A real-time calculation method for airborne SAR ground distance based on deformation CORDIC

Abstract

The application discloses a kind of real-time computing method of airborne SAR ground distance based on deformation CORDIC, belong to airborne synthetic aperture radar imaging signal processing technical field.The present application scheme is adopted four-step calculation process of pre-processing, block cascaded normalization, deformation hyperbolic CORDIC iterative calculation, denormalization for the problems of large resource consumption, high calculation delay, algorithm control complexity in high-resolution large bit-width scene.The method is first adjusted to full scale near by input data high bit through normalization to compress operation bit width, and the deformation hyperbolic CORDIC of introducing expected value iteration term eliminates the repeated iteration requirement of classical algorithm.The present application avoids the use of large bit-width multiplier, effectively reduces hardware resource occupation and calculation delay, while ensuring the calculation precision under large bit-width fixed-point input, can satisfy the real-time imaging demand of high-resolution airborne SAR.

Description

Technical Field

[0001] This invention relates to the field of airborne synthetic aperture radar imaging signal processing technology, and in particular to a method for real-time calculation of airborne SAR ground distance based on deformed CORDIC. Background Technology

[0002] In airborne SAR imaging, the radar system transmits linear frequency modulated signals and receives ground echoes, acquiring slant range sampling values ​​corresponding to different range gates. To obtain azimuth-free imaging results, the actual ground distance must be calculated from the slant range of each sampling point, and then the echo data is interpolated and stretched based on the ground distance value. When the flight platform altitude is known, the ground distance can be calculated using the Pythagorean theorem, i.e., the ground distance equals the arithmetic square root of the difference between the square of the slant range and the square of the platform altitude. As the resolution and swath width of airborne SAR imaging continue to increase, the number of ground distance sampling points that need to be calculated within a single pulse period increases significantly, and the accuracy requirements for the calculation results also increase substantially. When the slant range reaches the hundreds of kilometers, the bit width of the sampling data can typically reach more than 35 fixed points under high-resolution accuracy requirements. Currently, there are two main technical solutions in the industry for implementing this square root operation: one is a square operation-subtraction operation-CORDIC circular mode square root scheme based on a large bit-width multiplier; the other is a direct calculation scheme based on the classic hyperbolic CORDIC algorithm.

[0003] For the square-subtraction-CORDIC square root scheme, when the input bit width is large, the large-bit-width multiplier consumes a large amount of DSP computing resources, usually requiring multiple cascaded DSP units. Simultaneously, both the subtractor and the square root module need to process intermediate data with doubled bit width, easily leading to long computational delays, internal chip wiring congestion, and timing convergence difficulties. For the classic hyperbolic CORDIC scheme, repeated calculations are required in the 3k+1th iteration to ensure convergence, resulting in complex system control logic and cumbersome scale factor calculations, making it equally unsuitable for high-precision, large-bit-width computational scenarios.

[0004] In summary, these current technical solutions cannot simultaneously meet the multiple requirements of low latency, low resource consumption, and high accuracy for ground distance calculation in high-resolution airborne SAR imaging. Summary of the Invention

[0005] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0006] In view of the aforementioned existing problems, this invention is proposed. Therefore, this invention provides a real-time airborne SAR ground distance calculation method based on deformable CORDIC to solve the problems mentioned in the background art.

[0007] To address the aforementioned technical problems, this invention provides the following technical solution: a real-time airborne SAR ground distance calculation method based on deformed CORDIC, comprising: Obtain a first input value representing the slant range and a second input value representing the altitude of the flight platform, and preprocess the first input value and the second input value to obtain a first intermediate value and a second intermediate value; The first intermediate value and the second intermediate value are normalized. The high-order part of the first intermediate value is adjusted to near the preset full scale, and the total displacement during the normalization process is recorded to obtain the normalized first operand and the second operand. The normalized first and second operands are input into the deformed hyperbolic CORDIC cell for iterative calculation. An expected value iteration term is introduced in the iterative calculation to avoid repeated iterations, and the iterative result is obtained. The iteration results are denormalized based on the total displacement to restore the numerical scale and obtain the calculated ground distance.

[0008] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention uses block detection and cascaded shifting normalization processing to dynamically adjust wide-bit inputs to near full scale, so that subsequent CORDIC iterations do not need to process the full input bit width. This significantly reduces the operation bit width and computation delay while ensuring computational accuracy, and improves computational accuracy in small-signal input scenarios.

[0009] 2. This invention employs a modified hyperbolic CORDIC algorithm with an expected value iteration term. By comparing the expected value iteration term with the iteration variable, the iteration direction is controlled, eliminating the requirement for repeated iterations in the 3k+1th iteration of the classic hyperbolic CORDIC algorithm. This reduces the system control complexity and hardware implementation difficulty, and improves the stability of iteration convergence.

[0010] 3. In addition, the overall solution of this invention does not require the deployment of a large bit-width multiplier, which effectively reduces the pressure of LUT, wiring congestion and delay, while taking into account the calculation accuracy under large bit-width fixed-point input. It can simultaneously meet the multiple application requirements of low latency, low resource consumption and high accuracy of ground distance calculation for high-resolution airborne SAR imaging. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a schematic diagram illustrating the geometric relationship between airborne SAR slant range, altitude, and ground distance according to an embodiment of the present invention; Figure 2 This is a flowchart illustrating the overall calculation process according to one embodiment of the present invention; Figure 3 This is a normalization flowchart according to one embodiment of the present invention; Figure 4 This is a flowchart illustrating a modified CORDIC calculation method according to an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the application of the ground distance calculation module in the airborne SAR imaging algorithm according to an embodiment of the present invention. Detailed Implementation

[0012] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0013] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0014] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0015] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0016] Example 1

[0017] Reference Figures 1 to 4 This is the first embodiment of the present invention, which provides a method for real-time calculation of airborne SAR ground distance based on deformed CORDIC, including: Specifically, in airborne SAR imaging, the radar transmits a linear frequency modulated signal and receives the echo, obtaining the slant range corresponding to different range gates. To obtain an azimuth-free image, the actual ground distance must be calculated from the slant range of each sampling point, and then the data must be interpolated and stretched. For example... Figure 1 As shown, when the altitude of the flight platform is known, the first... The distance between each location can be calculated using the Pythagorean theorem, that is:

[0018] In the formula, Indicates the first The actual distance between each sampling point; Indicates the first The slant distance corresponding to each sampling point; This indicates the known altitude of the flight platform.

[0019] Furthermore, to address the issues of high DSP resource consumption, long latency, and difficulty in timing convergence caused by the traditional square-subtraction-CORDIC square root scheme in high-resolution, wide-swath scenarios (input data often reaches 35 bits or more), as well as the complex control of the classic hyperbolic CORDIC scheme, this embodiment provides a ground distance calculation method with normalization and modified CORDIC iteration. For example... Figure 2 The overall calculation process shown includes the following four steps: S1: Numerical preprocessing.

[0020] Furthermore, obtain the first input value representing the slope distance. and a second input value characterizing the altitude of the flight platform In this embodiment, and All are signed fixed-point number formats, and all have a bit width of [missing information]. .

[0021] Specifically, will and Compare the absolute values ​​of each value and use the larger value as the first intermediate value. Use the smaller value as the second intermediate value. (Right now , Simultaneously, an imaginary number flag is generated, which is used to indicate that the input data does not hold true in terms of physical geometry. For example, when the slope distance is less than the height, the square root of the difference of squares is negative, resulting in an imaginary number result.

[0022] In an implementable process, the representation method is as follows:

[0023] in, Represented as an imaginary number, when True means . and These are functions for finding the maximum and minimum values, respectively.

[0024] S2: Normalization process.

[0025] Furthermore, due to the large input bit width, in order to fully utilize the effective bit width in subsequent CORDIC iterations and increase the effective iteration count, it is necessary to... and Simultaneously magnify it, making its high-level value close to full scale. For example... Figure 3 The normalization process shown includes the following sub-steps: S201: First normalization.

[0026] Specifically, the first intermediate value binary bits A group of bits is divided into groups starting from the most significant bit. The data is divided into blocks, padded with zeros if necessary. A bitwise OR operation is performed on all bits within each block to obtain an N-bit value. It is important to emphasize that the choice of N is related to the operating clock speed and the speed of the target chip. A lower operating clock speed and a higher chip speed allow for a larger N. For example, in AMD (Xilinx) chips, LUT6 is the basic lookup table unit, and N is typically chosen to be 5-12. The synthesis result's path and fan-out can meet most operating conditions of chips with speeds below -2 GHz and below 350 MHz, demonstrating good applicability. Once N is determined, the following can be obtained: Detect the position P of the first (most significant) non-zero block (numbered starting from 0, where 0 represents the most significant block). Shift both R and A left by M×P bits simultaneously, so that the most significant non-zero block of R is moved to the most significant M bits.

[0027] S202: Cascade normalization (optional).

[0028] Specifically, when For larger datasets, normalization modules can be cascaded to further inspect and shift the data. In this case, only the data after the initial shift needs to be processed. highest The bits are used as weights and input to the next-level module. After detection, the data is shifted left again. This step can be cascaded multiple times; assuming the total number of cascades is... Then the block size at each level and the position of the non-zero block are denoted as follows: and corresponding (in , ).

[0029] In an feasible process, when M is large, such as M greater than 8, and the precision of input values ​​less than 8 bits is sensitive, the modules can be cascaded to further detect and shift the data.

[0030] S203: Zero-padding extension.

[0031] Specifically, the shifted data is padded with zeros at the least significant bit to expand it to the instantiation bit width of the CORDIC module. Let the number of CORDIC iterations be n. To ensure accuracy, the following must be satisfied: , usually choose . Recommended value Increasing the low-bit width further improves output accuracy, but the benefits diminish; when At that point, there will be no more gains in accuracy.

[0032] Furthermore, after the above processing, the total displacement during the normalization process... and the normalized first operand of the output Second operand The calculation formula is as follows:

[0033]

[0034]

[0035] In the formula, Indicates the total number of bits shifted left; Indicates the total number of cascaded normalizations; Indicates the first Number of bits in the group during level normalization; Indicates the first The highest non-zero block position detected during level normalization; This indicates a binary left shift operation.

[0036] S3: Iterative calculation of deformed hyperbolic CORDIC.

[0037] Specifically, the normalized first operand Second operand Input is fed into the deformed hyperbolic CORDIC cell. The classic hyperbolic CORDIC algorithm is in the... Repeated calculations are required in subsequent iterations to ensure convergence, leading to complex system control. This embodiment constructs a new expected value iteration term based on the original algorithm. ,pass Iterative changes and By comparing items, redundant iterations are eliminated, significantly reducing the implementation difficulty. For example... Figure 4 As shown, the specific calculation process is as follows: S301: Pre-calculated constant table ( and gain compensation factor .

[0038] Specifically, this gain compensation factor Represented as:

[0039] S302: Initialize variables:

[0040] In the formula, for To the initial value; for To initialize; This is the initial value for the expected value iteration term.

[0041] S303: Iterative Calculation: Let the total number of iterations be... For the first The next iteration ( The calculation formula is as follows:

[0042] In the formula, For the first The rotation direction of the next iteration; and The first After the next iteration Xianghe To numerical values; For the first The expected value of the iteration term after the next iteration; For the first The preset parameters for the next iteration. It is a symbolic function, and when hour ,when hour .

[0043] S304: Parameter Table Hardware optimization: due to The value of rapidly approaches 1 as the number of iterations increases. To reduce the overhead of the hardware multiplier, this embodiment... The update method has been optimized in segments based on the number of iterations. Taking a 35-bit unsigned number as an example, as shown in Table 1:

[0044] (i) In the first to fourth iterations, i.e. T[1] to T[4] change significantly, a hardware multiplier is used for update calculation; for example, the hexadecimal values ​​of T[1] to T[4] are 0x5A82799A0, 0x478DDE6E6, 0x41F83D9AC, and 0x407F80FD8, respectively. (ii) In the 5th to 16th iterations, i.e. T[5] to T

[16] can be approximately updated by replacing the multiplier with a combination of shift and addition operations; for example, T[5] to T[6] uses 3 additions, T[7] to T[8] uses 2 additions, and T[9] to T

[16] uses 1 addition; (iii) In the 17th iteration and thereafter, The value tends to remain unchanged (e.g., it can be approximated as 0x400000000), at which point the expected value iteration term remains unchanged, and no additional computing resources are consumed.

[0045] S305: Coefficient Correction: After iteration, adjust the output results. Perform rotation coefficients (gain compensation factor) Correction, to obtain the corrected result. :

[0046] S4: Denormalization process.

[0047] Furthermore, based on the total displacement recorded in S2 Regarding the corrected results A reverse right shift operation is performed to restore the numerical scale and obtain the final ground distance calculation result. :

[0048] In the formula, This indicates a binary right shift operation.

[0049] Final output For unsigned fixed-point numbers, their bit width is restored to 1. .

[0050] In addition, this embodiment also verifies the convergence effectiveness of CORDIC, as well as bit width and overflow protection.

[0051] For the convergence of the modified CORDIC: The expected angle of the vector rotation is: That is, when Change to At that time, the range of angle changes .

[0052] The total rotation angle supported by CORDIC is:

[0053] Therefore, corresponding to any All algorithms converge.

[0054] Regarding bit width and overflow protection: make 1.646760258121, order The results are shown in Table 2:

[0055] It should be noted that this embodiment uses a 54-bit input width implemented in an FPGA as an example, and compares the method of this embodiment with the traditional square-subtraction-CORDIC square root scheme, as shown in Table 3.

[0056]

[0057] Based on the results in this table, it can be seen that the traditional scheme requires two 54×54 multipliers, one 107-bit subtractor, and one 107-bit 54×2-stage pipelined square root CORDIC, consuming approximately 26 DSP48 cores in total. Furthermore, the ultra-wide bit-width addition needs to be split into two stages of computation, consuming approximately 36,956 LUTs, with a maximum latency of 117 clock cycles. In contrast, the scheme in this embodiment requires only one shift decision network, one shift recovery network, and one 60-bit 54-stage pipelined deformed hyperbolic CORDIC. Through block-priority encoding and block floating-point normalization, the wide-bit input is dynamically compressed, eliminating the need for subsequent CORDICs to process the full input bit width; simultaneously, the deformed hyperbolic CORDIC eliminates repeated iterations. Ultimately, this scheme consumes approximately 42 DSP48 cores and 9,891 LUTs, with a maximum latency of 74 clock cycles. In terms of full-scale accuracy, this scheme not only achieves approximately 10 -8 The relative error (which can be approached 10 through the protection bit) -9Furthermore, by effectively utilizing high-end bits through normalization, the calculation accuracy of small signals is higher, perfectly meeting the needs of high-resolution real-time imaging of airborne SAR.

[0058] Example 2

[0059] Reference Figure 5 This is the second embodiment of the present invention, which provides an application of the above-mentioned airborne SAR ground distance real-time calculation method based on deformed CORDIC in the FPGA implementation of SAR imaging algorithm.

[0060] Specifically, such as Figure 5 As shown, the deformed CORDIC ground distance calculation module is set in the SAR imaging pipeline inside the FPGA. Its front stage can be a wavefront calculation module or a slant range / height data generation module, and its back stage can be an interpolation algorithm module or other imaging calculation module. This module receives a first input value r and a second input value a in fixed-point format, and outputs the ground distance calculation result b and an optional imaginary flag according to S1~S4 in Embodiment 1. .

[0061] Furthermore, the deformed CORDIC ground distance calculation module can be reused in a time-division multiplexing manner as an independent square root basic calculation unit: when the input data is slant range and platform height, it is used to calculate ground distance; when the input data is a wavefront-related distance quantity, it is used for wavefront calculation; and when the input data is a rotational distance difference-related quantity, it is used for rotational distance difference calculation. Through a unified fixed-point interface and pipeline control interface, the module can be reused between different SAR imaging sub-processes.

[0062] In the hardware implementation, the module's inputs and outputs all use fixed-point interfaces and are connected to preceding and following modules via valid signals, data ready signals, or pipelined registers; when the imaginary flag... When true, the subsequent module can mark the corresponding sampling point as abnormal, clamp it to 0, or trigger resampling processing, thereby preventing the square root result of the negative square difference from entering the subsequent interpolation or imaging calculation.

[0063] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for real-time calculation of airborne SAR ground distance based on deformed CORDIC, characterized in that, include: Obtain a first input value representing the slant range and a second input value representing the altitude of the flight platform, and preprocess the first input value and the second input value to obtain a first intermediate value and a second intermediate value; The first intermediate value and the second intermediate value are normalized. The high-order part of the first intermediate value is adjusted to near the preset full scale, and the total displacement during the normalization process is recorded to obtain the normalized first operand and the second operand. The normalized first and second operands are input into the deformed hyperbolic CORDIC cell for iterative calculation. An expected value iteration term is introduced in the iterative calculation to avoid repeated iterations, and the iterative result is obtained. The iteration results are denormalized based on the total displacement to restore the numerical scale and obtain the calculated ground distance.

2. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 1, characterized in that, The preprocessing includes: Take the absolute value of the first input value and the second input value respectively to obtain the first intermediate value and the second intermediate value.

3. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 1, characterized in that, The normalization process includes: Divide the binary bits of the first intermediate value into multiple data blocks; Detect the position of the highest-order non-zero data block among the plurality of data blocks; Based on the position, a displacement is determined, and the first intermediate value and the second intermediate value are simultaneously shifted to the left.

4. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 3, characterized in that, The normalization process also includes: After completing a left shift operation, the high-order part of the first intermediate value after the shift is used as the new input. The data block division, non-zero data block position detection and left shift operation are repeated to achieve cascaded normalization.

5. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 1, characterized in that, Before the iterative calculation of the deformed hyperbolic CORDIC unit begins, an initialization operation is performed, which includes: Adding the normalized first operand to the second operand yields an initial value in the X direction, and subtracting them yields an initial value in the Y direction.

6. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 1 or 5, characterized in that, In each iteration of the deformed hyperbolic CORDIC unit, the expected value iteration term is updated according to a preset parameter table; the direction of iteration is determined by the sign of the current Y-axis value.

7. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 6, characterized in that, The update method for the expected value iteration term varies according to the number of iterations, including: In the initial few iterations, updates are performed using a multiplier; In the subsequent intermediate iterations, approximate updates are performed using a combination of shift and addition operations; In subsequent iterations, the expected value iteration term is kept unchanged.

8. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 1, characterized in that, After the iterative calculation of the deformed hyperbolic CORDIC unit is completed, a step of gain compensation correction is also included for the output result of the iterative calculation.

9. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 1, characterized in that, The denormalization process includes: The iterative result or the result after gain compensation correction is then shifted to the right in the opposite direction according to the total displacement.

10. The method for real-time calculation of airborne SAR ground distance based on deformed CORDIC as described in claim 1, characterized in that, Both the first input value and the second input value are in fixed-point number format.

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