Insect radar body parameter inversion method based on minimum polarization RCS

Abstract

The application discloses an insect radar body size parameter inversion method based on minimum polarization RCS. Firstly, the relationship between a polarization pattern shape and a scattering matrix eigenvalue is derived based on a symmetrical insect model, and on the basis, an analytic expression of minimum polarization RCS is derived, and finally, the relationship between the minimum polarization RCS and insect body length and weight is analyzed, and an empirical formula for inversing the insect body length and weight based on the minimum polarization RCS is given. The application provides an insect radar target body size parameter inversion method with good polarization error resistance and high precision, which is helpful to realize accurate species identification of migratory pests and improve the management ability of the migratory pests.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of insect radar, and particularly relates to an insect radar body size parameter inversion method based on minimum polarization RCS. BACKGROUND

[0002] Insect radar is an effective tool for studying migratory insects. Based on the measurement results of the insect radar, the body length, body weight, body width, wing beat frequency, horizontal speed, orientation and other parameters of the insects can be inverted. According to the inverted insect parameters, the migratory insects can be identified and the trajectory can be predicted, which is of great significance for studying the behavior of migratory insects and preventing migratory pests.

[0003] The body length and body weight of insects are important biological parameters of migratory insects, and accurate body length and body weight inversion results are of great significance for accurate species identification of migratory insects.

[0004] Based on the good mapping relationship between the radar cross-section (RCS) of the insect radar and the body length and body weight of the insects, the insect radar can realize the inversion of the body size parameters. So far, the method for inverting the body length and body weight of the insects with high precision in a single frequency band has poor polarization phase error resistance performance, and the inversion method with good polarization phase error resistance performance has poor inversion precision. Therefore, it is urgent to develop a body size parameter inversion method with high inversion precision and good polarization phase error resistance performance. SUMMARY

[0005] Therefore, the application provides an insect radar target body size parameter inversion method based on minimum polarization RCS, which has good polarization error resistance performance and body size parameter inversion precision, which helps to realize accurate species identification of migratory pests.

[0006] The application is an insect radar target body size parameter inversion method based on minimum polarization RCS, which provides an insect body size parameter inversion method with good polarization error resistance performance and high precision, and the specific steps include:

[0007] Step 1, polarization pattern shape discrimination;

[0008] Step 2, analytical calculation of minimum polarization RCS;

[0009] Step 3, construction of insect body length and body weight inversion method based on minimum polarization RCS. BRIEF DESCRIPTION OF DRAWINGS

[0010] Fig. 1 is a schematic diagram of insect polarization patterns: Fig. 1(a) is a circular polarization pattern; Fig. 1(b) is an "8" shaped polarization pattern; and Fig. 1(c) is a "cross" shaped polarization pattern.

[0011] Fig. 2 is a diagram showing the relationship between the minimum polarization RCS and the body length and weight of insects: Fig. 2(a) is a diagram showing the relationship between the minimum polarization RCS and the body length of insects; Fig. 2(b) is a diagram showing the relationship between the minimum polarization RCS and the weight of insects.

[0012] Fig. 3 is a diagram showing the accuracy comparison between the present method and the traditional method under different polarization errors: Fig. 3(a) is a diagram showing the body length inversion error comparison between different methods under different phase inconsistencies; Fig. 3(b) is a diagram showing the weight inversion error comparison between different methods under different phase inconsistencies; Fig. 3(c) is a diagram showing the body length inversion error comparison between different methods under different amplitude inconsistencies; Fig. 3(d) is a diagram showing the weight inversion error comparison between different methods under different amplitude inconsistencies. DETAILED DESCRIPTION

[0013] The present application provides an insect radar target body size parameter inversion method based on minimum polarization RCS, the basic idea of which is to first calculate the polarization pattern type according to the eigenvalue of the insect scattering matrix, then calculate the minimum polarization RCS of the corresponding polarization pattern type according to the polarization pattern type, and finally invert the body length and weight of the insect based on the mapping curve of the minimum polarization RCS and the body length and weight of the insect.

[0014] The present application will be described in detail below with reference to the accompanying drawings and examples.

[0015] Step one: polarization pattern shape discrimination

[0016] Suppose the polarization scattering matrix (PSM, Polarization Scattering Matrix) of the insect is

[0017]

[0018] where s 11 , s 12 , s 21 and s 22 are the amplitudes of the HH, HV, VH and VV polarization channels, and β, β' and γ are the phases of the HV, VH and VV polarization channels, respectively. For a single base station radar, s 12 =s 21 , β=β'.

[0019] The two eigenvalues μ1 and μ2 of the polarization scattering matrix can be calculated from equation (1), without loss of generality, assuming |μ1|≥|μ2|, then

[0020]

[0021]

[0022] The physical meaning of these two eigenvalues is the RCS when the polarization direction is parallel and perpendicular to the body axis of the insect.

[0023] Insects are typically symmetrical about their body axis. For symmetrical targets, if their body axis is parallel to the H or V polarization direction, the target scattering matrix cross-channel is 0. Assuming the insect is perfectly symmetrical about its body axis and is a parallel insect, when the insect's body axis is parallel to the H polarization, its scattering matrix can be expressed by eigenvalues ​​as:

[0024]

[0025] in:

[0026] A = |μ1| / |μ2| (5)

[0027] The relative amplitudes of the large and small eigenvalues ​​of the scattering matrix are named the difference eigenvalue amplitudes. According to the definition of A, it is easy to obtain A≥1; φ=arg(μ1 / μ2), which is the relative phase of the large and small eigenvalues ​​of the scattering matrix, where arg(·) represents the phase operation, and φ is named the difference eigenvalue phase.

[0028] The polarization pattern of an insect represents its RCS (Rapid Cross Section) under different polarization directions and can be calculated from the scattering matrix:

[0029]

[0030] Where θ represents the polarization direction, and σ(θ) represents the RCS of the insect when the polarization direction is θ.

[0031] The polarization pattern of a symmetrical target is completely symmetrical about the body axis. Based on the number of extreme points in the polarization pattern, the polarization pattern can be divided into three types: the polarization pattern has no extreme points, indicating that the target's RCS is not sensitive to the polarization direction, and the polarization pattern is circular (Fig. 1(a)); the polarization pattern has a pair of minimum points and a pair of maximum points, and the polarization pattern is shaped like an "8" (Fig. 1(b)); the polarization pattern has two pairs of maximum values ​​and two pairs of minimum values, and the polarization pattern is shaped like a cross (Fig. 1(c)).

[0032] Next, we will introduce a method for determining the shape of polarization patterns. By definition, the problem of determining the shape of polarization patterns is transformed into a problem of determining the number of σ extrema.

[0033] Based on the symmetry of the polarization pattern, it is only necessary to... Internal discussion.

[0034] If the insect's pattern is a figure-eight, then σ only has a maximum value when θ = 0. There exists a local minimum, that is, σ exists at... Monotonically decreasing, the problem is transformed into: It can be written as:

[0035]

[0036] According to equation (7), when A = 1 and φ = 0, All At this point, the polarization pattern is circular. The following discussion will focus on the case where A = 1 and φ = 0 do not simultaneously satisfy the conditions.

[0037] When sin2θ is greater than zero, according to equation (7), we can... Simplified to:

[0038] Acos 2 θ(cosφ-A)+sin 2 θ(1-Acosφ)≤0 (8)

[0039] Since A≥1 and A=1 and φ=0 do not satisfy simultaneously, we have A-cosφ>0. Therefore, equation (8) can be transformed into:

[0040]

[0041] By definition, the "8"-shaped polarization pattern requires equation (9) to always hold, therefore equation (9) is equivalent to:

[0042]

[0043] Known At that time, cot 2 If θ∈(0, +∞), then Acot 2 If θ∈(0,+∞), then equation (10) is equivalent to:

[0044]

[0045] Right now:

[0046] Acosφ≥1 (12)

[0047] Therefore, when Acosφ≥1 and A=1 and φ=0 do not simultaneously satisfy the condition, All and The polarization pattern is not always equal to 0; at this time, the polarization pattern is... The interval is monotonically decreasing, with no extreme points, and forms a figure-eight shape. Conversely, when Acosφ < 1, No longer satisfied Always less than 0, this means that the polarization pattern is in There are extreme points, and the polarization pattern is a cross shape.

[0048] The above derivation is based on the assumption that the insects are parallel and their body axes are parallel to the horizontal polarization direction. The following proves that the conclusion also applies to parallel or perpendicular insects whose body axes are not parallel to the polarization direction.

[0049] When the body axis of a parallel insect makes an angle ω with the horizontal polarization direction, its scattering matrix S ω It is obtained from the rotation angle ω of S0, that is:

[0050]

[0051] Its polarization pattern σ ω for:

[0052]

[0053] Comparing equation (6), it is found that when the angle between the body axis of a parallel insect and the horizontal polarization direction is ω, its polarization pattern is equivalent to translating ω units on the θ axis (or rotating ω around the horizontal polarization direction), and the shape and size of the polarization pattern do not change. After rotating the scattering matrix of a vertical insect by 90°, its form and parameter relationship are consistent with those of a parallel insect, which is essentially also a problem of scattering matrix rotation, and it will not change the size and shape of the polarization pattern. Therefore, the above conclusion applies to non-parallel insects and insects whose body axis is at a certain angle to the horizontal polarization direction.

[0054] Therefore, the above conclusions can be summarized as follows: the relationship between insect polarization pattern type and scattering matrix characteristics:

[0055]

[0056] Step 2: Analytical Calculation of Minimum Polarization RCS

[0057] After determining the shape of the insect polarization pattern, the next step is to calculate the minimum polarization RCSσ of the insect based on its shape. min .

[0058] For figure-eight or circular polarization patterns (Acosφ≥1), the minimum value of σ occurs at 0 or... At, σ min RCS corresponding to small eigenvalues:

[0059] σ min =|μ2| 2 (15)

[0060] For a cross-shaped polarization pattern (Acosφ < 1), σ is at 0 and All are local maxima, at which point σ is at... There exists a unique local minimum point θ′ such that Right now:

[0061] σmin = σ(θ') (16)

[0062] The following is θ' and σ min . Bring θ' into equation (7) to get:

[0063]

[0064] According to the condition, 2sin2θ' is greater than 0, then can be simplified as:

[0065] Acos 2 θ'(cosφ-A)+sin 2 θ'(1-Acosφ)=0 (18)

[0066] Replace sin 2 θ' in equation (18) with 1-cos 2 θ' to get:

[0067]

[0068] Replace cos 2 θ' in equation (18) with 1-sin 2 θ' to get:

[0069]

[0070] Substitute equations (19) and (20) into equation (6) to get:

[0071]

[0072] Thus, the complete expression of σ min is obtained, that is, the analytical expression of the minimum polarization RCS:

[0073]

[0074] Step three: Construction of insect body length and weight inversion method based on minimum polarization RCS

[0075] Based on equation (22), the minimum polarization RCS σ min of 157 insects measured in the microwave darkroom at X-band (9.5 GHz) was calculated, and the relationship between σ min and insect body length (Figure 2(a)) and body weight (Figure 2(b)) was obtained. The results show that σ min has a clear positive correlation with body weight and body length. As shown in Figure 2(a), below 30 mm, σ min and body length have a good mapping relationship, and above 30 mm, the relationship between σ min and body length becomes poor, but there is still a mapping relationship as a whole; as shown in Figure 2(a), in the whole body type section, σmin There is a very good correlation between it and body weight.

[0076] σ min The relationships with body length and weight were fitted using third-order and second-order polynomials, respectively, i.e., empirical formulas for retrieving insect body length and weight based on minimum polarization RCS:

[0077]

[0078]

[0079] Among them 1g(σ mm ()∈[-6.71,-3.36]. The fitting result is shown as the solid line in Figure 2.

[0080] Goodness-of-fit is used to evaluate the fit of the regression results to the inversion of body length and weight. Goodness-of-fit ranges from 0 to 1, with a value closer to 1 indicating a better fit between the regression curve and the observed values. Mean Relative Error (MRE) is used to evaluate the error between the estimated body length and weight and the measured body length and weight. MRE is defined as:

[0081]

[0082] Among them, M i and E i These represent the estimated value and the true value, respectively, and N is the sample size.

[0083] In the above text, σ min The goodness of fit for the fitted body weight was 0.93, and the MRE was 12.18%. The goodness of fit for the fitted body length was 0.79, and the MRE was 13.23%. Formulas (23) and (24) can be used to utilize σ min Empirical formulas for retrieving insect body length and weight, with body length inversion results in millimeters and weight inversion results in milligrams.

[0084] To verify the improvement in accuracy and anti-polarization error performance of the insect body shape parameter inversion method based on minimum polarization RCS described above compared with traditional methods, a comparison was made based on data from 157 insects measured in a microwave anechoic chamber, and compared with two existing single-band insect body shape parameter inversion methods: the determinant method (“An Insect Feature Parameter Inversion Method Based on the Determinant of Polarization Power Matrix”, Patent No.: ZL201710671464.9) and the eigenvalue method (“An Insect Feature Parameter Inversion Method Based on the Eigenvalue of Polarization Power Matrix”, Patent No.: ZL201710671461.5).

[0085] The insect scattering matrix obtained by measuring a fully polarized system can be expressed as:

[0086]

[0087] where s ij (i,j = h,v) represents the four elements of the ideal scattering matrix; M represents the measured scattering matrix, g contains the gain and attenuation of the signal in transmission, which can be compensated by effective RCS scaling, and is independent of polarization error, so in the simulation below it is assumed that g = 1; a r represents the amplitude and phase inconsistency between the H and V receiving channels of the system; a t represents the amplitude and phase inconsistency between the H and V transmitting channels of the system; C i (i = 1, 2, 3, 4) represents the cross-talk between the H and V channels when transmitting and receiving. C i (i = 1, 2, 3, 4) is usually small, and based on the measured polarization isolation of the insect radar system, it is set to C i (i = 1, 2, 3, 4) = -25 dB.

[0088] Based on this model, assuming that the amplitude and phase inconsistency of the transmitting and receiving channels is the same, and taking the scattering matrix of 157 insects as the true value, different amplitude and phase inconsistencies are set to the insect scattering matrix, so that the precision of the four methods for estimating body length and body weight under different polarization errors can be simulated.

[0089] Considering that in an actual system, after effective polarization calibration, the polarization error of the system will be controlled within a certain range, therefore, the amplitude inconsistency set in the simulation is within ±1.5 dB, and the phase inconsistency is within ±15°.

[0090] First, the influence of phase inconsistency on the body shape inversion precision of the three methods is simulated. The phase inconsistency of the system is set to vary in the range of -15° to 15°, and the amplitude inconsistency of the system is set to be error-free. The simulation results of the influence of phase inconsistency on the precision of estimating body length and body weight by the three methods are shown in Figures 3(a) and 3(b). In estimating body length and body weight, the eigenvalue method is most affected by phase error, and when the phase error increases, the average relative error of the estimated body length and body weight rapidly increases, while the method proposed in the present application and the determinant method are almost not affected.

[0091] Secondly, the influence of the simulation amplitude inconsistency on the precision of the three methods. The range of the system amplitude inconsistency is set from -1.5dB to 1.5dB, and the system phase inconsistency is set as no error. The simulation results of the influence of the amplitude inconsistency on the precision of the three methods in estimating the body length and the body weight are shown in FIG. 3(c) and FIG. 3(d). In estimating the body length and the body weight, the three methods are influenced by the amplitude error in different degrees. In estimating the body length, the determinant method is most influenced by the amplitude error, and the method proposed in the present application is least influenced. In estimating the body weight, the determinant method is least influenced, and the other two methods are nearly influenced. However, when the amplitude inconsistency is small, the precision of the method proposed in the present application in estimating the body weight is obviously higher than that of the determinant method.

[0092] The above 157 insects data based on the darkroom measurement is not used to limit the protection scope of the present application; the above is only the preferred embodiment of the present application, and is not used to limit the protection scope of the present application. The present application can have other various embodiments. Those skilled in the art can make various corresponding changes and modifications according to the present application without departing from the spirit and essence of the present application, but these corresponding changes and modifications should belong to the protection scope of the claims attached to the present application.

Claims

1. A minimum polarization RCS-based insect radar body size parameter inversion method, characterized in that, Comprising the following steps: Step one, polarization direction pattern shape discrimination; "Insect polarization direction pattern type and scattering matrix characteristic relationship" is: ； wherein is the relative amplitude of the large and small eigenvalues of the scattering matrix, is the relative phase of the large and small eigenvalues of the scattering matrix. Step two, analytical calculation of minimum polarization RCS; "Analytical expression of minimum polarization RCS" is: ； wherein, is the minimum polarized RCS of the insect, is the smallest eigenvalue of the insect scattering matrix; Step three, construction of insect body length and weight inversion method based on minimum polarization RCS.

2. The insect radar body size parameter inversion method based on minimum polarization RCS according to claim 1, characterized in that The "empirical formula for inverting insect body length and weight based on minimum polarization RCS" in the step three is: ； ； wherein .

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