected on the column space of the directional matrix (that is, μ = 1) can be defined as its maximum upper bound θ sup_max . According to formula 3-11, the expression of the maximum upper bound θ sup_max is obtained as:

[0086]

[0087] Radiation source directional system performance evaluation method

[0088] According to the definition of the upper bound of the directional error of the radiation source, the least square directional performance of the radiation source can be described by the least square directional error upper bound.

[0089] First, according to the error relationship of the least square direction of the radiation source , the directional error θ of the radiation source is obtained.

[0090] Second, the upper bound θ sup of the directional error θ is obtained:

[0091]

[0092] wherein μ is the ratio of the square of the modulus of the projection vector of the directional noise vector v on the column space of the directional matrix |v| 2 and the square of the modulus of ε 2 ; ε is the directional noise vector; σ minis the minimum nonzero singular value of the steering matrix; η is the conversion coefficient of the irradiance of the radiation source on the array mounting plane and its measured value; r is the radiation source vector.

[0093] In the third step, the maximum value θ sup of the expression is obtained: sup_max

[0094]

[0095] The value of θ sup_max can then be used to determine the performance of the radiation source steering system.

[0096] However, in practical applications, the steering noise caused by the internal and external environment of the steering system is usually random and unknown, so the projection of the steering noise in the column space of the least squares steering matrix is also usually random and unknown.

[0097] In the following, the maximum upper bound of the radiation source steering error is used to indirectly evaluate the least squares steering performance of the radiation source based on the characteristics of the steering interference energy distribution.

[0098] Characteristics of the steering interference energy distribution

[0099] In practical applications, the radiation energy of any radiation source cannot be unbounded. Therefore, the interference energy on the array mounting plane caused by the multipath propagation in the external environment and other interference radiation sources is always bounded. Since the interference energy on the array mounting plane is bounded, according to the law of conservation of energy, the noise component caused by the internal interference of the steering system (including the internal working noise of the irradiance measurement device and the position error of the array mounting plane) in the measured value of the irradiance at each array element is also bounded. Thus, the interference energy in the measured value of the irradiance at each array element is bounded.

[0100] Let the number of array elements constituting the least squares steering matrix be m (m > 3). When the value of m is finite, since the interference energy in the measured value of the irradiance at each array element is bounded, the steering interference energy |ε| 2 must be bounded. Conversely, when the value of m is large enough, the steering interference energy |ε| 2 may be bounded or unbounded. However, since the interference energy in the measured value of the irradiance at each array element is bounded, the average energy |ε| 2 / m must be bounded. For example, when m → ∞, the energy of the steering noise caused by the failure of a finite number of array elements is always bounded, but for atmospheric uniform scattering, the steering noise it produces in the array irradiance measurement is a constant, and its total energy |ε| 2 → ∞ but the average energy |ε| 2 / m is bounded.

[0101] ​In summary, the directional interference energy of a radiation source may be bounded or unbounded, but its average energy is always bounded. Therefore, the directional noise of a radiation source can be divided into two categories: noise with bounded energy and noise with unbounded energy but bounded average energy.

[0102] Performance evaluation methods for directional systems with two different types of noise

[0103] Based on the above-mentioned interference energy distribution characteristics, the directional noise of the radiation source can be classified into the following categories: 1) performance evaluation under the scenario where the directional interference energy is bounded; 2) performance evaluation under the scenario where the directional interference energy is unbounded but the average energy is bounded.

[0104] 1) Total energy of directional noise |ε| 2 There exists a bounded value

[0105] According to the definition of a radiation source vector, the magnitude |r| of the radiation source vector is independent not only of the least-squares orientation matrix of the radiation source orientation but also of the orientation noise. Therefore, in the error relationship of the least-squares orientation of the radiation source, the magnitude |r| of the radiation source vector is constant. Furthermore, the conversion coefficient η for the irradiance measurement of each array element is usually also a constant. Thus, it can be seen from Equation 3-12 that the maximum upper bound θsup of the radiation source orientation error is... _max The minimum non-zero singular value σ of the least squares orientation matrix min It is confirmed that they satisfy the following relationship:

[0106]

[0107] Define the interference coefficient of the least squares orientation matrix as 1 / σ min , and label it as κ. Because sinθ sup_max With θ sup_max Monotonically increasing (θ) sup_max Within the range of 0 to π / 2, the orientation error of the radiation source is θ. sup_max It cannot be less than 0. From equation 3-13, we can obtain κ and θ. sup_max Satisfying Relationship:

[0108] θ sup_max ∝κ (3-14)

[0109] Based on the above analysis, in applications where directional interference energy is bounded, the maximum upper bound of the radiation source's directional error is determined not only by the interference coefficients of the least squares orientation matrix, but also by the co-current changes in the same direction. In practical applications, since the mounting planes of the constituent elements of the least squares orientation matrix on the polyhedron are always known, it can be assumed that the least squares orientation matrix itself is also always known. Therefore, in this application scenario, the interference coefficients of the least squares orientation matrix can be used to evaluate the least squares directional performance of the radiation source.

[0110] 2) the average energy of the directional noise |ε| 2 There is a bounded value for m

[0111] According to formula 3-12, the maximum upper bound of the radiation source directional error is determined by the number of elements m of the least square directional matrix and its minimum non-zero singular value σ min Determination, they satisfy the relationship:

[0112]

[0113] Define the average interference coefficient of the least square directional matrix as Marked as κ a . According to formula 3-15, κ a And θ sup_fi Satisfy the relationship:

[0114] θ sup_max ∝κ a (3-16)

[0115] According to the above analysis, in the application scenario where the directional interference energy is unbounded but the average energy is bounded, the maximum upper bound of the radiation source directional error is not only determined by the average interference coefficient of the least square directional matrix, but also changes in the same direction. Similarly, since the least square directional matrix is always known, in this application scenario, the least square directional performance of the radiation source can be evaluated by using the average interference coefficient of the least square directional matrix.

[0116] Radiation source directional system directional matrix optimization method

[0117] Reducing the maximum upper bound of the radiation source directional error will generally improve the directional accuracy of the radiation source. According to the above radiation source directional system performance evaluation method, the radiation source directional noise is composed of two types of noise with bounded energy and unbounded energy but bounded average energy. However, under the interference of these two types of noise, the maximum upper bound of the radiation source directional error is determined by the least square directional matrix. Based on this idea, the least square directional matrix that makes the maximum upper bound of the radiation source directional error smaller can be selected to generally improve the directional accuracy of the radiation source, thereby realizing the optimization of the radiation source directional performance.

[0118] The steps of the radiation source directional system directional matrix optimization method are as follows:

[0119] First, establish the radiation source directional matrix;

[0120] Second, find the non-zero singular value of the directional matrix;

[0121] Third, according to the minimum non-zero singular value σ min Of the directional matrix and the number of elements m of the directional matrix, determine the optimal directional matrix of the radiation source directional system.

[0122] According to the characteristics of the directional interference energy distribution, the performance of the least square directional radiation source can be optimized by the following method:

[0123] The directional noise in the directional application of the radiation source is divided into the following three types:

[0124] The first type is the bounded energy noise (the square of the modulus of the directional noise vector is bounded, i.e. |ε 2 is bounded), which is usually generated by the internal interference of the directional system;

[0125] The second type is the noise with unbounded energy but bounded average energy (the square of the modulus of the directional noise vector is unbounded, but the ratio of the square of the modulus of the directional noise vector to the number of array elements m is bounded, i.e. |ε 2 is unbounded, and |ε 2 / m is bounded), which is usually generated by the external environmental interference;

[0126] The third type is the mixed noise with bounded energy and unbounded energy but bounded average energy.

[0127] When the interference energy is bounded, the minimum of the least square directional matrix interference coefficient k should be taken as the criterion to select the optimal directional matrix to minimize the maximum upper bound of the directional error of the radiation source.

[0128] That is, in all the directional matrices of the radiation source directional system, the directional matrix with the maximum minimum non-zero singular value σ min is the optimal directional matrix.

[0129] When the interference energy is unbounded but the average interference energy is bounded, the minimum of the mean value of the least square directional matrix interference coefficient κ a should be taken as the criterion to select the optimal directional matrix to minimize the maximum upper bound of the directional error of the radiation source.

[0130] That is, in all the directional matrices of the radiation source directional system, the matrix with the minimum value of κ is the optimal directional matrix.

[0131] When both the bounded interference energy and the unbounded interference energy but the average interference energy are bounded exist, since it is composed of the first type and the second type of directional noise, the minimum of both the least square directional matrix interference coefficient and the mean value of the interference coefficient should be taken as the criterion to select the optimal directional matrix to minimize the maximum upper bound of the directional error of the radiation source. That is, the matrix with both the interference coefficient κ and the mean value of the interference coefficient κ a are minimum is the optimal directional matrix.

[0132] According to the optimization criterion of the optimal steering matrix above, the optimal steering matrix of the third type of directional noise is also the optimal steering matrix of the first type and the second type of directional noise. Therefore, it is applicable to the optimization of the least square direction finding performance of the radiation source under any directional noise interference.

[0133] Selection of the optimal steering matrix

[0134] According to the definition of the least square direction finding matrix H, it is composed of the unit normal vectors of the installation planes of the m array elements on the directional array, and is a column full rank matrix of m x 3. According to the properties of singular values, the matrix H T The trace of H is equal to the sum of the squares of the singular values of the steering matrix H, and the matrix H T The trace of H is equal to m. Therefore, it can be deduced that the sum of the squares of the singular values of the steering matrix H is equal to m. Considering that the steering matrix H is column full rank, the number of its non-zero singular values is equal to 3 and their sum of squares is m, so the minimum non-zero singular value σ min The inequality should be satisfied:

[0135]

[0136] When the non-zero singular values of the steering matrix H are equal,

[0137] According to the definition of the interference coefficient κ of the least square direction finding matrix, from equation 3-16, we have:

[0138]

[0139] As can be seen from equation 3-17, if the number of array elements constituting the steering matrix is given, the minimum value of κ exists and is determinable. In practical applications, the number of array elements of the directional array is determined, and the least square direction finding matrix is composed of the unit normal vectors of the installation planes of the array elements. Therefore, the maximum number of array elements constituting the least square direction finding matrix is also determined, and accordingly the minimum value of the interference coefficient always exists and is determinable. Therefore, the minimum value of the interference coefficient of the least square direction finding matrix under the condition that the number of array elements of the steering matrix is given is defined as κ min .

[0140] Assuming that the non-zero singular values of the steering matrix H are equal, i.e. From equation 3-17, we have:

[0141]

[0142] Similarly, κ a_min is defined as the minimum value of the interference coefficient κ a of the least square direction finding mean value. According to the relationship between the least square direction finding interference coefficient and the mean value interference coefficient, from equation 3-18, we have:

[0143]

[0144] When the non-zero singular values of the least square steering matrix are equal, it can be seen from the equations 3-18 and 3-19 that both the interference coefficient and the mean interference coefficient of the least square steering matrix are its minimum values. According to the selection criterion of the optimal steering matrix, it can be deduced that for the directional noise with arbitrary energy distribution, the optimal steering matrix of the least square steering of the radiation source satisfies the basic characteristic that the non-zero singular values are equal.

[0145] Optimization method of the directional array of the radiation source directional system

[0146] The interference energy affecting the radiation source directional system is classified, and according to the directional matrix non-zero singular value, the optimal directional array is determined according to the directional matrix non-zero singular value for different interference energy distribution characteristics.

[0147] According to the optimization method of the directional matrix of the radiation source directional system, the performance of the least square steering of the radiation source can be optimized by its optimal steering matrix. However, according to the definition of the least square steering matrix, its optimal steering matrix is composed of the unit normal vectors of the array element installation plane. Therefore, the optimization of the performance of the least square steering of the radiation source is the optimization of the directional array structure design.

[0148] In practical applications, the number of constituent elements of the radiation source directional array is bounded, so the maximum number of available elements of the directional array design is determinable. It is assumed that the number of elements of the directional array design is m. Since the number of elements constituting the least square steering matrix cannot be greater than the total number of elements of the array, it can be known that there is no least square steering matrix with more than m elements in the array.

[0149] According to equation 3-18, to obtain the optimal steering matrix under the condition of unbounded interference energy, that is, the interference coefficient is equal to the minimum value The structure of the array should satisfy:

[0150] (1) There is a directional matrix with m constituent elements, that is, all the elements of the directional array are irradiated by the radiation source;

[0151] (2) The directional matrix with m constituent elements has the same non-zero singular value.

[0152] According to equation 3-19, when the non-zero singular values of the least square steering matrix are equal, the minimum value of the mean interference coefficient of the least square steering matrix is a constant Therefore, for any matrix satisfying the basic characteristics of the optimal steering matrix of the least square steering of the radiation source, its mean interference coefficient is the minimum value Therefore, to obtain the optimal steering matrix under the condition that the interference energy is unbounded but the mean value of the interference energy is bounded, the structure of the array should satisfy:

[0153] (1) There exists a non-zero singular value equal to the steering matrix.

[0154] The implementation array structure of the optimal steering matrix under the condition of unbounded interference energy and bounded average interference energy is compared with that of the optimal steering matrix under the condition of unbounded interference energy. It is known that the implementation array of the latter is necessarily the implementation array of the former. In addition, according to the optimal steering matrix selection criterion of the third type of directional noise, the optimal steering matrix of the third type of directional noise is necessarily the optimal steering matrix of the first and second types of directional noise. Therefore, for any energy distribution of directional noise, the implementation array of the optimal steering matrix can be designed according to the following criteria:

[0155] (1) All elements of the array are illuminated by the radiation source in the given detection field of view;

[0156] (2) The directional matrix formed by all elements of the array has the same non-zero singular value.

Claims

1. A method of optimizing a directional array of a directional source orientation system, characterized by, The noise energy affecting the radiation source orientation system is classified, and according to different noise energy distribution characteristics, the optimal orientation array is determined according to the non-zero singular value of the orientation matrix; When the interference energy is bounded, all the array elements of the directional array are illuminated by the radiation source on a given detection field of view, and the minimum nonzero singular value σ of the directional matrix composed of all the array elements is min satisfies the relationship: Wherein, m is the number of elements constituting the orientation matrix, m≥3; The orientation array corresponding to the orientation matrix is an optimal orientation array; When the interference energy is unbounded, but the average value of the interference energy is bounded, there is at least one minimum nonzero singular value σ of a directional matrix of all directional matrices formed by the illuminated elements of the directional array min satisfies the relationship: Wherein, m is the number of elements constituting the orientation matrix, m≥3; The orientation array corresponding to the orientation matrix is an optimal orientation array; When both bounded and unbounded but average bounded interference energy exist simultaneously, all the elements of the directional array are illuminated by the radiation source in the given detection field of view, and the minimum nonzero singular value σ min satisfies the relationship: Wherein, m is the number of elements constituting the orientation matrix, m≥3; The orientation array corresponding to the orientation matrix is an optimal orientation array. Wherein, m is the number of elements constituting the orientation matrix, m≥3; The orientation array corresponding to the orientation matrix is an optimal orientation array.

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