Beidou insar dem error compensation method based on multi-satellite data combination

Abstract

The application discloses a Beidou InSAR DEM error compensation method based on multi-satellite data jointing. In a Beidou InSAR system, multiple Beidou satellites are used as transmitters to obtain interference phases under different angles, so that PS points observed by multiple satellites at the same time can be obtained, interference phases observed by multiple satellites are combined, DEM phase error coefficients of each satellite are obtained based on a bistatic configuration, and DEM error estimation at the position is realized through least square. DEM error values of each PS point are estimated, DEM error results of the whole scene are corrected through NL filtering, and high-precision whole-scene DEM error estimation results can be obtained. DEM error compensation can be realized according to the system configuration and the whole-scene DEM error estimation results, and the precision of deformation inversion is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bistatic synthetic aperture radar, and particularly relates to a method for compensating DEM phase error of a BeiDou satellite bistatic InSAR system. BACKGROUND

[0002] The BeiDou-InSAR (BeiDou based Interferometric Synthetic Aperture Radar System) system can be used for monitoring scene deformation. The system uses an on-orbit BeiDou satellite as a transmitter, and a static receiver is arranged on the ground to form a bistatic SAR system, and then a deformation monitoring is realized by using a re-orbit SAR image. The system inherits the advantages of the BeiDou positioning system and the radar system, and can realize three-dimensional deformation measurement of a scene by a single device. Compared with the traditional deformation detection method, the system has the advantages of low cost and low monitoring period.

[0003] However, the bistatic configuration of the BeiDou InSAR makes the range-doppler equation complex. Under the influence of the DEM error, the PS point will have a nonlinear focusing position offset, so that the calculation and estimation of the bistatic range and DEM interference phase error of the PS point are difficult, the DEM error compensation is more difficult, and the deformation inversion accuracy is reduced. Therefore, it is necessary to propose a DEM error compensation method. SUMMARY

[0004] Therefore, the application provides a multi-satellite data jointed BeiDou InSAR DEM error compensation method. In the BeiDou InSAR system, multiple BeiDou satellites are used as transmitters to obtain interference phases at different angles, so that PS points observed by multiple satellites at the same time can be obtained. By jointly observing the interference phases of multiple satellites, DEM phase error coefficients of each satellite are obtained based on the bistatic configuration, and the DEM error at the position is estimated by least squares. The DEM error values of each PS point are estimated, and the DEM error results of the whole scene are corrected by NL filtering, so that high-precision whole-scene DEM error estimation results can be obtained. According to the system configuration and the whole-scene DEM error estimation results, the DEM error compensation can be realized, and the deformation inversion accuracy can be improved.

[0005] The specific scheme of the application is as follows:

[0006] The multi-satellite data jointed BeiDou InSAR DEM error compensation method comprises the following steps.

[0007] Step one, whole-scene DEM error estimation;

[0008] Step two, NL filtering;

[0009] Step three, DEM error compensation;

[0010] The present application has the following beneficial effects:

[0011] The present application solves the problem of low three-dimensional deformation inversion precision caused by DEM phase error in the interference processing of the Beidou satellite bistatic InSAR system, realizes DEM error estimation of the whole scene by combining multi-satellite observation data, compensates the DEM phase error in the interference phase, and improves the precision of Beidou InSAR deformation inversion. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 The NL filtering algorithm diagram of the embodiment of the present application.

[0013] Figure 2 The two demonstration point position diagrams of the embodiment of the present application.

[0014] Figure 3 The precision of demonstration point 1 before compensation of the embodiment of the present application.

[0015] Figure 4 The precision of demonstration point 2 before compensation of the embodiment of the present application.

[0016] Figure 5 The precision of demonstration point 1 after compensation of the DEM phase error of the embodiment of the present application.

[0017] Figure 6 The precision of demonstration point 2 after compensation of the DEM phase error of the embodiment of the present application. DETAILED DESCRIPTION

[0018] The present application will be described in detail below in combination with the drawings and embodiments.

[0019] The Beidou InSAR DEM error compensation method of multi-satellite data combination specifically includes the following steps:

[0020] Step one: whole scene DEM error estimation

[0021] For any position G under multi-satellite observation, it is assumed that it can be observed by K different satellites at the same time. Since the DEM errors of different satellites observing the same point are basically the same, the atmospheric errors are basically the same, therefore, the differences between the observation phases of different satellites are mainly because the system configurations of different observation satellites are different, K dem different, resulting in different DEM error phases, that is:

[0022]

[0023] The above formula is written in matrix form:

[0024]

[0025] wherein: is a Kx1 matrix, containing the observed phases; β is a 2x1 matrix, containing the DEM error and atmospheric phase at the position G to be estimated; denotes the phase noise, K dem is the DEM coefficient, expressed as:

[0026]

[0027] wherein,

[0028] t k denotes the aperture center time of the k-th day image, t n is the reference time, Q' denotes the position of the target Q after imaging, P S (t k ) is the position of the satellite at t k , P S (t n ) is the position of the satellite at t n , P s (t k , t n ) denotes the average of the satellite positions at t k and t n , P Q′ (t n ) denotes the three-dimensional coordinates of Q', P E denotes the three-dimensional coordinates of the echo antenna, V s denotes the satellite velocity.

[0029] Herein, contains the deformation phase, but the deformation phase can be removed by subsequent DEM filtering, without affecting the estimation result of the DEM.

[0030] Further, the accurate DEM error at the position G can be obtained by least squares:

[0031]

[0032] The first term in β is the accurate DEM error at the position G.

[0033] For all the correlation results of the first day, the DEM error of the PS point on all the correlations of the day can be estimated.

[0034] Step two: NL filtering

[0035] Because the SNR of Beidou InSAR system is low, and the estimation accuracy of DEM error is directly related to the number of associated satellites. When the number of associated satellites is small, the estimation result of the point will have a large deviation. Therefore, the DEM error obtained initially needs to be further processed to improve the accuracy.

[0036] The method of NL filter is used to process the DEM error obtained initially. The traditional filtering methods include Lee filter, Frost filter and non-local filter (NL, non-local filter) and the like. Among them, the NL filter fully considers the similarity and redundancy of the data itself and applies it to the denoising process. The main idea is to expand the local or semi-local model to the non-local model based on the similarity of the data itself, and let the weighted average value of all pixel points similar to the structure of the current pixel point as the gray estimation value of the current pixel point.

[0037] In the traditional image filtering, the main steps can be represented as:

[0038] Let the discretized image be p={p(i)|i∈Ω}, wherein Ω is the support domain. The DEM error value of any pixel i in the image is obtained by weighted average of its adjacent pixels:

[0039]

[0040] Among them, S(i) represents the search window centered on pixel i. w(i,j) represents the weight function, which is determined by the similarity between pixel i and pixel j, and satisfies 0≤w(i,j)≤1. Let N(i) represent the neighborhood centered on pixel i with fixed size, which is generally set as square. The weight w(i,j) can be represented as:

[0041]

[0042] Among them, h represents the decay factor, represents the Euclidean distance under Gaussian weighting, and α represents the standard deviation of the Gaussian kernel.

[0043] However, for the filtering of DEM error in Beidou InSAR, the traditional NL filter cannot be directly used, and needs to be improved. First, the preliminary estimation result of DEM error is a discrete point, only the position P ΔG The error estimation result can be obtained. Therefore, in formula 8, the Gaussian kernel needs to be rewritten in a discrete form:

[0044]

[0045] Among them, Z1(i,j) is a normalization function.

[0046] At the same time, for long time PS points, each interferometric pair can get an estimation of DEM error. However, due to the existence of focusing position error, that is, P ΔG There is random jitter. Even for a PS point series, its position is different every day, changing randomly in a small range. Traditional kernel function adopts exponential form, which decreases quickly in nearby area. In Beidou InSAR, more weight should be given to nearby area. At the same time, since DEM error does not have spatial coherence after a certain distance, the coefficient should decrease quickly with the increase of N1(i, j). Based on this, the weight kernel function needs to be further modified. Here, the new kernel function is defined as:

[0047]

[0048] where h1is the new smoothing index, and has:

[0049]

[0050] Secondly, in traditional NL filter, the neighborhood of a pixel, that is, N(i) is generally square. However, for Beidou InSAR system, the system has difference in spatial resolution. Therefore, in the filtering algorithm, the influence of resolution unit shape on spatial position distribution should also be considered. Here, the shape of the neighborhood is changed to an ellipse based on two-dimensional resolution, and its schematic diagram is shown in Figure 1 The square area is the search area, and the elliptical area is the neighborhood. ρ r , ρ a are the resolutions in range and azimuth directions, respectively, and α NL represents the expansion coefficient. This coefficient depends on the density of scene PS points. When the point density is high, the coefficient is low, and vice versa. In this way, the number of points in each direction of the area N can be equal, ensuring the average of the scene.

[0051] Through the NL filter, the preliminary estimated DEM error of the first day can be converted into the final DEM error of the first day scene, that is:

[0052] ΔDEM = NL_filter(ΔDEM coa ) (12)

[0053] For long time monitoring, the DEM information of the scene is unchanged, so after a period of DEM error estimation, the estimation value can be compensated to the DEM information as the correction of DEM, and then no longer DEM error estimation is performed.

[0054] Step three: DEM error compensation

[0055] For any PS point Q, its DEM error estimation result can be obtained from the full scene DEM error estimation result estimated in step two, and the phase error introduced by the DEM error can be expressed as:

[0056]

[0057] Traverse all PS points in the scene, the DEM phase error result of each PS point can be obtained, and the final differential phase is the phase caused by deformation:

[0058]

[0059] In the embodiment, a 1200m*1200m deformation scene is selected, and 8 Beidou IGSO satellites are selected as the transmitter, and the total experimental time is 22 days. The processing result of Beidou2 IGSO3 is taken as an example to show the phase error compensation result.

[0060] Two PS points are selected, and the positions are [157, 218] and [304, 266], and the positions are shown by white points in Figure 2 The interference phase accuracy of the two demonstration points before compensation is shown in Figure 3 , Figure 4 The average accuracy of the two PS points is 23.0525mm and 16.9324mm. The result after DEM error compensation is shown in Figure 5 , Figure 6 The accuracy of the two PS points is 17.4168mm and 7.5528mm.

[0061] Table 1 accuracy comparison

[0062]

[0063] According to the result in Table 1, it can be seen that the deformation inversion accuracy after the Beidou InSAR DEM error compensation method of multi-satellite data joint processing proposed in the present application is improved compared with that before processing, which proves the effectiveness of the present application.

[0064] To sum up, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for error compensation of BeiDou InSAR DEM based on multi-satellite data, characterized in that, The method includes the following steps: Step 1: Full-scene DEM error estimation; The error estimation matrix for the full-scene DEM is in the form of: ； in: K represents the number of observation satellites. yes The matrix contains the observed phase; yes The matrix contains the positions to be estimated. DEM error and atmospheric phase; Indicates phase noise, The DEM coefficient is expressed as follows: ； in, ; ； Indicates the first At the aperture center time of the celestial image, For reference time, Indicate target Position after imaging for The position of the satellite at all times. for The position of the satellite at all times. express Time and The average position of satellites at any given time. express The three-dimensional coordinates Represents the three-dimensional coordinates of the echo antenna. Indicates satellite speed; Step 2: NL filtering; Step 3: DEM error compensation.

2. The BeiDou InSAR DEM error compensation method based on multi-satellite data as described in claim 1, characterized in that... In step two, the Gaussian kernel is in discrete form: ； in, For normalization function, Represented by pixels A neighborhood of fixed size centered on the center. Indicates the attenuation factor. This represents the Euclidean distance under Gaussian weighting. This represents the standard deviation of the Gaussian kernel.

3. The BeiDou InSAR DEM error compensation method based on multi-satellite data as described in claim 2, characterized in that... In step two, the kernel function for the weights is defined as: ； in, For the new smoothing index: 。 4. The BeiDou InSAR DEM error compensation method based on multi-satellite data fusion as described in claim 1, characterized in that... In step two, the preliminary estimated DEM error for the first day is converted into the final DEM error for the first day scene: 。 5. The BeiDou InSAR DEM error compensation method based on multi-satellite data fusion as described in claim 1, characterized in that... In step three, the phase error introduced by the DEM error is expressed as: ； By iterating through all the PS points in the scene, we can obtain the DEM phase error result for each PS point. The final differential phase is the phase caused by deformation. 。

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