Frequency modulation continuous wave ice radar imaging method based on improved distance Doppler algorithm

Abstract

The invention provides a multilayer medium efficient imaging method suitable for frequency modulation continuous wave ice radar data, and belongs to the field of frequency modulation continuous wave ice radar imaging. Comprising the steps of multi-layer medium signal model construction, improved distance-Doppler algorithm implementation, distance migration accurate correction and azimuth focusing processing. According to the method, a multi-layer medium signal model containing refractive index and propagation velocity changes is established for the problem of target distance distortion caused by propagation velocity differences of electromagnetic waves in different media such as ice and snow; based on the model, a traditional distance-Doppler algorithm process is improved, distance migration caused by multiple layers of media is accurately corrected by introducing a medium-dependent distance migration factor, and efficient azimuth focusing is achieved. And finally, a high-resolution ice layer internal structure image can be generated, and the method is suitable for polar region large-range ice cover detection and rapid processing of a large amount of ice radar data.

Description

Technical Field

[0001] This invention relates to the field of ice radar signal processing, and specifically to a high-efficiency imaging method for frequency-modulated continuous wave ice radar suitable for multi-layered media environments. Background Technology

[0002] Frequency-modulated continuous wave (FM-CW) ice radar imaging algorithms can be broadly categorized into time-domain and frequency-domain algorithms. Time-domain algorithms primarily employ back-projection, which offers relatively simple imaging processing and can directly address errors caused by radar platform motion in the time domain. However, these algorithms are computationally intensive and have relatively low processing efficiency. To address these issues, FM-CW ice radar primarily utilizes frequency-domain algorithms. The ω-K algorithm is a fundamental frequency-domain algorithm that, theoretically, can achieve very high imaging accuracy because it does not employ any approximation methods in signal processing. However, this algorithm requires the computationally intensive stolt interpolation method when handling range migration, which significantly reduces imaging speed. In contrast, frequency scaling algorithms do not require interpolation and compensate for range migration through a frequency scaling transform function. Although the imaging accuracy of the frequency scaling algorithm is lower than that of the ω-K algorithm, it can improve imaging speed. However, in practical applications, due to the large volume of data from ice-detecting radar, it is necessary to use efficient focusing imaging techniques to alleviate the computational burden. Therefore, this paper proposes a range-Doppler algorithm suitable for FM-CW ice radar data processing. This method performs range migration correction and quadratic range compression, thus maintaining the same imaging accuracy as the frequency scaling algorithm. Furthermore, the range-Doppler algorithm requires only three Fast Fourier Transform (FFT) or Inverse Fast Fourier Transform (IFT) operations and four complex multiplications, while the frequency scaling algorithm requires three FFT or IFT operations and six complex multiplications. Compared to the frequency scaling algorithm, the proposed algorithm significantly improves processing speed, thereby more effectively meeting the high-efficiency detection requirements of ice layer data.

[0003] To achieve efficient and high-resolution ice layer imaging, this method proposes an improved range-Doppler algorithm. A multi-medium signal model is designed, which comprehensively considers the variations in refractive index and propagation velocity of frequency-modulated continuous wave (FMCH) ice radar, and an imaging algorithm suitable for multi-medium media is developed. Based on the refraction phenomenon of multi-medium media, this method can accurately correct for the range variation from radar to target caused by the multi-medium media, thus enabling accurate range migration interpolation. This adaptability allows for high-resolution imaging of FMCH ice radar data in multi-medium media. Summary of the Invention

[0004] To overcome the problems of insufficient range offset correction and difficulty in balancing imaging accuracy and efficiency in existing frequency-modulated continuous wave (FM-CW) ice radar imaging algorithms when processing multi-layered media, this invention proposes an FM-CW ice radar imaging method based on an improved range-Doppler algorithm. The advantages of this method are: First, it fully considers the differences in refractive index and propagation velocity of different media, introduces a multi-layered medium signal model, and accurately corrects the range variation between the radar and the target caused by the multi-layered medium, thereby obtaining the range migration and achieving high-resolution imaging; Second, it designs a new signal processing flow, including echo signal processing, application of the multi-layered medium range model, and definition of an azimuth compression matched filter, which can significantly improve processing speed while ensuring imaging accuracy, meeting the high-efficiency imaging requirements of ice radar data; Third, through point target simulation experiments and actual data processing tests, the advantages of this method in terms of signal-to-noise ratio and imaging time are verified. Compared with frequency scaling algorithms, the algorithm of this invention significantly improves imaging efficiency while maintaining high accuracy, especially performing excellently when processing complex ice layer data. The overall flowchart of the method is shown below. Figure 1 As shown, it mainly consists of three steps: establishing a multi-layer medium range model, echo signal preprocessing, range-Doppler domain transformation, layer-dependent range migration correction, medium adaptive secondary range compression and azimuth compression and imaging.

[0005] (1) Establish a multi-layer media propagation model:

[0006] The true geometric path between the radar and the target is converted into a single-layer equivalent slant range, allowing subsequent migration correction to be completed within a single frame. The difference in refractive index between snow and ice causes optical path elongation; therefore, refractive index weighting is introduced. Based on the refractive index n of the snow layer... snow and the refractive index n of the ice layer ice The slant range R0 between the radar and the target is modeled as:

[0007] R0 = h + n snow d snow +n ice d ice (Formula 1) Where h represents the vertical height from the radar platform above the ice surface to the target, derived from actual measurements taken by the flight platform. d snow The depth of the target within the snow layer is determined by inversion from prior drilling or coarse imaging. d ice The depth of the target within the ice layer is determined by prior drilling or coarse imaging inversion. The refractive index of the snow layer is n. snow The default value is 1.3, based on statistical results of measured data on Antarctic snow cover. The refractive index of the ice layer is n. ice The value is 1.78, which is the statistical result of measured data on Antarctic ice sheets and is considered a constant.

[0008] (2) Echo signal preprocessing:

[0009] The raw echo received by the frequency modulated continuous wave radar After performing residual video phase removal processing, we obtain:

[0010]

[0011] Where C is the amplitude of the radar echo, and its value has no effect on imaging. T p The duration of the signal sweep frequency is determined by the radar system settings. π is the mathematical constant Pi. j is the imaginary unit, and c is the electromagnetic wave propagation speed, a physical constant. τ is the target echo delay, which is twice the electromagnetic wave propagation time from the point target to the radar. a is the frequency modulation slope of the frequency-modulated continuous wave, determined by the radar system settings. rect is a rectangular function, and λ is the radar wavelength, determined by the radar system settings. L sar R(t) represents the radar aperture, set according to the radar system. m () represents the slant range from the target to the radar. t is the time delay t = the echo signal arriving at the radar after a single pulse transmission. m Let ν represent the time variable for different pulse transmissions / receptions as the radar platform moves along its flight trajectory, and let ν be the speed of the radar platform, obtained from measured data. exp is the natural exponential function.

[0012] (3) Range-Doppler domain transformation:

[0013] The signal is converted to the range-Doppler domain using a fast Fourier transform in the azimuth direction. The signal is:

[0014]

[0015] Where f m Here, is the azimuth frequency, which is the Doppler frequency along the flight path, and d is the depth of the target being detected, derived from prior drilling or coarse imaging. Doppler frequency shift correction is required in the range-Doppler domain. The Doppler frequency shift correction term H1 is defined as follows:

[0016]

[0017] After complex multiplication correction, the radar echo signal expression is as follows:

[0018]

[0019] The snow distance migration factor is a dimensionless coefficient that quantifies the combined effects of electromagnetic wave refraction and geometry in snow. It is used to correct the slope of the slant-range-time trajectory for conversion into a range-Doppler migration curve. Its definition is:

[0020] The ice range migration factor is a dimensionless coefficient that quantifies the combined effects of electromagnetic wave refraction and geometry in ice. It is used to correct the slope of the range-time trajectory when converting it into a range-Doppler migration curve. Its definition is:

[0021] The air distance migration factor is a dimensionless coefficient that quantifies the combined effects of refraction and geometry of electromagnetic waves in air. It is used to correct the slope of the slant-range-time trajectory for conversion into a range-Doppler migration curve. Its definition is:

[0022]

[0023] (4) Medium-adaptive quadratic distance compression:

[0024] Design a quadratic distance compression compensation function H2 based on a multilayer medium signal model:

[0025]

[0026] in for The conjugate term is used to achieve phase compensation through complex multiplication; after compensation, the radar echo signal expression is:

[0027]

[0028] (5) Layer-dependent distance migration correction:

[0029] Construct a media-adaptive correction function to eliminate distance migration caused by multiple media layers:

[0030]

[0031] Where R rd (f m Range migration is a physical quantity that represents the continuous variation in echo delay between adjacent pulses caused by the relative motion between the radar and the target, resulting in a curved deviation of the target trajectory in the range-Doppler domain. Range migration correction is performed by interpolating the signal, using 8-point sinc interpolation to align the curve to the same range gate, achieving an interpolation accuracy of <0.02m. After range migration correction, the expression for the radar echo signal becomes...

[0032]

[0033] (6) Azimuth compression and imaging:

[0034] Applying an azimuth matched filter, the azimuth compression term H3 is:

[0035] After azimuth compression, the expression for the radar echo signal after azimuth compression is:

[0036]

[0037] in Here, is the range frequency, which is the frequency across the track direction. Finally, through inverse fast Fourier transform, the expression for the focused radar echo signal is:

[0038]

[0039] Among them B a The azimuth Doppler bandwidth is given. At this point, a focused radar echo signal has been obtained. The radar echo matrix obtained by arranging the multiple radar echoes collected along the track along the range direction is processed in the above manner for each echo. The two-dimensional radar echo matrix then becomes a focused frequency-modulated continuous wave ice radar image.

[0040] Beneficial effects

[0041] This invention proposes an imaging method for frequency-modulated continuous wave (FMCH) ice radar data. This method can obtain higher resolution images of the interior of the ice layer while maintaining a certain imaging efficiency, and can be applied to large amounts of FMCH ice radar data. Attached Figure Description

[0042] Figure 1 This is the overall flowchart of the algorithm of this invention.

[0043] Figure 2 The image shows the results of frequency-modulated continuous wave ice radar imaging for example survey line 1.

[0044] Figure 3 The image shows the results of frequency-modulated continuous wave ice radar imaging for example survey line 2. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the specific embodiments shown in the accompanying drawings.

[0046] Figure 1 This is a flowchart of an imaging method for frequency-modulated continuous wave ice radar data proposed in this invention, which includes secondary range compression, range migration correction and azimuth compression.

[0047] In implementing this invention, a manned or unmanned aircraft platform suitable for polar operations is first selected, or a ground-based snowmobile is chosen to collect radar data. Before the operation, a digital elevation model of the snow surface below the flight path is obtained using a laser altimeter or photogrammetry. Simultaneously, on-site detection of the snow / ice layer is carried out at several representative points to measure snow thickness, snow density, ice temperature, and dielectric constant, establishing a parameter table for the "snow-ice" dual-layer medium. This parameter table is input into the airborne processing terminal for real-time imaging.

[0048] During flight, the radar continuously receives frequency-modulated continuous wave echoes reflected from the snow-ice interface, the internal layers of ice, and the base. The raw data includes a difference frequency signal in the fast time dimension and a synthetic aperture signal in the slow time dimension. After acquisition, a data integrity check is first performed at the ground station: abnormal frames caused by radio frequency interference, altimeter jumps, or drastic attitude changes are removed; then, inertial navigation data is used to compensate for platform motion errors to obtain a focused two-dimensional echo matrix.

[0049] According to claim 1, the broken-line path of the radar wave in the actual snow-ice bilayer medium is calculated by range gates using snow thickness, ice thickness, and corresponding refractive index, to obtain the corrected slant range. The resulting multilayer medium range migration is written into memory for direct lookup in subsequent range migration corrections, avoiding redundant calculations.

[0050] A Fast Fourier Transform (FFT) is performed on the range-Doppler domain signal after deskewing. Phase compensation is then performed using the quadratic range compression function shown in Equation 9. In practice, the compression function is constructed as a complex lookup table and multiplied point-by-point by its conjugate with the range-Doppler domain data; this step requires only one complex multiplication and is negligible in time. After compression, the range pulse, which was originally broadened due to medium refraction, is refocused, and the range sidelobes are significantly reduced.

[0051] In the range-Doppler domain, the range migration of the multi-layered medium obtained in step (iv) is used to perform azimuth-by-azimuth interpolation correction on the entire data. An 8-point sinc function is selected as the interpolation kernel to balance accuracy and efficiency. After correction, the energy of the same target is straightened in the range direction, and the corrected internal layered signals are highlighted.

[0052] On the range migration-corrected data, an azimuth-matched filter is constructed, the modulation frequency of which is determined by the platform velocity, radar wavelength, and slant range. In actual processing, the filter coefficients are first pre-stored as complex vectors, then frequency-domain matched filtering is performed on each range gate, and finally an inverse Fourier transform is performed along the azimuth direction to obtain a fully focused two-dimensional image.

[0053] Figure 2 , 3These are the frequency-modulated continuous wave ice radar imaging results from example survey lines 1 and 2. The imaging results from example survey lines 1 and 2 show that the internal reflective layer structure of the ice sheet is clear and continuous, and details such as the ice-snow interface and internal ice layering are fully presented without significant distortion. It effectively handles range migration in multi-layered media, accurately compensating for range cell offsets caused by refractive index differences in the range-Doppler domain, thus solving the imaging blurring problem of traditional algorithms in multi-layered ice-snow structures. Furthermore, compared with traditional frequency-domain imaging algorithms, this algorithm has a simpler process. These advantages make the improved range-Doppler algorithm particularly suitable for efficient detection of large-scale polar ice layers, providing a reliable foundation for real-time on-site processing and subsequent scientific analysis.

[0054] It should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in various embodiments can also be appropriately combined and implemented according to the understanding of those skilled in the art.

[0055] The detailed descriptions listed above are merely specific descriptions of feasible embodiments of the present invention and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the inventive technique should be included within the scope of protection of the present invention.

Claims

1. A method for frequency-modulated continuous-wave ice radar imaging based on an improved range-Doppler algorithm, characterized in that, The method comprises the following steps: (1) establishing a multi-layer medium propagation model: The true geometric path between the radar and the target is converted into a single-layer equivalent slant range, so that subsequent migration correction can be completed in a single framework. The difference in refractive index of snow and ice causes the optical path to be elongated, so the refractive index is introduced. According to the snow layer refractive index n snow And the ice layer refractive index n ice The slant range R0 between the radar and the target is modeled as: R0 = h + n snow d snow +n ice d ice (Formula 1) where h is the vertical height of the radar platform above the ice surface to the target, derived from flight platform measurements, d snow is the depth of the target in the snow layer, derived from prior boreholes or coarse imaging inversion, d ice is the depth of the target in the ice layer, derived from prior boreholes or coarse imaging inversion, the snow layer refractive index is n snow 1.3 by default, based on statistical results of Antarctic snow layer measured data, the ice layer refractive index is n ice 1.78, which is the statistical result of Antarctic ice layer measured data, and is regarded as a constant, (2) echo signal preprocessing: Raw echo received by a frequency modulated continuous wave radar performing residual video phase processing to obtain: where C is the amplitude of the radar return, which has no effect on imaging, T p is the signal sweep duration, which is set by the radar system, π is the constant of the circle, j is the imaginary unit, c is the electromagnetic wave propagation speed, which is a physical constant, τ is the target return delay, which is twice the time of flight of the electromagnetic wave from the target to the radar, a is the frequency modulation slope of the FMCW radar, which is set by the radar system, rect is the rect function, λ is the radar wavelength, which is set by the radar system, L sar is the radar aperture, which is set by the radar system, R(t m ) is the slant range of the target to the radar, is the delay time of the return signal to the radar after a single pulse transmission, t m is the time variable of different pulse transmissions / receptions when the radar platform moves along the flight trajectory, v is the radar platform movement speed, which is obtained according to the measured data, exp is the natural exponential function, (3) range-doppler domain transformation: The signal is converted to the range-doppler domain by azimuth fast Fourier transform, and the signal is: where f m is the azimuthal frequency, which is the Doppler frequency along the track direction, d is the depth of the target to be detected, which is obtained from prior borehole or coarse imaging inversion, the Doppler shift correction is needed in the range-Doppler domain, and the Doppler shift correction term H1 is defined as follows: Through complex multiplication correction, the radar echo signal expression is as follows: Wherein the distance migration factor of snow is a dimensionless coefficient for quantifying the combined effect of refraction and geometry of electromagnetic waves in snow, used to convert the slant range-time trajectory to the slope correction of the range-doppler domain migration curve, and its definition is: The range migration factor of ice is a dimensionless coefficient that quantifies the combined effect of refraction and geometry of electromagnetic waves in ice, used to convert the slant range-time trajectory to the slope correction of the range-Doppler domain migration curve, and it is defined as: The range migration factor of air is a dimensionless coefficient quantifying the joint effect of refraction and geometry of electromagnetic waves in air, used to convert the slant range-time trace to the slope correction of the range-Doppler domain migration curve, which is defined as: (4) medium adaptive secondary range compression: According to the multi-layer medium signal model, a secondary range compression compensation function H2 is designed: wherein is the conjugate term, the phase compensation is realized by complex multiplication; after compensation, the radar echo signal expression is: (5) layer-dependent range migration correction: A medium adaptive correction function is constructed to eliminate the range migration caused by the multi-layer medium: wherein R rd (f m ) is the range migration, which is a physical quantity that the echo delay caused by the relative motion between radar and target changes continuously between adjacent pulses, so that the target trajectory presents a curved offset in the range-Doppler domain. Through interpolation of the signal, the range migration correction is performed, an 8-point sinc interpolation is adopted to align the curve to the same range gate, the interpolation accuracy is <0.02 m, and after the range migration correction, the expression of the radar echo signal after the range migration correction becomes (6) azimuth compression and imaging: The azimuth compression term H3 is: After azimuth compression, the azimuth-compressed radar return signal expression is wherein is the range bin, is the distance to frequency, which is the frequency across the range direction, and finally the focused radar echo signal expression is where B a is the azimuth Doppler bandwidth. At this time, the radar echo signal of one focusing has been obtained, and the radar echo matrix obtained by arranging the multi-channel radar echo collected along the track direction along the range direction. Each channel of the radar echo is processed as described above, and the radar two-dimensional echo matrix becomes a focused frequency-modulated continuous wave ice radar image.

2. The method of claim 1, wherein the improved range-Doppler algorithm-based imaging method for frequency-modulated continuous wave ice radar is characterized by: By considering the refractive index difference between snow and ice layers, a multi-layer medium propagation model describing the slant range between the radar and the target is established, which can accurately simulate the propagation path and time delay of radar signals in different media, thereby laying a foundation for subsequent range migration correction and imaging accuracy improvement.

3. The method of claim 1, wherein the improved range Doppler algorithm-based frequency-modulated continuous wave ice radar imaging method is characterized by: The original echo signal received by the frequency-modulated continuous wave radar is processed to remove residual video phase, eliminating the redundant phase information introduced by radar platform motion or other factors, making the echo signal purer and providing high-quality input data for subsequent signal processing steps.

4. The method of claim 1, wherein the improved range Doppler algorithm-based frequency-modulated continuous wave ice radar imaging method is characterized by: The signal is converted from the time domain to the range-doppler domain by azimuth fast Fourier transform (formula 3), a range migration factor is defined to adapt to the multi-layer medium environment, and the signal is processed in this domain. This transformation can effectively separate the range and Doppler information of the signal, providing convenience for further imaging processing, while considering the influence of multi-layer medium on signal propagation.

5. The method of claim 1, wherein the improved range-Doppler algorithm-based frequency-modulated continuous wave ice radar imaging method is characterized by: A medium adaptive correction function (formula 6, 7, 8) is constructed to correct the range migration caused by the multi-layer medium. This correction function dynamically adjusts the correction parameters according to the propagation characteristics of different media, accurately compensates for the change in distance between the radar and the target caused by the change in refractive index of the medium, and improves the resolution and accuracy of imaging.

6. The method of claim 1, wherein the improved range-Doppler algorithm-based frequency-modulated continuous wave ice radar imaging method is characterized by: The secondary range compression term compensation function (formula 9) is derived based on the frequency-modulated continuous wave signal model, considering the refractive index of different media in the application scenario of ice radar with multi-layer medium.

7. The method of claim 1, wherein the improved range-Doppler algorithm-based frequency-modulated continuous wave ice radar imaging method is characterized by: The azimuth matching filter (formula 13) is applied to concentrate energy on the azimuth position of the target by using the characteristics of the matching filter, realize azimuth focusing, convert the processed signal from the frequency domain back to the time domain by inverse fast Fourier transform, and finally output clear imaging results. It can effectively present the detailed features of the internal structure of the ice layer, and meet the demand of ice radar for high-resolution imaging.

8. The method of claim 1, wherein the improved range-Doppler algorithm-based frequency-modulated continuous wave ice radar imaging method is characterized by: Compared with the traditional frequency scaling algorithm, the method significantly reduces the computational complexity while ensuring high precision, only requiring three fast Fourier transform or inverse fast Fourier transform operations and four complex multiplications, reducing the computational complexity of two complex multiplications compared with the frequency scaling algorithm, greatly improving the processing efficiency, and being able to support the fast processing of a large amount of ice radar data, meeting the actual application requirements of ice layer detection.

9. The method of claim 1, wherein the improved range-Doppler algorithm-based frequency-modulated continuous wave ice radar imaging method is characterized by: Through point target simulation experiments and actual data processing tests, as shown in FIGS. 2 and 3, the advantages of the method in signal-to-noise ratio and imaging time are verified. Whether in an idealized point target simulation environment or in a complex actual ice layer detection scene, the method shows good imaging effect, can accurately detect and identify weak signals inside the ice layer, has high practicability and reliability, and provides strong technical support for detailed analysis of the ice layer structure.

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