High-precision monopulse angle measurement method based on third-order Taylor expansion

Abstract

The high-precision monopulse angle measurement method based on third-order Taylor expansion is suitable for detecting a target object by an airborne radar, and comprises the following steps: establishing an array echo model of a non-ideal radar; performing self-calibration of the non-ideal radar based on the array echo model; radar non-ideal compensation is carried out on the sum and difference beam weights of the airborne radar; beam forming is carried out according to echoes, detected by the airborne radar, of the target object; and determining an angle measurement model of the sum-difference monopulse, performing third-order Taylor expansion on the angle measurement model, and determining an angle estimation value. Compared with a rationality radar monopulse angle measurement technology based on first-order Taylor expansion, non-ideal error compensation is carried out on the radar, third-order Taylor expansion is carried out on the monopulse ratio, angle measurement deviation caused by radar non-ideal and fixed angle discrimination slopes is compensated, and the angle measurement precision is effectively improved within the main beam range.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a high-precision single pulse angle measurement method based on third-order Taylor expansion. Background Art

[0002] The acquisition of the angle of the target is the basis for the effectiveness of airborne radar systems such as surveillance, detection, and fire control. Therefore, high-precision estimation of the angle parameters of the target is a key core capability of modern airborne radars. With the introduction of concepts such as distributed interference environment and network-centric information processing, the interference scenarios of the composite electromagnetic environment faced by airborne radars are becoming more and more complex. The long-term use of airborne radars under high-intensity interference causes some channels to work abnormally. Multi-channel airborne radars have non-ideal errors, which makes it difficult for the sum-difference single pulse technology to meet the needs of modern airborne radar platforms for high-precision measurement of target angles.

[0003] The sum-difference monopulse technology applied to an ideal airborne radar can accurately measure the angle information of the target. The algorithm is generally based on the first-order Taylor expansion of the monopulse ratio proposed by Nickel, and the angle detection curve is approximated by a straight line with a fixed slope. Since the ideal angle detection curve has a large nonlinearity at a distance away from the beam pointing angle, the angle measurement deviation at these positions is large. In addition, in order to expand the linear angle measurement range and reduce the nonlinearity of the adaptive monopulse angle detection curve, Yu KaiBor et al. proposed a method of using three-point or multi-point slope constraints at the deviation from the beam pointing to optimize the difference beam pattern, but there are certain limitations:

[0004] 1) The algorithm has limited scope for expanding the linear angle measurement range of the target and depends on the prerequisite constraints, so it cannot be applied to the adaptive beamforming algorithm under specific interference;

[0005] 2) The algorithm does not take into account the radar non-ideal error. The angle measurement accuracy is greatly affected by the inconsistency error of the radar channel, and it is impossible to ensure high-precision angle measurement under long-term use of the airborne radar;

[0006] 3) The algorithm adds additional constraints, which correspondingly reduces the degrees of freedom of the adaptive algorithm, resulting in a decrease in the output signal-to-interference-noise ratio of the adaptive difference beam, worsening the shape of the difference beam pattern, and significantly increasing its sidelobe level. Summary of the invention

[0007] In view of this, the high-precision single-pulse angle measurement method based on the third-order Taylor expansion of the present invention can compensate for the random angle measurement error in the entire airspace caused by radar non-ideality and the mean angle measurement deviation caused by the fixed angle detection slope when the ideal radar single-pulse angle measurement method has non-ideal radar and the target deviates from the beam pointing angle, thereby greatly improving the angle measurement accuracy of non-ideal airborne radars.

[0008] A high-precision single pulse angle measurement method based on third-order Taylor expansion is suitable for airborne radar detection of targets. The high-precision single pulse angle measurement method includes:

[0009] S101: Establishing an array echo model of a non-ideal radar;

[0010] S102: performing self-calibration of a non-ideal radar based on the array echo model;

[0011] S103: performing radar non-ideal compensation using sum and difference beam weights of the airborne radar;

[0012] S104: performing beam forming according to the echo of the target object detected by the airborne radar;

[0013] S105: Determine an angle measurement model for a single sum and difference pulse, perform a third-order Taylor expansion on the angle measurement model, and determine an angle estimation value.

[0014] Beneficial Effects

[0015] The angle measurement method that only uses the first-order Taylor expansion for the ideal airborne radar single pulse has the problem of angle measurement deviation when the airborne radar is irrational and deviates from the beam pointing angle. The high-precision single pulse angle measurement method based on the third-order Taylor expansion of the present invention can compensate for the random angle measurement error in the entire airspace caused by the non-ideal radar and the mean angle measurement deviation caused by the fixed angle detection slope, and obtain a true fitting angle detection curve within a large angle measurement range. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 It is a schematic diagram of the process of the present invention;

[0018] Figure 2 Schematic diagram of the first-order single pulse angle estimation accuracy;

[0019] Figure 3 Schematic diagram of the third-order single pulse angle estimation accuracy. DETAILED DESCRIPTION

[0020] The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.

[0021] The following describes the embodiments of the present disclosure through specific examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present disclosure.

[0022] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this device and / or practice this method.

[0023] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present disclosure, and only show the components related to the present disclosure rather than being drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout type may also be more complicated.

[0024] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, one skilled in the art will appreciate that aspects may be practiced without these specific details.

[0025] The traditional method only uses the first-order Taylor expansion angle measurement method for the ideal airborne radar single pulse. When the airborne radar is irrational or deviates from the beam pointing angle, there is an angle measurement deviation problem. To avoid this problem, the present invention proposes a high-precision single pulse angle measurement method based on the third-order Taylor expansion, such as Figure 1 As shown, the random angle measurement error in the whole airspace caused by the non-ideal radar and the average angle measurement deviation caused by the fixed angle measurement slope can be compensated, and the true fitting angle measurement curve can be obtained within a large angle measurement range. This method is suitable for the detection of targets by airborne radar. The high-precision single pulse angle measurement method includes:

[0026] S101: Establishing an array echo model of a non-ideal radar;

[0027] S102: performing self-calibration of a non-ideal radar based on an array echo model;

[0028] S103: The “sum and difference beam” weight of the airborne radar is used to perform radar non-ideal compensation;

[0029] S104: performing beam forming according to the echo of the target object detected by the airborne radar;

[0030] S105: Determine the angle measurement model of the sum and difference single pulses, perform third-order Taylor expansion on the angle measurement model, and determine the angle estimation value, thereby achieving high-precision angle estimation within the beam width.

[0031] The method of the present invention can be applied to a multi-channel array of any structure, and can compensate for the generalized single pulse angle measurement deviation caused by the single pulse ratio slope error, which is of great significance for improving the angle measurement accuracy of the radar.

[0032] As a specific implementation method provided in this case, S101 includes:

[0033] Get the target echo y received by the non-ideal airborne radar and express it as:

[0034] In the formula, represents the target steering vector of the non-ideal radar, represents the guiding vector of the target of the ideal radar, Γ represents the non-ideal diagonal matrix of the radar, θ t and They represent the pitch angle and azimuth angle of the target respectively, s is the time domain waveform of the echo signal, and n is the noise of the airborne radar receiver.

[0035] As a specific implementation method provided in this case, S102 includes:

[0036] S201: Calculate the covariance matrix R=yy of the target echo y H , where H represents the conjugate transpose;

[0037] S202: Perform eigenvalue decomposition on the covariance matrix R to obtain the noise subspace U n and the maximum eigenvalue λ of the covariance matrix R;

[0038] S203: According to the noise subspace U n and the maximum eigenvalue λ to search for the peak, the peak search cost function satisfy:

[0039] In the formula, θ and Respectively represent the angle value of the target; the maximum peak value is calculated Among them, θ max and Respectively represent the maximum peak value P max Corresponding elevation and azimuth angles;

[0040] S204: Order The mismatch matrix Γ can be obtained;

[0041] S205: Substitute the mismatch matrix Γ into In order to obtain the steering vector of all possible angles where the target of the non-ideal radar may be located

[0042] Relative to the hypothesis The ideal airborne radar array model has the problem of full airspace angle measurement deviation when the radar is not ideal, and the deviation will cause serious deterioration of the airborne radar angle measurement performance. The method of the present invention can compensate for the full airspace angle measurement deviation caused by the mismatch matrix Γ of the non-ideal airborne radar, and can still have the performance of high-precision angle measurement when some radio frequency transceiver components of the airborne radar fail.

[0043] As a specific implementation method provided in this case, S103 includes:

[0044] S301: Compensate for “sum beam” weights in, is the “sum beam” weight coefficient obtained by using the anti-jamming ADBF method under ideal airborne radar;

[0045] S302: Compensate for azimuth difference beam weight in, is the azimuth difference beam weight coefficient obtained by using the anti-jamming ADBF method under ideal airborne radar;

[0046] S303: Compensate for the pitch difference beam weight in, is the elevation difference beam weight coefficient obtained by using the anti-interference ADBF method under ideal airborne radar.

[0047] Further, S104 includes extracting a “sum and difference beam” echo of the target object according to the position of the target object, and the “sum and difference beam” echo includes a “sum beam” echo, an “azimuth dimension difference beam” echo, and a “pitch dimension difference beam” echo, which are respectively expressed as:

[0048] “Sum beam” echo

[0049] “Azimuth difference beam” echo

[0050] “Elevation beam” echo

[0051] As a specific implementation method provided in this case, "determining the angle measurement model of the sum and difference single pulses, and performing a third-order Taylor expansion on the angle measurement model" in S105 includes:

[0052] According to the formula of sum-difference single pulse ratio, the third-order Taylor expansion is performed to obtain the cost function vector l(u s , v s ), expressed as:

[0053]

[0054] , where l1(u s ,v s ) and l2(u s ,v s ) are the elements of the first and second rows of the cost function vector, θ0 and denote the elevation and azimuth angles of the sum beam, respectively. is the azimuth cosine, F u =|y Δ,u / y ∑ |、F v =|y Δ,v / y ∑ | are the single pulse ratios in azimuth and elevation dimensions respectively;

[0055] is the second-order partial derivative of the single pulse ratio, and is the third-order partial derivative of the single pulse ratio, and is the fourth-order partial derivative of the single pulse ratio, It is represented by the partial derivative symbol;

[0056] It should be pointed out that: compared with the traditional method of using only the first-order Taylor expansion angle measurement method, there is a problem of fixed angle measurement deviation in the main beam area when deviating from the beam pointing angle. The deviation will cause serious deterioration of the angle measurement performance of the airborne radar. The method of the present invention can compensate for this problem by fixing the angle slope F of the airborne radar. uu and F vv The compensation is to reduce the angle measurement deviation of the airborne radar to the target by the third-order Taylor expansion, so as to obtain the true fitting angle detection curve in a large angle measurement range. ∑ ,y Δ,u and Δ,vThe above-mentioned third-order Taylor expansion can compensate for the random angle measurement error in the entire spatial domain caused by the amplitude and phase errors, and improve the angle measurement accuracy of the single-pulse algorithm.

[0057] Determining the angle estimate value in S105 includes:

[0058] The above equation is a nonlinear system of equations, which can be solved by Newton's iteration method, where:

[0059] Get the azimuth cosine value of the target angle (u s ,v s ), the initial angle value of the target object is The iterative formula of Newton's iteration method can be expressed as:

[0060]

[0061] in, and denote the i-th iteration values ​​of azimuth and elevation cosine respectively, and They represent the i+1th iteration values ​​of the azimuth and elevation cosines, respectively. Generally, the Newton iteration method used in angle estimation only requires 1-2 iterations to significantly improve the angle measurement accuracy of the single pulse algorithm.

[0062] Furthermore, it also includes a convergence test on the angle estimate, wherein:

[0063] S401: Cost function l(u s ,v s ) is an elementary function. s -δ,u s +δ] is continuous, and δ is the minimum value;

[0064] S402: obtained by Newton iteration method and Finally, they converge to u s and v s , and (u0,v0) as The initial value of , then the Newton iteration is expressed as:

[0065]

[0066] S403: If the result of the Newton iteration is exactly the same as the angle measurement result of the first-order expansion, it means that the Newton iteration algorithm can converge quickly. Otherwise, it means that the Newton iteration algorithm cannot be used and needs to be corrected.

[0067] For example:

[0068] Overview: Conventional low sidelobe DBF technology or anti-interference ADBF technology is used to calculate the sum and difference beam weights, and conventional target detection methods are used to obtain the detected target echo; finally, a sum and difference single pulse angle measurement model is established, a third-order Taylor expansion is performed, and the Newton iteration method is used to solve the target, and the target is calculated to achieve high-precision angle estimation within the beam width. Taking a two-dimensional active phased array radar as an example, the simulation parameters are as follows:

[0069] 1) Radar system parameters: uniform array with triangular grid, number of array elements N = 35, all-digital channel, beam pointing That is, (u0, v0) = (0.5, 0.707);

[0070] 2) Non-ideal parameter settings between radar channels: the amplitude error is randomly distributed within the 2dB range, and the phase error is randomly distributed within the ±15° range;

[0071] 3) The angle range of the target object is:

[0072] (u0,v0)∈([u0-0.021,u0+0.021],[v0-0.021,v0+0.021]); The u and v angles of the target object are used to estimate DOA in steps of 0.007, and 1000 Monte Carlo simulations are performed at each angle;

[0073] 4) The number of radar echo snapshots is single snapshot, the unit level SNR = 0 dB, and the maximum number of iterations is i = 3.

[0074] 1) Obtaining the target echo y of the non-ideal radar;

[0075] Based on non-ideal echo model Calculate the mismatch matrix Γ, specifically:

[0076] Calculate the covariance matrix R = yy H , perform eigenvalue decomposition on the covariance matrix R and obtain the noise subspace U n , and the maximum eigenvalue λ of the covariance matrix R; perform spectral peak search Among them, θ and Respectively represent all angles where the target may be located. The maximum peak value is calculated where θ max and Respectively represent the maximum peak value P max The corresponding elevation and azimuth angles; according to The mismatch matrix Γ is calculated;

[0077] So, substitute the mismatch matrix Γ into In the example above, we obtain the guidance vectors of all possible angles where the target of the non-ideal radar may be located.

[0078] 2) Perform radar non-ideal compensation on the “sum and difference beam” weights of the airborne radar, specifically:

[0079] Compensation and Beam Weights: in represents the sum beam weight coefficient obtained by the anti-jamming ADBF method under ideal airborne radar;

[0080] Compensate for the azimuth difference beam weight: in represents the azimuth difference beam weight coefficient obtained by the anti-jamming ADBF method under ideal airborne radar;

[0081] Compensate for the elevation difference beam weight: in It represents the elevation difference beam weight coefficient obtained by the anti-jamming ADBF method under ideal airborne radar.

[0082] 3) Obtain the echo of the target detected by the airborne radar, and specifically extract the "sum and difference beam" echo of the target according to the position of the target, including:

[0083] a) “Sum beam” echo

[0084] b) Azimuth difference beam echo

[0085] c) Elevation beam echo

[0086] 4) Establishing the sum-difference single pulse angle measurement model and performing third-order Taylor expansion

[0087] Based on the single pulse ratio formula, a third-order Taylor expansion is performed to obtain the function:

[0088]

[0089] 5) Newton iteration method to solve the angle estimate

[0090] The above formula is a nonlinear equation system, which can be solved by Newton iteration method to obtain the azimuth cosine value of the target angle (u s ,v s ). The initial target value is At this time, the iteration formula of Newton's iteration method is:

[0091]

[0092] This method can compensate for the random angle measurement deviation in the entire airspace caused by radar non-ideality and the fixed angle measurement deviation caused by the first-order single pulse ratio slope error, and it is superior to the conventional single pulse algorithm with only two iterations. Figure 2 The first-order monopulse angle estimation results using the conventional monopulse algorithm for non-ideal airborne radar are given. Figure 3 The effect diagram of the third-order single pulse angle estimation result of the non-ideal airborne radar of the present invention is given. Compared with the first-order single pulse angle estimation algorithm without compensation for the mismatch matrix, the estimated offset at the beam pointing not equal to the target angle within the beam width of the present invention is significantly reduced. Therefore, the method of the present invention can compensate for the random angle measurement error in the entire airspace caused by the non-ideal radar and the mean angle measurement deviation caused by the fixed angle detection slope, greatly improving the angle measurement accuracy of the non-ideal airborne radar.

[0093] The above is only a specific implementation of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present disclosure should be included in the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be based on the protection scope of the claims.

Claims

1. A high-precision single pulse angle measurement method based on third-order Taylor expansion, suitable for airborne radar detection of targets, characterized in that: The high-precision single pulse angle measurement method comprises: S101: Establishing an array echo model of a non-ideal radar; S102: performing self-calibration of a non-ideal radar based on the array echo model; S103: performing radar non-ideal compensation using sum and difference beam weights of the airborne radar; S104: performing beam forming according to the echo of the target object detected by the airborne radar; S105: Determine an angle measurement model for a single sum and difference pulse, perform a third-order Taylor expansion on the angle measurement model, and determine an angle estimation value.

2. The high-precision single pulse angle measurement method according to claim 1, characterized in that: S101 includes: Get the target echo y received by the non-ideal airborne radar and express it as: In the formula, represents the target steering vector of the non-ideal radar, represents the guiding vector of the target of the ideal radar, Γ represents the non-ideal diagonal matrix of the radar, θ t and They represent the pitch angle and azimuth angle of the target respectively, s is the time domain waveform of the echo signal, and n is the noise of the airborne radar receiver.

3. The high-precision single pulse angle measurement method according to claim 2, characterized in that: S102 includes: S201: Calculate the covariance matrix R=yy of the target echo y H , where H represents the conjugate transpose; S202: Decomposing the covariance matrix R by eigenvalue to obtain the noise subspace U n and the maximum eigenvalue λ of the covariance matrix R; S203: Based on the noise subspace U n and the maximum eigenvalue λ to search for the peak, the peak search cost function satisfy: In the formula, θ and Respectively represent the angle value of the target; the maximum peak value is calculated Among them, θ max and Respectively represent the maximum peak value P max Corresponding elevation and azimuth angles; S204: Order The mismatch matrix Γ can be obtained; S205: Substitute the mismatch matrix Γ into In order to obtain the steering vector of all possible angles where the target of the non-ideal radar may be located 4. The high-precision single pulse angle measurement method according to claim 3, characterized in that: S103 includes: S301: Compensation and beam weighting in, is the sum beam weight coefficient obtained by using the anti-jamming ADBF method under ideal airborne radar; S302: Compensate for azimuth difference beam weight in, is the azimuth difference beam weight coefficient obtained by using the anti-jamming ADBF method under ideal airborne radar; S303: Compensate for the pitch difference beam weight in, is the elevation difference beam weight coefficient obtained by using the anti-interference ADBF method under ideal airborne radar.

5. The high-precision single pulse angle measurement method according to claim 4, characterized in that: S104 includes extracting the sum and difference beam echoes of the target object according to the position of the target object. The sum and difference beam echoes include sum beam echoes, azimuth dimension difference beam echoes and elevation dimension difference beam echoes, which are respectively expressed as: and beam echo Azimuth difference beam echo Elevation beam echo 6. The high-precision single pulse angle measurement method according to claim 5, characterized in that: Determining the angle measurement model of the sum and difference single pulse in S105 and performing a third-order Taylor expansion on the angle measurement model includes: According to the formula of sum-difference single pulse ratio, the third-order Taylor expansion is performed to obtain the cost function vector l(u s , v s ), expressed as: In the formula, l1(u s ,v s ) and l2(u s ,v s ) are the elements of the first and second rows of the cost function vector, θ0 and denote the elevation and azimuth angles of the sum beam respectively, is the azimuth cosine, F u =|y Δ,u / y ∑ |、F v =|y Δ,v / y ∑ | are the single pulse ratios in azimuth and elevation dimensions respectively; is the second-order partial derivative of the single pulse ratio, and is the third-order partial derivative of the single pulse ratio, and is the fourth-order partial derivative of the single pulse ratio, Represented as partial derivative symbol.

7. The high-precision single pulse angle measurement method according to claim 6, characterized in that: Determining the angle estimate value in S105 includes: The Newton iteration method is used to solve the problem, where Get the azimuth cosine value of the target angle (u s ,v s ), the initial angle value of the target object is The iterative formula of Newton's iteration method can be expressed as: in, and denote the i-th iteration values ​​of azimuth and elevation cosine respectively, and Represent the i+1th iteration values ​​of azimuth and elevation cosine respectively.

8. The high-precision single pulse angle measurement method according to claim 7, characterized in that: The method further includes performing a convergence check on the angle estimate, wherein: S401: Cost function l(u s ,v s ) is an elementary function. s -δ,u s +δ] is continuous, and δ is the minimum value; S402: obtained by Newton's iteration method and Finally, they converge to u s and v s , and (u0,v0) as The initial value of , then the Newton iteration is expressed as: S403: If the result of the Newton iteration is exactly the same as the angle measurement result of the first-order expansion, it means that the Newton iteration algorithm can converge quickly.

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