Optimal matching double-star SAR fusion imaging method based on CRLB

Abstract

The invention discloses an optimal matching double-star SAR fusion imaging method based on CRLB. A global navigation satellite system (GNSS) has the advantages of all-weather operation, wide space coverage and the like, and although a GNSS-R SAR technology in which reflected signals of the GNSS are used for imaging of a ground synthetic aperture radar (SAR) is low in cost and wide in application, the resolution ratio of the GNSS is poor due to the fact that the bandwidth of the GNSS signals is limited. According to the method, an SAR fusion imaging system model composed of a plurality of satellites and a single ground fixed GNSS receiver is established, the mutual relation between a fuzzy function of a GNSS signal and Fisher information is explored, and a system Cramer-Rao lower bound (CRLB) influenced by a bistatic set geometric configuration is deduced. On the basis, a CRLB expression is adopted to identify satellites in the optimal resolution direction of the ground target, and according to the principle that the included angle between the optimal resolution directions is as close as 90 degrees as possible, the imaging results of the selected satellites are subjected to incoherent fusion. By means of the method, unnecessary redundant imaging processing is avoided, and it is ensured that imaging resources are utilized most reasonably. And the resolution performance of the system is improved in a more efficient manner.

Description

Technical Field

[0001] The invention belongs to the field of electronic signal processing and relates to an optimal matching dual-satellite SAR fusion imaging method based on CRLB. Background Art

[0002] The Global Navigation Satellite System (GNSS) has all-weather operability and wide spatial coverage, enabling global positioning, navigation, and time synchronization. By using GNSS reflected signals for ground-based synthetic aperture radar (SAR) imaging, that is, synthetic aperture radar imaging (GNSS-R SAR) technology using GNSS reflected signals. With its advantages of low cost, all-weather operation, and wide coverage, this technology has been widely used in the fields of sea surface height measurement, wind speed estimation, and ground imaging.

[0003] GNSS-R SAR technology captures satellite transmitted signals and signals reflected from targets without the need for dedicated transmitters, which has significant economic benefits. However, GNSS signals have limited bandwidth and face the problem of low resolution in practical applications. Existing solutions all have certain limitations. Although selecting a high-bandwidth signal source can improve the resolution to a certain extent, it cannot fundamentally solve the problem and may over-rely on the transmission signal; extending the observation time will increase the storage and computing burden; in terms of algorithms, the incoherent fusion of multiple satellite imaging results can improve the system resolution, but when the relative geometric configuration between the selected satellite and the receiver is similar, the effectiveness of the fusion processing is significantly reduced.

[0004] In view of this problem, the present invention discloses an optimal matching dual-satellite SAR fusion imaging method based on the Cramer-Rao Lower Bound (CRLB). The method establishes a SAR fusion imaging system model consisting of multiple satellites and a single ground-fixed GNSS receiver, and derives the CRLB affected by the geometric configuration of the dual-base setting based on the mathematical relationship between the ambiguity function of the GNSS signal and the Fisher information. On this basis, the CRLB expression is used to identify the satellite with the optimal resolution direction for the ground target, and a dual-satellite SAR imaging fusion method based on optimal matching is proposed. Specifically, the derived CRLB expression is used to perform a one-dimensional search on the angle to determine the deflection angle corresponding to the minimum CRLB value, thereby determining the optimal resolution direction of all satellites in the scene. Then, based on the principle that the angle between the optimal resolution directions should be as close to 90 degrees as possible, two optimally matched satellites are selected, and their imaging results are fused. Summary of the invention

[0005] The present invention proposes an optimal matching dual-satellite SAR fusion imaging method based on CRLB. First, by establishing the relationship between the GNSS signal ambiguity function and the Fisher information, the CRLB of ground target parameter estimation is derived, thereby further calculating the optimal resolution direction of ground target detection. Secondly, the optimal matching dual-satellite selection principle is determined based on CRLB. Finally, the incoherent fusion method is used to optimize the results of SAR imaging of two optimal matching satellites. The present invention avoids redundant operations while improving the system resolution, and also provides a theoretical basis for the selection of satellites. Specifically, the following steps are included:

[0006] Step 1: The geometric configuration of the GPS SAR imaging system is defined in a three-dimensional Cartesian coordinate system, such as Figure 1 As shown in Figure 1. It includes GPS satellites as transmitters, ground-fixed receivers, and ground targets.

[0007] The GPS signal is represented by the carrier data code and the PRN code. The original signal is converted into a two-dimensional form after orthogonal demodulation, including a two-dimensional direct wave and a two-dimensional reflected wave. d (η,τ),s r (η,τ), respectively:

[0008]

[0009] Where τ is the fast time, σ is the target scattering coefficient, λ is the wavelength, and c is the speed of light. d and D rRepresents the distance of direct wave and reflected wave propagation respectively. By using the GNSS software receiver to demodulate the direct wave signal, the coordinates of the satellite at each slow moment can be obtained through the demodulated navigation message. Then, with the receiver as the origin, the grid point coordinates of the imaging scene and the satellite coordinates are converted into East-North-Up (ENU) coordinates.

[0010] Step 2: Define the ambiguity function as the cross-correlation function of two adjacent target echoes. Define the ground target in the polar coordinate frame through Taylor expansion theory to obtain the decoupled ambiguity function of delay and Doppler. Assume that point O and point P are on the ground, take O as the origin, and define the point target in polar coordinates to more effectively represent the position estimation accuracy of the target in various angular directions. Figure 1 The polar coordinates of point P are expressed as (ρcosθ, ρsinθ, 0), and the ambiguity functions of O and P in the time domain and frequency domain are expressed as:

[0011]

[0012]

[0013] S O represents the echo at point O, S P represents the echo of point P, η∈[0,T]. K is the normalization coefficient. The change of K has the same effect on all angles, so the effect of the change of K is omitted. In the above formula, f and η are severely coupled. For GPSL1 signal, the system parameters meet the following conditions:

[0014]

[0015] The bandwidth B L1 is 2.046MHZ, and the decoupled fuzzy function can be expressed as:

[0016]

[0017] τ d (ρ,θ) and f d (ρ, θ) represent the time delay and Doppler frequency generated by the target P in the system respectively.

[0018] According to the relationship between the fuzzy function and the Fisher information, the Fisher information matrix is ​​obtained Where SNR is the signal-to-noise ratio. We can further obtain J 12 =J 21 =0

[0019] Substitute the coordinates of point P into:

[0020]

[0021] Where f0 is the carrier frequency, λ0 is the carrier wavelength, and v x and v y is the instantaneous velocity of the satellite at η0. The definition of η=[ρ,θ] gives the Jacobian matrix Ψ as According to the properties of Fisher information, the Fisher information matrix of η is obtained

[0022] Combining the relationship between the Fisher information matrix and CRLB, the CRLB expression of the parameter ρ is obtained by matrix inversion, and finally the CRLB expression is derived as follows:

[0023]

[0024] Among them, t1, t2, f1, f2, Г, Ε, Η are variables defined to simplify the final result:

[0025]

[0026] CRLB is related to the signal-to-noise ratio (SNR), bandwidth (B), synthetic aperture time (T), target polar angle (σ), satellite position and velocity. Figure 2 (a) The variation of CRLB at different azimuths is shown in polar coordinates. There are two directions where CRLB has the maximum and minimum values, and these two directions are perpendicular to each other. Figure 2 (b) shows the CRLB one-dimensional direction angle search result, which is consistent with Figure 2 (a) Consistency.

[0027] Step 3: According to the CRLB expression, determine the optimal resolution direction of all satellites by performing a one-dimensional search on the angle. For the i-th satellite, its CRLB expression and optimal resolution angle are defined as CRLB(ρ) i and θ i ,satisfy Then, two satellites with the best resolution direction difference closest to 90 degrees are selected from the collected satellite data and used as the best matching satellite pair for fusion imaging, that is:

[0028]

[0029] Step 4: Use the imaging algorithm to perform imaging operations on the selected matching satellites. The target satellites determined based on the CRLB expression and the satellite selection criteria are imaged using the back projection (BP) algorithm. The specific method is:

[0030] After matching and filtering the echo signal and the reference point signal, the range compression output signal is obtained:

[0031] s(η)=s inv (η)exp{j4πf0R(η) / c}

[0032] In the formula, A represents the amplitude, f0 is the carrier frequency, and R(η) is the distance between the radar and the point target. The imaging scene is then divided into grids, and the echo data of all grid points are obtained by sinc interpolation:

[0033]

[0034] The grid point echo data obtained by interpolation is compensated for phase information:

[0035] s(η)=s inv (η)exp{j4πf0R(η) / c}

[0036] In the formula, s inv (η) is the grid point echo data, and R(η) is the distance between the radar and the grid point. For all grid points, the grid point echo data in each azimuth are phase compensated and superimposed.

[0037] Step 5: Perform incoherent fusion on the imaging results of the two satellites to obtain high-resolution images. First, normalize the two images separately. The normalization formula is:

[0038]

[0039] Among them, I(x,y) is the pixel value of the original data at position (x,y), I min and I max are the minimum and maximum pixel values ​​in the image respectively. Then, the normalized images are superimposed:

[0040] I fusion (x,y)=ω1·I norm1 (x,y)+ω2·I norm2 (x,y)

[0041] Among them, I norm1 (x,y) and I norm2 (x, y) are the pixel values ​​of the two normalized images at (x, y), and ω1 and ω2 are weight coefficients.

[0042] The above method can effectively simplify the processing process, avoid redundant operations, and significantly improve the overall efficiency of synthetic aperture radar (SAR) imaging. This method achieves more efficient SAR imaging and reduces computational complexity and storage requirements by optimizing satellite selection and imaging fusion strategy.

[0043] In the present invention, the BP imaging algorithm effectively reduces the error caused by approximate operations for the nonlinear trajectory of GPS satellites. Its robustness makes it unaffected by the change of radar motion trajectory, making it suitable for various imaging scenarios. Since the PRN code has a strong autocorrelation characteristic, the BP imaging algorithm is used to process the signal, and the pure reference signal is reconstructed by demodulating the direct wave information and the reflected signal is correlated to achieve distance compression, and the final imaging result is obtained by integrating in the azimuth direction.

[0044] After adopting the above-mentioned solution, the present invention can achieve the following beneficial effects:

[0045] 1. Based on CRLB, with the help of satellite orbit parameter information, the theoretical analytical formula of the resolution characteristics of the system composed of any satellite and receiver for ground targets is accurately calculated, providing a key theoretical basis for achieving high-precision imaging.

[0046] 2. Incoherent fusion of the imaging results of the two satellites improves the system resolution. In addition, the fused imaging results have a clearer correspondence with the satellite images of the scene map.

[0047] 3. By using the "star selection principle", the two most suitable satellites can be efficiently screened and determined for SAR imaging. This process avoids unnecessary redundant imaging processing and ensures the most reasonable use of imaging resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of the GPS SAR imaging system.

[0049] Figure 2 The changes of CRLB under different conditions. (a) The changes of CRLB value under different direction angles. (b) The results of one-dimensional angle search.

[0050] Figure 3 Flowchart for optimized matching of dual-satellite fusion imaging. DETAILED DESCRIPTION

[0051] Step 1: Define the SAR imaging system in a three-dimensional Cartesian coordinate system, including GPS satellites as transmitters, ground-fixed receivers, and ground targets. First, use a dual-channel GNSS receiver to simultaneously capture direct and reflected wave signals from the satellite, use a GNSS software receiver to track the GPS satellites, and calculate the orbital parameters of each satellite based on the direct wave signals. Subsequently, the longitude and latitude coordinates of the receiver and the imaging grid points are converted to ENU coordinates.

[0052] Step 2: Use the CRLB expression to evaluate and select the best matching satellite pair. The ambiguity function is the cross-correlation function of the echoes of two adjacent targets. The ground target is defined in the polar coordinate frame through Taylor expansion theory. By analyzing the ambiguity function of the signal, the decoupled ambiguity function of delay and Doppler is obtained:

[0053]

[0054] τ d (ρ,θ) and f d (ρ, θ) represent the time delay and Doppler frequency generated by the target P in the system respectively.

[0055] According to the relationship between the fuzzy function and the Fisher information, the Fisher information matrix is ​​obtained Related elements in J 11 , J 12 , J 21 , J 22 After that, the specific matrix element values ​​obtained by decoupling the Doppler frequency and time delay are used to obtain the expressions of time delay and Doppler frequency through operations such as coordinate substitution. After defining the relevant variables, the Fisher information matrix about the parameter η is obtained based on the Fisher information property.

[0056] Then, according to the relationship between the Fisher information matrix and CRLB, the CRLB expression CRLB(ρ) of the parameter ρ is obtained through matrix inversion.

[0057] Step 3: Use the CRLB expression to determine the best ground resolution direction for each satellite. After acquiring a large number of satellite data, select two satellites whose resolution direction difference is closest to 90 degrees, and use these two satellites to perform SAR imaging and incoherent fusion related operations.

[0058] Step 4: Generate a reference signal for distance compression based on the satellite direct wave signal tracking results. The satellite direct wave signal tracking results can obtain PRN code, carrier phase, Doppler frequency shift, code delay and navigation information, etc. Use this information to generate the corresponding pure signal locally as a reference signal, and perform correlation processing with the reflected signal to achieve distance compression. Combined with satellite data, the BP algorithm is used to image the two satellites.

[0059] Step 5: Finally, the imaging results of the two best matching satellites are incoherently fused to obtain a high-resolution image.

[0060] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A CRLB-based optimal matching dual-satellite SAR image fusion imaging method, comprising the following steps: Step 1: Establish a GNSS SAR imaging system in a three-dimensional Cartesian coordinate system, including GPS satellites as transmitters, ground-fixed receivers, and ground targets. Use a dual-channel GNSS receiver to simultaneously capture direct and reflected wave signals from satellites, use a GNSS software receiver to track GPS satellites, and calculate the orbital parameters of each satellite based on the direct wave signal. Step 2: According to the relationship between the ambiguity function of the GNSS signal and the Fisher information matrix and CRLB, the CRLB expression related to the signal-to-noise ratio, bandwidth, synthetic aperture time, target polar angle, satellite position and speed is derived through matrix inversion: Where Γ, E, and H are variables defined to simplify the final result, respectively: Among them J ** are the elements in the information matrix, t1, t2, f1, f2 are: in, f0 is the carrier frequency, λ0 is the carrier wavelength, v x and v y is the instantaneous velocity of the satellite at η0. According to the orbital parameters of each satellite, the derived CRLB is used to evaluate the optimal resolution direction of each satellite, that is, the direction where CRLB takes the minimum value. Under the same conditions, the CRLB(ρ) values ​​of different angular directions are different. Step 3: After determining the best ground resolution direction of each satellite, select the two satellites whose resolution direction difference is closest to 90 degrees and use them as the best matching satellites for incoherent fusion. The satellite selection principle is: Where i and j are the serial numbers of the two satellites selected, CRLB(ρ) i and θ i are their respective CRLB expressions and optimal resolution angles, satisfying: Step 4: Generate a reference signal for distance compression based on the satellite direct wave signal tracking results. The best matching satellites are processed separately. The PRN code, carrier phase, Doppler frequency shift, code delay and navigation information can be obtained from the satellite direct wave signal tracking results. Use this information to generate the corresponding pure signal locally as a reference signal, and perform correlation processing with the reflected signal to achieve distance compression. Combined with satellite data, imaging is performed using the back projection algorithm (BP). Step 5: Perform incoherent fusion of the imaging results of the two best matching satellites to obtain a high-resolution image. Normalize the two images involved in the fusion to obtain: norm1 (x,y) and I norm2 (x,y). Finally, the normalized images are superimposed to obtain the final image: I fusion (x,y)=ω1·I norm1 (x,y)+ω2·I norm2 (x,y) Where ω1 and ω2 are weight coefficients.

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