An ISAR optimal imaging time period selection method and system based on D-S evidence theory

Abstract

The application discloses an ISAR optimal imaging time period selection method and system based on D-S evidence theory, and the method comprises the following steps: obtaining the number of distance units occupied by a sub-aperture image according to the sub-aperture image; obtaining Doppler broadening according to the envelope summation result of the distance units; obtaining image contrast according to the sub-aperture image; calculating the information entropy of the sub-aperture image, and calculating the target-background ratio of the sub-aperture image; obtaining the probability distribution function after sub-aperture image fusion based on the D-S evidence theory; selecting the central moment corresponding to the maximum sub-aperture image in all the probability distribution functions after fusion as the optimal imaging moment; performing ISAR imaging according to a preset time length search range with the optimal imaging moment as the center, and obtaining the optimal imaging time period based on the imaging result. The application can not only screen out an arc data segment with high azimuth resolution, but also consider the focusing quality of the image.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a method and system for selecting the optimal imaging time period for ISAR based on DS evidence theory. Background Technology

[0002] Inverse Synthetic Aperture Radar (ISAR) is a radar imaging technique that can acquire high-resolution images of non-cooperative moving targets, such as ships, aircraft, and satellites. ISAR imaging typically targets non-cooperative targets. For stationary targets, the Doppler frequency generated by the target's scattering points can be considered constant during the radar observation time. Therefore, using the traditional range-Doppler algorithm for imaging within the imaging accumulation time can yield good results. However, with the development of ISAR imaging technology and the increasing demands of observation, the observation scenarios and targets are constantly expanding. For non-stationary targets, such as ships and aircraft, directly imaging them using the traditional range-Doppler algorithm is difficult to achieve good results. Ships, in addition to their own maneuvering, are also affected by wave surges, exhibiting a motion dominated by their own maneuvering and simple harmonic vibrations. Aircraft targets, under the combined influence of their own maneuvering and atmospheric disturbances, exhibit a three-dimensional random vibration motion dominated by their own maneuvering. Both share a common characteristic: the target's motion state is unstable throughout the entire aperture time. To obtain good imaging results, it is necessary to select data from ISAR echo data for imaging, which is the optimal imaging time period selection technique.

[0003] Existing optimal imaging time period selection techniques can be broadly categorized into two types: image analysis-based selection algorithms and Doppler information-based selection algorithms. The first type of traditional algorithm does not consider any information about target motion; it selects the optimal imaging time period solely by evaluating certain indicators of the target image. The second type of traditional algorithm estimates the target's motion characteristics by estimating the Doppler broadening or Doppler center of the target's scattering points to select the optimal imaging time period.

[0004] However, while image analysis-based optimal imaging timing algorithms can determine image focus quality, they neglect target motion information, and the selected data segments may not be able to interpret the target shape. Optimal imaging timing methods based on Doppler information estimation can select arc segments with high azimuth resolution, but the imaging results may suffer from severe defocusing. Furthermore, low signal-to-noise ratios and abundant clutter severely interfere with Doppler broadening calculations, making these methods less robust and often ineffective at low signal-to-noise ratios. Neither approach can simultaneously achieve both high image focus quality and azimuth resolution.

[0005] Therefore, how to effectively select the optimal imaging time period in ISAR echo data has become an urgent problem to be solved. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides a method and system for selecting the optimal imaging time period for ISAR based on DS evidence theory.

[0007] The technical problem to be solved by this invention is achieved through the following technical solution:

[0008] A method for selecting the optimal imaging time period for ISAR based on DS evidence theory, the method comprising:

[0009] Acquire sub-aperture images of ISAR;

[0010] The number of distance cells occupied by the sub-aperture image is obtained based on the sub-aperture image;

[0011] Doppler broadening is obtained based on the summation of the envelope of the distance cell;

[0012] The image contrast is obtained based on the sub-aperture image;

[0013] Calculate the information entropy of the sub-aperture image, and calculate the target-to-background ratio of the sub-aperture image;

[0014] Based on the DS evidence theory, data fusion is performed according to the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the Doppler broadening, the image contrast, the information entropy, and the target-to-background ratio to obtain the probability allocation function after the sub-aperture image fusion.

[0015] The center time corresponding to the sub-aperture image with the largest probability assignment function among all fused images is selected as the optimal imaging time.

[0016] Centered on the optimal imaging time, ISAR imaging is performed according to a preset time search range to obtain the optimal imaging time period based on the imaging results.

[0017] Optionally, sub-aperture images of ISAR are acquired, including:

[0018] Let t m For azimuth slow time, then based on the scattering point p at time t m The instantaneous slant range caused by the rotational motion is used to obtain the slant range R between the scattering point p and the radar. p (t m The slant distance R p (t m ) is represented as:

[0019] R p (t m )=R0(t m )+ΔR p (t m )=R0+r(t m )+y p ·cosθ(t m )-x p ·sinθ(t m )

[0020] Wherein, R0(t) m ) represents the slant range history between the target's rotation center and the radar, ΔR p (t m ) represents the scattering point p at time t m The instantaneous slant range caused by rotational motion, R0 is the initial distance between the radar and the target position, and r(t) is the instantaneous slant range caused by rotational motion. m (x) represents the instantaneous change in slant distance caused by the target's translational motion. p ,y p Let θ be the coordinates of the scattering point p, and sinθ(t) be the coordinates of the scattering point p. m ) for t m The sine value, cosθ(t) m ) for t m The cosine value;

[0021] According to the Taylor expansion formula of trigonometric functions, sinθ(t) m )≈θ(t m )=ω e ·t m ,cosθ(t m )≈1, the slope distance R p (t m This can be represented as:

[0022] R p (t m )=R0+r(t m )+y p -x p ·ω e ·t m

[0023] Where, ω e (t m )=ω e ω e (t m The effective rotational speed is the target.

[0024] Based on the slope distance R p (t mThe echo signal at the scattering point p is obtained by combining the linear frequency modulated signal emitted by the radar with the echo signal emitted by the scattering point p. The echo signal at the scattering point p is expressed as follows:

[0025]

[0026] in, The echo signal is from scattering point p. For fast time, rect[·] is the unit rectangular window function, c is the electromagnetic wave propagation speed, and T is the time constant. p Where f is the pulse width, j is the imaginary unit, and f is the pulse width. c γ is the carrier frequency, and γ is the modulation frequency of the linear frequency modulated signal;

[0027] The echo signal from the scattering point p is divided into several sub-aperture echo signals, and the sub-aperture echo signals are subjected to carrier frequency removal and range pulse compression to obtain compressed sub-aperture echo signals. The compressed sub-aperture echo signals are represented as follows:

[0028]

[0029] in, For the compressed sub-aperture echo signal, σ p Let be the back-box scattering coefficient of scattering point p, sinc{·} be the sigma function, B be the bandwidth, and λ be the wavelength of the electromagnetic wave.

[0030] The total sub-aperture echo signal is obtained based on the compressed sub-aperture echo signal, and the total sub-aperture echo signal is expressed as follows:

[0031]

[0032] in, For the total echo signal of the sub-aperture;

[0033] The total echo signal of the sub-aperture is subjected to translational motion compensation to obtain the translationally compensated total echo signal of the sub-aperture, which is expressed as follows:

[0034]

[0035] in, The signal is after translational motion compensation;

[0036] The total echo signal of the sub-aperture after translational motion compensation is discretized to obtain the discretized total echo signal of the sub-aperture, which is expressed as follows:

[0037]

[0038] Where S(n; m) is the discretized signal, m is the index of the azimuth cell, and n is the index of the range cell. For fast time sampling intervals, Δt m Slow time sampling interval;

[0039] The discretized sub-aperture total echo signal is subjected to a Fourier transform in the azimuth dimension to obtain the sub-aperture image. The sub-aperture image in the data domain is represented as follows:

[0040]

[0041] Where I(n,k) is the sub-aperture image in the data domain, k is the index of the Doppler cell, and Δf a T is the Doppler frequency interval. a This is the interval for coherent processing.

[0042] Optionally, obtaining the number of distance cells occupied by the sub-aperture image based on the sub-aperture image includes:

[0043] The first sum envelope is obtained by summing the envelopes of each azimuth cell containing the sub-aperture image. The first sum envelope is expressed as:

[0044]

[0045] Where P1 is the first and envelope, M is the number of azimuth cells occupied by the sub-aperture image, and p 1m Let m be the envelope of the m-th orientation unit;

[0046] The first sum and envelope are compared with the first threshold. The first position in the first sum and envelope that is greater than the first threshold is selected as the lowest distance sequence number, and the last position that is greater than the first threshold is selected as the highest distance sequence number.

[0047] The number of distance cells occupied by the sub-aperture image is obtained based on the difference between the lowest distance sequence number and the highest distance sequence number.

[0048] Optionally, Doppler broadening is obtained based on the envelope summation result of the distance cell, including:

[0049] Summing the N distance cells yields the second sum envelope, which is expressed as:

[0050]

[0051] Where P2 is the second sum and envelope, N is the number of distance cells, and p 2n Let n be the envelope of the nth distance unit;

[0052] The second sum and envelope are compared with the second threshold. The first position in the second sum and envelope that is greater than the second threshold is selected as the first sequence number, and the last position that is greater than the second threshold is selected as the second sequence number.

[0053] Multiplying the first and second sequence numbers by the coefficients respectively yields f. min and f max ;

[0054] According to f max and f min The difference is widened by Doppler.

[0055] Optionally, the image contrast is represented as:

[0056]

[0057] Where IC is the image contrast, E{·} is the calculated mean, |I(n,k)| represents the amplitude of the pixel position (n,k) in the sub-aperture image, k is the index of the Doppler unit, and n is the index of the distance unit.

[0058] Optionally, the information entropy is represented as:

[0059]

[0060]

[0061] Among them, E g Let be the information entropy, M be the number of azimuth cells in the sub-aperture image, N be the number of range cells, k be the index of the Doppler cell, and |I(n,k)| represent the amplitude of the pixel position (n,k) in the sub-aperture image.

[0062] Optionally, the target-to-background ratio is expressed as:

[0063]

[0064] Where TBR is the target-to-background ratio, |I(n,k)| represents the magnitude of the pixel position (n,k) in the sub-aperture image, T1 is the set of pixel units of the target, and T2 is the set of pixel units of the background.

[0065] Optionally, based on DS evidence theory, data fusion is performed according to the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the Doppler broadening, the image contrast, the information entropy, and the target-to-background ratio to obtain the fused probability allocation function, including:

[0066] The basic probability allocation function for obtaining the number of distance cells occupied by the sub-aperture image, the basic probability allocation function for Doppler broadening, the basic probability allocation function for image contrast, the basic probability allocation function for information entropy, and the basic probability allocation function for target-to-background ratio;

[0067] Based on the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the basic probability allocation function of Doppler broadening, the basic probability allocation function of image contrast, the basic probability allocation function of information entropy, and the basic probability allocation function of target-to-background ratio, data fusion is performed according to the DS synthesis rule to obtain the probability allocation function after sub-aperture image fusion.

[0068] Optionally, ISAR imaging is performed centered on the optimal imaging time and within a preset time search range to obtain the optimal imaging time period based on the imaging results, including:

[0069] Centered on the optimal imaging time, a preset search is performed within a preset time range according to time l, and [T] is then searched. opt -l / 2,T opt ISAR imaging was performed on the echoes within the time period +l / 2] to obtain the imaging results, where T opt The optimal imaging time;

[0070] The image with the highest contrast among all the imaging results is selected as the optimal cumulative duration l. opt ;

[0071] The optimal imaging time period is obtained based on the optimal cumulative duration lopt, and the optimal imaging time period is [T]. opt -l opt / 2,T opt +l opt / 2].

[0072] This invention also provides an optimal imaging time period selection system for ISAR based on DS evidence theory, the selection system comprising:

[0073] The acquisition module is used to acquire sub-aperture images of ISAR;

[0074] A distance cell number generation module is used to obtain the number of distance cells occupied by the sub-aperture image based on the sub-aperture image;

[0075] The Doppler broadening generation module is used to obtain Doppler broadening based on the envelope summation result of the distance cell;

[0076] An image contrast generation module is used to obtain the image contrast based on the sub-aperture image;

[0077] Information entropy generation module, used to calculate the information entropy of the sub-aperture image;

[0078] The target background ratio generation module is used to calculate the target background ratio of the sub-aperture image;

[0079] The probability allocation function generation module is used to perform data fusion based on the DS evidence theory, according to the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the Doppler broadening, the image contrast, the information entropy and the target-to-background ratio, to obtain the probability allocation function after the sub-aperture image fusion.

[0080] The optimal imaging time generation module is used to select the center time corresponding to the sub-aperture image with the largest probability allocation function among all fused images as the optimal imaging time.

[0081] The optimal imaging time period generation module is used to perform ISAR imaging based on the optimal imaging time as the center and according to a preset time period search range, so as to obtain the optimal imaging time period based on the imaging results.

[0082] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0083] This invention is based on DS evidence theory. It performs data fusion based on the basic probability allocation function of the number of range cells occupied by the sub-aperture image, Doppler broadening, image contrast, information entropy, and target-to-background ratio. The data fusion results are then used to select the optimal time period for ISAR echo data. This method can select arc data segments with high azimuth resolution while also taking into account the image focusing quality, thus improving the problem of balancing resolution and focusing quality in the selection of imaging time periods.

[0084] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0085] Figure 1 This is a flowchart illustrating an ISAR optimal imaging time period selection method based on DS evidence theory provided in an embodiment of the present invention.

[0086] Figure 2 This is a flowchart illustrating another method for selecting the optimal imaging time period for ISAR based on DS evidence theory, provided in an embodiment of the present invention.

[0087] Figure 3 This is a schematic diagram of an ISAR turntable imaging model provided in an embodiment of the present invention;

[0088] Figure 4 This is a schematic diagram of a simulated three-dimensional ship model provided in an embodiment of the present invention;

[0089] Figure 5 This is a schematic diagram of a ship's three-dimensional rolling motion provided in an embodiment of the present invention;

[0090] Figure 6a and Figure 6b This is a schematic diagram of experimental results based on ship simulation data provided in an embodiment of the present invention;

[0091] Figure 7a and Figure 7b A schematic diagram of experimental results based on aircraft measured data provided in an embodiment of the present invention;

[0092] Figure 8 This is a schematic diagram of an ISAR optimal imaging time period selection system based on DS evidence theory provided in an embodiment of the present invention. Detailed Implementation

[0093] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0094] Example 1

[0095] ISAR imaging typically targets non-cooperative targets. For targets undergoing non-stationary motion, such as ships oscillating in three dimensions on the sea surface, precessing missiles, and maneuvering aircraft, directly imaging using traditional range-Doppler algorithms is difficult to achieve good results. To obtain good imaging results, it is necessary to select data segments from the ISAR echo data for imaging, i.e., the optimal imaging time period selection technique. The main task of optimal imaging time period selection is to select data segments from ISAR echo data to achieve good imaging effects. This invention focuses on the data fusion problem of target Doppler information and image information in ISAR echo data, forming a method for fusion evaluation of image quality and solving the problem of optimal imaging time period selection in ISAR echo data.

[0096] Based on this, please see Figure 1 , Figure 1 This is a flowchart illustrating an ISAR optimal imaging time period selection method based on DS evidence theory provided by an embodiment of the present invention. The ISAR optimal imaging time period selection method based on DS evidence theory provided by the present invention includes:

[0097] Step 1: Obtain the sub-aperture image of ISAR.

[0098] In an optional embodiment, step 1 may specifically include:

[0099] Step 1.1, based on the scattering point p at t m The instantaneous slant range caused by rotational motion is used to obtain the slant range R between the scattering point p and the radar.p (t m ).

[0100] In this embodiment, the imaging target of ISAR is generally a non-cooperative target. The relative motion components between the target and the radar include translational and rotational components. Generally, the influence of the translational component on target imaging is not negligible. After translational compensation processing, the target can be transformed into a turntable model. A schematic diagram of the turntable model is shown below. Figure 3 The imaging principle of ISAR is explained below using the geometric model of the target's turntable.

[0101] Let the coordinates of the scattering point p on the target at the initial moment in the imaging plane be (x...). p ,y p If the scattering point p is at time t, then... m The instantaneous slant distance ΔR caused by rotational motion at any moment p (t m )for:

[0102] ΔR p (t m )=y p ·cosθ(t m )-x p ·sinθ(t m )

[0103] Wherein, sinθ(t) m ) for t m The sine value, cosθ(t) m ) for t m The cosine value, t m This refers to the location over a longer period of time.

[0104] Considering the instantaneous change in slant range caused by the initial slant range and translational motion, the slant range R between the scattering point p and the radar... p (t m This can be represented as:

[0105] R p (t m )=R0(t m )+ΔR p (t m )=R0+r(t m )+y p ·cosθ(t m )-x p ·sinθ(t m )

[0106] Wherein, R0(t) m R0 is the slant range history between the target's rotation center and the radar, and R0 is the initial distance between the radar and the target position. mR0+r(t) represents the instantaneous change in slant range caused by the target's translational motion. This change is the same for all points on the target. m The slant distance between the target's rotation center and the radar is indicated by ).

[0107] For optimal ISAR imaging timeframes, the coherence accumulation angle is typically small and changes smoothly. Furthermore, due to target inertia, its attitude changes are not overly complex. Therefore, the target's rotational motion can be approximated as uniform rotational speed. Let the effective rotational speed of the target be ω. e (t m According to the Taylor expansion formula of trigonometric functions, sinθ(t) m )≈θ(t m )=ω e ·t m ,cosθ(t m )≈1,R p (t m This can be expressed as:

[0108] R p (t m )=R0+r(t m )+y p -x p ·ω e ·t m

[0109] Where, ω e (t m )=ω e ω e (t m The effective rotational speed is the target.

[0110] Step 1.2, based on slant distance R p (t m The echo signal from the scattering point p is obtained by combining the linear frequency modulation (LFM) signal emitted by the radar with the echo signal emitted by the radar.

[0111] Specifically, assuming the radar transmits a linear frequency modulated signal, the echo signal from the scattering point p can be expressed as:

[0112]

[0113] in, The echo signal is from scattering point p. For fast time, rect[·] is the unit rectangular window function, c is the electromagnetic wave propagation speed, and T is the time constant. p Where f is the pulse width, j is the imaginary unit, and f is the pulse width. c γ is the carrier frequency, and γ is the modulation frequency of the LFM signal.

[0114] Step 1.3: Divide the echo signal from scattering point p into several sub-aperture echo signals, and perform carrier frequency removal and range pulse compression on the sub-aperture echo signals to obtain compressed sub-aperture echo signals.

[0115] Specifically, the echo signal from scattering point p is divided into multiple sub-aperture echo signals. The length of each sub-aperture is an empirical value, which can be estimated using the pulse repetition frequency and the target's motion information. Then, the sub-aperture echo signals are subjected to carrier frequency removal and range pulse compression. The compressed sub-aperture echo signal can then be expressed as:

[0116]

[0117] in, For the compressed sub-aperture echo signal, σ p Let be the back-box scattering coefficient of the scattering point p, sinc{·} be the sigma function, B be the bandwidth, and λ be the wavelength of the electromagnetic wave.

[0118] Step 1.4: Obtain the total sub-aperture echo signal based on the compressed sub-aperture echo signal.

[0119] Specifically, each sub-aperture echo signal also includes several sub-signals. Therefore, the total signal of the sub-aperture echo signal composed of these sub-signals (i.e., the total sub-aperture echo signal) is expressed as:

[0120]

[0121] in, This is the total echo signal of the sub-aperture.

[0122] Step 1.5: Perform translational motion compensation on the sub-aperture total echo signal to obtain the translationally compensated sub-aperture total echo signal. The translationally compensated sub-aperture total echo signal is expressed as:

[0123]

[0124] in, This is the signal after translational motion compensation.

[0125] Step 1.6: Discretize the total echo signal of the sub-aperture after translational motion compensation to obtain the discretized total echo signal of the sub-aperture. The discretized total echo signal of the sub-aperture is represented as follows:

[0126]

[0127] Where S(n; m) is the discretized signal, n is the index of the distance unit (i.e., the index of the fast time unit), and m is the index of the azimuth unit (i.e., the index of the slow time unit). For fast time sampling intervals, Δt m This is a slow sampling interval.

[0128] Step 1.7: Perform a Fourier transform on the discretized sub-aperture total echo signal in the azimuth dimension to obtain the sub-aperture image. The sub-aperture image in the data domain is represented as follows:

[0129]

[0130] Where I(n,k) is the sub-aperture image in the data domain, k is the index of the Doppler cell, and Δf a T is the Doppler frequency interval. a This is the interval for coherent processing.

[0131] Step 2: Obtain the number of distance cells occupied by the sub-aperture image based on the sub-aperture image.

[0132] In an optional embodiment, step 2 may specifically include:

[0133] Step 2.1: Summate the envelopes of each azimuth cell containing the sub-aperture image to obtain the first sum envelope, which is expressed as:

[0134]

[0135] Where P1 is the first and envelope, M is the number of azimuth cells occupied by the sub-aperture image, and p 1m Let be the envelope of the m-th orientation unit.

[0136] Step 2.2: Compare the first sum and envelope with the first threshold, select the first position in the first envelope that is greater than the first threshold as the lowest distance sequence number, and select the last position that is greater than the first threshold as the highest distance sequence number.

[0137] Specifically, the first sum and envelope are compared with the first threshold. The first position point in the first sum and envelope that is greater than the first threshold is selected as the lowest distance sequence number. After the lowest distance sequence number, multiple points will appear consecutively with the first sum and envelope that are also greater than the first threshold. The last position point after these consecutive points that is greater than the first threshold is also selected as the highest distance sequence number.

[0138] It should be noted that this embodiment does not specifically limit the first threshold, and those skilled in the art can set the first threshold according to actual needs.

[0139] Step 2.3: Calculate the number of distance cells occupied by the sub-aperture image based on the difference between the lowest and highest distance sequence numbers.

[0140] Specifically, the difference between the highest and lowest distance sequence numbers is the length between the two points. This length is approximately the number of distance cells occupied by the target. Therefore, this length is used as the number of distance cells d occupied by the sub-aperture image.

[0141] Step 3: Obtain Doppler broadening based on the summation of the envelopes of the distance cells.

[0142] In an optional embodiment, step 3 may specifically include:

[0143] Step 3.1: Summate the N distance cells to obtain the second sum envelope, which is represented as:

[0144]

[0145] Where P2 is the second sum and envelope, N is the number of distance cells, and p 2n Let be the envelope of the nth distance unit.

[0146] Step 3.2: Compare the second sum and envelope with the second threshold, select the first position in the second envelope sum that is greater than the second threshold as the first sequence number, and select the last position that is greater than the second threshold as the second sequence number.

[0147] Step 3.3: Multiply the first sequence number and the second sequence number by the coefficient PRF respectively to obtain f. min and f max .

[0148] Here, PRF stands for Pulse Repetition Frequency.

[0149] Step 3.4, according to f max and f min The difference is widened by Doppler.

[0150] Specifically, Doppler broadening and the effective rotation vector change synchronously. Based on the relationship between angular velocity and Doppler frequency, this problem can be equivalently represented as finding the time period during which the target's Doppler broadening is maximized and stable. The effective rotation vector is measured by calculating the Doppler broadening of the echo data, and the optimal imaging time is selected by choosing the data segment where the effective rotation vector is stable and has a large amplitude. In this embodiment, the corresponding f is calculated by summing the envelopes of each range cell. max and f min Calculate the difference f max -f min As a broadening of Doppler f ds That is, f ds =f max -f min .

[0151] Step 4: Obtain image contrast based on sub-aperture images.

[0152] In this embodiment, high-quality ISAR images are visually clear, with high contrast and distinct target structural features. From a signal perspective, they typically have a high peak-to-sidelobe ratio. This method uses image contrast as the criterion for judging ISAR images and as the condition for selecting the optimal imaging time period.

[0153] Specifically, the image contrast of each sub-aperture image is calculated, and the image contrast is defined as follows:

[0154]

[0155] Where IC is the image contrast, |I(n,k)| represents the magnitude of the pixel position (n,k) in the sub-aperture image, and E{·} is the calculated mean.

[0156] Image contrast is essentially the calculation of the normalized variance of an image. As shown in the above formula, when the image is poorly focused, the amplitude values ​​|I(n,k)| at each point in the image matrix are all around the image mean. At this time, the standard deviation of the image is smaller than when the image is well focused. Therefore, the better the image focus, the larger the IC will be.

[0157] Step 5: Calculate the information entropy of the sub-aperture image.

[0158] Specifically, the concept of entropy in information theory is used to describe the amount of information. It was later introduced into the field of image processing to measure the degree of focus of an image.

[0159] Here, the information entropy of each sub-aperture image is calculated, and the information entropy is expressed as:

[0160]

[0161]

[0162] Among them, E g Let M be the information entropy, N be the number of azimuth cells containing the sub-aperture image, k be the index of the Doppler cell, I(n,k) be the sub-aperture image in the data domain, and D be the information entropy. nk Let I(n,k) be the probability of I(n,k) in the image.

[0163] The lower the information entropy of an ISAR image, the more information it contains and the better its focusing performance; conversely, the image has poor focusing performance and is not clear.

[0164] Step 6: Calculate the target-to-background ratio of the sub-aperture image.

[0165] Specifically, a target-to-background ratio criterion is incorporated to characterize the SNR of target imaging. To calculate the target-to-background ratio, an appropriate threshold is selected to divide the imaging plane into a target region and a background region. Signals falling within the target region are defined as target signals, while those outside are considered background noise.

[0166] Calculate the target-to-background ratio for each sub-aperture image. First, select an appropriate threshold to divide the ISAR image into target and background regions. The formula for calculating the target-to-background ratio is as follows:

[0167]

[0168] Where T1 is the set of pixel units of the target, T2 is the set of pixel units of the background, and TBR is the target-to-background ratio, which is the ratio of target energy to background energy. TBR can effectively reduce the impact of false points on evaluation indicators, and at the same time, TBR also effectively characterizes the SNR of target imaging.

[0169] Step 7: Based on the DS evidence theory, perform data fusion according to the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, Doppler broadening, image contrast, information entropy and target-to-background ratio to obtain the probability allocation function after sub-aperture image fusion.

[0170] In an optional embodiment, step 7 may specifically include:

[0171] Step 7.1: Obtain the basic probability allocation function for the number of distance cells occupied by the sub-aperture image, the basic probability allocation function for Doppler broadening, the basic probability allocation function for image contrast, the basic probability allocation function for information entropy, and the basic probability allocation function for target-to-background ratio.

[0172] Specifically, different imaging times are denoted as Θ as the sample space. The corresponding data at each time are calculated and normalized before preprocessing, and their proportions are used as the basic probability allocation function. The formula for calculating the basic probability allocation function is as follows:

[0173]

[0174] Where m represents the basic probability assignment function, A q Let f represent the q-th sub-aperture image, where Q is the total number of sub-aperture images. There are J indices, and Z(j) represents the j-th index. These indices are the number of range cells occupied by the sub-aperture image, Doppler broadening, image contrast, information entropy, and target-to-background ratio. For example, using Doppler broadening f... ds For example, Doppler broadening f ds The formula for calculating the basic probability assignment function is:

[0175]

[0176] Among them, m1(A q Doppler broadening f for the q-th sub-aperture image ds The basic probability assignment function.

[0177] Step 7.2: Based on the basic probability allocation functions of the number of distance cells occupied by the sub-aperture image, the basic probability allocation function of Doppler broadening, the basic probability allocation function of image contrast, the basic probability allocation function of information entropy, and the basic probability allocation function of target-to-background ratio, data fusion is performed according to the DS synthesis rules to obtain the probability allocation function after sub-aperture image fusion.

[0178] Specifically, DS evidence theory is a theory for handling uncertain information; it can fuse uncertain information. DS evidence theory is an important extension of traditional Bayesian theory, capable of handling both single and combined hypotheses. Therefore, when using DS evidence theory to fuse ISAR data segments using multiple criteria, the probability assignment function after sub-aperture image fusion is calculated as follows:

[0179]

[0180]

[0181] in, Let be the probability assignment function after fusing the q-th sub-aperture image.

[0182] Step 8: Select the center time corresponding to the sub-aperture image with the highest probability among all fused probability assignment functions as the optimal imaging time.

[0183] Specifically, step 7 yields the probability allocation function for each fused sub-aperture image. The sub-aperture image with the highest probability is selected from the probabilities calculated by all fused probability allocation functions, and the center time corresponding to that sub-aperture image is taken as the optimal imaging time.

[0184] Step 9: Using the optimal imaging time as the center, perform ISAR imaging according to the preset time search range to obtain the optimal imaging time period based on the imaging results.

[0185] In an optional embodiment, step 9 may specifically include:

[0186] Step 9.1: Centered on the optimal imaging time, perform a preset search within a preset time range according to time duration l, and then search for [T]. opt -l / 2,T opt ISAR imaging was performed on the echoes within the time period +l / 2] to obtain the imaging results, where T opt This is the optimal imaging time.

[0187] Specifically, first, a preset search duration range is set, denoted as [l min ,l max Then, taking the optimal imaging time as the center, a preset search is performed within a preset time range according to duration l. This preset search can be performed sequentially within the preset time range according to duration l, or it can be performed at intervals according to duration l, thereby obtaining the value of each duration l within [T]. opt -l / 2,T opt Imaging results of ISAR imaging within the time period of +l / 2].

[0188] Step 9.2: Select the image with the highest contrast among all imaging results as the optimal accumulation time l. opt .

[0189] It should be noted that, in order to reduce the amount of computation during the search for the optimal cumulative duration in this embodiment, a large step size can be used for the search first, and then a small step size search can be performed to determine the optimal cumulative duration after narrowing down the range.

[0190] Step 9.3: Obtain the optimal imaging time period based on the optimal cumulative duration lopt. The optimal imaging time period is [T]. opt -l opt / 2,T opt +l opt / 2].

[0191] After obtaining the optimal imaging time period, this embodiment can perform ISAR imaging on the echoes during the optimal imaging time period to obtain the final imaging result.

[0192] The effectiveness of this invention can be verified using simulation and experimental data:

[0193] The invented algorithm was validated using simulated and measured ISAR data. The simulated target was a ship, and the model contained 295 scattering points. Its 3D model is shown below. Figure 4 In the simulation experiment, the ship's motion was set as translation and three-dimensional oscillation. In the three-dimensional oscillation motion (i.e., the actual motion), the ship experiences three-dimensional rotation due to wind speed and wave thrust. The ship's rotation along the X, Y, and Z axes manifests as roll, yaw, and pitch, respectively, which can be decomposed into three components along the XYZ axes: θ r θ p and θ y , representing the angles of roll, pitch, and yaw of the ship, respectively. A schematic diagram of their motion is shown below. Figure 5As shown. The angle between the ship's coordinate system and the radar line-of-sight is defined as α. The value of α changes as the ship's motion changes. The transformation from the ship's coordinate system to the radar coordinate system involves the rotation matrix rot(α):

[0194]

[0195] The ship's total rotation matrix is:

[0196] rot(θ r ,θ p ,θ y ) = roll(θ r )·pitch(θ p )·yav(θ y )

[0197] The ship's sway angle roughly follows a sine and cosine law, and the rotation angle can be expressed as:

[0198]

[0199] In the above formula, A i This is the amplitude value, used to represent the maximum value of the ship's rotation. The ship's initial phase is φ. i , indicating the ship's initial position, T i Indicates the period of a ship's movement.

[0200] The imaging results of this invention based on the selected imaging time period of the simulation data are as follows: Figure 6a and Figure 6b The target in the ISAR measured data is an aircraft target exhibiting maneuvering motion. The imaging results of this invention, based on the measured data and selecting an imaging time period, are as follows: Figure 7a and Figure 7b .

[0201] Based on the principle of ISAR imaging, this invention designs multiple evaluation indicators for ISAR imaging data segments of non-stationary targets such as ships and aircraft to improve the robustness of the selection of the optimal ISAR imaging time period. This invention uses DS evidence theory to perform decision-level fusion of data under multiple evaluation criteria of sub-aperture images to obtain the probability allocation of each fused sub-aperture image. The selection is made based on the result of the probability allocation to improve the accuracy of the selection of the optimal ISAR imaging time period.

[0202] First, the method proposed in this invention uses data fusion results to select the optimal time period for ISAR echo data, which can not only filter out arc data segments with high azimuth resolution, but also take into account the image focusing quality, thus improving the problem of difficulty in balancing resolution and focusing quality in the selection of imaging time period.

[0203] Second, the method proposed in this invention can reduce the problem of extreme data affecting selection when the target information is estimated incorrectly, and provide more effective data support for subsequent refined compensation or identification operations.

[0204] Third, the method proposed in this invention can select the optimal imaging time period for ISAR for various non-stationary targets, and the selection effect is good.

[0205] Example 2

[0206] Please see Figure 8 , Figure 8 This is a schematic diagram of an ISAR optimal imaging time period selection system based on DS evidence theory provided in an embodiment of the present invention. The ISAR optimal imaging time period selection system based on DS evidence theory provided in this embodiment of the present invention includes:

[0207] The acquisition module is used to acquire sub-aperture images of ISAR;

[0208] A distance cell number generation module is used to obtain the number of distance cells occupied by the sub-aperture image based on the sub-aperture image;

[0209] The Doppler broadening generation module is used to obtain Doppler broadening based on the envelope summation result of the distance cell;

[0210] An image contrast generation module is used to obtain the image contrast based on the sub-aperture image;

[0211] Information entropy generation module, used to calculate the information entropy of the sub-aperture image;

[0212] The target background ratio generation module is used to calculate the target background ratio of the sub-aperture image;

[0213] The probability allocation function generation module is used to perform data fusion based on the DS evidence theory, according to the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the Doppler broadening, the image contrast, the information entropy and the target-to-background ratio, to obtain the probability allocation function after the sub-aperture image fusion.

[0214] The optimal imaging time generation module is used to select the center time corresponding to the sub-aperture image with the largest probability allocation function among all fused images as the optimal imaging time.

[0215] The optimal imaging time period generation module is used to perform ISAR imaging based on the optimal imaging time as the center and according to a preset time period search range, so as to obtain the optimal imaging time period based on the imaging results.

[0216] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0217] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0218] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0219] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for selecting the optimal imaging time period for ISAR based on DS evidence theory, characterized in that, The selection method includes: Acquire sub-aperture images of ISAR; The number of distance cells occupied by the sub-aperture image is obtained from the sub-aperture image; Doppler broadening is obtained based on the summation of the envelope of the distance cell; The image contrast is obtained based on the sub-aperture image; Calculate the information entropy of the sub-aperture image, and calculate the target-to-background ratio of the sub-aperture image; Based on the DS evidence theory, data fusion is performed according to the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the Doppler broadening, the image contrast, the information entropy, and the target-to-background ratio to obtain the probability allocation function after the sub-aperture image fusion. The center time corresponding to the sub-aperture image with the largest probability assignment function among all fused images is selected as the optimal imaging time. Centered on the optimal imaging time, ISAR imaging is performed according to a preset time search range to obtain the optimal imaging time period based on the imaging results. Acquire sub-aperture images of ISAR, including: set up For azimuth slow time, then based on the scattering point p exist The scattering point is obtained from the instantaneous slant distance caused by the rotational motion. p Slant range between radar and The slant distance Represented as: in, The slant range history between the target's rotation center and the radar. For scattering points p exist The instantaneous slant distance caused by rotational motion at any given moment. The initial distance between the radar and the target position. The instantaneous change in slant distance caused by the translational motion of the target. For scattering points p coordinates for The sine value, for The cosine value; According to the Taylor expansion formula of trigonometric functions , The slant distance It can be represented as: in, , The effective rotational speed for the target; Based on the slope distance The scattering point is obtained from the linear frequency modulated signal emitted by the radar. p The echo signal, the scattering point p The echo signal is represented as: in, For scattering points p echo signal, To save time, For unit rectangular window functions, c The speed of electromagnetic wave propagation. The pulse width. The imaginary unit, For carrier frequency, The modulation frequency of a linear frequency modulated signal; The scattering point p The echo signal is divided into several sub-aperture echo signals, and the sub-aperture echo signals are subjected to carrier frequency removal and range pulse compression to obtain compressed sub-aperture echo signals. The compressed sub-aperture echo signals are represented as follows: in, This is the compressed sub-aperture echo signal. For scattering points p The back-box scattering coefficient, For the Singer function, For bandwidth, The wavelength of electromagnetic waves; The total sub-aperture echo signal is obtained based on the compressed sub-aperture echo signal, and the total sub-aperture echo signal is expressed as follows: in, For the total echo signal of the sub-aperture; The total echo signal of the sub-aperture is subjected to translational motion compensation to obtain the translationally compensated total echo signal of the sub-aperture, which is expressed as follows: in, The signal is after translational motion compensation; The total echo signal of the sub-aperture after translational motion compensation is discretized to obtain the discretized total echo signal of the sub-aperture, which is expressed as follows: in, The signal is discretized. This is the serial number of the azimuth unit. This is the index of the distance cell. For fast sampling intervals, Slow time sampling interval; The discretized sub-aperture total echo signal is subjected to a Fourier transform in the azimuth dimension to obtain the sub-aperture image. The sub-aperture image in the data domain is represented as follows: in, For sub-aperture images in the data domain, The serial number of the Doppler element. The Doppler frequency interval, This is the interval for coherent processing.

2. The method for selecting the optimal imaging time period for ISAR based on DS evidence theory according to claim 1, characterized in that, The number of distance cells occupied by the sub-aperture image is obtained based on the sub-aperture image, including: The first sum envelope is obtained by summing the envelopes of each azimuth cell containing the sub-aperture image. The first sum envelope is expressed as: in, For the first and envelope, M This represents the number of azimuth cells occupied by the sub-aperture image. For the first m The envelope of each directional unit; The first sum and envelope are compared with the first threshold. The first position in the first sum and envelope that is greater than the first threshold is selected as the lowest distance sequence number, and the last position that is greater than the first threshold is selected as the highest distance sequence number. The number of distance cells occupied by the sub-aperture image is obtained based on the difference between the lowest distance sequence number and the highest distance sequence number.

3. The method for selecting the optimal imaging time period for ISAR based on DS evidence theory according to claim 1, characterized in that, Doppler broadening is obtained based on the envelope summation result of the distance cell, including: right Summing the distance units yields a second sum envelope, which is expressed as follows: in, For the second and envelope, The number of distance cells. For the first n The envelope of a distance unit; The second sum and envelope are compared with the second threshold. The first position in the second sum and envelope that is greater than the second threshold is selected as the first sequence number, and the last position that is greater than the second threshold is selected as the second sequence number. Multiply the first and second sequence numbers by the coefficients respectively to obtain the corresponding results. and ; according to and The difference is widened by Doppler.

4. The method for selecting the optimal imaging time period for ISAR based on DS evidence theory according to claim 1, characterized in that, The image contrast is represented as: in, For image contrast, To calculate the mean, The pixel position in the sub-aperture image is n , k The range, The serial number of the Doppler element. This is the sequence number of the distance unit.

5. The method for selecting the optimal imaging time period for ISAR based on DS evidence theory according to claim 1, characterized in that, The information entropy is represented as: in, For information entropy, M This represents the number of azimuth cells containing the sub-aperture image. The number of distance cells. The serial number of the Doppler element. The pixel position in the sub-aperture image is n , k The range.

6. The method for selecting the optimal imaging time period for ISAR based on DS evidence theory according to claim 1, characterized in that, The target-to-background ratio is expressed as: in, For target background ratio, The pixel position in the sub-aperture image is n , k The range, The set of pixel units for the target. The set of pixel units for the background.

7. The method for selecting the optimal imaging time period for ISAR based on DS evidence theory according to claim 1, characterized in that, Based on DS evidence theory, data fusion is performed according to the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the Doppler broadening, the image contrast, the information entropy, and the target-to-background ratio, resulting in a fused probability allocation function, including: The basic probability allocation function for obtaining the number of distance cells occupied by the sub-aperture image, the basic probability allocation function for Doppler broadening, the basic probability allocation function for image contrast, the basic probability allocation function for information entropy, and the basic probability allocation function for target-to-background ratio; Based on the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the basic probability allocation function of Doppler broadening, the basic probability allocation function of image contrast, the basic probability allocation function of information entropy, and the basic probability allocation function of target-to-background ratio, data fusion is performed according to the DS synthesis rule to obtain the probability allocation function after sub-aperture image fusion.

8. The method for selecting the optimal imaging time period for ISAR based on DS evidence theory according to claim 1, characterized in that, Centered on the optimal imaging time, ISAR imaging is performed according to a preset time search range to obtain the optimal imaging time period based on the imaging results, including: Centered on the optimal imaging time, within a preset time range, search according to the duration... l Perform a preset search and... ISAR imaging was performed on the echoes within a certain time period to obtain the imaging results, among which... The optimal imaging time; Select the image with the highest image contrast from all the imaging results. l As the optimal cumulative duration ; Based on the optimal cumulative duration The optimal imaging time period is obtained, and the optimal imaging time period is: .

9. A system for selecting the optimal imaging time period for ISAR based on DS evidence theory, characterized in that, For executing the ISAR optimal imaging time period selection method based on DS evidence theory as described in any one of claims 1-8, the selection system comprises: The acquisition module is used to acquire sub-aperture images of ISAR; A distance cell number generation module is used to obtain the number of distance cells occupied by the sub-aperture image based on the sub-aperture image; The Doppler broadening generation module is used to obtain Doppler broadening based on the envelope summation result of the distance cell; An image contrast generation module is used to obtain the image contrast based on the sub-aperture image; Information entropy generation module, used to calculate the information entropy of the sub-aperture image; The target background ratio generation module is used to calculate the target background ratio of the sub-aperture image; The probability allocation function generation module is used to perform data fusion based on the DS evidence theory, according to the basic probability allocation function of the number of distance cells occupied by the sub-aperture image, the Doppler broadening, the image contrast, the information entropy and the target-to-background ratio, to obtain the probability allocation function after the sub-aperture image fusion. The optimal imaging time generation module is used to select the center time corresponding to the sub-aperture image with the largest probability allocation function among all fused images as the optimal imaging time. The optimal imaging time period generation module is used to perform ISAR imaging based on the optimal imaging time as the center and according to a preset time period search range, so as to obtain the optimal imaging time period based on the imaging results.

Images