Optimal matched dual-satellite SAR fusion imaging method based on CRLB

Abstract

The application discloses a kind of optimal matching double star SAR fusion imaging methods based on CRLB.Global navigation satellite system (GNSS) has the advantages such as all-weather operation and extensive spatial coverage, although the GNSS-R SAR technology for ground synthetic aperture radar (SAR) imaging using reflected signal of GNSS is low in cost and widely used, but because the bandwidth of GNSS signal is limited, its resolution is poor.The application establishes the SAR fusion imaging system model by multiple satellites and a single ground fixed GNSS receiver, explores the interrelation between the ambiguity function of GNSS signal and Fisher information, and deduces the system Cramer-Rao lower bound (CRLB) affected by the geometry configuration of bistatic setting.On this basis, the satellite in the optimal resolution direction for ground target is identified by using CRLB expression, and the imaging results of selected satellite are incoherently fused according to the principle that the included angle between optimal resolution directions is as close to 90 degrees as possible.Through this method, unnecessary redundant imaging processing is avoided, and imaging resources are most reasonably used.The resolution performance of the system is improved in a more efficient way.

Description

TECHNICAL FIELD

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

[0002] Global Navigation Satellite System (GNSS) has all-weather operability and wide spatial coverage, and can realize global positioning, navigation and time synchronization. By using GNSS reflection signals for ground synthetic aperture radar (SAR) imaging, that is, Global Navigation Satellite System-Reflectometry Synthetic Aperture Radar (GNSS-R SAR) technology realized by using GNSS reflection signals. The technology has been widely used in sea surface height measurement, wind speed estimation and ground imaging and other fields due to its advantages of low cost, all-weather operation and wide coverage.

[0003] GNSS-R SAR technology acquires satellite transmitted signals and signals reflected from targets without a dedicated transmitter, and has significant economic benefits. However, GNSS signal bandwidth is limited, and in actual application, low resolution is faced. Existing solutions 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 excessively rely on the transmission signal; prolonging the observation time will increase the storage and computing burden; in terms of algorithms, the incoherent fusion of imaging results of multiple satellites 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] To solve the problem, the application discloses a Cramer-Rao Lower Bound (CRLB) based optimal matching dual-satellite SAR fusion imaging method. SUMMARY

[0005] The application provides a CRLB based optimal matching dual-satellite SAR fusion imaging method, which firstly derives the CRLB of ground target parameter estimation by establishing the relationship between the GNSS signal ambiguity function and the Fisher information, and further calculates the best resolution direction of ground target detection. Secondly, the optimal matching dual-satellite selection principle is determined based on the CRLB. Finally, the non-coherent fusion method is used to optimize the SAR imaging results of the two optimal matching satellites. The application improves the system resolution while avoiding redundant operations, and provides a theoretical basis for satellite selection. Specifically, the application comprises the following steps:

[0006] Firstly, the geometric configuration of the GPS SAR imaging system is defined in a three-dimensional Cartesian coordinate system, as shown in the drawing. Figure 1 The system includes a GPS satellite as a transmitter, a ground fixed receiver and a ground target.

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

[0008]

[0009] Wherein, τ is fast time, sigma is a target scattering coefficient, lambda is a wavelength, and c is a light speed. d And D rrespectively. The direct wave signal is demodulated by using GNSS software receiver, and the coordinates of the satellite at each slow time can be obtained by the demodulated navigation message. Then the grid point coordinates of the imaging scene and the satellite coordinates are converted into East-North-Up (ENU) coordinates with the receiver as the origin.

[0010] Second step: define the ambiguity function as the cross-correlation function of the echoes of two adjacent targets, and define the ground target in polar coordinate frame by Taylor expansion theory to obtain the decoupled ambiguity function of time delay and Doppler. Let point O and point P be on the ground, and define the point target with polar coordinates with O as the origin, which can more effectively represent the estimation accuracy of the target in each angular direction, as shown in Figure 1 . The polar coordinates of point P are represented as (p cos θ, p sin θ, 0), and the ambiguity functions of O and P in time domain and frequency domain are represented as:

[0011]

[0012]

[0013] S O represents the echo of point O, and S P represents the echo of point P, and η ∈ [0, T]. K is a normalization coefficient. The change of K has the same effect on each angular direction, so the effect of the change of K is omitted. In the above formula, f is coupled with η, and for GPS L1 signal, the system parameters satisfy:

[0014]

[0015] where the bandwidth B L1 is 2.046 MHz, and the decoupled ambiguity function can be represented as:

[0016]

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

[0018] According to the relationship between the ambiguity function and the Fisher information, the Fisher information matrix is obtained, where SNR is the signal-to-noise ratio. Further, it is obtained that J 12 = J 21 = 0

[0019] Substitute the coordinates of point P into:

[0020]

[0021] where f0is the carrier frequency, λ0is the carrier wavelength, v x and v y is the instantaneous velocity of the satellite at η0. The definition of η = [ρ, θ] is established, and the Jacobian matrix Ψ is expressed as According to the properties of Fisher information, the Fisher information matrix of η is obtained as According to the properties of Fisher information, the Fisher information matrix of η is obtained as

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

[0023]

[0024] where t1, t2, f1, f2, Г, Ε, Η are variables defined for simplifying the final result:

[0025]

[0026] CRLB is related to signal-to-noise ratio (SNR), bandwidth (B), synthetic aperture time (T), target polar angle (σ), satellite position and velocity. Figure 2 (a) The change of CRLB under different azimuth angles is shown in polar coordinate form. The directions that make CRLB have maximum and minimum values respectively have two, and the two directions are perpendicular. Figure 2 (b) The one-dimensional direction angle search result of CRLB is given, which is consistent with Figure 2 (a).

[0027] Third step: According to the CRLB expression, the optimal resolution direction of all satellites is determined by one-dimensional search of angle. For the i-th satellite, its CRLB expression and optimal resolution angle are defined as CRLB(ρ) i and θ i , respectively, which satisfy Then select two satellites from the collected satellite data whose optimal resolution direction difference is closest to 90 degrees, and use them as the optimal matching satellite pair for fusion imaging, that is:

[0028]

[0029] Fourth step: Use imaging algorithm to image the selected matching satellites. According to the CRLB expression and the target satellite determined by the selected satellite, the back projection (BP) algorithm is used for imaging processing. The specific way is:

[0030] After matched filtering the echo signal with the reference point signal, the range-compressed output signal is obtained:

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

[0032] where A represents the amplitude, f0 is the carrier frequency, and R(η) is the distance between the radar and the point target. Subsequently, the imaging scene is divided into a grid, and the echo data of all grid points is obtained through sinc interpolation:

[0033]

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

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

[0036] where 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 direction is phase-compensated and superimposed.

[0037] Fifth step: Non-coherent fusion of the imaging results of the two satellites to obtain high-resolution images. First, normalize the two images respectively, and the normalization formula is:

[0038]

[0039] where 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, superimpose the normalized images:

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

[0041] where 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] Through the above method, the processing process can be effectively simplified, redundant operations can be avoided, and the overall efficiency of Synthetic Aperture Radar (SAR) imaging can be significantly improved. This method optimizes satellite selection and imaging fusion strategy, realizes more efficient SAR imaging, and reduces computational complexity and storage requirements.

[0043] In the application, the BP imaging algorithm effectively reduces the error caused by approximation operation on the nonlinear trajectory of the GPS satellite. Its robustness makes it not affected by the change of the radar trajectory, making it suitable for various imaging scenes. Since the PRN code has strong autocorrelation characteristics, the signal is processed by using the BP imaging algorithm, the direct wave demodulation information is reconstructed to realize distance compression, and the final imaging result is obtained by integrating in the azimuth direction.

[0044] After the above-mentioned scheme is adopted, the following beneficial effects can be achieved:

[0045] 1. Based on CRLB, the theoretical analytic expression of the resolution characteristics of the system composed of any satellite and the receiver to the ground target is accurately calculated by means of satellite orbit parameter information, which provides a key theoretical basis for realizing high-precision imaging.

[0046] 2. The imaging results of two satellites are incoherently fused to improve the system resolution. Moreover, the fused imaging result has a clearer corresponding relationship with the satellite image of the scene map.

[0047] 3. By using the “star selection principle”, the most matched two satellites for SAR imaging can be efficiently screened and determined. This process avoids unnecessary redundant imaging processing and ensures that the imaging resources are used most reasonably. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 It is a schematic diagram of a GPS SAR imaging system.

[0049] Figure 2 It is the change of CRLB under different conditions. (a) Change of CRLB value under different direction angles. (b) Result of one-dimensional angle search.

[0050] Figure 3 It is an optimization matching flowchart of double-satellite fusion imaging. DETAILED DESCRIPTION

[0051] First step: In the three-dimensional Cartesian coordinate system, define the SAR imaging system, including the GPS satellite as the transmitter, the ground fixed receiver and the ground target. First, use a double-channel GNSS receiver to simultaneously capture direct wave and reflected wave signals from the satellite, use a GNSS software receiver to track the GPS satellite, and calculate the orbit parameters of each satellite according to the direct wave signal. Then, convert the latitude and longitude coordinates of the receiver and the imaging grid points into ENU coordinates.

[0052] Second step: using CRLB expression to evaluate and select the optimal matching satellite pair. Ambiguity function is the cross-correlation function of adjacent two target echoes, the ground target is defined in polar coordinate frame by Taylor expansion theory, by analyzing the ambiguity function of the signal, the decoupling ambiguity function of time 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 target P in the system respectively.

[0055] According to the relationship between ambiguity function and Fisher information, the related elements J 11 , J 12 , J 21 , J 22 in Fisher information matrix are obtained. Then, the specific matrix element value decoupled from Doppler frequency and time delay is obtained through coordinate substitution and other operations to get the time delay and Doppler frequency expression. After defining the related variables, the Fisher information matrix about parameter η is obtained based on the Fisher information properties.

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

[0057] Third step: using CRLB expression to determine the best ground resolution direction of each satellite. After obtaining a large amount of satellite data, select two satellites whose resolution direction difference is closest to 90 degrees, and use these two satellites to carry out SAR imaging and non-coherent fusion related operations.

[0058] Fourth step: generate reference signal for range compression according to satellite direct wave signal tracking results. Satellite direct wave signal tracking results can obtain PRN code, carrier phase, Doppler shift, code delay and navigation information, etc. Using these information to generate corresponding pure signal as reference signal at local, and carry out correlation processing with reflected signal to realize range compression, combined with satellite data to use BP algorithm for imaging of two satellites.

[0059] Fifth step: finally, non-coherent fusion is carried out on the imaging results of the two optimal matching satellites to obtain high resolution image.

[0060] The above merely provides the specific implementation of the present application, any feature disclosed in the specification can be replaced by other equivalent or similar purpose alternative features unless specifically described, and all features disclosed or all steps in the method or process can be combined in any manner except for mutually exclusive features and / or steps.

Claims

1. A CRLB-based optimal matching dual-satellite SAR image fusion imaging method, comprising the following steps: Step 1: Build a GNSS SAR imaging system in a three-dimensional Cartesian coordinate system, including GPS satellites as transmitters, ground-based fixed receivers, and ground targets. Use a dual-channel GNSS receiver to simultaneously capture direct and reflected wave signals from the satellites. A GNSS software receiver tracks the GPS satellites and calculates the orbital parameters of each satellite based on the direct wave signals. Step 2: Based on 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 velocity 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: 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. 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 for 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 selection principle is as follows: 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 based on the satellite direct wave signal tracking results for range compression. The optimal matching satellites are processed separately. The satellite direct wave signal tracking results provide information such as the PRN code, carrier phase, Doppler shift, code delay, and navigation information. This information is used to generate a corresponding pure signal locally as a reference signal. This signal is correlated with the reflected signal to achieve range compression, and imaging is performed using the back-projection (BP) algorithm in combination with the satellite data. Step 5: Perform incoherent fusion on the imaging results of the two best matching satellites to obtain a high-resolution image, and normalize the two images involved in the fusion to obtain: I 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.

Images