A joint motion compensation method for low signal-to-noise ratio inverse synthetic aperture radar

Abstract

The present invention provides a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, which belongs to the field of radar signal processing and solves the problem of difficulty in accurate compensation of high-speed motion compensation and translation compensation under low signal-to-noise ratio conditions; including: constructing a joint motion compensation model according to a reference distance, a time domain echo after RVP compensation, a radial distance and a radial velocity; performing polynomial fitting on a set of observed radial distances to obtain an initial value set of polynomial coefficients of the radial distance of a space target; using the initial value set as input, using an RTH algorithm to solve the rough motion parameters of the space target, and then using a Nelder‑Mead algorithm to solve the precise motion parameters of the space target; performing joint motion compensation on the echo according to the precise motion parameters, and performing Fourier transform to obtain a high-quality ISAR image of the target. The present invention reduces the influence of high-speed motion residual errors on translation compensation through a joint motion compensation model, improves the accuracy of motion compensation under low signal-to-noise ratio conditions, and achieves high-quality imaging.

Description

Technical Field

[0001] The invention belongs to the field of radar signal processing, and particularly relates to motion compensation in inverse synthetic aperture radar imaging of space targets, and more particularly to a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method. Background Art

[0002] Inverse synthetic aperture radar (ISAR) is an important sensor for observing and imaging aerial and space targets. Compared with optical sensors, ISAR imaging radar is not affected by sky background light and cloud cover, has good all-weather and all-day working capabilities, and has a long detection distance, playing an important role in space target monitoring.

[0003] The targets observed by ISAR are generally non-cooperative targets. The motion parameters of non-cooperative targets cannot be predicted, which is the main challenge for high-quality ISAR imaging. Generally speaking, the motion of the target relative to the radar can be decomposed into two parts: translation and rotation. Rotation is exactly what is needed for imaging, while translation will cause the distance unit to be misaligned and introduce phase error. Therefore, it is necessary to compensate for the translation to achieve high-quality ISAR imaging.

[0004] The key to high-quality ISAR imaging lies in the accurate compensation of translational motion, also known as translation compensation. Current translation compensation methods are divided into two categories: one is the non-parametric translation compensation method, also known as the cascaded translation compensation method, which is divided into two steps: envelope alignment and phase correction. This type of method is easily affected by noise and has poor compensation effect under low signal-to-noise ratio conditions. The other is the parametric method, also known as the joint translation compensation method. This method uses entropy or contrast as the focus quality evaluation index of ISAR images. Then the motion of the target is modeled as a polynomial, and the motion parameters of the target are solved using the optimized image evaluation index. Based on this, the compensation term is constructed to achieve joint compensation of envelope alignment and phase correction. Due to the joint processing of envelope alignment and phase correction, this method has good noise resistance.

[0005] However, for space targets with high-speed motion, such as satellites, ballistic missiles, and spacecraft, the high-speed motion of the target will cause the one-dimensional range image of the target to be broadened and moved, so high-speed motion compensation is required. High-speed motion compensation and translation compensation are usually performed in cascade, so the residual error of high-speed motion compensation will reduce the accuracy of translation compensation. Under low signal-to-noise ratio conditions, that is, when the signal-to-noise ratio of the target echo is lower than 0dB, the high-speed motion of the target is difficult to compensate accurately, and the residual high-speed motion error will cause the failure of parametric and non-parametric translation compensation methods, reduce the imaging quality of space targets, and be unfavorable for target feature extraction and image interpretation. Summary of the invention

[0006] The present invention provides a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, which solves the technical problem of the difficulty in accurately compensating high-speed motion and translation under low signal-to-noise ratio conditions. The purpose of the present invention is to accurately compensate for the high-speed motion and translation of the target, achieve high-resolution ISAR imaging, and improve imaging quality. The present invention performs joint compensation for high-speed motion and translation, reduces the influence of high-speed motion residual errors on translation compensation, has higher motion compensation accuracy, and improves the motion compensation performance under low signal-to-noise ratio conditions by using the high signal-to-noise ratio gain accumulated by two-dimensional images.

[0007] To achieve the above object, the present invention provides a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, comprising:

[0008] Step 1: Perform Fourier transform on the initial time domain echo of the space target, transform it into the frequency domain to perform residual video phase RVP compensation, and obtain a one-dimensional range image; perform inverse Fourier transform on the one-dimensional range image to obtain the time domain echo after RVP compensation;

[0009] Step 2: Calculate the radial distance derivative to obtain the radial velocity from the space target to the radar; the radial distance is a high-order polynomial;

[0010] Step 3: Use the two-row orbital element TLE information of the space target to obtain the orbital position information of the space target within the imaging time, calculate the observed radial distance from the space target to the radar based on the orbital position information of the space target within the imaging time and combined with the radar position information, and save all the observed radial distances as an observed radial distance set;

[0011] Step 4: Perform polynomial fitting on the observed radial distance set to obtain a polynomial coefficient set of the observed radial distance set, use the polynomial coefficients of the observed radial distance set as initial values ​​of the polynomial coefficients of the radial distance, and save the initial values ​​of all polynomial coefficients of the radial distance as an initial value set;

[0012] Step 5: Obtain the reference distance recorded in the radar system information when performing Dechirp processing on the echo of the transmitted pulse, and construct a joint motion compensation model of the space target based on the time domain echo, radial distance and radial velocity after RVP compensation; discretize the joint motion compensation model to obtain a discretized joint motion compensation model;

[0013] Step 6: Initialize the positions of all red-tailed hawk individuals through the initial value set as the input of the red-tailed hawk algorithm RTH, obtain the first time domain echo corresponding to the position of each red-tailed hawk individual through the discretized joint motion compensation model, calculate the image entropy corresponding to the first time domain echo through the image entropy calculation model, search for the minimum position of the image entropy corresponding to the first time domain echo, and obtain the rough motion parameters of the spatial target;

[0014] Step 7: Initialize the rough motion parameters to the vertices of the simplex as the input of the Nelder-Mead algorithm, obtain the second time domain echo through the discretized joint motion compensation model, and calculate the image entropy corresponding to the second time domain echo through the image entropy calculation model; search for the minimum position of the image entropy corresponding to the second time domain echo to obtain the precise motion parameters of the space target;

[0015] Step 8: Input the radial distance and radial velocity corresponding to the obtained precise motion parameters into the discretized joint motion compensation model to obtain the third time domain echo after joint motion compensation processing. The third time domain echo is subjected to two-dimensional Fourier transform to obtain the ISAR image of the space target.

[0016] In step 1, the one-dimensional range image and the time domain echo after RVP compensation are:

[0017]

[0018] s(t r ,t m )=IFFT(R g (f r ,t m ));

[0019] Among them, R g (f r ,t m ) is a one-dimensional distance image, s(t r ,t m ) is the time domain echo after RVP compensation; FFT is Fourier transform, IFFT is inverse Fourier transform, s dc (t r ,t m ) is the initial time domain echo; is the RVP compensation item; t r For quick time, T p is the pulse width, n=1,2,…,N, is the distance unit number, N is the number of distance units; t m For slow time, T CPI is the radar imaging processing time; m = 1, 2, ..., M, is the transmission pulse number, M is the total number of transmission pulses; γ is the frequency modulation rate of the radar transmission signal; f r is the distance frequency, f s is the sampling rate.

[0020] In step 2, the radial distance is:

[0021]

[0022] Among them, R T (t m ; b) is the radial distance; b = [b0, b1, b2, b3, b4, b5] is the set of polynomial coefficients, b l is the coefficient corresponding to the l-order term; l is the different orders, l=0,1,2,3,4,5; m=1,2,…,M is the transmission pulse number, M is the total number of transmission pulses; Δt m is the pulse repetition interval;

[0023] Taking the derivative of the radial distance, we can get the radial velocity v(t m ; b) The method comprises:

[0024]

[0025] In step 3, the two-row orbital element TLE information of the space target is used to obtain the orbital position information of the space target within the imaging time. The method for calculating the observed radial distance from the space target to the radar based on the orbital position information of the space target within the imaging time and the radar position information is as follows:

[0026] R T (m) = Ed(P ECI (m),R ECI (m));

[0027] Among them, R T (m) is the observed radial distance, m = 1, 2, ..., M, is the transmitted pulse number, and M is the total number of transmitted pulses; Ed (·, ·) represents the Euclidean distance calculation operation; P ECI (m) is the slowing time t m Convert to Coordinated Universal Time UTCm Then, the space target is obtained at t using the two-row orbit element TLE information of the space target. UTCm The orbital position information in the ECI coordinate system at 1000 s; R ECI (m) is the radar at t UTCm Position information in the ECI coordinate system at the time;

[0028] All observed radial distances R T (m) is saved as the observed radial distance set R T ;

[0029] R T =[R T (1),…,R T (m),…,R T (M)].

[0030] In step 4, a polynomial fitting is performed on the observed radial distance set to obtain a polynomial coefficient set of the observed radial distance set, the polynomial coefficients of the observed radial distance set are used as initial values ​​of the polynomial coefficients of the radial distance, and the initial values ​​of all polynomial coefficients of the radial distance are saved as an initial value set. The method includes:

[0031] For the set of observed radial distances R T Perform a 5th-order polynomial fit to obtain the polynomial coefficient set of the observed radial distance set The expression is as follows:

[0032]

[0033] Where X = [1, 2, …, m, …, M], is the discrete slow time set, M is the total number of transmitted pulses; polyfit(·) represents the polynomial fitting operation; the polynomial coefficient corresponding to the l-order term of the observed radial distance set is The polynomial coefficient corresponding to the l-order term of the observed radial distance set As the radial distance R T (t m ; b) The polynomial coefficient b corresponding to the l-order term l The initial values ​​of all polynomial coefficients of radial distance are saved as the initial value set

[0034] In step 5, the joint motion compensation model of the spatial target is constructed as follows:

[0035]

[0036] in, is the time domain echo after joint motion compensation processing; s(t r ,t m ) is the time domain echo after RVP compensation; j is the imaginary unit; c is the speed of light; f c is the radar signal carrier frequency; R T (t m ; b) is the radial distance; R ref (t m ) is the reference distance for Dechirp processing of the echo of the mth transmitted pulse; γ is the modulation frequency of the radar transmitting signal; t r is the fast time; v(t m ; b) is the radial velocity.

[0037] In step 5, the discretized joint motion compensation model is:

[0038]

[0039] in, The time domain echo after joint motion compensation The discrete form of s(n,m) is the time domain echo s(t r ,t m ) in discrete form; R T (m; b) is the radial distance R T (t m ; b) Discrete form; R ref (m) is the reference distance R ref (t m ) is a discrete form; n is the distance unit number; v(m; b) is the radial velocity v(t m ; b) discrete form.

[0040] In step six, the positions of all red-tailed hawk individuals are initialized by an initial value set as the input of the red-tailed hawk algorithm RTH, the first time domain echo corresponding to the position of each red-tailed hawk individual is obtained by a discretized joint motion compensation model, the image entropy corresponding to the first time domain echo is calculated by an image entropy calculation model, and the minimum position of the image entropy corresponding to the first time domain echo is searched. The method for obtaining the rough motion parameters of the spatial target includes:

[0041] 6.1, according to the initial value set Determine upper bounds on polynomial coefficients and the lower bound Initialize the total number of red-tailed hawks, K, according to and Get the position of the kth red-tailed hawk among K red-tailed hawks t is the iteration number; k = 1, 2, 3, ..., K; set the maximum number of iterations T max ; t=1,2,3,…,T max ;

[0042] 6.2, t = 1, position Corresponding radial distance and radial velocity The radial distance and radial velocity Input the discretized joint motion compensation model to obtain the first time domain echo after joint motion compensation processing for:

[0043]

[0044] 6.3, the image entropy calculation model is:

[0045]

[0046] in, is the image entropy corresponding to the first time domain echo; ln(·) represents the natural logarithm operation, S I is the image corresponding to the first time domain echo The total energy of , k1 = 1, ..., N, is the image domain distance unit number, h = 1, ..., M, is the image domain orientation unit number;

[0047] 6.4, according to Sort the red-tailed hawk individuals by size and get the smallest The corresponding position of the red-tailed hawk completes an iterative search process;

[0048] 6.5, the iteration number t increases by 1, and the position of the red-tailed hawk individual k is updated Execute steps 6.2 to 6.5 until the number of iterations reaches the maximum value T. max , terminate the iterative search process and output the minimum The corresponding position of the red-tailed hawk individual is used to obtain the rough motion parameters of the space target.

[0049] In step 7, the rough motion parameters are initialized as the vertices of the simplex as the input of the Nelder-Mead algorithm, the second time domain echo is obtained by the discretized joint motion compensation model, and the image entropy corresponding to the second time domain echo is calculated by the image entropy calculation model; the method of searching for the minimum position of the image entropy corresponding to the second time domain echo to obtain the precise motion parameters of the space target includes:

[0050] 7.1, according to the Nelder-Mead algorithm, the rough motion parameters are initialized to the 7 vertices of the simplex vertex Corresponding to a set of target motion polynomial coefficients; l1 = 0, 1, 2, 3, 4, 5, 6 are vertex numbers; the stop condition is set to: is the vertex number of the stopping condition; TL is the error threshold; Ed(·,·) represents the Euclidean distance calculation operation;

[0051] 7.2. Input the radial distance and radial velocity corresponding to each vertex into the discretized joint motion compensation model to obtain the second time domain echo after joint motion compensation processing, and calculate the image entropy corresponding to the second time domain echo through the image entropy calculation model in accordance with The value of the vertex Reorder to meet If the stop condition is met, execute 7.9; otherwise, execute 7.3;

[0052] 7.3. Calculate the reflection point by discretizing the joint motion compensation model and the image entropy calculation model Image entropy Reflection Points ρ′ is the reflection coefficient; To discard the vertex with the largest image entropy After that, the centroids of the first 6 vertices are calculated;

[0053] 7.4, if The extension point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Extension Points γ′ is the expansion coefficient; if Then Replace with Continue with 7.2; otherwise, Replace with Continue with 7.2.

[0054] 7.5, if Then Replace with Continue with 7.2.

[0055] 7.6, if The shrinkage point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Pinch Point α′ is the contraction coefficient; if Then Replace with Continue to 7.2; otherwise, proceed to 7.8;

[0056] 7.7, if The inner contraction point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Inner contraction point if Inner contraction point Alternative Continue to 7.2; otherwise, proceed to 7.8;

[0057] 7.8, Calculating the Fallback Point σ′ is the backoff coefficient, except Replace all vertices other than with fallback points and continue with 7.2;

[0058] 7.9, stop the Nelder-Mead algorithm and get the precise motion parameter b of the space target fine , b fine The vertex with the smallest image entropy when the Nelder-Mead algorithm reaches the stopping condition The corresponding motion parameters.

[0059] In step eight, the radial distance and radial velocity corresponding to the obtained precise motion parameters are input into the discretized joint motion compensation model to obtain the third time domain echo after the joint motion compensation processing, and the method of obtaining the ISAR image of the space target by two-dimensional Fourier transform of the third time domain echo includes:

[0060] The third time domain echo is:

[0061]

[0062] in, is the third time domain echo; R T (m; b fine ) is the precise motion parameter b fine Corresponding radial distance; v(m; b fine ) is the precise motion parameter b fine The corresponding radial velocity;

[0063] The third time domain echo is transformed into the ISAR image of the space target by two-dimensional Fourier transform. fine )for:

[0064]

[0065] Beneficial effects:

[0066] 1. The present invention provides a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, constructs a joint motion compensation model for space targets, and simultaneously compensates for the high-speed motion and translation of the target, thereby reducing the influence of high-speed motion residual errors on translation compensation, improving the accuracy of motion compensation, and achieving high-quality ISAR imaging.

[0067] 2. The present invention provides a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, which fully considers the target radial velocity change within the imaging time and models the target motion as a high-order polynomial. It is more accurate than traditional high-speed motion compensation methods such as minimum entropy high-speed motion compensation and integral cubic phase function ICPF high-speed motion compensation.

[0068] 3. The present invention provides a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, which uses the image entropy after joint motion compensation as the objective function to achieve the solution of target motion parameters. Since the high signal-to-noise ratio gain accumulated by the two-dimensional image is utilized, the motion compensation performance under low signal-to-noise ratio conditions is improved.

[0069] 4. The present invention provides a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, which adopts a target motion parameter optimization method of first RTH coarse search and then Nelder-Mead precise search, which ensures the globality of parameter optimization and the accuracy of motion parameters, further reduces the amount of calculation required for optimization, and improves the speed of motion compensation. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a model of the space target used in the simulation experiment of the present invention.

[0071] Figure 2 It is the ideal ISAR image of the target when SNR=0dB.

[0072] Figure 3 It is the ISAR image of the target after motion compensation using the ME+MERA+MEPA method when SNR=0dB.

[0073] Figure 4 It is the ISAR image of the target after motion compensation using the ICPF+MICRA+MICPA method when SNR=0dB.

[0074] Figure 5 It is an ideal ISAR image of the target after motion compensation using the method of the present invention when SNR=0dB.

[0075] Figure 6 It is the ideal ISAR image of the target when SNR = -5dB.

[0076] Figure 7 It is the ISAR image of the target after motion compensation using the ME+MERA+MEPA method when SNR=-5dB.

[0077] Figure 8 It is the ISAR image of the target after motion compensation using the ICPF+MICRA+MICPA method when SNR=-5dB.

[0078] Fig. 9 It is an ideal ISAR image of the target after motion compensation using the method of the present invention when SNR=-5dB.

[0079] Fig.10 It is the ideal ISAR image of the target when SNR = -9dB.

[0080] Fig.11 It is the ISAR image of the target after motion compensation using the ME+MERA+MEPA method when SNR=-9dB.

[0081] Fig.12It is the ISAR image of the target after motion compensation using the ICPF+MICRA+MICPA method when SNR=-9dB.

[0082] Fig.13 It is an ideal ISAR image of the target after motion compensation using the method of the present invention when SNR=-9dB.

[0083] Fig.14 It is the ideal ISAR image of the target when SNR = -13dB.

[0084] Fig.15 It is the ISAR image of the target after motion compensation using the ME+MERA+MEPA method when SNR=-13dB.

[0085] Fig.16 It is the ISAR image of the target after motion compensation using the ICPF+MICRA+MICPA method when SNR=-13dB.

[0086] Fig.17 It is an ideal ISAR image of the target after motion compensation using the method of the present invention when SNR=-13dB. DETAILED DESCRIPTION

[0087] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0088] An embodiment of the present invention provides a low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, comprising:

[0089] Step 1: Perform Fourier transform on the initial time domain echo of the space target, transform it into the frequency domain to perform residual video phase RVP compensation, and obtain a one-dimensional range image; perform inverse Fourier transform on the one-dimensional range image to obtain the time domain echo after RVP compensation;

[0090] Step 2: Take the derivative of the radial distance to obtain the radial velocity from the space target to the radar; the radial distance is a high-order polynomial; this step obtains the polynomial of the radial velocity of the space target, taking into account the change of the radial velocity of the space target during the imaging time, which can improve the accuracy of high-speed motion compensation.

[0091] Step 3: Use the two-row orbital element TLE information of the space target to obtain the orbital position information of the space target within the imaging time, calculate the observed radial distance from the space target to the radar based on the orbital position information of the space target within the imaging time and combined with the radar position information, and save all the observed radial distances as an observed radial distance set;

[0092] Step 4: Perform polynomial fitting on the observed radial distance set to obtain the polynomial coefficient set of the observed radial distance set, use the polynomial coefficients of the observed radial distance set as the initial values ​​of the polynomial coefficients of the radial distance, and save the initial values ​​of all the polynomial coefficients of the radial distance as the initial value set; since the TLE information of the space target is fully utilized, the initial value set of the polynomial coefficients of the space target motion can be fitted, which narrows the scope of the parameter search and can greatly reduce the computational complexity of the motion parameter search.

[0093] Step 5: Obtain the reference distance recorded in the radar system information when performing Dechirp processing on the echo of the transmitted pulse, and construct a joint motion compensation model of the space target based on the time domain echo, radial distance and radial velocity after RVP compensation; discretize the joint motion compensation model to obtain a discretized joint motion compensation model; the discretized joint motion compensation model can be used to compensate for the high-speed motion and translational motion of the space target at the same time, reduce the influence of the residual error of high-speed motion on the translational compensation, and improve the accuracy of motion compensation.

[0094] Step 6: Initialize the positions of all red-tailed hawk individuals through the initial value set as the input of the red-tailed hawk algorithm RTH, obtain the first time domain echo corresponding to the position of each red-tailed hawk individual through the discretized joint motion compensation model, calculate the image entropy corresponding to the first time domain echo through the image entropy calculation model, search for the minimum position of the image entropy corresponding to the first time domain echo, and obtain the rough motion parameters of the spatial target; use the Red-tailed Hawk algorithm to search for rough motion parameters. The Red-tailed Hawk algorithm has the characteristics of strong evolutionary ability, fast search speed, and strong optimization ability, which can ensure the globality of parameter optimization.

[0095] Step 7: Initialize the rough motion parameters to the vertices of the simplex as the input of the Nelder-Mead algorithm, obtain the second time domain echo through the discretized joint motion compensation model, and calculate the image entropy corresponding to the second time domain echo through the image entropy calculation model; search for the minimum position of the image entropy corresponding to the second time domain echo to obtain the precise motion parameters of the spatial target; use the Nelder-Mead algorithm to search for precise motion parameters. The Nelder-Mead algorithm has the advantages of fast search speed and insensitivity to the choice of initial values, and can quickly obtain precise motion parameters.

[0096] Step 6 and step 7 of the embodiment of the present invention adopt a two-step motion parameter search method of first roughly searching the motion parameters and then using the Nelder-Mead algorithm to accurately search the motion parameters. This method fully utilizes the advantages of the Red-tailed Hawk algorithm and the Nelder-Mead algorithm, ensures the globality and accuracy of parameter optimization, reduces the amount of calculation for parameter optimization, and improves the speed of joint motion compensation for space targets.

[0097] Step 8: Input the radial distance and radial velocity corresponding to the obtained precise motion parameters into the discretized joint motion compensation model to obtain the third time domain echo after joint motion compensation processing. The third time domain echo is subjected to two-dimensional Fourier transform to obtain the ISAR image of the space target.

[0098] In step 1, the one-dimensional range image and the time domain echo after RVP compensation are:

[0099]

[0100] s(t r ,t m )=IFFT(R g (f r ,t m ));

[0101] Among them, R g (f r ,t m ) is a one-dimensional distance image, s(t r ,t m ) is the time domain echo after RVP compensation; FFT is Fourier transform, IFFT is inverse Fourier transform, s dc (t r ,t m ) is the initial time domain echo; is the RVP compensation item; t r For quick time, T p is the pulse width, for example, T p = 200us, n = 1, 2, ..., N, is the distance unit number, N is the number of distance units, for example, N = 1203; t m For slow time, T CPI is the radar imaging processing time, for example, T CPI =14s; m = 1, 2, ..., M, is the transmission pulse number, M is the total number of transmission pulses, for example, M = 1024; γ is the modulation frequency of the radar transmission signal, for example, γ = 10^13 Hz / s; f r is the distance frequency, f s is the sampling rate, for example, f s =10MHz.

[0102] In step 2, the radial distance is:

[0103]

[0104] Among them, R T (t m; b) is the radial distance; b = [b0, b1, b2, b3, b4, b5] is the set of polynomial coefficients, b l is the coefficient corresponding to the l-order term; l is the different orders, l=0,1,2,3,4,5; m=1,2,…,M is the transmission pulse number, M is the total number of transmission pulses; Δt m is the pulse repetition interval; considering that the imaging time is generally short and the motion of the space target is relatively stable, a fifth-order polynomial is sufficient to describe the motion of the target. Therefore, the motion of the space target is modeled as a fifth-order polynomial:

[0105] Taking the derivative of the radial distance, we can get the radial velocity v(t m ; b) The method comprises:

[0106]

[0107] In step 3, the two-row orbital element TLE information of the space target is used to obtain the orbital position information of the space target within the imaging time. The method for calculating the observed radial distance from the space target to the radar based on the orbital position information of the space target within the imaging time and the radar position information is as follows:

[0108] R T (m) = Ed(P ECI (m),R ECI (m));

[0109] Among them, R T (m) is the observed radial distance, m = 1, 2, ..., M, is the transmitted pulse number, and M is the total number of transmitted pulses; Ed (·, ·) represents the Euclidean distance calculation operation; P ECI (m) is the slowing time t m Convert to Coordinated Universal Time UTCm Then, the space target is obtained at t using the two-row orbit element TLE information of the space target. UTCm The orbital position information in the ECI coordinate system at 1000 s; R ECI (m) is the radar at t UTCm The position information in the ECI coordinate system at the time t m Convert to the corresponding coordinated universal time t UTCm It is from 22-Sept-2016 20:35:58 to 22-Sept-2016 20:36:12, a total of 14 seconds.

[0110] All observed radial distances R T (m) is saved as the observed radial distance set R T ;

[0111] R T =[R T(1),…,R T (m),…,R T (M)].

[0112] In step 4, a polynomial fitting is performed on the observed radial distance set to obtain a polynomial coefficient set of the observed radial distance set, the polynomial coefficients of the observed radial distance set are used as initial values ​​of the polynomial coefficients of the radial distance, and the initial values ​​of all polynomial coefficients of the radial distance are saved as an initial value set. The method includes:

[0113] For the set of observed radial distances R T Perform a 5th-order polynomial fit to obtain the polynomial coefficient set of the observed radial distance set The expression is as follows:

[0114]

[0115] Where X = [1, 2, …, m, …, M], is the discrete slow time set, M is the total number of transmitted pulses; polyfit(·) represents the polynomial fitting operation; the polynomial coefficient corresponding to the l-order term of the observed radial distance set is The polynomial coefficient corresponding to the l-order term of the observed radial distance set As the radial distance R T (t m ; b) The polynomial coefficient b corresponding to the l-order term l The initial values ​​of all polynomial coefficients of radial distance are saved as the initial value set

[0116] In step 5, the joint motion compensation model of the spatial target is constructed as follows:

[0117]

[0118] in, is the time domain echo after joint motion compensation processing; s(t r ,t m ) is the time domain echo after RVP compensation; j is the imaginary unit; c is the speed of light; f c is the radar signal carrier frequency, for example, f c =16GHz; R T (t m ; b) is the radial distance; R ref (t m ) is the reference distance for Dechirp processing of the echo of the mth transmitted pulse; γ is the modulation frequency of the radar transmitting signal; t r is the fast time; v(t m ; b) is the radial velocity.

[0119] In step 5, the discretized joint motion compensation model is:

[0120]

[0121] in, The time domain echo after joint motion compensation The discrete form of s(n,m) is the time domain echo s(t r ,t m ) in discrete form; R T (m; b) is the radial distance R T (t m ; b) Discrete form; R ref (m) is the reference distance R ref (t m ) is a discrete form; n is the distance unit number; v(m; b) is the radial velocity v(t m ; b) in discrete form; for example, and s(n,m) are both complex matrices with 1203 rows and 1024 columns.

[0122] In step six, the positions of all red-tailed hawk individuals are initialized by an initial value set as the input of the red-tailed hawk algorithm RTH, the first time domain echo corresponding to the position of each red-tailed hawk individual is obtained by a discretized joint motion compensation model, the image entropy corresponding to the first time domain echo is calculated by an image entropy calculation model, and the minimum position of the image entropy corresponding to the first time domain echo is searched. The method for obtaining the rough motion parameters of the spatial target includes:

[0123] 6.1, according to the initial value set Determine upper bounds on polynomial coefficients and the lower bound Initialize the total number of red-tailed hawks, K, according to and Get the position of the kth red-tailed hawk among K red-tailed hawks t is the iteration number; k = 1, 2, 3, ..., K; set the maximum number of iterations T max ; t=1,2,3,…,T max ;

[0124] 6.2, t = 1, position Corresponding radial distance and radial velocity The radial distance and radial velocity Input the discretized joint motion compensation model to obtain the first time domain echo after joint motion compensation processing for:

[0125]

[0126] 6.3, the image entropy calculation model is:

[0127]

[0128] in, is the image entropy corresponding to the first time domain echo; ln(·) represents the natural logarithm operation, S I is the image corresponding to the first time domain echo The total energy of , k1 = 1, ..., N, is the image domain distance unit number, h = 1, ..., M, is the image domain orientation unit number;

[0129] 6.4, according to Sort the red-tailed hawk individuals by size and get the smallest The corresponding position of the red-tailed hawk completes an iterative search process;

[0130] 6.5, the iteration number t increases by 1, and the position of the red-tailed hawk individual k is updated Execute steps 6.2 to 6.5 until the number of iterations reaches the maximum value T. max , terminate the iterative search process and output the minimum The corresponding position of the red-tailed hawk individual is used to obtain the rough motion parameters of the space target.

[0131] In step 7, the rough motion parameters are initialized as the vertices of the simplex as the input of the Nelder-Mead algorithm, the second time domain echo is obtained by the discretized joint motion compensation model, and the image entropy corresponding to the second time domain echo is calculated by the image entropy calculation model; the method of searching for the minimum position of the image entropy corresponding to the second time domain echo to obtain the precise motion parameters of the space target includes:

[0132] 7.1, according to the Nelder-Mead algorithm, the rough motion parameters are initialized to the 7 vertices of the simplex vertex Corresponding to a set of target motion polynomial coefficients; l1 = 0, 1, 2, 3, 4, 5, 6 are vertex numbers; the stop condition is set to: is the vertex number of the stopping condition; TL is the error threshold; Ed(·,·) represents the Euclidean distance calculation operation;

[0133] 7.2. Input the radial distance and radial velocity corresponding to each vertex into the discretized joint motion compensation model to obtain the second time domain echo after joint motion compensation processing, and calculate the image entropy corresponding to the second time domain echo through the image entropy calculation model in accordance with

[0134] The value of the vertex Reorder to meet If the stop condition is met, execute 7.9; otherwise, execute 7.3;

[0135] 7.3. Calculate the reflection point by discretizing the joint motion compensation model and the image entropy calculation model Image entropy Reflection Points ρ′ is the reflection coefficient; To discard the vertex with the largest image entropy After that, the centroids of the first 6 vertices are calculated;

[0136] 7.4, if The extension point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Extension Points γ′ is the expansion coefficient; if Then Replace with Continue with 7.2; otherwise, Replace with Continue with 7.2.

[0137] 7.5, if Then Replace with Continue with 7.2.

[0138] 7.6, if The shrinkage point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Pinch Point α′ is the contraction coefficient; if Then Replace with Continue to 7.2; otherwise, proceed to 7.8;

[0139] 7.7, if The inner contraction point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Inner contraction point if Inner contraction point Alternative Continue to 7.2; otherwise, proceed to 7.8;

[0140] 7.8, Calculating the Fallback Point σ′ is the backoff coefficient, except Replace all vertices other than with fallback points and continue with 7.2;

[0141] 7.9, stop the Nelder-Mead algorithm and get the precise motion parameter b of the space target fine , b fine The vertex with the smallest image entropy when the Nelder-Mead algorithm reaches the stopping condition The corresponding motion parameters.

[0142] In step eight, the radial distance and radial velocity corresponding to the obtained precise motion parameters are input into the discretized joint motion compensation model to obtain the third time domain echo after the joint motion compensation processing, and the method of obtaining the ISAR image of the space target by two-dimensional Fourier transform of the third time domain echo includes:

[0143] The third time domain echo is:

[0144]

[0145] in, is the third time domain echo; R T (m; b fine ) is the precise motion parameter b fine Corresponding radial distance; v(m; b fine ) is the precise motion parameter b fine The corresponding radial velocity;

[0146] The third time domain echo is transformed into the ISAR image of the space target by two-dimensional Fourier transform. fine )for:

[0147]

[0148] In order to facilitate those skilled in the art to understand the present invention, the present invention provides a specific example.

[0149] In this example, the inverse synthetic aperture radar is located at (29.7°N, 119.8°E), and the model of the space target is as follows: Figure 1 The TLE of the space target is shown in Table 1, and the radar imaging parameters are shown in Table 2. The number of red-tailed hawks K is set to 10, and the maximum number of iterations T max is 300; the error threshold TL of the Nelder-Mead algorithm is set to 10^-6. The values ​​of reflection coefficient, expansion coefficient, contraction coefficient and back-off coefficient are: ρ′=1, γ′=2, α′=1 / 2, σ′=1 / 2 respectively.

[0150] Table 1

[0151]

[0152] Table 2

[0153]

[0154] In order to illustrate the effectiveness of this method, simulation experiments were carried out under different signal-to-noise ratio conditions, and all experiments were compared with two motion compensation methods. The first method is a cascade motion compensation method using minimum entropy high-speed motion compensation, minimum entropy envelope alignment, and minimum entropy self-focusing, called: ME+MERA+MEPA method; the second method is a cascade motion compensation method using integral cubic phase function ICPF high-speed motion compensation, maximum contrast envelope alignment, and maximum contrast self-focusing, called: ICPF+MICRA+MICPA method.

[0155] When SNR = 0dB, Figure 3 , Figure 4 and Figure 5 It can be seen that the image quality obtained by the ME+MERA+MEPA method, ICPF+MICRA+MICPA method and the method of the present invention is similar, which is consistent with the ideal image. Figure 2 The target’s outline features can be clearly displayed. When SNR = -5dB, Figure 7 , Figure 8 and Fig. 9 It can be seen that the image quality obtained by the ME+MERA+MEPA method and the ICPF+MICRA+MICPA method begins to decline, the image becomes slightly defocused, and the component features of the target gradually blur. However, the ISAR image after motion compensation by the method of the present invention still has high quality and is consistent with the ideal image. Figure 6 Basically the same. When SNR = -9dB, from Fig.11 , Fig.12 and Fig.13 It can be seen that the image quality obtained by the ME+MERA+MEPA method and the ICPF+MICRA+MICPA method is reduced, the image is seriously defocused, and the component features of the target are seriously blurred. However, the ISAR image after motion compensation by the method of the present invention still has a high quality, which is comparable to the ideal image. Fig.10 Basically the same. When SNR = -13dB, from Fig.15 , Fig.16 and Fig.17 It can be seen that the image quality obtained by the ME+MERA+MEPA method and the ICPF+MICRA+MICPA method is seriously degraded, and the target cannot be distinguished from the image. However, the ISAR image after motion compensation by the method of the present invention still has high quality, and the component features of the target are more obvious, which is different from the ideal image. Fig.14 Basically the same. At the same time, in order to quantitatively prove the superiority of the method of the present invention, the image entropy after compensation by different methods is given as shown in Table 3:

[0156] Table 3

[0157]

[0158] It can be seen from Table 3 that, compared with the ME+MERA+MEPA method and the ICPF+MICRA+MICPA method, the image entropy obtained by the method of the present invention is smaller and closer to the ideal image entropy, which further demonstrates the effectiveness and superiority of the motion compensation method of the present invention.

[0159] From the above analysis, it can be seen that the residual error of high-speed motion compensation will affect the accuracy of translation compensation due to the cascade of high-speed motion compensation and translation compensation in the traditional cascade motion compensation algorithm, and the compensation accuracy is easily affected by low signal-to-noise ratio. In contrast, the proposed joint motion compensation method adopts the method of high-speed motion and translation joint compensation, which reduces the influence of high-speed motion residual error on translation compensation. At the same time, due to the use of the high signal-to-noise ratio gain of the two-dimensional image, accurate joint motion compensation can be achieved under low signal-to-noise ratio conditions, and high-resolution imaging of space targets can be achieved. Therefore, the proposed low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method solves the technical problem of the difficulty of high-speed motion and translation accurate compensation under low signal-to-noise ratio conditions, realizes the joint compensation of high-speed motion and translation of the target under low signal-to-noise ratio conditions, and can provide high-quality ISAR images for target recognition and state inversion based on ISAR images.

[0160] Therefore, the present invention has great application value.

[0161] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method, characterized in that: include: Step 1: Perform Fourier transform on the initial time domain echo of the space target, transform it into the frequency domain to perform residual video phase RVP compensation, and obtain a one-dimensional range image; Perform inverse Fourier transform on the one-dimensional range image to obtain the time domain echo after RVP compensation; Step 2: Calculate the radial distance derivative to obtain the radial velocity from the space target to the radar; the radial distance is a high-order polynomial; Step 3: Use the two-row orbital element TLE information of the space target to obtain the orbital position information of the space target within the imaging time, calculate the observed radial distance from the space target to the radar based on the orbital position information of the space target within the imaging time and combined with the radar position information, and save all the observed radial distances as an observed radial distance set; Step 4: Perform polynomial fitting on the observed radial distance set to obtain a polynomial coefficient set of the observed radial distance set, use the polynomial coefficients of the observed radial distance set as initial values ​​of the polynomial coefficients of the radial distance, and save the initial values ​​of all polynomial coefficients of the radial distance as an initial value set; Step 5: Obtain the reference distance recorded in the radar system information when performing Dechirp processing on the echo of the transmitted pulse, and construct a joint motion compensation model of the space target based on the time domain echo, radial distance and radial velocity after RVP compensation; discretize the joint motion compensation model to obtain a discretized joint motion compensation model; Step 6: Initialize the positions of all red-tailed hawk individuals through the initial value set as the input of the red-tailed hawk algorithm RTH, obtain the first time domain echo corresponding to the position of each red-tailed hawk individual through the discretized joint motion compensation model, calculate the image entropy corresponding to the first time domain echo through the image entropy calculation model, search for the minimum position of the image entropy corresponding to the first time domain echo, and obtain the rough motion parameters of the spatial target; Step 7: Initialize the rough motion parameters to the vertices of the simplex as the input of the Nelder-Mead algorithm, obtain the second time domain echo through the discretized joint motion compensation model, and calculate the image entropy corresponding to the second time domain echo through the image entropy calculation model; search for the minimum position of the image entropy corresponding to the second time domain echo to obtain the precise motion parameters of the space target; Step 8: Input the radial distance and radial velocity corresponding to the obtained precise motion parameters into the discretized joint motion compensation model to obtain the third time domain echo after the joint motion compensation processing, and obtain the ISAR image of the space target by performing two-dimensional Fourier transform on the third time domain echo; Among them, in step 1, the one-dimensional range image and the time domain echo after RVP compensation are respectively: s(t r ,t m )=IFFT(R g (f r ,t m )); Among them, R g (f r ,t m ) is a one-dimensional distance image, s(t r ,t m ) is the time domain echo after RVP compensation; FFT is Fourier transform, IFFT is inverse Fourier transform, s dc (t r ,t m ) is the initial time domain echo; is the RVP compensation item; t r For quick time, T p is the pulse width, n=1,2,…,N, is the distance unit number, N is the number of distance units; t m For slow time, T CPI is the radar imaging processing time; m = 1, 2, ..., M, is the transmission pulse number, M is the total number of transmission pulses; γ is the frequency modulation rate of the radar transmission signal; f r is the distance frequency, f s is the sampling rate; In step 2, the radial distance is: Among them, R T (t m ; b) is the radial distance; b = [b0, b1, b2, b3, b4, b5] is the set of polynomial coefficients, b l is the coefficient corresponding to the l-order term; l is the different orders, l=0,1,2,3,4,5; m=1,2,…,M is the transmission pulse number, M is the total number of transmission pulses; Δt m is the pulse repetition interval; Taking the derivative of the radial distance, we can get the radial velocity v(t m ; b) The method comprises: In step 3, the two-row orbital element TLE information of the space target is used to obtain the orbital position information of the space target within the imaging time. The method for calculating the observed radial distance from the space target to the radar based on the orbital position information of the space target within the imaging time and the radar position information is as follows: R T (m)=Ed(P ECI (m),R ECI (m)); Among them, R T (m) is the observed radial distance, m = 1, 2, ..., M is the transmitted pulse number, and M is the total number of transmitted pulses; Ed (·, ·) represents the Euclidean distance calculation operation; P ECI (m) is the slowing time t m Convert to Coordinated Universal Time UTCm Then, the space target is obtained at t using the two-row orbit element TLE information of the space target. UTCm The orbital position information in the ECI coordinate system at 1000 s; R ECI (m) is the radar at t UTCm Position information in the ECI coordinate system at the time; All observed radial distances R T (m) is saved as the observed radial distance set R T ; R T =[R T (1),···,R T (m),···,R T (M)]; In step 4, a polynomial fitting is performed on the observed radial distance set to obtain a polynomial coefficient set of the observed radial distance set, the polynomial coefficients of the observed radial distance set are used as initial values ​​of the polynomial coefficients of the radial distance, and the initial values ​​of all polynomial coefficients of the radial distance are saved as an initial value set. The method includes: For the observed radial distance set R T Perform a 5th-order polynomial fit to obtain the polynomial coefficient set of the observed radial distance set The expression is as follows: Where X = [1, 2, …, m, …, M] is the discrete slow time set, m = 1, 2, …, M is the transmission pulse number, and M is the total number of transmission pulses; polyfit(·) represents the polynomial fitting operation; the polynomial coefficient corresponding to the l-order term of the observed radial distance set is The polynomial coefficient corresponding to the l-order term of the observed radial distance set As the radial distance R T (t m ; b) The polynomial coefficient b corresponding to the l-order term l The initial values ​​of all polynomial coefficients of radial distance are saved as the initial value set In step 5, the joint motion compensation model of the spatial target is constructed as follows: in, is the time domain echo after joint motion compensation processing; s(t r ,t m ) is the time domain echo after RVP compensation; j is the imaginary unit; c is the speed of light; f c is the radar signal carrier frequency; R T (t m ; b) is the radial distance; R ref (t m ) is the reference distance for Dechirp processing of the echo of the mth transmitted pulse; γ is the modulation frequency of the radar transmitting signal; t r is the fast time; v(t m ; b) is the radial velocity.

2. A low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method as claimed in claim 1, characterized in that: In step 5, the discretized joint motion compensation model is: in, The time domain echo after joint motion compensation The discrete form of s(n,m) is the time domain echo s(t r ,t m ) in discrete form; R T (m; b) is the radial distance R T (t m ; b) Discrete form; R ref (m) is the reference distance R ref (t m ) is a discrete form; n is the distance unit number; v(m; b) is the radial velocity v(t m ; b) discrete form.

3. A low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method as claimed in claim 2, characterized in that: In step six, the positions of all red-tailed hawk individuals are initialized by an initial value set as the input of the red-tailed hawk algorithm RTH, the first time domain echo corresponding to the position of each red-tailed hawk individual is obtained by a discretized joint motion compensation model, the image entropy corresponding to the first time domain echo is calculated by an image entropy calculation model, and the minimum position of the image entropy corresponding to the first time domain echo is searched. The method for obtaining the rough motion parameters of the spatial target includes: 6.1, according to the initial value set Determine upper bounds on polynomial coefficients and lower bound Initialize the total number of red-tailed hawks, K, according to and Get the position of the kth red-tailed hawk among K red-tailed hawks t is the iteration number; k = 1, 2, 3, ..., K; set the maximum number of iterations T max ; t=1,2,3,…,T max ; 6.2, t = 1, position Corresponding radial distance and radial velocity The radial distance and radial velocity Input the discretized joint motion compensation model to obtain the first time domain echo after joint motion compensation processing for: 6.3, the image entropy calculation model is: in, is the image entropy corresponding to the first time domain echo; ln(·) represents the natural logarithm operation, S I is the image corresponding to the first time domain echo The total energy of , k1 = 1, ..., N is the image domain distance unit number, h = 1, ..., M is the image domain orientation unit number; 6.4, according to Sort the red-tailed hawk individuals by size and get the smallest The corresponding position of the red-tailed hawk completes an iterative search process; 6.5, the iteration number t increases by 1, and the position of the red-tailed hawk individual k is updated Execute steps 6.2 to 6.5 until the number of iterations reaches the maximum value T. max , terminate the iterative search process and output the minimum The corresponding position of the red-tailed hawk individual is used to obtain the rough motion parameters of the space target.

4. A low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method as claimed in claim 3, characterized in that: In step 7, the rough motion parameters are initialized as the vertices of the simplex as the input of the Nelder-Mead algorithm, the second time domain echo is obtained by the discretized joint motion compensation model, and the image entropy corresponding to the second time domain echo is calculated by the image entropy calculation model; The method of searching for the minimum position of the image entropy corresponding to the second time domain echo and obtaining the accurate motion parameters of the space target includes: 7.1, according to the Nelder-Mead algorithm, the rough motion parameters are initialized to the 7 vertices of the simplex vertex corresponds to a set of target motion polynomial coefficients; l1=0,1,2,3,4,5,6 are the vertex numbers; the stop condition is set as: l2=1,...,6 is the vertex number of the stopping condition; TL is the error threshold; Ed(·,·) represents the Euclidean distance calculation operation; 7.

2. Input the radial distance and radial velocity corresponding to each vertex into the discretized joint motion compensation model to obtain the second time domain echo after joint motion compensation processing, and calculate the image entropy corresponding to the second time domain echo through the image entropy calculation model in accordance with The value of the vertex Reorder to meet If the stop condition is met, execute 7.9; Otherwise, go to 7.

3. 7.

3. Calculate the reflection point by discretizing the joint motion compensation model and the image entropy calculation model Image entropy Reflection Points ρ′ is the reflection coefficient; To discard the vertex with the largest image entropy After that, the centroids of the first 6 vertices are calculated; 7.4, if The extension point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Extension Points γ′ is the expansion coefficient; if Then Replace with Continue with 7.2; otherwise, Replace with Continue with 7.

2. 7.5, if Then Replace with Continue with 7.

2. 7.6, if The shrinkage point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Pinch Point α′ is the contraction coefficient; if Then Replace with Continue to 7.2; otherwise, proceed to 7.8; 7.7, if The inner contraction point is calculated by the discretized joint motion compensation model and the image entropy calculation model Image entropy Inner contraction point if Inner contraction point Alternative Continue to 7.2; otherwise, proceed to 7.8; 7.8, Calculating the Fallback Point σ′ is the backoff coefficient, except Replace all vertices other than with fallback points and continue with 7.2; 7.9, stop the Nelder-Mead algorithm and get the precise motion parameter b of the space target fine , b fine The vertex with the smallest image entropy when the Nelder-Mead algorithm reaches the stopping condition The corresponding motion parameters.

5. The low signal-to-noise ratio inverse synthetic aperture radar joint motion compensation method according to claim 4, characterized in that: In step eight, the radial distance and radial velocity corresponding to the obtained precise motion parameters are input into the discretized joint motion compensation model to obtain the third time domain echo after the joint motion compensation processing, and the method of obtaining the ISAR image of the space target by two-dimensional Fourier transform of the third time domain echo includes: The third time domain echo is: in, is the third time domain echo; R T (m; b fine ) is the precise motion parameter b fine Corresponding radial distance; v(m; b fine ) is the precise motion parameter b fine The corresponding radial velocity; The third time domain echo is transformed into the ISAR image of the space target by two-dimensional Fourier transform. fine )for:

Images