A frequency point design method for multi-frequency interferometric phase unwrapping in InSAR

Abstract

This invention belongs to the field of interferometric radar technology and is a frequency point design method for multi-frequency interferometric phase unwrapping in InSAR. By optimizing the frequency ratio and increasing the theoretical interval between the centers of the intersection points of adjacent cutting planes, high-precision unwrapping of InSAR interferometric phases can be achieved.

Description

Technical Field

[0001] This invention belongs to the field of interferometric radar technology, specifically, it relates to a frequency point design method for multi-frequency interferometric phase unwrapping for InSAR. Background Technology

[0002] Interferometric Synthetic Aperture Radar (InSAR) has been widely used in fields such as geological disaster monitoring and early warning, surface subsidence monitoring, and topographic mapping.

[0003] InSAR measures elevation by coherently processing two complex SAR images of the same region and utilizing phase information. To ensure the feasibility and accuracy of interferometry, a sufficient height difference is required between the two flights, meaning the spatial baseline must be long enough. Under long baseline conditions, the gradient of the true phase change is large due to terrain undulations, resulting in very dense fringes in the interferometric phase map. In complex terrain, issues such as overlapping and shading caused by the geometry of SAR front-side-looking imaging can easily lead to phase jumps in the interferometric fringes. Conventional phase unwrapping methods are difficult to apply to InSAR phase maps for mapping complex terrain.

[0004] Conventional single-baseline phase unwrapping methods require the assumption of phase continuity, meaning the mapped area must have spatial continuity and the true phase difference between adjacent pixels in the interferometric phase map must not exceed π. Multi-baseline phase unwrapping effectively overcomes this limitation by combining long and short baselines, significantly improving the ambiguity height and finding successful applications in spaceborne / airborne InSAR. However, for airborne InSAR, the inconsistent flight paths and time-varying interferometric baselines (changing for different ground targets) result in an excessive number of baseline combinations during multiple flights, making conventional multi-spatial-baseline unwrapping methods unsuitable. Multi-frequency phase unwrapping, a branch of multi-baseline phase unwrapping, utilizes the combined processing of different frequencies during two flights to improve the ambiguity height without requiring multiple flights, reducing data acquisition difficulty. It also represents a phase unwrapping method that overcomes the phase continuity assumption.

[0005] Due to phase errors, pixels with the same ambiguity exhibit significant clustering. This phenomenon is influenced by the frequency ratio of different frequency points. If the frequency ratio is poorly designed, the theoretical interval between the centers of adjacent cleaving plane intersections will be very small, making it more sensitive to errors and thus affecting the final phase unwrapping accuracy. Therefore, it is necessary to study frequency design methods to improve the accuracy of phase unwrapping. Summary of the Invention

[0006] In view of this, the present invention provides a frequency point design method for multi-frequency interferometric phase unwrapping for InSAR, which achieves high-precision unwrapping of InSAR interferometric phase by increasing the theoretical interval between the centers of the intersection points of adjacent cut planes.

[0007] To achieve the above-mentioned objectives, the technical solution of this invention is as follows:

[0008] This invention proposes a frequency point design method for multi-frequency interferometric phase unwrapping in InSAR, comprising the following steps:

[0009] S1. Assume there are M different channels transmitting and receiving radar signals with different center frequencies. If N channels are randomly selected, there are a total of... In the middle combination, obtain all possible fuzzy number vector combinations k for each combination case. m .

[0010] S2. Construct an N-dimensional spatial linear equation regarding ambiguity, set a reference cutting plane, and obtain the intersection vector p of the N-dimensional spatial linear equation determined by any pixel and the cutting plane. m .

[0011] S3. Take all possible fuzzy number vectors k obtained in S1. m Substitute the position vector p of the intersection point with the cutting plane m In this process, we obtain the position vectors of all possible intersection points.

[0012] S4. Calculate the maximum unambiguous height h of the multi-frequency points at this time. 2πN .

[0013] S5. Construct an objective function based on minimizing the Euclidean distance between the position vectors of the intersection points with the cutting plane, and satisfy that the ratios of the simplest integer ratios of each frequency point are mutually exclusive, and the maximum unambiguous height is greater than the maximum terrain height.

[0014] S6. Iterate through all possible frequency points to obtain the optimal N frequency points.

[0015] Furthermore, the expression for all possible fuzzy number vectors in S1 is:

[0016]

[0017] Where, k m Let M represent the ambiguity of the interferogram corresponding to the m-th frequency point, and M represent the product of the ratios of the simplest integer ratios of all frequency points. This represents the ratio of the simplest integer ratio corresponding to the m-th frequency point.

[0018] Furthermore, the spatial linear equation for ambiguity constructed in S2 is:

[0019]

[0020] Where f1, f2, ..., f N k represents different center frequencies. n (s) represents the ambiguity of the s-th pixel in the interferometric phase image corresponding to the n-th frequency point, k n This represents the spatial coordinate axis corresponding to the nth frequency point.

[0021] Considering the influence of noise, the spatial line equation corresponding to each pixel is:

[0022]

[0023] Where Δk n (s) represents the change in ambiguity of the s-th pixel in the interferometric phase diagram corresponding to the n-th frequency point due to phase error.

[0024] Let any one dimension be the cutting plane, that is, let k x =0, then the equation of the line and k x The position of 0 in N-1 dimensional space can be represented as

[0025]

[0026] Where i = 1, 2, K, N, i ≠ x

[0027] Furthermore, the objective function in S5 based on minimizing the Euclidean distance between the intersection point vectors of the cutting plane and the cutting plane is:

[0028]

[0029]

[0030] m1, m2 ∈ [0, 2M-1], m1 ≠ m2

[0031] i = 1, 2, K, N, i ≠ x

[0032] h 2πN ≥h z

[0033] Among them, f1 * f2 * ,L, The ratio representing the simplest integer ratio of each frequency point. h represents the spatial position vector of any possible intersection point of an N-dimensional line and a cutting plane. 2πN h represents the maximum unambiguous height that multi-frequency phase unwrapping can handle at this point. z This represents the maximum terrain elevation.

[0034] Beneficial effects: This invention provides a frequency point design method for multi-frequency interferometric phase unwrapping in InSAR. By optimizing the frequency points of the signal and increasing the theoretical interval between the centers of the intersection points of adjacent cut planes, the robustness of density clustering and the reliability of determining the fuzzy pairs corresponding to each cluster center based on the Chinese remainder theorem are enhanced, thereby improving the accuracy of interferometric phase unwrapping and helping to achieve high-precision unwrapping of InSAR interferometric phases. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the implementation of the present invention. Detailed Implementation

[0036] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] like Figure 1 As shown, this invention provides a frequency point design method for multi-frequency interferometric phase unwrapping in InSAR, specifically including the following steps:

[0038] S1. Assume there are M different channels transmitting and receiving radar signals with different center frequencies. If N channels are randomly selected, there are a total of... In the middle combination, obtain all possible fuzzy number vector combinations k for each combination case. m .

[0039] Taking two frequency points as an example, the expression for all possible fuzzy number vectors is:

[0040]

[0041] Where k1(s) and k2(s) represent the ambiguity corresponding to the s-th pixel in the interferogram for the 1st and 2nd frequency points, respectively, and f1 * f2 * This represents the ratio of the simplest integer ratios corresponding to the 1st and 2nd frequency points.

[0042] Taking three frequency points as an example, all possible fuzzy number vectors are:

[0043]

[0044] Where, k m (s) represents the ambiguity corresponding to the s-th pixel in the interferogram at the m-th frequency point, and M represents the product of the ratios of the simplest integer ratios of all frequency points. This represents the ratio of the simplest integer ratio corresponding to the m-th frequency point.

[0045] Extending to N frequency points, all possible ambiguity vectors are:

[0046]

[0047] Where, k m (s) represents the ambiguity corresponding to the s-th pixel in the interferogram at the m-th frequency point, and M represents the product of the ratios of the simplest integer ratios of all frequency points. This represents the ratio of the simplest integer ratio corresponding to the m-th frequency point.

[0048] S2. Construct an N-dimensional spatial linear equation regarding ambiguity, set a reference cutting plane, and obtain the intersection vector p of the N-dimensional spatial linear equation determined by any pixel and the cutting plane. m .

[0049] Taking two frequency points as an example, the two-dimensional linear equation for ambiguity is:

[0050]

[0051] Where f1 and f2 represent different center frequencies, and k1(s) and k2(s) represent the ambiguity of the s-th pixel in the interferometric phase diagram corresponding to the first and second frequency points, respectively. This represents the s-th pixel in the interference phase diagram corresponding to the 1st and 2nd frequency points, representing the entangled phase.

[0052] The purpose of phase unwrapping is to obtain integer ambiguities k1(s) and k2(s). For any pixel, its ambiguity vector is uniquely determined. Therefore, (4) can be rewritten as

[0053]

[0054] Where k1-k2 represents the plane containing the line, f1 * f2 * It represents the ratio of the simplest integer ratio of two frequency points f1 and f2.

[0055] Extending to N frequency points, the N-dimensional linear equation for ambiguity is:

[0056]

[0057] Where f1, f2, ..., f N k represents different center frequencies. n (s) represents the ambiguity of the s-th pixel in the interferometric phase image corresponding to the n-th frequency point, k n This represents the spatial coordinate axis corresponding to the nth frequency point.

[0058] Choose any plane parallel to the spatial coordinate axes as the reference cutting plane.

[0059] Taking two frequency points as an example, and taking k1 = 0 as the reference secant plane, then the coordinates of the intersection point with the secant plane are:

[0060]

[0061] Taking the three-frequency point as an example, and taking k2 = 0 as the reference secant plane, then the coordinates of the intersection point with the secant plane are:

[0062]

[0063] Extend to N frequency points, take k x If 0 is taken as the reference cutting plane, then the coordinates of the intersection point with the cutting plane are...

[0064]

[0065] S3. Take all possible fuzzy number vectors k obtained in S1. m Substitute the position vector p of the intersection point with the cutting plane m In this process, we obtain the position vectors of all possible intersection points.

[0066] Taking two frequency points as an example, all possible intersection points can be represented as follows:

[0067]

[0068] Extend to N frequency points, take k x With 0 as the reference cutting plane, the vectors representing the positions of all possible intersection points can be expressed as follows:

[0069]

[0070] in Let represent the ratio of the simplest integer ratios corresponding to the m-th frequency point, where m = 1, 2, K, N, m ≠ x. M represents the product of the ratios of the simplest integer ratios of all frequency points.

[0071] S4. Calculate the maximum unambiguous height h of the multi-frequency phase unwrapping at this time. 2πN .

[0072] Assuming the center frequency is f1, the maximum unambiguous height during single-frequency phase unwrapping is: Where λ1 is the signal wavelength, R is the slant range from the target to the radar (usually the slant range at the center of the scene is used for unified calculation), and B is the baseline length.

[0073] The multi-frequency phase unwrapping method improves the ambiguity height by jointly processing different frequencies. The maximum unambiguity height using the multi-frequency phase unwrapping method is...

[0074]

[0075] Where f1, f2, ..., f N f1 represents different center frequencies. * f2 * ,L, The ratio representing the simplest integer ratio of each frequency point.

[0076] S5. Construct an objective function based on minimizing the Euclidean distance between the position vectors of the intersection points with the cutting plane, and satisfy that the ratios of the simplest integer ratios of each frequency point are mutually exclusive, and the maximum unambiguous height is greater than the maximum terrain height.

[0077] Taking two frequency points as an example, without considering the influence of phase error on phase unwrapping, all possible intersection points are shown in (10). The objective function is constructed by minimizing the distance between the intersection points.

[0078]

[0079] Among them, f1 * f2 * The ratio representing the simplest integer ratio of two frequency points. It represents the spatial position vector of the intersection point of any straight line and the cutting plane.

[0080] Considering the effect of phase error,

[0081]

[0082] Where Δk n (s) represents the change in ambiguity of the s-th pixel in the n-th interferometric phase image due to phase error.

[0083] (14) can be rewritten as

[0084]

[0085] The lines corresponding to the same ambiguity vector no longer coincide, but instead shift vertically from their theoretical positions. Assume the ambiguity change Δk is caused by the phase error. i If the standard deviation of (i = 1, 2) is σ, then The standard deviation is

[0086] Then we have the objective function that considers phase error.

[0087]

[0088] When the terrain height is too high, an inappropriate frequency ratio can cause the extended maximum unambiguous height to fall short of the terrain height, still failing to completely overcome the phase continuity assumption. Therefore, terrain constraints must also be considered.

[0089] h 2πN ≥h z (17)

[0090] Where h 2πNh represents the maximum unambiguous height achieved using the multi-frequency phase unwrapping method. z This represents the maximum elevation of the terrain.

[0091] In summary, considering phase error, the objective function for the two frequency points is:

[0092]

[0093] Extending to N frequencies, the objective function based on minimizing the Euclidean distance between the intersection vectors of the cutting plane and the N-frequency points is:

[0094]

[0095] Among them, f1 * f2 * ,L, The ratio representing the simplest integer ratio of each frequency point. h represents the spatial position vector of any possible intersection point of an N-dimensional line and a cutting plane. 2πN h represents the maximum unambiguous height that multi-frequency phase unwrapping can handle at this point. z This represents the maximum terrain elevation.

[0096] S6. Iterate through all possible frequency points to maximize the objective function and obtain the ratio f1 of the simplest integer ratio of the optimal frequency points. * f2 * ,L, Choose an appropriate frequency point based on the system's own conditions.

[0097] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for InSAR multi-frequency point interferometric phase unwrapping frequency point design, characterized in that, The method comprises the following steps: Step one, assuming there are M different channels transmitting and receiving radar signals of different center frequencies, any of which are selected N , a total of combinations, get all possible ambiguity number vector combinations under each combination ; Step two, construct the equation of straight line in n-dimensional space about ambiguity N The equation of straight line in n-dimensional space, set the reference tangent plane, get the position vector of intersection point of the straight line and the tangent plane determined by any pixel N The equation of straight line in n-dimensional space and the position vector of intersection point of the tangent plane ; Step three, obtain all possible fuzzy number vectors from step one Substitute the intersection position vector of the tangent plane In this way, all possible intersection position vectors are obtained; Step four, calculate the maximum unambiguous height of multi-frequency points at this time ; Step five, constructing a target function based on the minimum Euclidean distance between the position vectors of the intersection points of the cutting planes, and satisfying the ratio exclusion of the minimum integer ratios of each frequency point and the maximum unambiguous height being greater than the maximum terrain height; wherein the target function is expressed as: ； wherein, a ratio representing the simplest integer ratio of the frequencies, a ratio representing the simplest integer ratio of the frequencies, N a spatial position vector of the intersection of a straight line in the n-dimensional space with the dissection plane, a standard deviation representing the change in ambiguity caused by the phase error, a maximum unambiguous height representing the maximum unambiguous height that can be processed at this time by multi-frequency phase unwrapping, a maximum terrain height representing the maximum terrain height, Q a product representing the ratio of the simplest integer ratio of the frequencies. Step six, traversing all possible frequency points to maximize the target function to obtain the optimal N frequency points.

2. The InSAR-oriented multi-frequency-point interferometric phase-unwrapping frequency-point design method of claim 1, wherein, The expression of all possible ambiguity number vectors in step one is ； wherein, represents the ambiguity of the interference pattern corresponding to the m Q represents the ambiguity of the interference pattern corresponding to the m represents the ratio of the simplest integer ratios of the respective frequencies.​​ 3. The InSAR-oriented multi-frequency-point interferometric phase un-wrapping frequency point design method of claim 1, wherein, The constructed spatial straight line equation about the ambiguity in step two is ； wherein, denotes different center frequencies, denotes the spatial coordinate axis corresponding to the n th frequency point, s denotes the ambiguity corresponding to the th pixel in the interference phase map corresponding to the n th frequency point, Considering the noise influence, the spatial straight line equation corresponding to each pixel is ； wherein, represents the change in the ambiguity of the pixel in the interference phase map corresponding to the n th frequency point due to the phase error; and s th pixel in the interference phase map corresponding to the th frequency point due to the phase error. Let any one dimension be the cut plane, i.e. let Then the line equation is In N -1 dimensional space, the position can be represented as ； wherein .

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