A method for modeling atmospheric effects on imaging of an aerial target by a vehicular sar system

Abstract

The application discloses a modeling method for atmospheric influence on aerial target imaging of a vehicle-mounted SAR system. The method respectively constructs wide-area space-time variable models for different scales of atmospheric disturbance influence, adopts a high-precision numerical weather model to combine a space-time variable wide-area ray tracing method to model a conventional troposphere phase error, and adopts a turbulence power spectrum model to combine a method of a multi-phase screen theory to model a troposphere turbulence. The application discloses an influence mechanism of atmospheric disturbance on signal propagation of the vehicle-mounted SAR system, and provides theoretical support for realizing high-precision atmospheric disturbance compensation of the vehicle-mounted SAR system.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture radar technology, and particularly relates to a method for modeling the atmospheric effects of a vehicle-mounted SAR system on imaging aerial targets. Background Technology

[0002] Synthetic aperture radar (SAR), as an active remote sensing sensor, utilizes the movement of the radar carrier to create a large-aperture antenna, thereby acquiring high-resolution radar image data. It is unaffected by adverse weather conditions and possesses all-weather, 24 / 7 observation capabilities. It has wide applications in military and civilian fields. Vehicle-mounted SAR uses a vehicle as a platform, creating a synthetic aperture through vehicle movement to acquire high-resolution radar images of aerial targets. Vehicle-mounted SAR systems offer significant advantages in miniaturization, flexibility, and rapid response.

[0003] During SAR imaging, electromagnetic waves propagate through the atmosphere. The non-uniform atmospheric medium causes the signal propagation path to bend, resulting in a phase delay between the propagation path and the theoretical path, which may lead to defocusing in the SAR imaging results. Because vehicle-mounted SAR systems detect aerial targets at long distances, they require long-term image accumulation to obtain high-resolution images, making them severely affected by wide-area spatiotemporal atmospheric disturbances, leading to a significant deterioration in SAR imaging quality. The spatiotemporal variability of the troposphere is the most severe and has the greatest impact on imaging.

[0004] Because vehicle-mounted SAR systems have long synthetic aperture times and irregular trajectories, and the atmosphere exhibits wide-area, spatiotemporally variable, and multi-scale characteristics, traditional modeling methods for the impact of atmospheric disturbances on vehicle-mounted SAR imaging are based on the spatiotemporally frozen model assumption, which assumes that the troposphere remains constant within the imaging synthetic aperture time and imaging scene, and that meteorological parameters do not change with time and space. Therefore, it is necessary to consider methods applicable to modeling the impact of wide-area spatiotemporally variable atmospheric effects on vehicle-mounted SAR imaging. Summary of the Invention

[0005] To address the issues of long accumulation times and irregular trajectories of sounding targets in vehicle-mounted SAR systems, and the wide-domain spatiotemporal variability of atmospheric effects leading to the failure of traditional atmospheric influence models, this invention provides a method for modeling atmospheric influences on aerial target imaging using vehicle-mounted SAR systems. This method constructs wide-domain spatiotemporal variable models for atmospheric disturbances at different scales, revealing the mechanism by which atmospheric disturbances affect SAR signal propagation, and providing theoretical support for achieving high-precision atmospheric disturbance compensation in vehicle-mounted SAR systems.

[0006] The technical solution for implementing the present invention is as follows:

[0007] Step 1: Based on the multi-scale characteristics of atmospheric effects, the influence mechanism of conventional tropospheric turbulence at the large scale and tropospheric turbulence at the small scale are analyzed respectively.

[0008] Step 2: For conventional tropospheric modeling, phase error is the primary consideration. A high-precision numerical meteorological model combined with a spatiotemporally variable wide-area ray tracing method is used for modeling. The radio wave propagation characteristics of the troposphere are typically represented by the refractive index N.

[0009]

[0010] Where k1, k2, and k3 are constants, and T, P, and e represent the temperature, pressure, and water vapor pressure of the atmosphere at different altitudes, respectively.

[0011] First, the refractive index of each layer over a wide area is calculated based on a numerical meteorological model. Considering the time-varying nature of the atmosphere, meteorological parameters are updated every half hour. Then, the propagation path of the signal is estimated using the spatiotemporally variable wide-area ray tracing method, and the path is integrated with the refractive index to obtain the atmospheric delay error Δr(P,t). a Construct a conventional tropospheric spatiotemporal phase error model Δφ trop :

[0012]

[0013] Where, q i Δr represents the time derivatives of Δr, and P represents different positions.

[0014] Step 3: Tropospheric turbulence is modeled using a turbulence power spectrum model combined with multiphase screen theory. The amplitude and phase fluctuations introduced by tropospheric turbulence are modeled using a modified turbulence power spectrum. A filter is constructed based on the turbulence power spectrum function. After filtering the complex Gaussian random number sequence, an inverse discrete Fourier transform (IDFT) is performed to obtain the random phase φ introduced by the troposphere. turb The tropospheric transfer function D is calculated based on the multiphase screen theory. TF The amplitude fluctuation of the signal is obtained. and phase fluctuations Right now:

[0015]

[0016] To address the low time correlation of turbulence, the turbulence error is re-estimated every five minutes.

[0017] Step 4: Combining the modeling results of conventional tropospheric and tropospheric turbulence influences, the vehicle-mounted SAR echo signal model under atmospheric disturbances is obtained.

[0018]

[0019] Where r(t) a ) for ta The instantaneous slant range from the vehicle-mounted SAR to the target at any given moment, A r (·) and A a (·) represent the distance and orientation envelope functions, respectively, and k r λ is the signal modulation frequency, and λ is the signal wavelength. The conventional tropospheric phase error calculated in step 2, and These are the amplitude fluctuations and phase fluctuations of the tropospheric turbulence estimated in step 3, respectively. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the processing flow of the present invention.

[0021] Figure 2 This is a flowchart illustrating the specific processing steps of the present invention.

[0022] Figure 3 This is a schematic diagram of the propagation of vehicle-mounted SAR signals under atmospheric disturbance.

[0023] Figure 4 The simulation results show the conventional tropospheric time delay error within the synthetic aperture time.

[0024] Figure 5 Simulation results of tropospheric turbulence phase error within the synthetic aperture time.

[0025] Figure 6 Simulation results of total tropospheric phase error. Detailed Implementation

[0026] The overall processing flow diagram of the present invention is shown below. Figure 1 As shown. Due to the long time and irregular trajectory of the synthetic aperture of vehicle-mounted SAR, atmospheric effects have wide-area spatiotemporal variability. The atmospheric influence on different radar locations varies, so it is necessary to construct a multi-scale spatiotemporal variability atmospheric model.

[0027] The invention will now be described in detail with reference to the accompanying drawings, and the specific processing steps are shown in the flowchart below. Figure 2 As shown.

[0028] Step 1: Based on the multi-scale characteristics of atmospheric effects, the influence of the troposphere on signal propagation can be divided into two parts: the large-scale conventional troposphere and the small-scale tropospheric turbulence. The influence mechanisms of each part will be analyzed separately. Furthermore, atmospheric disturbances exhibit spatiotemporal variability, meaning that atmospheric disturbances change with time and space, and the atmospheric influence on different synthetic apertures is inconsistent over time. A schematic diagram of vehicle-mounted SAR signal propagation under atmospheric disturbances is shown below. Figure 3 As shown.

[0029] The conventional troposphere mainly refers to the slowly varying portion of the troposphere. Due to the non-uniformity of the refractive index in the troposphere, the signal propagation speed changes accordingly, and the path becomes curved, resulting in time delay errors and curvature errors during signal propagation. The main consideration is the phase error. Tropospheric turbulence is caused by rapid fluctuations in the refractive index under certain sudden and extreme weather conditions, leading to random fluctuations in signal amplitude and phase.

[0030] Step 2: Phase error modeling of the conventional troposphere is performed using a numerical meteorological model combined with the spatiotemporally variable wide-area ray tracing method.

[0031] 1) Numerical meteorological model calculates the refractive index and altitude of each atmospheric layer.

[0032] The spatiotemporal distribution characteristics of the tropospheric refractive index N are related to the spatiotemporal distributions of three factors: temperature T, vapor pressure e, and pressure P. The refractive index is expressed as...

[0033]

[0034] Where, N d This is the refractive index term, N w The refractive index is the wet term. Dry air pressure P d =Pe(hPa), T is temperature (K), Thayer gives the reference values ​​for k1, k2 and k3 as follows: k1 = 77.604 ± 0.014, k2 = 64.79 ± 0.08, k3 = 377600 ± 400.

[0035] The water vapor parameter provided by the numerical meteorological model is specific humidity. First, the specific humidity q is converted into the water vapor pressure e required for the refractive index:

[0036]

[0037] Since the elevation system of numerical meteorological models is geopotential height, while the elevation system of radar is geodetic height, it is necessary to convert geopotential height to geodetic height. First, convert the geopotential data to geopotential height:

[0038] H g =Φ / g0 (7)

[0039] In the formula, is the potential height (m), and Φ is the potential (m). 2 / s 2 g0 = 9.80665 m / s 2 is the gravitational acceleration constant.

[0040] Then the potential height is converted to positive height H. N

[0041]

[0042] In the formula, g(λ,β,H) N The value is the gravitational acceleration that varies with longitude λ, latitude β, and orthometric height. Based on the geoid difference provided by the EGM96 model, the orthometric height is converted to geodetic height.

[0043] H = H N +N H (9)

[0044] In the formula, N H H represents the geoid difference, and H represents the geodetic height. After unifying the elevation system, the atmospheric refractive index of each layer is calculated using meteorological parameters from each layer.

[0045] 2) Calculation of phase error using the spatiotemporally variable wide-area ray tracing method

[0046] The propagation path of electromagnetic wave signals in the atmosphere is simulated by the spatiotemporally variable wide-area ray tracing method. The atmospheric time delay error Δr is obtained by path integration of the refractive index and then converted into phase error.

[0047] Δr=10 -6 ∫N·dH (10)

[0048] The specific steps are as follows:

[0049] i. Calculate the refractive index based on the numerical meteorological model and construct a three-dimensional atmospheric refractive index network. Since the signal travels across a wide area in the atmosphere, it is necessary to consider the spatial variability of the atmosphere. The required spatial range of the numerical meteorological data should include the regions that the signal traverses when passing through the atmosphere.

[0050] ii. Considering the time-varying nature of the atmosphere, and based on the fact that the large-scale background troposphere still maintains temporal correlation within a day, the parameters of the numerical meteorological model are updated every half hour to improve the accuracy of the modeling results.

[0051] iii. From the radar position, along the direction of the ray projection onto the ground, select a distance d that should encompass the area projected onto the ground along the signal's path as it propagates through the atmosphere. When the signal incident angle is θ, and the top layer height of the numerical meteorological model data is H... TOP It needs to satisfy d > tanθ·H TOP A range of 1500km can be used. Samples are taken on d at 1km intervals to obtain the latitude and longitude of each point.

[0052] iv. Based on the coordinates of each point on d and the three-dimensional atmospheric refractive index network provided by the numerical meteorological model, resampling is performed to obtain a two-dimensional refractive index grid on the plane where the signal propagation path lies. The grid is cell-based in the horizontal direction, and the height of each layer in the vertical direction is divided by the actual interval of the horizontal grid.

[0053] v. Calculate the ray propagation path using the spatiotemporally variable wide-area ray tracing method to obtain the delay in the line-of-sight direction.

[0054] ◆Calculation starts from the bottom layer near the ground.

[0055] ◆ Determine whether the cell has passed through its top boundary based on the angle of incidence and the coordinates of the point of entry into the current layer. The cell height is the height difference Δh between two adjacent layers provided by the numerical meteorological model. The piercing point location is (x... in ,z in Based on the angle of incidence, the coordinates (x, y) of the point that exits this layer are obtained. out ,z out ),in

[0056] x out =x in +tanθ·Δh (11)

[0057] If x out Greater than This means it did not cross the top of the cell, so calculate the coordinates (x, y) of leaving this cell. n ,z n ), and calculate the next cell; if not greater than If the value is passed through, the calculation for the next layer will proceed.

[0058]

[0059] ◆Calculate the slope path s within the corresponding cell based on the coordinates of the puncture point. i Integrating, we obtain the slant range delay r. i And add it to the delay r of this layer.

[0060] r=Σ10 -6 ·Ns i (13)

[0061] ◆ Iterate until the ray reaches the top layer.

[0062] ◆Due to the limited altitude of data provided by numerical meteorological models, the top layer is far below 60 km. However, there is almost no water vapor influence above the top layer. The atmospheric delay from the top layer to 60 km is calculated using the Saastamoinen dry delay model, ultimately yielding the total delay Δr. The specific calculation method is as follows:

[0063]

[0064] In the formula, This is a correction for the gravitational acceleration caused by the Earth's rotation. Where h is latitude and h is altitude (km), it is expressed as:

[0065]

[0066] vi. Since the radar position is changing, take a coordinate at intervals according to the synthetic aperture path, and repeat steps iii to v above to obtain the atmospheric delay Δr corresponding to the entire aperture path.

[0067] vii. Considering the two-way propagation effect of SAR signals, a spatiotemporal variable phase error model is constructed as follows:

[0068]

[0069] In the formula, q i Δr represents the time derivatives of Δr, and P represents different positions.

[0070] Step 3: The influence of tropospheric turbulence is modeled and analyzed using the turbulent power spectrum model combined with the multiphase screen theory.

[0071] The refractive index variation caused by turbulence follows a power-law spectral distribution, and its power spectrum adopts the modified turbulent power spectrum:

[0072] Φ n (κ)=0.033C n 2 (κ 2 +κ0 2 ) -11 / 6 ·exp(-κ 2 / κ l 2 )·[1+1.802(κ / κ l -0.254(κ / κ) l ) 7 / 6 (17)

[0073] Where L0 is the external scale of turbulence, ranging from meters to hundreds of meters in size; l0 is the internal scale of turbulence, ranging from millimeters in size. Let κ be the space wavenumber. x =2π / x,κ y =2π / y,κ z =2π / z, κ l =3.3 / l0,κ0=2π / L0. is the tropospheric refractive index structure constant, used to characterize turbulence intensity.

[0074] Based on phase screen theory, tropospheric turbulence is modeled as a phase screen and the free space outside the phase screen. Using phase screen theory, turbulence is simulated as multiple thin phase screens, with the energy of each layer integrated onto different thin phase screens.

[0075] The refractive index power spectrum and the resulting phase power spectrum Φ s (κ) relations are represented as:

[0076] Φ s(κ)=2πk 2 ∫ Δx Φ n (κ)dh (18)

[0077] Where k = 2π / λ, and Δx is the turbulent thickness. In the phase screen simulation, Φ is used. s (κ) Construct a filter to filter the complex Gaussian random number sequence, and then obtain the random phase fluctuations through the inverse discrete Fourier transform (IDFT):

[0078]

[0079] Where, r m A Hermitian complex Gaussian random variable with zero mean and unit variance.

[0080] The tropospheric transfer function D is calculated based on the phase screen theory. TF The amplitude fluctuation of the signal is obtained. and phase fluctuations Right now:

[0081]

[0082] Where u is the horizontal spatial position. This is the transfer function of the i-th phase screen. If the transmission passes through multiple phase screens, the transfer function for the entire tropospheric turbulence is:

[0083]

[0084] Considering the time-varying nature of tropospheric turbulence, the time correlation of small-scale turbulence is only on the order of minutes. Therefore, the amplitude and phase errors of turbulence are recalculated every five minutes.

[0085] Step 4: Considering the large-scale conventional tropospheric influence model (16) and combining it with the small-scale tropospheric turbulence influence model (20), the vehicle-mounted SAR echo signal model under atmospheric disturbance is obtained.

[0086]

[0087] Where r(t) a ) for t a The instantaneous slant range from the vehicle-mounted SAR to the target at any given moment, A r (·) and A a (·) represent the distance and orientation envelope functions, respectively, and k r λ is the signal modulation frequency, and λ is the signal wavelength. The conventional tropospheric phase error calculated in step 2, and These are the amplitude fluctuations and phase fluctuations of the tropospheric turbulence estimated in step 3, respectively.

[0088] This completes all the steps.

[0089] The following provides an implementation example with specific parameters.

[0090] An irregular trajectory was randomly selected as the synthetic aperture path for microwave vehicle-mounted SAR for simulation analysis. The path was approximately 1045 km long, and the synthetic aperture time was approximately 10 hours. A typical temperate zone scenario from 8:00 to 18:00 in February was selected, and the tropospheric influence was modeled and simulated using measured tropospheric data. The numerical meteorological model used high-precision ECMWF (European Centre for Medium-Range Weather Forecasts) ERA-5 reanalysis data. This product can provide hourly meteorological data with a spatial resolution of 0.25°×0.25° and 37 vertical layers. The air pressure, temperature, specific humidity, and surface gravitational potential data of the 37 layers of the ERA5 product were selected. The observed spatial target was a small near-Earth celestial body.

[0091] First, following step 1, the tropospheric atmospheric disturbance is modeled in two parts.

[0092] Step 2 involves constructing a conventional tropospheric error model using a high-precision numerical meteorological model combined with a spatiotemporally variable wide-area ray tracing method. The variation of the time delay error within the synthetic aperture time is then obtained as follows: Figure 4 .

[0093] Step 3 involves using a turbulent power spectrum model combined with multiphase screen theory to model the effects of tropospheric turbulence, resulting in the variation of turbulent phase error as shown below. Figure 5 .

[0094] Perform step 4, combining the modeling results of the influence of conventional troposphere and tropospheric turbulence, to obtain the total tropospheric phase error, such as... Figure 6 .

[0095] Therefore, this invention can construct a spatiotemporally variable error model for wide-area spatiotemporally variable atmospheric disturbances, taking into account the characteristics of long accumulation time and irregular trajectory of sounding targets in vehicle-mounted SAR systems. The above examples demonstrate the effectiveness of this method.

[0096] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for modeling the atmospheric effects of a vehicle-mounted SAR system on imaging aerial targets, characterized in that... The steps of this method include: The first step is to divide the atmospheric impact into two parts: conventional troposphere and tropospheric turbulence, and to analyze the impact mechanism of each part separately. The second step is to model the phase error of the conventional troposphere using a numerical meteorological model combined with the spatiotemporally variable wide-area ray tracing method. The third step is to model and analyze the influence of tropospheric turbulence using the turbulence power spectrum model combined with the multiphase screen theory. Fourthly, combining the conventional tropospheric error model calculated in the second step and the tropospheric turbulence influence model estimated in the third step, the vehicle-mounted SAR echo signal model under atmospheric disturbance is obtained as follows: ； in, for The instantaneous slant range from the vehicle-mounted SAR to the target at any given moment. and These are the distance and orientation envelope functions, respectively. It is frequency modulation of the signal. It is the signal wavelength; This is a typical tropospheric phase error. and These represent the amplitude fluctuations and phase fluctuations of tropospheric turbulence, respectively.

2. The atmospheric impact modeling method for imaging aerial targets by a vehicle-mounted SAR system according to claim 1, characterized in that: In the first step, considering the multi-scale characteristics of atmospheric effects, the influence of atmospheric disturbances is divided into large-scale conventional troposphere and small-scale tropospheric turbulence.

3. The atmospheric impact modeling method for imaging aerial targets by a vehicle-mounted SAR system according to claim 1, characterized in that: In the second step, meteorological parameters from the high-precision ECMWF ERA5 model are used to calculate the refractive index and corresponding altitude of each atmospheric layer; the refractive index is expressed as... ； in, This is the refractive index term. For refractive index (wet term); dry air pressure T is the temperature (K), given by Thayer. , and Reference value: , , .

4. The atmospheric impact modeling method for imaging aerial targets by a vehicle-mounted SAR system according to claim 3, characterized in that: The geopotential height of the ECMWF ERA5 model is converted to the geodetic height used by the radar's elevation system; first, the ERA5 geopotential data is converted to geopotential height. Then convert the potential height to positive height. Then, based on the EGM96 geoid model, the orthographic height was converted into geodetic height: ； in, The difference in geoid level, For the earth's height; To follow longitude ,latitude And the gravitational acceleration that changes with positive altitude, is the gravitational acceleration constant.

5. The atmospheric impact modeling method for imaging aerial targets by a vehicle-mounted SAR system according to claim 1, characterized in that: In the second step, the delay calculation based on the ERA5 model is performed in two parts. For the ERA5 data below the top layer, the refractive index of two adjacent isobaric surfaces is averaged, and the tropospheric delay is calculated using the spatiotemporally variable wide-area ray tracing method. Then, the Saastamoinen dry delay model is introduced to calculate the tropospheric delay above the top layer, finally obtaining the total tropospheric delay. The specific calculation method is as follows: ； ； in, This is a correction for the gravitational acceleration caused by the Earth's rotation. The latitude of the radar. Altitude (km).

6. The atmospheric impact modeling method for imaging aerial targets by a vehicle-mounted SAR system according to claim 5, characterized in that: Considering the two-way propagation effect of SAR signals, a spatiotemporal phase error model is constructed. 。 7. The atmospheric impact modeling method for imaging aerial targets by a vehicle-mounted SAR system according to claim 1, characterized in that: In the third step, a modified turbulent power spectrum is used to describe the change in refractive index caused by turbulence; ； in, The external scale of turbulence ranges from meters to hundreds of meters in size. It is a turbulent internal scale, with a size on the order of millimeters; For space wavenumber, , , ; is the tropospheric refractive index structure constant, used to characterize turbulence intensity.

8. A method for modeling the atmospheric effects of a vehicle-mounted SAR system on imaging aerial targets according to claim 7, characterized in that: Phase power spectrum based on turbulence A filter is constructed, and after filtering the complex Gaussian random number sequence, an inverse discrete Fourier transform (IDFT) is performed to obtain the random phase introduced by the troposphere. ; ； in, A Hermitian complex Gaussian random variable with zero mean and unit variance.

9. A method for modeling atmospheric effects on aerial target imaging using a vehicle-mounted SAR system according to claim 8, characterized in that: Calculation of tropospheric transfer function based on multiphase screen theory The amplitude fluctuation of the signal is obtained. and phase fluctuations ,Right now: 。

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