CN116609781B - A method for error compensation of BeiDou InSAR DEM based on multi-satellite data - Google Patents

Abstract

This invention discloses a method for DEM error compensation using multi-satellite data fusion in BeiDou InSAR. In the BeiDou InSAR system, multiple BeiDou satellites are used as transmitters to obtain interferometric phase at different angles, thus obtaining PS points observed simultaneously by multiple satellites. By fusion of the interferometric phase from multi-satellite observations, and based on a bistatic configuration, the DEM phase error coefficient of each satellite is obtained. Least squares are then used to estimate the DEM error at that location. The DEM error value for each PS point is estimated accordingly, and then NL filtering is used to correct the DEM error result for the entire scene, resulting in a high-precision full-scene DEM error estimation result. Finally, based on the system configuration and the full-scene DEM error estimation result, DEM error compensation can be achieved, improving the accuracy of deformation inversion.

Description

Beidou InSAR DEM error compensation method combining multiple star data

Technical Field

The invention belongs to the technical field of bistatic synthetic aperture radars, and particularly relates to a method for compensating DEM phase errors by a Beidou satellite bistatic InSAR system.

Background

The InSAR system of Beidou satellite (BeiDou-InSAR, beiDou based Interferometric Synthetic Aperture RADAR SYSTEM) can be used to monitor scene deformation. According to the system, an on-orbit Beidou satellite is used as a transmitter, a static receiving mechanism is arranged on the ground to form a double-base SAR system, and then deformation monitoring is realized by using a heavy-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 an opposite scene through a single device. Compared with the traditional deformation detection method, the system has the advantages of low cost, low monitoring period and the like.

However, the distance Doppler equation is complicated due to the bistatic configuration of the Beidou InSAR, under the influence of the DEM error, the PS point can generate nonlinear focusing position offset, so that the calculation and estimation difficulty of the bistatic distance of the PS point and the DEM interference phase error are increased, the DEM error compensation is more difficult, and the deformation inversion precision is reduced, so that the DEM error compensation method is necessary to be provided.

Disclosure of Invention

In view of the above, the invention provides a Beidou InSAR DEM error compensation method combining multi-star data. In the Beidou InSAR system, a plurality of Beidou satellites are used as transmitters to obtain interference phases under different angles, so that PS points observed by the plurality of satellites at the same time can be obtained, the interference phases observed by the plurality of satellites are combined, then the DEM phase error coefficient of each satellite is obtained based on a bistatic configuration, and the DEM error estimation at the position is realized through least square. And estimating the DEM error value of each PS point, and correcting the DEM error result of the whole scene through NL filtering to obtain a high-precision full-scene DEM error estimation result. And then according to the system configuration and the full-scene DEM error estimation result, the DEM error compensation can be realized, and the accuracy of deformation inversion is improved.

The specific scheme of the invention is as follows:

a Beidou InSAR DEM error compensation method combining multi-star data comprises the following steps:

step one, estimating the error of a full scene DEM;

Step two, NL filtering;

Step three, DEM error compensation;

The invention has the following beneficial effects:

the method solves the problem of low three-dimensional deformation inversion precision caused by DEM phase errors when the Beidou satellite bistatic InSAR system performs interference processing, realizes full-scene DEM error estimation by combining multi-satellite observation data, compensates the DEM phase errors in interference phases, and improves the precision of the Beidou InSAR deformation inversion.

Drawings

Fig. 1 is a schematic diagram of NL filtering algorithm according to an exemplary embodiment of the present invention.

FIG. 2 is a schematic diagram of two exemplary point locations according to an exemplary embodiment of the present invention.

Fig. 3 shows the accuracy of an exemplary point 1 before uncompensation in accordance with an exemplary embodiment of the invention.

Fig. 4 shows the accuracy of an exemplary point 2 before uncompensated, in accordance with an exemplary embodiment of the invention.

Fig. 5 illustrates the accuracy of the exemplary point 1 compensated DEM phase error according to an exemplary embodiment of the invention.

Fig. 6 illustrates the accuracy of the exemplary point 2 compensated DEM phase error in accordance with an exemplary embodiment of the invention.

Detailed Description

The invention will now be described in detail by way of example with reference to the accompanying drawings.

The Beidou InSAR DEM error compensation method based on multi-star data combination specifically comprises the following steps:

Step one, full scene DEM error estimation

For position G under any multi-satellite observation, it is assumed that it can be observed by K different satellites simultaneously. Since DEM errors of different satellites observing the same point are basically consistent, and atmospheric errors are basically consistent, the difference between the observed phases of different satellites is mainly caused by different system configurations of different satellites, and different K _dem results in different DEM error phases, namely:

Writing the above into a matrix form:

wherein: is a Kx1 matrix containing the observed phase, and beta is a2 x 1 matrix containing the DEM error and the atmospheric phase of the position G to be estimated; Representing phase noise, K _dem is a DEM coefficient, and the expression is:

wherein, the

T _k denotes the aperture center time of the kth 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 time t _k, P _S(t_n) is the position of the satellite at time t _n, P _s(t_k,t_n) denotes the average of the satellite positions at time t _k and time t _n, P _Q′(t_n) denotes the three-dimensional coordinates of Q', P _E denotes the three-dimensional coordinates of the echo antenna, and V _s denotes the satellite speed.

Where the number of the elements in the process is,The deformation phase is included, but can be removed through subsequent DEM filtering, and the estimation result of the DEM is not affected.

Further, the exact DEM error at the correlated pair G position may be obtained by least squares:

the first term in β is the exact DEM error at position G.

For all correlation results for the first day, the DEM error for PS points on all correlations for that day can be estimated.

NL filtering

Because the signal-to-noise ratio of the Beidou InSAR system is low, meanwhile, the estimation accuracy of the DEM error is directly related to the number of the point-associated satellites. When the number of associated satellites is small, a large deviation in the estimation results of this point occurs. Therefore, further processing of the preliminarily obtained DEM errors is required to improve accuracy.

The initially obtained DEM error is processed here by NL filtering. Conventional filtering methods include Lee filtering, post filtering, non-local filtering (NL, nonlocal filter), and the like. The NL filter fully considers the similarity and redundancy of the data, and applies the data to the denoising process. The main idea is to extend a local or semi-local model into a non-local model based on the similarity of the data, so that the weighted average value of all pixels similar to the current pixel in structure is used as the gray level estimation value of the current pixel.

In conventional image filtering, the main steps can be expressed as:

let the discretized image be p= { p (i) |i e Ω }, where Ω is the support domain. The DEM error value of any pixel i in the image is obtained by weighted average of adjacent pixels:

Where S (i) denotes a search window centered at pixel i. w (i, j) represents a weight function which is determined by the similarity between pixel i and pixel j, while satisfying 0≤w (i, j). Ltoreq.1. Let N (i) denote a neighborhood of fixed size centered on pixel i, typically square, and the weights w (i, j) can be expressed as:

wherein h represents an attenuation factor, The Euclidean distance under Gaussian weighting is shown, and α is the standard deviation of the Gaussian kernel.

However, for filtering DEM errors in beidou InSAR, a conventional NL filter cannot be directly used, and a certain improvement is required. First, the preliminary estimation result of the DEM error is a discrete point, and only the position P _ΔG corresponding to the correlation pair G can obtain the error estimation result. Therefore, in equation 8, the gaussian kernel needs to be rewritten into a discrete form:

Wherein Z ₁ (i, j) is a normalization function.

Meanwhile, for a long-time PS point, each interference pair can obtain an estimation result of DEM errors. However, there is random jitter due to the presence of focus position errors, i.e., P _ΔG. Even for a sequence of PS points, the position of each day is different, varying randomly over a small range. The conventional kernel function takes the form of an index, where coefficients fall off faster, whereas in Beidou InSAR, more weight should be given to the neighborhood. Meanwhile, since the DEM error does not have spatial coherence after a certain distance, the coefficient should be rapidly reduced with the increase of N ₁ (i, j). Based on this, further modification of the kernel function of the weights is required. Here, a new kernel function is defined as:

wherein h ₁ is a new smoothness index, which has:

Second, in a conventional NL filter, the neighborhood of picture elements, i.e. N (i), is typically chosen to be square. However, for the Beidou InSAR system, the system is spatially resolved differently. Therefore, the effect of the shape of the resolving element on the spatial position distribution should also be taken into account in the filtering algorithm. Here, the shape of the neighborhood is changed to an ellipse based on two-dimensional resolution, a schematic view of which is shown in fig. 1. In the figure, the square area is a search area, and the elliptical area is a neighborhood. ρ _r,ρ_a is the resolution in the distance and azimuth directions, respectively, and α _NL represents the expansion coefficient. The coefficient depends on the density of the scene PS points, and is lower when the point density is higher, and vice versa. In this way, the number of points of the region N in each direction can be made equal, and the average of the scene is ensured.

Through the NL filter, the preliminary estimated DEM error of the first day may be converted into the final DEM error of the first day scene, i.e.:

ΔDEM=NL_filter(ΔDEM_coa) (12)

For long-time monitoring, the DEM information of the scene is unchanged, so after a period of DEM error estimation, the estimated value can be used as correction compensation of the DEM to the DEM information, and then the DEM error estimation is not performed.

Step three, DEM error compensation

For any PS point Q, the DEM error estimation result can be obtained from the full-scene DEM error estimation result estimated in the step two, and then the phase error introduced by the DEM error can be expressed as;

Traversing 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:

In this embodiment, a deformation scene of 1200 m×1200 m is selected, 8 beidou IGSO satellites are selected as the transmitter, and the experiment time is 22 days in total. In this embodiment, the result of phase error compensation is shown by taking the processing result of Beidou2 IGSO3 as an example.

Two PS points were selected, the positions of which were [157,218], [304,266], the positions of which are shown as white points in fig. 2. The interferometric phase precision before two exemplary point compensations is shown in fig. 3 and 4, and the average precision of two PS points is 23.0525mm and 16.9324mm. The result of DEM error compensation is shown in FIGS. 5 and 6, and the accuracy of the two PS points is 17.4168mm and 7.5528mm.

Table 1 precision comparison

According to the results of table 1, it can be seen that the deformation inversion accuracy after being processed by the multi-star data combined Beidou InSAR DEM error compensation method provided by the invention is improved compared with that before being processed, and the effectiveness of the invention is proved.

In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. The Beidou InSAR DEM error compensation method based on multi-star data combination is characterized by comprising the following steps of:

step one, estimating the error of a full scene DEM;

The full scene DEM error estimation matrix form is:

;

wherein: K represents the number of satellites in view, Is thatComprises an observation phase; Is that Comprises a matrix of positions to be estimatedDEM error and atmospheric phase; Representing the phase noise of the signal and, For DEM coefficients, the expression is:

;

wherein, the ;

;

Represent the firstThe aperture center of the day image is at the moment,For the reference time to be used,Representing objectsThe position after the imaging is performed,Is thatThe position of the satellite at the moment in time,Is thatThe position of the satellite at the moment in time,Representation ofTime of dayThe average of the time-of-day satellite positions,Representation ofIs provided with a plurality of three-dimensional coordinates,Representing the three-dimensional coordinates of the echo antenna,Representing satellite velocity;

Step two, NL filtering;

and thirdly, performing DEM error compensation.

2. The multi-star data combined Beidou InSAR DEM error compensation method of claim 1 is characterized in that in the second step, a Gaussian kernel is in a discrete form:

;

wherein, the As a function of the normalization,Expressed in picture elementsIs a neighborhood of fixed size for the center,The attenuation factor is indicated as such,Representing the euclidean distance under gaussian weighting,The standard deviation of the gaussian kernel is shown.

3. The multi-star data combined Beidou InSAR DEM error compensation method of claim 2, wherein in the step two, a kernel function of the weight is defined as:

;

wherein, the For a new smoothness index:

。

4. The multi-star data combined Beidou InSAR DEM error compensation method of claim 1 is characterized in that in the second step, the preliminarily estimated first-day DEM error is converted into a final first-day scene DEM error:

。

5. the multi-star data combined Beidou InSAR DEM error compensation method of claim 1, wherein in the third step, the phase error introduced by the DEM error is expressed as:

;

Traversing 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:

。