CN103675775A - Method for analyzing influences of background ionosphere on GEO SAR imaging - Google Patents

Abstract

The invention discloses a method for analyzing influences of a background ionosphere on GEO SAR imaging. The method includes the steps that a GEO SAR echo signal model influenced by a time-varying ionosphere is established, image offset and defocusing phase which are used for analyzing influences on imaging are derived on the basis of the model, and then judgment of the influences on imaging is performed; during analysis, GEO SAR echo signals influenced by the time-varying ionosphere and the measuring data of the ionosphere total electron content TEC on the propagation paths of the GEO SAR signals are obtained, polynomial fitting is performed on the TEC measuring data three times, a constant term and coefficients of first three items are obtained, echo signal parameters and TEC coefficients are substituted into a derived expression of the image offset and the defocusing phase, and compared with a threshold value, the influences of the background ionosphere on GEO SAR imaging are obtained. According to the method, modeling is performed specifically and is accurate, and imaging analysis is performed on the basis of the accurate model so that the analysis accuracy can be improved.

Description

The analytical approach of background ionosphere to GEO SAR Imaging

Technical field

The present invention relates to a kind of geostationary orbit synthetic-aperture radar ionospheric effect analytical approach, belong to Synthetic Aperture Radar Technique field.

Background technology

Synthetic aperture radar (SAR) is a kind of high-resolution microwave remotely sensed image radar of round-the-clock, round-the-clock, can be arranged on the flying platforms such as aircraft, satellite, guided missile.Since the invention fifties in last century, in a lot of fields, application more and more widely, fields such as disaster control, vegetational analysis, microwave remote sensing have been obtained.

Geostationary orbit synthetic-aperture radar (GEO SAR) is the SAR satellite operating on the synchronous elliptical orbit of the 36000km height earth.Than low rail SAR(LEO SAR, orbit altitude is lower than 1000Km), GEO SAR has that areas imaging is large, revisit time is short, anti-strike and the feature such as anti-lethality is strong, has become at present study hotspot both domestic and external.

Ionospheric effect is an importance of GEO SAR research.Low rail SAR compares with tradition, because GEO SAR reaches kilosecond magnitude (low rail SAR is only about a second) aperture time, therefore aperture time internal ionization layer variation will become and can not ignore, Freezing Model hypothesis in the low rail SAR of tradition will lose efficacy, and must consider the impact on GEO SAR imaging under the situation of change of ionosphere.This does not all have and relates in existing GEO SAR research.

So, a kind of background ionosphere is proposed to GEO SAR Influence Analysis on Imaging method, to GEO SAR ionospheric effect research and follow-up GEO SAR imaging processing and differential interferometry, process significant.

Summary of the invention

The present invention proposes the analytical approach of a kind of background ionosphere to GEO SAR Imaging, while having set up, become the GEO SAR echo signal model under ionosphere effect, based on this model inference, go out for analyzing the image shift amount of Imaging and defocusing the quantitative computing formula of phase place, and then carry out the judgement of Imaging.This analytical approach is carried out modeling targetedly, and modeling is accurate, carries out imaging analysis just can improve precision of analysis based on accurate model.

The present invention is achieved through the following technical solutions.

Background ionosphere, to a GEO SAR Influence Analysis on Imaging method, comprises the steps:

While first, setting up, become GEO SAR echo modeling under ionosphere effect:

When radar signal is passed ionosphere, under the effect of ionosphere, will make signal produce an additive phase, consider GEO SAR round trip propagation effect, this phase error is

$\mathrm{\Δ\φ}=-\frac{4\mathrm{\π}(\mathrm{\Δt}\·c)}{\mathrm{\λ}}\≈-\frac{2\mathrm{\π}\·80.6\·\mathrm{TEC}}{\mathrm{cf}}---\left(1\right)$

Wherein, Δ t is the radar signal time delay that background ionosphere causes, the wavelength that λ is radar signal, and TEC is the total electron content on travel path, and c is the light velocity, and f is signal frequency.

In low rail SAR, in the synthetic aperture time, TEC is definite value.Yet the singularity due to GEO SAR ionosphere problem, need to re-start modeling to TEC, consider the variation of TEC in the long synthetic aperture time, TEC can be expressed as slow time t _afunction TEC (t _a):

TEC(t _a)＝TEC ₀+ΔTEC(t _a) (2)

Wherein, TEC ₀for TEC (t _a) constant component, it is temporal evolution not, this part can affect distance to imaging, will cause SAR image along distance to skew and distance to defocusing.Δ TEC (t _a) be TEC (t _a) changing unit, it will affect orientation to imaging, can cause SAR image along orientation to skew and orientation to defocusing.Δ TEC (t _a) can be expressed as the form of slow time all-order derivative

ΔTEC(t _a)＝k ₁·t _a+k ₂·t _a ²+k ₃·t _a ³+... (3)

Wherein, k _ifor the derivative of TEC to each rank i of slow time.

TEC (t so _a)=TEC ₀+ k ₁t _a+ k ₂t _a ²+ k ₃t _a ³+ ..., by TEC polyfit, can obtain constant term TEC ₀, 1 item coefficient k ₁, 2 item coefficient k ₂, 3 item coefficient k ₃value Deng each item coefficient.

As shown in Figure 1, satellite platform flies with speed v, the angle of squint that θ is point target, R ₀for the shortest oblique distance, R _pfor the center oblique distance of aperture center to target, t _afor the slow time, P is point target position vector, R _real(t _a; P) be t _aradar is to the instantaneous oblique distance of point target P constantly.

Point target echoed signal can be expressed as

$s(t_a,t)=A_r\left(t\right)A_a\left(t_a\right)\exp \left[{\mathrm{j\πk}}_r{(t-\frac{{2R}_{\mathrm{real}}(t_a;P)}{c})}^2\right]\exp [-j\mathrm{4\π}\frac{R_{\mathrm{real}}(t_a;P)}{\mathrm{\λ}}]---\left(4\right)$

A _r() and A _a() be respectively distance to orientation to envelope function, k _rfor the frequency modulation rate of chirp signal, λ is signal wavelength.Consider the impact of ionosphere on GEO SAR echoed signal, be subject to the echoed signal under ionosphere effect to be

$s(t_a,t)=A_r\left(t\right)A_a\left(t_a\right)\exp \left[{\mathrm{j\πk}}_r{(t-\frac{{2R}_{\mathrm{real}}(t_a;P)}{c})}^2\right]\exp [-j\mathrm{4\π}\frac{R_{\mathrm{real}}(t_a;P)}{\mathrm{\λ}}]\exp \left(\mathrm{\Δ\φ}\right)---\left(5\right)$

In conjunction with (1) (2) formula, obtain

$\begin{array}{c}s(t_a,t)=A_r\left(t\right)\·A_a\left(t_a\right)\·\exp \left[{\mathrm{j\πk}}_r{(t-\frac{{2R}_{\mathrm{real}}(t_a;P)}{c})}^2\right]\·\exp [-j4\mathrm{\π}\frac{R_{\mathrm{real}}(t_a;P)}{\mathrm{\λ}}]\\ \·\exp [-\frac{2\mathrm{\π}\·80.6\·({\mathrm{TEC}}_0+\mathrm{\ΔTEC}\left(t_a\right))}{\mathrm{cf}}]\end{array}---\left(6\right)$

(6) formula is done to distance after Fourier transform, be subject to the echoed signal under ionosphere effect apart from frequency-domain expression to be

$\begin{array}{c}S(f_r,t_a)=A_r\left(f_r\right)\·A_a\left(t_a\right)\·\exp [-j\frac{{4\mathrm{\π}(f_r+f_0)R}_{\mathrm{real}}(t_a;P)}{c}]\·\exp (-j\frac{{{\mathrm{\πf}}_r}^2}{k_r})\\ \·\exp [-\frac{2\mathrm{\π}\·80.6\·({\mathrm{TEC}}_0+\mathrm{\ΔTEC}\left(t_a\right))}{\mathrm{cf}}]\end{array}---\left(7\right)$

Wherein, f _rfor distance is to frequency, f ₀for signal center frequency.

Separately, (7) formula can turn to the phase error that ionosphere constant component and changing unit are caused

$\begin{array}{c}S(f_r,t_a)=A_r\left(f_r\right)\·A_a\left(t_a\right)\·\exp [-j\frac{{4\mathrm{\π}(f_r+f_0)R}_{\mathrm{real}}(t_a;P)}{c}]\·\exp (-j\frac{{{\mathrm{\πf}}_r}^2}{k_r})\\ \·\exp [-\frac{2\mathrm{\π}\·80.6\·{\mathrm{TEC}}_0}{c(f_r+f_0)}]\·\exp [-\frac{2\mathrm{\π}\·80.6\·\mathrm{\ΔTEC}\left(t_a\right)}{{\mathrm{cf}}_0}]\end{array}---\left(8\right)$

In definition (8) $\exp [-\frac{2\mathrm{\π}\·80.6\·{\mathrm{TEC}}_0}{c(f_r+f_0)}]={\mathrm{\φ}}_{\mathrm{iono}},\exp [-\frac{2\mathrm{\π}\·80.6\·\mathrm{\ΔTEC}\left(t_a\right)}{{\mathrm{cf}}_0}]={\mathrm{\φ}}_{\mathrm{\Δiono}};$

In formula (8), φ _ionofor the phase error that ionosphere constant component causes, φ _{Δ iono}for the phase error that between different pulses, ionosphere changing unit causes.Wherein, φ _ionoto adjust the distance and impact to imaging, and φ _{Δ iono}to imaging, impact orientation.Due to f _rwith respect to f ₀very little, when analyzing ionosphere and change orientation to Imaging, do not consider f _rimpact.

Background ionosphere to GEO SAR distance to Influence Analysis on Imaging

(8) formula is carried out to range pulse compression, and reference signal form is

$H_r=\exp \left(j\frac{{{\mathrm{\πf}}_r}^2}{k_r}\right)---\left(9\right)$

Signal form after pulse compression is

$\begin{array}{c}S(f_r,t_a)=A_r\left(f_r\right)\·A_a\left(t_a\right)\·\exp [-j\frac{4\mathrm{\π}(f_r+f_0)R_{\mathrm{real}}(t_a;P)}{c}]\\ \·\exp [-\frac{2\mathrm{\π}\·80.6\·{\mathrm{TEC}}_0}{c(f_r+f_0)}]\·\exp [-\frac{2\mathrm{\π}\·80.6\·\mathrm{\ΔTEC}\left(t_a\right)}{{\mathrm{cf}}_0}]\end{array}---\left(10\right)$

In formula (10), due to

existence, the signal distance after pulse compression is to will be no longer a complete sinc function, but there will be target location skew and distance to blooming effect.

Adjust the distance when affecting in analysis background ionosphere, by φ _ionoat f=f ₀taylor expansion is done at place, and makes a concrete analysis of each effect and impact thereof.

${\mathrm{\&phi;}}_{\mathrm{iono}}={\mathrm{\&phi;}}_{\mathrm{iono}}{|}_{f=0}+\frac{{\&PartialD;\mathrm{\&phi;}}_{\mathrm{iono}}}{\&PartialD;f}{|}_{f={\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}\&CenterDot;(f-f_0)+\frac{1}{2!}\frac{{\&PartialD;}^2{\mathrm{\&phi;}}_{\mathrm{iono}}}{{\&PartialD;}^{2}f}{|}_{f={\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}\&CenterDot;{(f-f_0)}^2+\frac{1}{3!}\frac{{\&PartialD;}^3{\mathrm{\&phi;}}_{\mathrm{iono}}}{{\&PartialD;}^{3}f}{|}_{f={\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}\&CenterDot;{(f-f_0)}^3+...\left(1\right)$

In definition (11):

${\mathrm{\&phi;}}_{\mathrm{iono}}{|}_{f=0}={\mathrm{\&phi;}}_0\left(f\right)$

$\frac{{\&PartialD;\mathrm{\&phi;}}_{\mathrm{iono}}}{\&PartialD;f}{|}_{f={\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}\&CenterDot;(f-f_0)={\mathrm{\&phi;}}_1\left(f\right)$

$\frac{1}{2!}\frac{{\&PartialD;}^2{\mathrm{\&phi;}}_{\mathrm{iono}}}{{\&PartialD;}^{2}f}{|}_{f={\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}\&CenterDot;{(f-f_0)}^2={\mathrm{\&phi;}}_2\left(f\right)$

$\frac{1}{3!}\frac{{\&PartialD;}^3{\mathrm{\&phi;}}_{\mathrm{iono}}}{{\&PartialD;}^{3}f}{|}_{f={\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}\&CenterDot;{(f-f_0)}^3={\mathrm{\&phi;}}_3\left(f\right)$

In formula (11), first φ ₀(f) be constant term, it can not have any impact to imaging.Second φ ₁(f) be once item of frequency of distance, it can affect imaging subject location, but can not cause image defocus.The 3rd φ ₂(f) the and four φ ₃(f) and more high-order term can cause image defocus, but their can impact focusing on multi-form.

φ ₁(f) mainly can make image produce along distance to skew, but it does not affect figure image focu.φ ₁(f) concrete form is as follows

${\mathrm{\&phi;}}_1\left(f\right)=\frac{2\mathrm{\&pi;}\&CenterDot;80.6{\mathrm{TEC}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}^2}\&CenterDot;(f-f_0)---\left(12\right)$

The distance that background ionosphere causes to image shift amount is:

$\mathrm{\&Delta;L}=\frac{80.6\&CenterDot;{\mathrm{TEC}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}^2}---\left(13\right)$

From (13) formula, the distance that background ionosphere causes is to image shift and two factor analysis: signal frequency and TEC value.Signal frequency is lower, and image distance is larger to side-play amount; TEC value is higher, and image distance is larger to side-play amount.

φ ₂(f) can cause that main lobe broadening, secondary lobe raise, impact distance is to image quality.The quadratic term expression that propagation constant is launched is:

${\mathrm{\&phi;}}_2\left(f\right)=\frac{2\mathrm{\&pi;}\&CenterDot;80.6{\mathrm{TEC}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}^3}{(f-f_0)}^2---\left(14\right)$

The size of quadratic phase error is

${\mathrm{\&phi;}}_2\left(f\right)=\frac{40.3\mathrm{\&pi;}\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="TEC"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">TEC</figure-callout>}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}^3}\&CenterDot;B^2---\left(15\right)$

From formula (15), signal bandwidth B, signal frequency, TEC ₀value all can impact focusing on.The distance that introduce in ionosphere is to quadratic phase error and signal bandwidth, TEC ₀value is directly proportional, and is inversely proportional to signal frequency.

φ in formula (11) ₃(f) by bring distance to asymmetric secondary lobe, and then impact focusing on, its expression is as follows

${\mathrm{\&phi;}}_3\left(f\right)=\frac{2\mathrm{\&pi;}\&CenterDot;80.6\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="TEC"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">TEC</figure-callout>}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}^4}{(f-f_0)}^3---\left(16\right)$

Three phase error sizes are

${\mathrm{\&phi;}}_3\left(f\right)=\frac{20.15\mathrm{\&pi;\&pi;}\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="TEC"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">TEC</figure-callout>}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}^4}{B}^3---\left(17\right)$

From formula (17), signal bandwidth, signal frequency, TEC ₀value all can impact cubic term bit error.Specifically, TEC and signal bandwidth are directly proportional to three phase errors; Signal frequency and three phase errors are inversely proportional to.

Background ionosphere to GEO SAR orientation to Influence Analysis on Imaging

Consider TEC changing pattern pattern (3), ionosphere changes the phase error phi causing _{Δ iono}can be write as

${\mathrm{\&phi;}}_{\mathrm{\&Delta;iono}}=\exp [-\frac{2\mathrm{\&pi;}\&CenterDot;80.6}{{\mathrm{cf}}_0}({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&CenterDot;t_a\&CenterDot;k_2\&CenterDot;{t_a}^2+{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3\&CenterDot;{t_a}^3+...)]---\left(18\right)$

Therefore, apart from the signal (10) after pulse compression, can be written as

$\begin{array}{c}S(f_r,t_a)=A_r\left(f_r\right)\&CenterDot;A_a\left(t_a\right)\&CenterDot;\exp [-j\frac{4\mathrm{\&pi;}(f_r+f_0)R_{\mathrm{real}}(t_a;P)}{c}\\ \&CenterDot;\exp [-\frac{2\mathrm{\&pi;}\&CenterDot;80.6\&CenterDot;\mathrm{TE}{C}_0}{c(f_r+f_0)}]\&CenterDot;\exp [-\frac{2\mathrm{\&pi;}\&CenterDot;80.6}{{\mathrm{cf}}_0}({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&CenterDot;t_a+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\&CenterDot;{t_a}^2+{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3\&CenterDot;{t_a}^3+...)]\end{array}---\left(19\right)$

In definition (19) $\exp [-\frac{2\mathrm{\&pi;}\&CenterDot;80.6\&CenterDot;\mathrm{TE}{C}_0}{c(f_r+f_0)}]={\mathrm{\&phi;}}_{\mathrm{iono}},\exp [-\frac{2\mathrm{\&pi;}\&CenterDot;80.6}{{\mathrm{cf}}_0}({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&CenterDot;t_a+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\&CenterDot;{t_a}^2+{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3\&CenterDot;{t_a}^3+...)]={\mathrm{\&phi;}}_{\mathrm{\&Delta;iono}};$

According to SAR image-forming principle, therefrom extract orientation to Chirp signal, at φ _{Δ iono}the lower orientation of impact to Chirp signal is

$s\left(t_a\right)=\mathrm{rect}\left(\frac{t_a}{T_a}\right)\exp ({\mathrm{j\&pi;f}}_{\mathrm{dr}}\&CenterDot;{t_a}^2)\exp [-\frac{2\mathrm{\&pi;}\&CenterDot;80.6}{{\mathrm{cf}}_0}({\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\&CenterDot;t_a+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\&CenterDot;{t_a}^2+{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3\&CenterDot;{t_a}^3...)]---\left(20\right)$

Wherein, T _afor synthetic aperture time, f _drfor orientation is to frequency modulation rate.

The azimuth spectrum expression formula that can obtain under ionosphere effect is

$\mathrm{\&phi;}\left(f_a\right)=A\&CenterDot;\exp (-\frac{2\mathrm{\&pi;}\&CenterDot;80.6{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{{\mathrm{cf}}_0{f}_{\mathrm{dr}}}\&CenterDot;f_a)\&CenterDot;\exp (-\frac{\mathrm{\&pi;}}{f_{\mathrm{dr}}-\frac{161.2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}}\&CenterDot;{f_a}^2)\&CenterDot;\exp (-\frac{161.2\&CenterDot;\mathrm{\&pi;}\&CenterDot;{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3}{{\mathrm{cf}}_0{{\mathrm{<figure-callout\; id="3"\; label="f\; dr"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{dr}}}^3}\&CenterDot;{f_a}^3)---\left(21\right)$

Wherein, f _afor orientation is to frequency, A is the constant component in azimuth spectrum;

In definition (21):

$\exp (-\frac{2\mathrm{\&pi;}\&CenterDot;80.6{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{{\mathrm{cf}}_0{f}_{\mathrm{dr}}}\&CenterDot;f_a)={\mathrm{\&phi;}}_{a1}$

$\exp (-\frac{\mathrm{\&pi;}}{f_{\mathrm{dr}}-\frac{161.2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{{\mathrm{cf}}_0}}{f_a}^2)={\mathrm{\&phi;}}_{a2}$

$\exp (-\frac{161.2\&CenterDot;\mathrm{\&pi;}\&CenterDot;{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3}{{\mathrm{cf}}_0{{\mathrm{<figure-callout\; id="3"\; label="f\; dr"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{dr}}}^3}\&CenterDot;{f_a}^3){=\mathrm{\&phi;}}_{a3}$

From formula (21), the variation of TEC can cause that image orientation is to skew and orientation to image defocus in the synthetic aperture time.

φ in formula (21) _a1the orientation that item causes to image shift amount is

${\mathrm{\&Delta;L}}_a=v_{\mathrm{nadir}}\&CenterDot;\frac{80.6{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{{\mathrm{cf}}_0{f}_{\mathrm{dr}}}---\left(22\right)$

Wherein, for aspect is to frequency modulation rate, θ is radar angle of squint, R ₀for the shortest oblique distance, v _satellitefor satellite velocities, v _nadirfor substar speed.Through type (22) can find out, when GEO SAR satellite orbit is fixedly time, orientation is to size and signal frequency and the TEC first order derivative k of side-play amount ₁relevant.

φ in formula (21) _a2item expression is

${\mathrm{\&phi;}}_{a2}=\exp (-\frac{\mathrm{\&pi;}}{f_{\mathrm{dr}}-\frac{161.2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}}\&CenterDot;{f_a}^2)---\left(23\right)$

The orientation that ionosphere causes to quadratic phase error size is

${\mathrm{\&phi;}}_{a2}=\exp (-\frac{{{\mathrm{\&pi;<figure-callout\; id="2"\; label="f\; dr"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{dr}}}^2}{4(f_{\mathrm{dr}}-\frac{161.2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{{\mathrm{cf}}_0})}\&CenterDot;{T_a}^2)---\left(24\right)$

This phase error can make image orientation defocus to occurring, and is subject to following factor impact.TEC second order rate of change k ₂larger, signal frequency is lower, the synthetic aperture time is longer, quadratic phase error is larger.

Three times phase error expression formula is as follows

${\mathrm{\&phi;}}_{a3}=\exp (-\frac{161.2{\mathrm{\&pi;<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3}{{\mathrm{cf}}_0{{\mathrm{<figure-callout\; id="3"\; label="f\; dr"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{dr}}}^3}\&CenterDot;{f_a}^3)---\left(25\right)$

The orientation that ionosphere causes to three phase error sizes is

${\mathrm{\&phi;}}_{a3}=\exp (-\frac{20.15{\mathrm{\&pi;<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3}{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}\&CenterDot;{T_a}^3)---\left(26\right)$

Cubic term can cause asymmetric secondary lobe, and then impact focuses on.From formula (25), can find out, signal frequency is lower, TEC tri-rank rate of change k ₃larger, the synthetic aperture time is longer, cubic term impact is more serious.

Based on above-mentioned modeling and analytic process, the background ionosphere that the present invention proposes, to geostationary orbit synthetic aperture radar image-forming impact analysis method, comprises the steps:

When step 1, acquisition, become the GEO SAR echoed signal under ionosphere effect, and total electron content TEC measurement data in GEO SAR signal propagation path, TEC measurement data is carried out to 3 order polynomial matchings, obtain constant term TEC ₀, 1 item coefficient k ₁, 2 item coefficient k ₂with 3 item coefficient k ₃;

Step 2, analysis background ionosphere to GEO SAR distance to Imaging;

1. the distance that adopts formula (13) to calculate to be caused by background ionosphere is to image shift amount Δ L;

2. the GEO SAR signal distance that adopts formula (15) to calculate to be caused by background ionosphere is to quadratic term error φ ₂; Work as φ ₂value be greater than the quadratic term threshold value T of setting ₁time, confirm that main lobe broadening, secondary lobe rising that background ionosphere causes cause image distance to defocusing; Preferably, quadratic term threshold value T ₁=0.78rad;

3. the GEO SAR signal distance that adopts formula (17) to calculate to be caused by background ionosphere is to cubic term error φ ₃; Work as φ ₃value be greater than the cubic term threshold value T of setting ₂time, confirm that the asymmetric secondary lobe that background ionosphere causes causes image distance to defocusing; Preferably, described cubic term threshold value T ₂=0.39rad;

Step 3, analysis background ionosphere to GEO SAR orientation to Imaging;

1. the orientation that adopts formula (22) to calculate to be caused by background ionosphere is to image shift amount Δ L _a;

2. the GEO SAR aspect that adopts formula (24) to calculate to be caused by background ionosphere is to quadratic term error φ _a2; Work as φ _a2value be greater than described quadratic term threshold value T ₁time, confirm that background ionosphere causes that image orientation is to defocusing;

3. the GEO SAR aspect that adopts formula (26) to calculate to be caused by background ionosphere is to cubic term error φ _a3; Work as φ _a3value be greater than described cubic term threshold value T ₂time, confirm that background ionosphere causes that image orientation is to defocusing.

Beneficial effect:

The present invention is first in conjunction with the feature of GEO SAR ionosphere problem, while having set up, become the GEO SAR echo signal model under ionosphere effect, then based on this model inference, go out for analyzing the image shift amount of Imaging and defocusing phase place, finally according to image shift amount and defocus phase place judge background ionosphere whether to GEO SAR two dimension (apart to orientation to) imaging impacts, and has good effect.

Accompanying drawing explanation

Fig. 1 is GEO SAR three dimensional signal model.

Fig. 2 is the TEC on receiver A and B travel path.

Fig. 3 is that the distance that causes of background ionosphere is to image shift amount.

Fig. 4 is the lower distance of background ionosphere impact to pulse compression result: wherein (a) is receiver A, (b) is receiver B.

Fig. 5 is that the orientation that causes of background ionosphere is to image shift amount.

Fig. 6 is the lower orientation of background ionosphere impact to pulse compression result: wherein (a) is receiver A, (b) is receiver B.

Fig. 7 is process flow diagram of the present invention.

Embodiment

Below in conjunction with the accompanying drawing embodiment that develops simultaneously, describe the present invention.

In this example, correlation parameter is as follows:

Semi-major axis of orbit: 42164.17Km, orbit inclination: 53 ⁰, track eccentricity: 0.07, argument of perigee: 270 ⁰

Right ascension of ascending node: 265 ⁰, antenna size: 30m, frequency range: L-band (0.24m wavelength), bandwidth: 80MHz, 120MHz, aperture time: 500 seconds, 1000 seconds, 1500 seconds.

Meanwhile, adopt Klobuchar model and Big Dipper Navsat to obtain ionospheric data, two receivers are set, lay respectively at mid latitudes, geographic coordinate is 43 ° 34 ' of north latitude, 120 ° 16 ' of east longitude; Region of the equator, geographic coordinate is 3 ° 52 ' of north latitude, east longitude 120 ^°4 '.Obtain on August in 2013 29 TEC data as shown in Figure 2.

Adopt background ionosphere of the present invention to geostationary orbit synthetic aperture radar image-forming impact analysis method, complete background ionosphere under this parameter to the emulation of GEO SAR Imaging, referring to Fig. 7, idiographic flow is as follows.

Step 1, becomes the GEO SAR echoed signal under ionosphere effect during acquisition, extract signal center frequency f ₀, bandwidth B and synthetic aperture time T _adeng echo parameter; Obtain the TEC measurement data in GEO SAR signal propagation path.According to TEC measurement data, TEC measurement data is carried out to 3 order polynomial matchings, obtain constant term TEC ₀, 1 item coefficient k ₁, 2 item coefficient k ₂with 3 item coefficient k ₃.

Following table 1 is TEC constant term and each rank coefficient on receiver A and B travel path.Wherein, TEC unit is TECU, 1TECU=1 * 10 ¹⁶e ^-/ m ³, S is second.

Step 2, analysis background ionosphere is the impact to imaging on GEO SAR distance.

1. in formula (2), the constant component of TEC will be adjusted the distance and be impacted to focusing, impact be divided into distance to image shift and distance to image defocus two parts.

The distance that background ionosphere causes to image shift amount is:

$\mathrm{\&Delta;L}=\frac{80.6\&CenterDot;{\mathrm{TEC}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}^2}$

The distance that the ionosphere that receiver A and B place record causes to image shift amount as shown in Figure 3.The image distance that receiver A place data cause is 6m left and right to side-play amount, and the image distance that receiver B place data cause can reach nearly 38m to side-play amount maximum.

2. distance can cause image defocus to quadratic phase error, and quadratic phase error size is

${\mathrm{\&phi;}}_2=\frac{40.3\mathrm{\&pi;}\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="TEC"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">TEC</figure-callout>}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}^3}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">B</figure-callout>}}^2$

Work as φ ₂value be greater than the quadratic term threshold value T of setting ₁time, confirm that main lobe broadening, secondary lobe rising that background ionosphere causes cause image distance to defocusing.

It has been generally acknowledged that when quadratic phase error is greater than 0.78rad, can impact focusing on.Distance under quadratic phase error impact to pulse compression result as shown in Figure 4.The ionosphere numerical value recording due to receiver A place is less, by above formula, calculates the not enough 0.78rad of phase error that it causes, so it is adjusted the distance and does not impact to focusing on.The ionosphere numerical value that receiver B place records is larger, and when 80MHz and 120MHz bandwidth, its distance causing has reached 1.02rad and 2.30rad to quadratic phase error, has started to impact focusing on.As can be seen from Figure 4, when signal bandwidth reaches 120MHz, distance is no longer-theoretical value of 13.2dB to have deteriorated into-12.33dB to the peak sidelobe ratio after pulse pressure.

3. calculate the GEO SAR signal distance that caused by background ionosphere to cubic term error φ ₃:

${\mathrm{\&phi;}}_3=\frac{20.15\mathrm{\&pi;}\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="TEC"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">TEC</figure-callout>}}_0}{{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}^4}{\mathrm{<figure-callout\; id="3"\; label="B"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">B</figure-callout>}}^3$

Work as φ ₃value be greater than the cubic term threshold value T of setting ₂time, confirm that the asymmetric secondary lobe that background ionosphere causes causes image distance to defocusing.For quadratic phase error, choose while being greater than 0.39rad, think and can impact focusing on.

In this example, distance is less to three phase errors, at this, does not consider.

Step 3, analysis background ionosphere is the impact to imaging on GEO SAR orientation.

1. each item of TEC can impact to focusing orientation, and wherein TEC linear change is partly that 1 item can cause that image produces orientation to skew, and nonlinearities change part can cause that image orientation is to defocusing.

Orientation to image shift amount is

${\mathrm{\&Delta;L}}_a=v_{\mathrm{nadir}}\&CenterDot;\frac{80.6{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}{{\mathrm{cf}}_0{f}_{\mathrm{dr}}}$

The orientation that ionosphere measured data causes to image shift amount as shown in Figure 5.The image orientation that receiver A place data cause is 0.2m left and right to side-play amount, and the image orientation that receiver B place data cause approaches 3.2m to side-play amount maximum.

2. the orientation that ionized layer TEC second derivative causes to quadratic phase error size is

${\mathrm{\&phi;}}_{a2}=\exp (-\frac{{{\mathrm{\&pi;<figure-callout\; id="2"\; label="f\; dr"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{dr}}}^2}{4(f_{\mathrm{dr}}-\frac{161.2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000436177500000021.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{{\mathrm{cf}}_0})}\&CenterDot;{T_a}^2)$

Work as φ _a2value be greater than described quadratic term threshold value T ₁time, confirm that background ionosphere causes that image orientation is to defocusing.

In the present embodiment, think equally when quadratic phase error is greater than 0.78rad, can impact focusing on.Orientation under quadratic phase error impact to pulse compression result as shown in Figure 6.The TEC rate of change that receiver A place data record is also little, calculates its phase error causing be less than 0.78rad by above formula, can to focusing, not impact orientation.The data TEC rate of change that receiver B place records is larger, when aperture time, reaches 1000 seconds and 1500 seconds time, orientation phase error reaches 1.34rad and 2.56rad, will to focusing, impact orientation.From the result of Fig. 6, can find out, when the synthetic aperture time is 1500s, orientation is to deteriorated into-11.33dB of peak sidelobe ratio.

3. calculate the GEO SAR aspect that caused by background ionosphere to cubic term error φ _a3:

${\mathrm{\&phi;}}_{a3}=\exp (-\frac{20.15{\mathrm{\&pi;<figure-callout\; id="3"\; label="k"\; filenames="HDA0000436177500000032.png"\; state="\{\{state\}\}">k</figure-callout>}}_3}{{\mathrm{<figure-callout\; id="0"\; label="cf"\; filenames="HDA0000436177500000011.png,HDA0000436177500000022.png"\; state="\{\{state\}\}">cf</figure-callout>}}_0}\&CenterDot;{T_a}^3)$

Work as φ _a3value be greater than described cubic term threshold value T ₂time, confirm that background ionosphere causes that image orientation is to defocusing.

In this example, orientation is less to three phase errors, at this, does not consider.

By simulation result, can find out and utilize the validity of this methods analyst background ionosphere to GEO SAR Imaging.

Above-described specific descriptions; object, technical scheme and beneficial effect to invention further describe; institute is understood that; the foregoing is only specific embodiments of the invention; the protection domain being not intended to limit the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (2)

1. the analytical approach of background ionosphere to GEO SAR Imaging, is characterized in that, comprises the steps:

When step 1, acquisition, become the geostationary orbit synthetic-aperture radar GEO SAR echoed signal under ionosphere effect, extract signal center frequency f ₀, bandwidth B and synthetic aperture time T _a, and obtain GEO SAR signal propagation path upper ionized layer total electron content TEC measurement data, and TEC measurement data is carried out to 3 order polynomial matchings, obtain constant term TEC ₀, 1 item coefficient k ₁, 2 item coefficient k ₂with 3 item coefficient k ₃;

Step 2, analysis background ionosphere to GEO SAR distance to Imaging;

1. calculate the distance that caused by background ionosphere to image shift amount Δ L;

$\mathrm{\&Delta;L}=\frac{80.6\&CenterDot;{\mathrm{TEC}}_0}{{f_0}^2}$

2. calculate the GEO SAR signal distance that caused by background ionosphere to quadratic term error φ ₂:

${\mathrm{\&phi;}}_2=\frac{40.3\mathrm{\&pi;}\&CenterDot;{\mathrm{TEC}}_0}{{{\mathrm{cf}}_0}^3}\&CenterDot;B^2$

Wherein, c is the light velocity;

Work as φ ₂value be greater than the quadratic term threshold value T of setting ₁time, confirm that main lobe broadening, secondary lobe rising that background ionosphere causes cause image distance to defocusing;

3. calculate the GEO SAR signal distance that caused by background ionosphere to cubic term error φ ₃:

${\mathrm{\&phi;}}_3=\frac{20.15\mathrm{\&pi;}\&CenterDot;{\mathrm{TEC}}_0}{{{\mathrm{cf}}_0}^4}{B}^3$

Work as φ ₃value be greater than the cubic term threshold value T of setting ₂time, confirm that the asymmetric secondary lobe that background ionosphere causes causes image distance to defocusing;

Step 3, analysis background ionosphere to GEO SAR orientation to Imaging;

1. calculate the orientation that caused by background ionosphere to image shift amount Δ L _a;

${\mathrm{\&Delta;L}}_a=v_{\mathrm{nadir}}\&CenterDot;\frac{80.6k_1}{{\mathrm{cf}}_0{f}_{\mathrm{dr}}}$

Wherein, v _nadirfor the substar speed of GEO SAR, f _drfor aspect is to frequency modulation rate;

2. calculate the GEO SAR aspect that caused by background ionosphere to quadratic term error φ _a2:

${\mathrm{\&phi;}}_{a2}=\exp (-\frac{{{\mathrm{\&pi;f}}_{\mathrm{dr}}}^2}{4(f_{\mathrm{dr}}-\frac{161.2k_2}{{\mathrm{cf}}_0})}\&CenterDot;{T_a}^2)$

Work as φ _a2value be greater than described quadratic term threshold value T ₁time, confirm that background ionosphere causes that image orientation is to defocusing;

3. calculate the GEO SAR aspect that caused by background ionosphere to cubic term error φ _a3:

${\mathrm{\&phi;}}_{a3}=\exp (-\frac{20.15{\mathrm{\&pi;k}}_3}{{\mathrm{cf}}_0}\&CenterDot;{T_a}^3)$

Work as φ _a3value be greater than described cubic term threshold value T ₂time, confirm that background ionosphere causes that image orientation is to defocusing.

2. the method for claim 1, is characterized in that, described quadratic term threshold value T ₁=0.78rad, described cubic term threshold value T ₂=0.39rad.

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