Array aperture expansion method based on motion platform distance Doppler domain extrapolation

Abstract

The invention relates to an array aperture expansion method based on motion platform distance Doppler domain extrapolation, and belongs to the technical field of radar array signal processing. Comprising the following steps: receiving echo data of a target by using a motion array, and performing down-conversion and time domain segmentation processing on each array element data; performing distance Doppler transformation and target detection on the baseband data of each array element and each time period to obtain distance Doppler unit data of a target; target distance and speed are obtained and are suitable for moving target detection; and extrapolation processing is carried out based on target distance Doppler unit data of different array elements and different time periods, an estimated value of virtual array element data is obtained, and array aperture expansion is realized. The method is suitable for a shipborne high-frequency ground wave system radar, and through the distance Doppler domain processing and time domain segmentation technology, the problems that the radar array aperture is small and the radar angle measurement performance is reduced due to the limited space of a shipborne platform are solved.

Description

Technical Field

[0001] The invention relates to an array aperture expansion method based on moving platform range Doppler domain extrapolation, and belongs to the technical field of radar array signal processing. Background Art

[0002] High-frequency ground-wave over-the-horizon radar (HFGSWR) operates in the 3-30 MHz frequency band, utilizing vertically polarized electromagnetic waves propagating across the sea surface. This enables detection of targets beyond the horizon, unaffected by weather, and possesses significant military and civilian applications. Shipborne HFGSWR systems further enhance the radar's flexibility and detection range by deploying antenna arrays onboard ships. However, spatial limitations of shipborne platforms result in a relatively small antenna array aperture, which reduces the radar's angle estimation performance and limits its effectiveness. To address this issue, various array aperture expansion methods have been proposed. However, these existing aperture expansion methods still have limitations in practical applications. For example, traditional aperture expansion methods typically rely on time-domain signal processing, making them unsuitable for use in strong clutter scenarios. For example: the publication number is CN116520276A, and the name of the invention is "Motion Synthetic Array Aperture Expansion Method Based on Generalized Coprime Arrays". Its technical solution discloses a coprime array synthetic aperture method, which utilizes the time domain information of the echo signal and synthesizes a virtual aperture based on the array motion, increases the flexibility of signal processing, improves the number of estimable signal sources, and enhances the angular resolution capability of the radar; however, it is not suitable for scenarios where non-target signals dominate, and the more complex solution method affects its real-time performance.

[0003] Therefore, it is urgent to propose an array aperture expansion method based on the range-Doppler domain extrapolation of the moving platform to solve the above technical problems. Summary of the Invention

[0004] To address the above-mentioned issues, a method for array aperture expansion based on range-Doppler domain extrapolation of a moving platform is provided. A brief overview of the invention is provided below to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive overview of the invention. It is not intended to identify key or important aspects of the invention, nor is it intended to limit the scope of the invention.

[0005] The technical solution of the present invention:

[0006] A method for array aperture expansion based on range-Doppler domain extrapolation of a moving platform comprises the following steps:

[0007] Step 1: Use the motion array to receive the target's echo data, and perform down-conversion and time-domain segmentation processing on each array element;

[0008] Step 2: Perform range-Doppler transform and target detection on the baseband data of each array element and each time period to obtain the range-Doppler unit data of the target; obtain the target range and speed, which is suitable for moving target detection;

[0009] Step 3: Based on the target range Doppler unit data of different array elements and different time periods, extrapolation processing is performed to obtain the estimated value of the virtual array data to achieve array aperture expansion.

[0010] Preferably: in step 1, the receiving antenna is arranged in a uniform linear array on one side of the moving platform, the platform moves in a uniform linear motion, the target moves in a stationary or uniform linear motion and is located in the far field of the antenna; down-conversion processing is performed by removing the carrier frequency in the target echo signal to obtain the baseband echo signal of the target; time domain segmentation processing is performed by uniformly segmenting the echo signal received by each antenna in the time domain, and ensuring that the time length of each segment is an integer multiple of the pulse repetition period.

[0011] Preferably, in step 1, the transmission signal used is a periodic linear frequency modulation pulse signal, which is expressed as:

[0012]

[0013] Among them, τ p is the pulse width, μ=B / τ p is the FM slope, B is the FM bandwidth, f c is the carrier frequency, t is the fast time variable, and rect(·) is the rectangular window function;

[0014] The target echo signal after down-conversion and time domain segmentation processing is expressed as:

[0015]

[0016] Where seg(k) represents the target echo signal in the kth period, t slow is a slow time variable, which is an integer multiple of the pulse repetition period, i represents the i-th target, m represents the m-th array element, d represents the array element spacing, θ i represents the azimuth of the i-th target, c represents the speed of light, is the baseband echo signal of target i received by the reference array element in time period k, which is expressed as:

[0017]

[0018] in, represents the distance of target i changing with slow time in time period k.

[0019] Preferably, the range Doppler unit data of the target in step 2 is expressed as:

[0020]

[0021] Where RD[·] represents the range-Doppler transform processing, u k and v k represents the uth order of the range Doppler spectrum at time period k k distance unit and the vth k Speed unit.

[0022] Preferably, in step 3, the range Doppler unit extrapolation processing adopts forward extrapolation processing, backward extrapolation processing or forward and backward extrapolation processing.

[0023] Preferably, the forward extrapolation process in step 3 includes the following steps:

[0024] Based on the range Doppler unit data of M array elements in K time periods, a forward-moving space-time two-dimensional extrapolation window of size K×(p+1) is constructed. When the two-dimensional window moves forward to position j, the data in the window is expressed as:

[0025]

[0026] Based on the two-dimensional window data at different positions, the least squares solution of the linear equation system and the forward extrapolation coefficient is constructed as follows:

[0027]

[0028] Among them, W f and w f They are respectively composed of the first p columns of data and the (p+1)th column of data of the two-dimensional window data at different positions, and are expressed as:

[0029]

[0030] Based on the solved forward extrapolation coefficient z f The real array data of time period k is forward extrapolated to obtain the estimated value of virtual array data in time period k. The extrapolation process is expressed as:

[0031]

[0032] The target range Doppler unit data of the extended array in time period k based on forward extrapolation is obtained and expressed as:

[0033]

[0034] Preferably, the backward extrapolation process in step 3 includes the following steps:

[0035] Based on the range Doppler unit data of M array elements in K time periods, a backward-moving space-time two-dimensional extrapolation window of size K×(p+1) is constructed. When the two-dimensional window moves backward to position j (1≤j≤Mp), the data in the window is expressed as:

[0036]

[0037] Based on the two-dimensional window data at different positions, the least squares solution of the linear equation system and the backward extrapolation coefficient is expressed as:

[0038]

[0039] Among them, W b and w b They are respectively composed of the last p columns of data and the first column of data of the two-dimensional window data at different positions, and are expressed as:

[0040]

[0041] Based on the solved backward extrapolation coefficient z b The virtual array data in period k is then extrapolated backward to obtain the estimated value of the virtual array data in period k. The extrapolation process is expressed as:

[0042]

[0043] The target range Doppler unit data of the extended array in time period k based on backward extrapolation is obtained and expressed as:

[0044]

[0045] Preferably, in step 3, the forward and backward extrapolation processing is performed simultaneously to obtain the target range Doppler unit data of the extended array.

[0046] The present invention has the following beneficial effects:

[0047] 1. The present invention performs range Doppler transformation and target detection on the baseband data of each array element and each time period, obtains the range and velocity information of the target and clutter, and realizes the resolution of the target and clutter;

[0048] 2. The present invention uses the target range Doppler unit data based on different array elements and different time periods to perform extrapolation processing to achieve array aperture expansion, with low algorithm complexity and good real-time performance;

[0049] 3. The present invention separates target and clutter information in the echo signal through range-Doppler transform, and then performs extrapolation based on the target information to achieve array aperture expansion, thereby solving the problem that traditional extrapolation methods fail in shipborne high-frequency ground-wave over-the-horizon radar scenarios due to the presence of strong clutter;

[0050] 4. By performing time-domain segmentation on the echo signals received by the shipborne platform before range-Doppler transformation, the present invention solves the problem of performance degradation or even failure of the extrapolated aperture expansion method when a large number of targets are present in a single range-Doppler unit. Finally, the present invention solves the problem of reduced antenna array aperture due to spatial limitations of the shipborne platform, which leads to a decrease in radar array angular measurement performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Flowchart of the present invention.

[0052] Figure 2 Schematic diagram of the motion of the motion platform and the target in an embodiment of the present invention.

[0053] Figure 3 It is the far-field equivalent motion model of the moving platform and target in the embodiment of the present invention.

[0054] Figure 4 4 is a signal processing flow chart of an embodiment of the present invention.

[0055] Figure 5 This is a principle diagram of forward extrapolation coefficient estimation when the range Doppler unit is used to forward extrapolate aperture expansion in an embodiment of the present invention.

[0056] Figure 6 This is a principle diagram of estimating virtual array data by forward extrapolation when the range Doppler unit is used to forward extrapolate the aperture expansion in an embodiment of the present invention.

[0057] Figure 7 This figure shows the result of performing azimuth estimation using a conventional beamforming method after performing forward extrapolation, backward extrapolation, and forward and backward extrapolation aperture expansion on the array in a single-target scenario in an embodiment of the present invention.

[0058] Figure 8 This figure shows the result of using a conventional beamforming method to perform azimuth estimation after performing forward extrapolation, backward extrapolation, and forward and backward extrapolation aperture expansion on the array in a two-target scenario in an embodiment of the present invention.

[0059] Figure 9 This figure shows the root mean square error results of azimuth estimation using a conventional beamforming method after forward extrapolation aperture expansion of the array based on different numbers of extrapolated virtual array elements in a single-target scenario in an embodiment of the present invention.

[0060] Figure 10 This figure shows the root mean square error results of azimuth estimation using a conventional beamforming method after forward extrapolation aperture expansion of the array based on different numbers of time periods in a single-target scenario in an embodiment of the present invention.

[0061] Figure 11 This figure shows the root mean square error results of azimuth estimation using a conventional beamforming method after forward extrapolation aperture expansion of the array based on different ship speed errors in a single-target scenario in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] To make the objectives, technical solutions, and advantages of the present invention more clearly apparent, the present invention is described below using specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely illustrative and are not intended to limit the scope of the present invention. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present invention.

[0063] Specific implementation method 1: Combination Figure 1-11 This embodiment describes an array aperture expansion method based on moving platform range Doppler domain extrapolation, including the following steps:

[0064] Step 1: Use the motion array to receive the target's echo data, and perform down-conversion and time-domain segmentation processing on each array element;

[0065] Step 2: Perform range-Doppler transform and target detection on the baseband data of each array element and each time period to obtain the range-Doppler unit data of the target; obtain the target range and speed, which is suitable for moving target detection;

[0066] Step 3: Extrapolate the target range Doppler unit data of different array elements and different time periods to obtain an estimated value of the virtual array data, thereby achieving array aperture expansion; the algorithm has low complexity and good real-time performance; the present invention is applicable to shipborne high-frequency ground wave radars, and solves the problems of small radar array aperture and reduced radar angle measurement performance caused by limited space on the shipborne platform through range Doppler domain processing and time domain segmentation technology.

[0067] Specific implementation method 2: Combination Figure 1-11 The present embodiment is described. The present embodiment is an array aperture expansion method based on Doppler domain extrapolation of a moving platform. In step 1, the moving array includes a receiving antenna and a platform. The radar transmitting system is a one-transmit-multiple-receiver system. The receiving antenna of the radar is a uniform linear array on one side of the moving platform. The platform moves in a uniform linear motion. The target moves in a stationary or uniform linear motion and is located in the far field of the antenna. Down-conversion processing is achieved by removing the carrier frequency in the target echo signal, thereby obtaining the baseband echo signal of the target. Time domain segmentation processing is achieved by uniformly segmenting the echo signal received by each antenna in the time domain, and ensuring that the time length of each segment is an integer multiple of the pulse repetition period.

[0068] Specific implementation method three: Combination Figure 1-11This embodiment describes an array aperture expansion method based on range-Doppler domain extrapolation of a moving platform. In step 1, the transmitting signal used by the antenna is a periodic linear frequency modulation pulse signal, which is specifically expressed as follows:

[0069]

[0070] Among them, τ p is the pulse width, μ=B / τ p is the FM slope, B is the FM bandwidth, f c is the carrier frequency, t is the fast time variable, rect(·) is the rectangular window function, and j is the imaginary unit;

[0071] The target echo signal after down-conversion and time domain segmentation is expressed as (ignoring the noise term):

[0072]

[0073] Where seg(k) represents the target echo signal in the kth period, t slow is a slow time variable, which is an integer multiple of the pulse repetition period, i represents the i-th target, m represents the m-th array element, d represents the array element spacing, θ i represents the azimuth of the i-th target, c represents the speed of light, N represents the total number of targets, is the baseband echo signal of target i received by the reference array element in time period k, which is expressed as:

[0074]

[0075] in, represents the distance of target i changing with slow time in time period k.

[0076] Specific implementation method four: Combination Figure 1-11 This embodiment describes an array aperture expansion method based on range-Doppler domain extrapolation of a moving platform. In step 2, range-Doppler transform and target detection are performed on the target echo baseband data of each array element and each time period, and the obtained target range-Doppler unit data is expressed as:

[0077]

[0078] Where RD[·] represents the range-Doppler transform processing, u k and v k represents the uth order of the range Doppler spectrum at time period k k distance unit and the vth k Speed unit.

[0079] Specific implementation method five: Combination Figure 1-11This embodiment is described as an array aperture expansion method based on range-Doppler domain extrapolation of a moving platform. In step 3, the range-Doppler unit extrapolation processing adopts forward extrapolation processing, backward extrapolation processing, or forward and backward extrapolation processing.

[0080] Specific implementation method six: combination Figure 1-11 This embodiment describes an array aperture expansion method based on range Doppler domain extrapolation of a moving platform. In step 3, the forward extrapolation process is performed based on target range Doppler unit data of multiple different time periods and different array elements to obtain M f The target range Doppler unit data of a virtual array element includes the following steps:

[0081] Based on the range-Doppler unit data of K time periods and M array elements obtained in steps 1 and 2, a forward-moving space-time two-dimensional extrapolation window of size K×(p+1) is constructed (where p is the forward extrapolation order). When the two-dimensional window moves forward to position index value j (1≤j≤Mp), the data within the window is expressed as:

[0082]

[0083] Furthermore, based on the two-dimensional window data at different positions, a system of linear equations is constructed and the least squares solution of the forward extrapolation coefficient is obtained as follows:

[0084]

[0085] Among them, H is the conjugate transpose, W f and w f They are respectively composed of the first p columns of data and the (p+1)th column of data of the two-dimensional window data at different positions, and are expressed as:

[0086]

[0087] Then, based on the solved forward extrapolation coefficient z f The real array data of time period k is forward extrapolated to obtain the estimated value of virtual array data in time period k. The extrapolation process is expressed as:

[0088]

[0089] Finally, the target range Doppler unit data of the extended array in time period k based on forward extrapolation is obtained, which is expressed as:

[0090]

[0091] Specific implementation method seven: combination Figure 1-11This embodiment describes an array aperture expansion method based on the range Doppler domain extrapolation of a moving platform. In step 3, the backward extrapolation process is performed based on target range Doppler unit data of multiple different time periods and different array elements to obtain M b The target range Doppler unit data of a virtual array element comprises the following steps:

[0092] Based on the range-Doppler unit data of K time periods and M array elements obtained in steps 1 and 2, a backward-moving space-time two-dimensional extrapolation window of size K×(p+1) is constructed (p is the backward extrapolation order). When the two-dimensional window moves backward to position j (1≤j≤Mp), the data in the window is expressed as:

[0093]

[0094] Furthermore, based on the two-dimensional window data at different positions, a system of linear equations is constructed and the least squares solution of the backward extrapolation coefficient is obtained as follows:

[0095]

[0096] Among them, W b and w b They are respectively composed of the last p columns of data and the first column of data of the two-dimensional window data at different positions, and are expressed as:

[0097]

[0098] Then, based on the solved backward extrapolation coefficient z b The virtual array data in period k is then extrapolated backward to obtain the estimated value of the virtual array data in period k. The extrapolation process is expressed as:

[0099]

[0100] Finally, the target range Doppler unit data of the extended array in time period k based on backward extrapolation is obtained, which is expressed as:

[0101]

[0102] Specific implementation method eight: combination Figure 1-11 The present embodiment is described. This embodiment provides an array aperture expansion method based on moving platform range Doppler domain extrapolation. The forward and backward extrapolation processing in step 3 refers to simultaneously performing the above-mentioned forward extrapolation and backward extrapolation processing to obtain the target range Doppler unit data of the expanded array. The forward extrapolation processing is used for preliminary processing, and then the backward extrapolation processing is used for correction processing. The fused information is used to apply to complex scenarios and achieve accurate prediction and compensation.

[0103] Example 1:

[0104] Combine Figures 1-6 , this example proposes an array aperture expansion method based on moving platform range Doppler domain extrapolation, the method comprising the following steps:

[0105] Step 1: Use the motion array to receive the target's echo data, and perform down-conversion and time-domain segmentation processing on each array element;

[0106] Step 2: Perform range-Doppler transform and target detection on the baseband data of each array element and each time period to obtain the range-Doppler unit data of the target;

[0107] Step 3: Extrapolate the target range Doppler unit data of different array elements and different time periods to obtain the estimated value of the virtual array data, thereby achieving array aperture expansion.

[0108] In step 1, the motion diagrams and far-field equivalent motion models of the motion platform and target are as follows: Figure 2 、 Figure 3 As shown, the signal processing process involved in step 1 is as follows Figure 4 As shown. The radar adopts a one-transmit-multiple-receive system, with array element 1 transmitting the signal and array elements 1 to M receiving the echo signal; the receiving antenna is a uniform linear array with an interval of d and is located on one side of the moving platform. The platform moves at a constant speed, and the target moves at a stationary or constant speed and is located in the far field of the antenna. Down-conversion processing refers to removing the carrier frequency from the target echo signal to obtain the baseband echo signal of the target; time domain segmentation processing refers to uniformly segmenting the echo signals received by each antenna in the time domain, and ensuring that the time length of each segment is an integer multiple of the pulse repetition period. The transmitting signal used in the present invention is a periodic linear frequency modulation pulse signal, which is specifically expressed as:

[0109]

[0110] Among them, τ p is the pulse width, μ=B / τ p is the FM slope, B is the FM bandwidth, f c is the carrier frequency, t is the fast time variable, and rect(·) is the rectangular window function. The target echo signal after down-conversion and time domain segmentation is expressed as (ignoring the noise term):

[0111]

[0112] Where seg(k) represents the target echo signal in the kth period, t slow is a slow time variable, which is an integer multiple of the pulse repetition period, i represents the i-th target, m represents the m-th array element, d represents the array element spacing, θ irepresents the azimuth of the i-th target, c represents the speed of light, is the baseband echo signal of target i received by the reference array element in time period k, which is expressed as:

[0113]

[0114] in, represents the distance of target i changing with slow time in time period k.

[0115] In step 2, the signal processing involved is as follows Figure 4 This step is based on the down-conversion and time domain segmentation processing in step 1. The target echo baseband data of each array element and each time period are respectively subjected to range Doppler transformation and target detection to obtain the target range Doppler unit data, which is expressed as:

[0116]

[0117] Where RD[·] represents the range-Doppler transform processing, u k and v k represents the uth order of the range Doppler spectrum at time period k k distance unit and the vth k Speed unit.

[0118] In step 3, the signal processing involved is as follows Figure 4 As shown. This step is to perform extrapolation processing on the basis of the target range Doppler unit data of each array element in each time period obtained in step 2 to achieve array aperture expansion. Among them, the range Doppler unit extrapolation processing includes three methods: forward extrapolation processing, backward extrapolation processing, and forward and backward extrapolation processing. This embodiment mainly uses the forward extrapolation processing as an example to illustrate. Forward extrapolation processing refers to forward prediction based on the target range Doppler unit data of multiple different time periods and different array elements to obtain M f The target range Doppler unit data of the virtual array element. Specifically, Figure 5 As shown in FIG1 , based on the range-Doppler unit data of M array elements in K time periods obtained in steps 1 and 2, a forward-moving space-time two-dimensional extrapolation window of size K×(p+1) is constructed (where p is the forward extrapolation order). When the two-dimensional window moves forward to position j (1≤j≤Mp), the data within the window is expressed as:

[0119]

[0120] Furthermore, based on the two-dimensional window data at different positions, a system of linear equations is constructed and the least squares solution of the forward extrapolation coefficient is obtained as follows:

[0121]

[0122] Among them, W f and w f They are respectively composed of the first p columns of data and the (p+1)th column of data of the two-dimensional window data at different positions, and are expressed as:

[0123]

[0124] Then, if Figure 6 As shown, based on the solved forward extrapolation coefficient z f The real array data of time period k is forward extrapolated to obtain the estimated value of virtual array data in time period k. The extrapolation process is expressed as:

[0125]

[0126] Finally, the target range Doppler unit data of the extended array in time period k based on forward extrapolation is obtained, which is expressed as:

[0127]

[0128] The following is an analysis of the performance of this example:

[0129] The simulation parameters are set as follows:

[0130] 1. Uniform linear array, 8 elements, 15m spacing;

[0131] 2. Transmit signal carrier frequency 10MHz, bandwidth 30kHz, pulse width 4×10 -4 s, pulse repetition period 4×10 -3 s, sampling rate 60kHz;

[0132] 3. The shipborne platform moves in a uniform linear motion at a speed of 7.5 m / s;

[0133] 4. Target 1 moves in a straight line at a constant speed, with a distance of 50 km, a speed of 80 m / s, and an azimuth of 20 degrees;

[0134] 5. Target 2 moves in a straight line at a constant speed, with a distance of 50 km, a speed of 80 m / s, and an azimuth of 30 degrees;

[0135] 6. The number of time domain segments is 2, and the interval between each segment is 2s;

[0136] 7. The number of virtual array elements in the forward extrapolation is 4, the number of virtual array elements in the backward extrapolation is 4, and the extrapolation order is 2.

[0137] First, under given simulation parameters, the result diagram of azimuth estimation using conventional beamforming method is given after forward extrapolation, backward extrapolation and forward and backward extrapolation aperture expansion of the array in a single target scenario, as shown in the figure below. Figure 7As shown in the figure; and in the two-target scenario, after the array is forward extrapolated, backward extrapolated, and the aperture is expanded forward and backward, the result of azimuth estimation using the conventional beamforming method is shown in the figure, Figure 8 As shown in the figure, for single or multiple targets, the angle estimation spectrum of the proposed method is more concentrated than that of the real array, indicating that the proposed method can effectively expand the virtual aperture of the array, thereby improving the angular resolution capability of the array. Figure 8 It can also be seen that the peak of the angle estimation spectrum of the proposed method is closer to the true orientation of the target, indicating that the method proposed in the present invention can also effectively improve the angle measurement accuracy of the array.

[0138] Secondly, under given simulation parameters, the root mean square error results of the azimuth estimation using the conventional beamforming method after forward extrapolation aperture expansion of the array based on different numbers of extrapolated virtual array elements in a single target scenario are given, as shown in the figure below. Figure 9 The corresponding numerical results are shown in Table 1. The graph shows that the root mean square error (RMS) of the extrapolated array is lower than that of the actual array, demonstrating that the proposed method can effectively improve the accuracy of the angle of arrival estimation. As the number of extrapolated elements increases from 3 to 15, the virtual aperture of the array becomes larger, which improves the accuracy of the angle of arrival estimation. However, it should be noted that when the number of extrapolated elements increases from 15 to 17, the RMS error does not continue to decrease, but instead increases due to errors in the extrapolation process itself, which means that the accuracy of the angle of arrival estimation actually decreases.

[0139] Table 1

[0140]

[0141] Then, under given simulation parameters, the root mean square error results of the azimuth estimation using the conventional beamforming method after the array is forward extrapolated and the aperture is expanded based on different time periods in a single target scenario are given, as shown in the figure below. Figure 10 The corresponding numerical results are shown in Table 2. The graph shows that the root mean square error (RMS) of the extrapolated array is lower than that of the actual array, indicating that the proposed method can effectively improve the accuracy of arrival angle estimation. The figure also shows that as the number of time periods K increases, the number of observations used to estimate the forward extrapolation coefficients increases, the estimation accuracy improves, the RMS error of the extrapolated array decreases, and the angle estimation performance of the proposed method improves.

[0142] Table 2

[0143]

[0144]

[0145] Finally, under given simulation parameters, the root mean square error results of the azimuth estimation using the conventional beamforming method after the array is forward extrapolated and the aperture is expanded based on different ship speed errors in a single target scenario are given, as shown in the figure below. Figure 11 The corresponding numerical results are shown in Table 3. The graph shows that the arrival angle estimation accuracy of the proposed method decreases as the ship speed error increases. When the ship speed error is small (e.g., 5% or 10%), the root mean square error of the extrapolated array is still lower than that of the actual array. However, when the ship speed error is large (e.g., 20%), the root mean square error of the extrapolated array becomes higher than that of the actual array, and the performance of the proposed method deteriorates.

[0146] Table 3

[0147]

[0148] Experiments have shown that the method of the present invention is effective and realizes array aperture expansion based on range Doppler domain extrapolation of the moving platform, thereby improving the angular measurement performance of the array.

[0149] The present invention aims to propose a new technical solution based on time-Doppler domain extrapolation processing. By optimizing the signal processing method of traditional high-frequency ground wave radar, the system can overcome the space limitations of the shipborne platform, significantly improve the angle estimation accuracy of the high-frequency ground wave over-the-horizon radar system, and enhance its detection capability in complex marine environments.

[0150] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutations and combinations. Therefore, the present invention will no longer describe the technical solutions after permutations and combinations one by one, but it should be understood that the technical solutions after permutations and combinations have been disclosed by the present invention.

[0151] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for array aperture expansion based on range-Doppler domain extrapolation of a moving platform, characterized by: The following steps are involved: Step 1: Use the motion array to receive the target's echo data, and perform down-conversion and time-domain segmentation processing on each array element; Step 2: Perform range-Doppler transform and target detection on the baseband data of each array element and each time period to obtain the range-Doppler unit data of the target; Step 3: Based on the target range Doppler unit data of different array elements and different time periods, extrapolation processing is performed to obtain the estimated value of the virtual array data to achieve array aperture expansion.

2. The array aperture expansion method based on moving platform range Doppler domain extrapolation according to claim 1, characterized in that: In step 1, the receiving antenna is arranged in a uniform linear array on one side of the moving platform. The platform moves at a constant speed, and the target moves at a stationary or constant speed and is located in the far field of the antenna. Down-conversion processing is performed by removing the carrier frequency from the target echo signal to obtain the target's baseband echo signal. Time domain segmentation processing is performed by uniformly segmenting the echo signals received by each antenna in the time domain, and ensuring that the time length of each segment is an integer multiple of the pulse repetition period.

3. The array aperture expansion method based on moving platform range Doppler domain extrapolation according to claim 2, characterized in that: In step 1, the transmission signal used is a periodic linear frequency modulation pulse signal, which is expressed as: Among them, τ p is the pulse width, μ=B / τ p is the FM slope, B is the FM bandwidth, f c is the carrier frequency, t is the fast time variable, and rect(·) is the rectangular window function; The target echo signal after down-conversion and time domain segmentation processing is expressed as: Where seg(k) represents the target echo signal in the kth period, t slow is a slow time variable, which is an integer multiple of the pulse repetition period, i represents the i-th target, m represents the m-th array element, d represents the array element spacing, θ i represents the azimuth of the i-th target, c represents the speed of light, is the baseband echo signal of target i received by the reference array element in time period k, which is expressed as: in, represents the distance of target i changing with slow time in time period k.

4. The array aperture expansion method based on moving platform range-Doppler domain extrapolation according to claim 3, characterized in that: The range Doppler unit data of the target in step 2 is expressed as: Where RD[·] represents the range-Doppler transform processing, u k and v k represents the uth order of the range Doppler spectrum at time period k k distance unit and the vth k Speed unit.

5. The array aperture expansion method based on moving platform range Doppler domain extrapolation according to claim 4, characterized in that: In step 3, the range-Doppler unit extrapolation process adopts forward extrapolation process, backward extrapolation process or forward and backward extrapolation process.

6. The array aperture expansion method based on moving platform range Doppler domain extrapolation according to claim 5, characterized in that: The forward extrapolation process in step 3 includes the following steps: Based on the range Doppler unit data of M array elements in K time periods, a forward-moving space-time two-dimensional extrapolation window of size K×(p+1) is constructed. When the two-dimensional window moves forward to position j, the data in the window is expressed as: Based on the two-dimensional window data at different positions, the least squares solution of the linear equation system and the forward extrapolation coefficient is constructed as follows: Among them, W f and w f They are respectively composed of the first p columns of data and the (p+1)th column of data of the two-dimensional window data at different positions, and are expressed as: Based on the solved forward extrapolation coefficient z f The real array data of time period k is forward extrapolated to obtain the estimated value of virtual array data in time period k. The extrapolation process is expressed as: The target range Doppler unit data of the extended array in time period k based on forward extrapolation is obtained and expressed as:

7. The array aperture expansion method based on moving platform range Doppler domain extrapolation according to claim 6, characterized in that: The backward extrapolation process in step 3 includes the following steps: Based on the range Doppler unit data of M array elements in K time periods, a backward-moving space-time two-dimensional extrapolation window of size K×(p+1) is constructed. When the two-dimensional window moves backward to position j (1≤j≤Mp), the data in the window is expressed as: Based on the two-dimensional window data at different positions, the least squares solution of the linear equation system and the backward extrapolation coefficient is expressed as: Among them, W b and w b They are respectively composed of the last p columns of data and the first column of data of the two-dimensional window data at different positions, and are expressed as: Based on the solved backward extrapolation coefficient z b The virtual array data in period k is then extrapolated backward to obtain the estimated value of the virtual array data in period k. The extrapolation process is expressed as: The target range Doppler unit data of the extended array in time period k based on backward extrapolation is obtained and expressed as:

8. The array aperture expansion method based on moving platform range Doppler domain extrapolation according to claim 7, characterized in that: In step 3, the forward and backward extrapolation processing is performed simultaneously, and the target range Doppler unit data of the extended array is obtained.

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