CN105842672A - Low-frequency broadband satellite-borne SAR imaging ionosphere phase error compensation method - Google Patents

Abstract

The invention provides a low-frequency broadband satellite-borne SAR imaging ionosphere phase error compensation method, which is characterized in that series decomposition is carried out on ionosphere phase error to three terms based on Legendre orthogonal basis, and the obtained errors are mutually orthogonal, so that the problem of order coupling of an existing assessment method is solved; then, based on an expression of each order derived based on an orthogonal model, influence of zero-order phase error on broadening of direction images, first-order phase error on translation of distance images, on pulse broadening caused by second-order phase error and on pulse distortion caused by third-order phase error are quantitatively evaluated; and based on the influence, ionosphere total electron content TEC information can be obtained, and ionosphere influence compensation can be carried out on the images. The method can accurately reflect the influence of true ionosphere phase error on low-frequency broadband satellite-borne SAR imaging, and thus ionosphere influence compensation precision is improved.

Description

A kind of broad band low frequency Space-borne SAR Imaging ionosphere phase error compensation method

Technical field

The present invention relates to a kind of broad band low frequency Space-borne SAR Imaging ionosphere phase error compensation method, belong to synthetic aperture Field of radar and ionospheric radio propagation field, be mainly used in improving broad band low frequency Space-borne SAR Imaging ionosphere compensation precision.

Background technology

It is conceived to the demands such as the interior high-resolution identification to forest cover and underground vanishing target of global range, is operated in VHF/ One of low frequency satellite-borne synthetic aperture radar (Synthetic Aperture Radar, SAR) System Development trend of uhf band is Towards bigger relative bandwidth design.But, due to its work on ionosphere or among, the phase of echo of these frequency ranges is not Can avoid being affected, and carrier frequency is the lowest, bandwidth is the biggest, affect the most serious so that the service behaviour of SAR system drastically under Fall.In order to more thoroughly suppress ionospheric impact, it is carried out Accurate Model and assessment is premise and key.Therefore, modeling The service behaviour of broad band low frequency Spaceborne SAR System after ionosphere compensates directly is determined with the accuracy of assessment.

Currently for the ionosphere effect of the low frequency and narrow bandwidth SAR signals such as PALSAR and BIOMASS SAR, due to its phase place by mistake Difference secondary and above every less can ignore, Taylor series expansion becomes analysis and compensates each order error SAR is become picture element Amount affects most common method.But, when low frequency SAR signal bandwidth increases, secondary and three error term quickly increase can not Ignore, if still by every non-orthogonal Taylor series ionospheric error being analyzed and compensating, owing to high-order term comprising Low order item composition increase the most accordingly, now will produce obvious errors, detailed problems is as follows:

First, according to Fourier transform property, zero degree item error can't produce impact on SAR image distance to compression, But orientation can be caused to decline to image resolution ratio.Generally, orientation is more sensitive to zero degree phase error to picture quality, because of This needs more accurate assessment.And along with the increase of bandwidth, do not consider in quadratic phase error due to existing method Zero degree component, therefore can not compensate well for the impact that zero degree phase error is brought.

Second, one time phase error can cause image distance to translation, although for scene single-point situation, image shift is not Can affect image image quality, but actual scene is made up of many point targets, this skew can cause local resolution to decline. Along with bandwidth increases, existing compensation method does not consider the component of degree n n in three phase errors, and therefore also resulting in can not The error ignored.

3rd, quadratic phase error can cause distance to pulse stretching (after pulse pressure), causes resolution ratio to decline, due to existing The quadratic phase error that method is assessed contains zero degree item, therefore needs to improve its precision.

4th, three times phase error can cause distance asymmetrical distortion after pulse pressure, for PALSAR or BIOMASS SAR Deng narrowband systems, three phase error magnitudes are the least can be ignored.And when analyzing big bandwidth, the first order in existing method becomes Branch causes obvious error.

Summary of the invention

The purpose of the present invention: overcome the deficiencies in the prior art, it is provided that a kind of broad band low frequency Space-borne SAR Imaging ionosphere phase place Error compensating method, overcomes each order phase error coupled problem that Taylor series expansion obtains, is effectively increased ionosphere shadow Ring the precision compensated.

The technical solution used in the present invention is:

A kind of broad band low frequency Space-borne SAR Imaging ionosphere phase error compensation method, comprises the steps:

(1) obtain the broad band low frequency satellite-borne SAR echo-signal under ionosphere effect, build for this satellite-borne SAR echo-signal The ionosphere zero degree that the Legendre's orthogonal series that is based on launches is to three phase errors；

(2) determine ionosphere zero degree phase error on orientation to the impact of image quality, i.e. determine ionosphere zero degree phase place The orientation that error causes is to maximum secondary phase error, and then determines the first vertical total electron content value TEC₁；

(3) determine that one time, ionosphere phase error is adjusted the distance the impact to image quality, i.e. determine one time, ionosphere phase place The image distance that error causes is to translational movement, and then determines the second vertical total electron content value TEC₂；

(4) determine that ionosphere quadratic phase error is adjusted the distance the impact to image quality, i.e. determine that ionosphere causes away from Descriscent maximum secondary phase error, and then determine the 3rd vertical total electron content value TEC₃；

(5) determine that three times, ionosphere phase error is adjusted the distance the impact to image quality, i.e. determine that ionosphere causes away from Maximum three phase errors in descriscent, and then determine the 4th vertical total electron content value TEC₄；

(6) according to four the TEC values determined in step (2)～(5), vertical total electron content mean value TEC is calculated_Averagely；

(7) according to the TEC obtained in step (6)_Averagely, determine that the ionosphere zero degree in step (1) is to three phase errors； (detailed description of the invention illustrates TEC_AveragelySubstitute in step 1 formula)

(8) according to the ionosphere zero degree determined in step (7) to three phase errors, satellite-borne SAR image is compensated, Obtain removing the borne SAR image of ionosphere effect.

In described step (1), the phase error of zero degree to three times is followed successively by Δ φ_0Le(f_τ)、Δφ_1Le(f_τ)、Δφ_2Le (f_τ)、Δφ_3Le(f_τ), obtain especially by equation below:

${\mathrm{\Δ\φ}}_{0Le}\left(f_{\mathrm{\τ}}\right)=\frac{A_0\·TEC}{B}ln\left(\frac{2f_0+B}{2f_0-B}\right)$

${\mathrm{\Δ\φ}}_{1Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC\·f_{\mathrm{\τ}}(\frac{12}{B^2}-\frac{12f_0}{B^3}ln(\frac{2f_0+B}{2f_0-B}\left)\right)$

$\begin{array}{c}{\mathrm{\Δ\φ}}_{2Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC(\frac{30f_{\mathrm{\τ}}^2}{B^3}-\frac{5}{2B})\\ \·(-\frac{1}{2}\ln (\frac{2f_0+B}{2f_0-B})-\frac{6f_0}{B}+\frac{6f_0^2}{B^2}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\end{array}$

$\begin{array}{c}{\mathrm{\Δ\φ}}_{3Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC(\frac{140f_{\mathrm{\τ}}^3}{B^4}-\frac{21f_{\mathrm{\τ}}}{B^2})\\ \·(-\frac{4}{3}+\frac{3f_0}{B}\ln (\frac{2f_0+B}{2f_0-B})+\frac{20f_0^2}{B^2}-\frac{20f_0^3}{B^3}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\end{array}$

Wherein, f₀For carrier frequency, B is transmitted bandwidth, A₀For constant, and A₀=40.28；f_τ∈ [-B/2, B/2] is SAR signal Spectral range, TEC is vertical total electron content value.

Described step (2) determining, orientation that ionosphere zero degree phase error causes, to maximum secondary phase error, is entered And determine the first vertical total electron content value TEC₁, particularly as follows:

Wherein L_sFor length of synthetic aperture, TEC₀It is defined as thunder Reach TEC value during distance objective minimum oblique distance, TEC₀=TEC₁/ cos θ, θ are radar downwards angle of visibility, f₀For carrier frequency, B is for launching band Width, c is the light velocity, ΔΦ_a2LeFor orientation to maximum secondary phase error.

Described step (3) determines that image distance that one time, ionosphere phase error causes, to translational movement, and then determines second Vertical total electron content value TEC₂, particularly as follows:

Wherein, Δ L_rLeFor image distance to flat Shifting amount,

Described step (4) determines that distance that ionosphere causes, to maximum secondary phase error, and then determines that the 3rd is vertical total Electron content value TEC₃, particularly as follows:

Wherein, ΔΦ_r2LeFor distance to maximum secondary phase error.

Described step (5) determines that distance that ionosphere causes, to maximum three phase errors, and then determines that the 4th is vertical total Electron content value TEC₄, particularly as follows:

Wherein, ΔΦ_r3LeFor distance to maximum three phase errors.

TEC in step (6)_Averagely=(TEC₁+TEC₂+TEC₃+TEC₄)/4。

The present invention the most desirable following technique effect:

(1) ionosphere phase error is decomposed by the inventive method based on Legendre's orthogonal basis, perfect can distinguish each rank The impact on SAR image of the secondary error, solves existing Taylor series expansion appraisal procedure each order coupled problem.

(2) present invention derives zero degree based on this orthogonal model, to three ionosphere phase errors, SAR image is become picture element The Mathematical Modeling of amount impact, owing to now higher order term error does not contains lower term composition, the Mathematical Modeling therefore obtained relatively Taylor's level It is more accurate that number method of deploying obtains.Affect model based on these and then can get four total electron content TEC values, final To its mean value.Now utilize the TEC mean value obtained that the satellite-borne SAR image by ionosphere effect is compensated.Due to This method perfect can distinguish the impact on SAR image of each order error, solves the most independent the asking of each order of existing appraisal procedure Topic, improves ionosphere effect compensation precision.

Accompanying drawing explanation

Fig. 1 is the flow chart of the inventive method；

Fig. 2 is three phase error simulation result schematic diagrams that Taylor series expansion obtains；

Fig. 3 is three phase error simulation result schematic diagrams that the present invention obtains；

Fig. 4 is the simulation result schematic diagram that true error is compensated by the ionosphere phase error that the present invention obtains, wherein, and figure 4 (a) is the one-dimensional result that satellite-borne SAR image ionosphere effect compensates；Upper figure in Fig. 4 (a) is to be tied by ionosphere effect Really, shown in middle figure for utilizing Taylor series expansion to compensate by the SAR image of ionosphere effect, figure below is for utilizing Legendre's level Number launches to compensate the SAR image by ionosphere effect；Fig. 4 (b) is the two-dimensional simulation result that in Fig. 4 (a), upper figure is corresponding, Fig. 4 C () is the two-dimensional simulation result that middle figure is corresponding；Fig. 4 (d) is the two-dimensional simulation result that figure below is corresponding.

Detailed description of the invention

Below in conjunction with the accompanying drawings and give an actual example, to the spaceborne image quality of the broad band low frequency by ionosphere effect according to the present invention Appraisal procedure is described in detail, and used main radar and Ionospheric Parameters are as shown in table 1.

Table 1 ionosphere and radar parameter

As it is shown in figure 1, the one for the present invention is launched to carry out broad band low frequency Space-borne SAR Imaging based on Legendre's orthogonal series Ionosphere effect compensation method flow chart, what the method included specifically comprises the following steps that

(1) obtain the broad band low frequency satellite-borne SAR echo-signal under ionosphere effect, build for this satellite-borne SAR echo-signal The ionosphere zero degree that the Legendre's orthogonal series that is based on launches is to three phase errors；

Ionosphere is a kind of dispersive medium, and when SAR signal is propagated wherein, in signal bandwidth, the time delay of different spectral is not With, therefore can cause the phase term that echo is extra, its two dimension echo-signal is represented by:

$\begin{array}{c}{s}_{r\_iono}(\mathrm{\τ},\mathrm{\η})=w_a\[\mathrm{\η}\]\·\exp (-{\mathrm{j\πK}}_a{\mathrm{\η}}^2)\\ \·ifft\[W\left(f_{\mathrm{\τ}}\right)\·\exp \left({\mathrm{j\Δ\φ}}_{iono}\right(f_{\mathrm{\τ}}\left)\right)\·\exp (-j2{\mathrm{\πf}}_{\mathrm{\τ}}\·\frac{2R\left(\mathrm{\η}\right)}{c})\]\end{array}---\left(1\right)$

In above formula, τ, η represent the fast time of SAR and slow time variable respectively.w_a[η] is that orientation is to envelope, W (f_τ) be away from The Fourier transformation form of descriscent envelope, K_aFor orientation to chirp rate, R (η) is when slow time η, radar and target away from From, c is the light velocity, f_τ∈ [-B/2, B/2] is SAR signal spectrum scope, and B is signal bandwidth.Δφ_iono(f_τ) be and ionized The true additive phase of layer impact, its expression formula can be written as:

${\mathrm{\Δ\φ}}_{iono}\left(f_{\mathrm{\τ}}\right)=\frac{A_0\·TEC}{f_{\mathrm{\τ}}+f_0}---\left(2\right)$

Wherein A₀=4 π 40.28/c, f₀For signal carrier frequency, TEC is ionosphere total electron content (Total Electron Content).If launching by tradition Taylor series, above formula can be approximately

Wherein, Δ φ_0Ta,Δφ_1Ta,Δφ_2Ta, and Δ φ_3TaIt is the zero degree that obtains of Taylor series expansion respectively, once, Secondary and three phase errors.Typically for the ionosphere effect of low frequency and narrow bandwidth SAR signal, due to its phase error secondary And above the most every less can ignore, therefore above formula can the most accurately assess the impact that ionosphere is brought.But, when relatively When bandwidth increases, owing to Taylor expansion is every and non-orthogonal, high-order term error contains low order composition, such as cubic term and contains one Secondary item, now will produce the error can not ignore.Fig. 2 show the parameter utilizing table 1, three phase error Δ obtained φ_3TaSimulation result, it can be seen that linear segment enough causes bigger assessment errors.Therefore, for broad band low frequency satellite-borne SAR Signal ionosphere effect is assessed, and needs to set up every orthogonal series expansion method, and the present invention enters based on Legendre's orthogonal basis Row progression decomposes, and can again approximate true phase error:

Wherein, Δ φ_0Le(f_τ),Δφ_1Le(f_τ),Δφ_2Le(f_τ), and Δ φ_3Le(f_τ) it is based on Legnedre series exhibition Opening the optimal zero degree obtained, once, secondary, three times phase error expresses formula.L_nFor Legendre's basic function, it is represented by:

$\begin{array}{cc}{L}_0\left(f_{\mathrm{\τ}}\right)=\frac{1}{\sqrt{B}},& L_1\left(f_{\mathrm{\τ}}\right)=\sqrt{\frac{3}{B}}\·\frac{2f_{\mathrm{\τ}}}{B}\\ L_2\left(f_{\mathrm{\τ}}\right)=\sqrt{\frac{5}{B}}\·(\frac{6{f_{\mathrm{\τ}}}^2}{B^2}-\frac{1}{2}),& L_3\left(f_{\mathrm{\τ}}\right)=\sqrt{\frac{7}{B}}\·(\frac{20{f_{\mathrm{\τ}}}^3}{B^3}-\frac{3f_{\mathrm{\τ}}}{B})\end{array}---\left(5\right)$

And a_nFor corresponding coefficient

$a_n={\∫}_{-B/2}^{B/2}{L}_n\left(f_{\mathrm{\τ}}\right)\·{\mathrm{\Δ\φ}}_{iono}\left(f_{\mathrm{\τ}}\right){\mathrm{df}}_{\mathrm{\τ}}---\left(6\right)$

Therefore, the expression formula of each term coefficient can be written as:

$\begin{array}{c}{a}_0=\sqrt{\frac{1}{B}}{A}_0\·TEC\ln \left(\frac{2f_0+B}{2f_0-B}\right)\\ a_1=\sqrt{\frac{3}{B}}{A}_0\·TEC(2-\frac{2f_0}{B}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\\ a_3=\sqrt{\frac{5}{B}}{A}_0\·TEC(-\frac{1}{2}\ln (\frac{2f_0+B}{2f_0-B})-\frac{6f_0}{B}+\frac{6f_0^2}{B^2}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\\ a_3=\sqrt{\frac{7}{B}}{A}_0\·TEC(-\frac{4}{3}+\frac{3f_0}{B}\ln (\frac{2f_0+B}{2f_0-B})+\frac{20f_0^2}{B^2}-\frac{20f_0^3}{B^3}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\end{array}---\left(7\right)$

Finally, each order optimum phase error expression launching to obtain based on Legnedre series can be written as:

$\begin{array}{c}{\mathrm{\Δ\φ}}_{0Le}\left(f_{\mathrm{\τ}}\right)=\frac{A_0\·TEC}{B}\ln \left(\frac{2f_0+B}{2f_0-B}\right)\\ {\mathrm{\Δ\φ}}_{1Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC\·f_{\mathrm{\τ}}(\frac{12}{B^2}-\frac{12f_0}{B^3}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\\ {\mathrm{\Δ\φ}}_{2Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC(\frac{30f_{\mathrm{\τ}}^2}{B^3}-\frac{5}{2B})\·(-\frac{1}{2}\ln (\frac{2f_0+B}{2f_0-B})-\frac{6f_0}{B}+\frac{6f_0^2}{B^2}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\\ {\mathrm{\Δ\φ}}_{3Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC(\frac{140f_{\mathrm{\τ}}^3}{B^4}-\frac{21f_{\mathrm{\τ}}}{B^2})\·(-\frac{4}{3}+\frac{3f_0}{B}\ln (\frac{2f_0+B}{2f_0-B})+\frac{20f_0^2}{B^2}-\frac{20f_0^3}{B^3}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\end{array}---\left(8\right)$

The simulation parameter of similar Fig. 2, shown in Fig. 3 for three phase error af_3LeSimulation result, now can see Go out owing to having orthogonality, Δ φ_3LeIn do not comprise linear segment, therefore three times, ionosphere phase error can correctly be described The impact that image is brought.In like manner, other order error is Optimal Error statement.

(2) determine ionosphere zero degree phase error on orientation to the impact of image quality, i.e. determine ionosphere zero degree phase place The orientation that error causes is to maximum secondary phase error, and then determines the first vertical total electron content value TEC₁；

When only considering zero degree phase error, broad band low frequency satellite-borne SAR echo expression formula can be written as:

$S_{r\_iono}(\mathrm{\τ},\mathrm{\η})=w_a\[\mathrm{\η}\]\·\sin c\[B\·(\mathrm{\τ}-\frac{2R\left(\mathrm{\η}\right)}{c})\]\·\exp (-{\mathrm{j\πK}}_a{\mathrm{\η}}^2)\·\exp \left({\mathrm{j\Δ\φ}}_{0Le}\right(\mathrm{\η}\left)\right)---\left(9\right)$

When the vertical TEC value in scene is invariable, now Δ φ_0LeAlong orientation to the change of slow time be due to often Oblique TEC value difference suffered by individual slow time echo causes, and tiltedly the change of TEC value is to be become by the spacing of radar with target Change causes, it may be assumed that

$TEC\left(\mathrm{\η}\right)={\mathrm{TEC}}_0\·\sqrt{R_0^2+{\left(V\mathrm{\η}\right)}^2}\≈{\mathrm{TEC}}_0+{\mathrm{TEC}}_0\frac{V^2{\mathrm{\η}}^2}{2R_0^2}---\left(10\right)$

Wherein TEC₀It is defined as TEC value during distance by radar target minimum oblique distance, TEC₀=TEC₁/ cos θ, θ are under radar Visual angle.In the result of above formula, the quadratic term about the slow time can cause orientation to pulse stretching, i.e. resolution ratio declines, and typically uses Big quadratic phase error describes the spreading characteristic after pulse pressure, and its expression formula can be written as:

${\mathrm{\Δ\Φ}}_{a2Le}=ln\left(\frac{2f_0+B}{2f_0-B}\right)\frac{A_0{\mathrm{TEC}}_0}{B}\·\frac{V^2{\mathrm{\η}}^2}{2R_0^2}{|}_{\mathrm{\η}=0}^{\mathrm{\η}=T_a/2}=\frac{20.14{\mathrm{\πL}}_s^2}{{\mathrm{cBR}}_0^2}ln\left(\frac{2f_0+B}{2f_0-B}\right){\mathrm{TEC}}_0---\left(11\right)$

Wherein L_s=T_aV is length of synthetic aperture.ΔΦ_a2LeAvailable adaptive iteration backoff algorithm is calculated, for Common sense in the field.When determining that orientation that ionosphere zero degree phase error causes, and then can be true after maximum secondary phase error Fixed first vertical total electron content value TEC₁。

(3) determine that one time, ionosphere phase error is adjusted the distance the impact to image quality, i.e. determine one time, ionosphere phase place The image distance that error causes is to translational movement, and then determines the second vertical total electron content value TEC₂；

Determine that image distance that one time, ionosphere phase error causes, to translational movement, and then determines that second vertical total electronics contains Value TEC₂, particularly as follows:

${\mathrm{\ΔL}}_{rLe}=40.28\·{\mathrm{TEC}}_2\·(\frac{12}{B^2}-\frac{12f_0}{B^3}ln(\frac{2f_0+B}{2f_0-B}\left)\right)---\left(12\right)$

Wherein, Δ L_rLeFor image distance to translational movement, can be obtained by image strong point coordinate, existing Taylor series expansion The translation expression formula obtained is unrelated with bandwidth, and as can be seen from the above equation, the image translation that linear term causes is to have with bandwidth Close.

(4) determine that ionosphere quadratic phase error is adjusted the distance the impact to image quality, i.e. determine that ionosphere causes away from Descriscent maximum secondary phase error, and then determine the 3rd vertical total electron content value TEC₃；

Quadratic phase error can cause distance expansion after image pulse pressure, causes resolution ratio to decline, its maximum caused Quadratic phase error expression formula is:

$\begin{array}{c}{\mathrm{\Δ\Φ}}_{r2Le}={\mathrm{\Δ\φ}}_{2Le}\left(f_{\mathrm{\τ}}\right){|}_{f_{\mathrm{\τ}}=0}^{f_{\mathrm{\τ}}/B/2}=\frac{1208.4{\mathrm{\πTEC}}_3}{cB}\\ \·\left(\frac{6f_0^2}{B^2}\ln \right(\frac{2f_0+B}{2f_0-B})-\frac{1}{2}\ln (\frac{2f_0+B}{2f_0-B})-\frac{6f_0}{B})\end{array}---\left(13\right)$

Determine that distance that ionosphere causes is to maximum secondary phase error ΔΦ_r2LeAfter, and then determine the 3rd vertical total electricity Sub-content value TEC₃.Wherein, ΔΦ_r2LeFor distance to maximum secondary phase error, its available adaptive iteration backoff algorithm meter Obtain, for common sense in the field.

(5) determine that three times, ionosphere phase error is adjusted the distance the impact to image quality, i.e. determine that ionosphere causes away from Maximum three phase errors in descriscent, and then determine the 4th vertical total electron content value TEC₄；

Three times phase error can cause distance pulse after pulse pressure asymmetrical distortion situation, this asymmetrical distortion occur The appearance of false target can be caused time serious, three the phase error forms derived based on Legendre, maximum three times can be obtained The expression formula of phase error:

$\begin{array}{c}{\mathrm{\Δ\Φ}}_{r3Le}={\mathrm{\Δ\φ}}_{3Le}\left(f_{\mathrm{\τ}}\right){|}_{f_{\mathrm{\τ}}=B/2}^{f_{\mathrm{\τ}}=-B/2}=\frac{2255.68{\mathrm{\πTEC}}_4}{cB}\\ \·(\frac{4}{3}-\frac{3f_0}{B}\ln (\frac{2f_0+B}{2f_0-B})-\frac{20f_0^2}{B^2}+\frac{20f_0^3}{B^3}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\end{array}---\left(14\right)$

Determine that distance that ionosphere causes is to maximum three phase error ΔΦs_r3LeAfter, and then determine the 4th vertical total electricity Sub-content value TEC₄.Wherein, ΔΦ_r3LeFor distance to maximum three phase errors.It is possible with adaptive iteration backoff algorithm It is calculated.

(6) according to four the TEC values determined in step (2)～(5), vertical total electron content mean value TEC is calculated_Averagely；

TEC_Averagely=(TEC₁+TEC₂+TEC₃+TEC₄)/4 (15)

(7) according to the TEC obtained in step (6)_Averagely, determine that the ionosphere zero degree in step (1) is to three phase errors；

The TEC that will obtain_AveragelyThe ionosphere zero degree that in mean value substitution step (1), Legnedre series are launched to obtain is to three times In phase error, obtain the phase error estimated.

(8) according to the ionosphere zero degree determined in step (7) to three phase errors, satellite-borne SAR image is compensated, Obtain removing the borne SAR image of ionosphere effect；

In order to preferably describe the appraisal procedure superiority that the present invention proposes, We conducted point target simulating, verifying, as Shown in Fig. 4, simulation parameter used is as shown in table 1, the peak sidelobe ratio (Peak Side-lobe Ratio:PSLR) of simulation result As shown in table 2 with integration secondary lobe ratio (Integrate Side-lobe Ratio:ISLR).The upper figure of Fig. 4 (a) is by true electricity Absciss layer phase error (i.e. Δ φ_iono) pulse pressure that obtains is as a result, it is possible to see now picture quality degradation, Fig. 4 (b) is right The two-dimensional simulation result answered.Shown in middle figure for utilizing Taylor series expansion to compensate by the image of ionosphere effect, Fig. 4 (c) Corresponding two-dimensional simulation result, after compensating as can be seen from Table 2, picture quality is still not up to requirement, illustrates now based on Taylor's exhibition The approximation opened can not react true phase error situation well.It should be noted that this difference can not be by adding Higher order time error (such as four times, five times, six inferior) is improved.Shown in figure below for utilize Legnedre series launch compensate By the image of ionosphere effect, Fig. 4 (d) is corresponding two-dimensional simulation result, and the image after now compensating has returned to ideal Situation, illustrates that each order error launched based on Legnedre series can be good at reacting true ionospheric error situation.

Table 2 emulating image quality assessment result

Image evaluation	PSLR(dB)	ISLR(dB)
			Fig. 4 (c)	-8.46	-8.36
Fig. 4 (d)	-13.55	-10.74

The content not being described in detail in description of the invention belongs to the known technology of those skilled in the art.

Claims (7)

1. a broad band low frequency Space-borne SAR Imaging ionosphere phase error compensation method, it is characterised in that comprise the steps:

(1) obtain the broad band low frequency satellite-borne SAR echo-signal under ionosphere effect, set up base for this satellite-borne SAR echo-signal In Legendre's orthogonal series launch ionosphere zero degree to three phase errors；

(2) determine ionosphere zero degree phase error on orientation to the impact of image quality, i.e. determine ionosphere zero degree phase error The orientation caused is to maximum secondary phase error, and then determines the first vertical total electron content value TEC₁；

(3) determine that one time, ionosphere phase error is adjusted the distance the impact to image quality, i.e. determine one time, ionosphere phase error The image distance caused is to translational movement, and then determines the second vertical total electron content value TEC₂；

(4) determine that ionosphere quadratic phase error is adjusted the distance the impact to image quality, i.e. determine distance that ionosphere causes to Maximum secondary phase error, and then determine the 3rd vertical total electron content value TEC₃；

(5) determine that three times, ionosphere phase error is adjusted the distance the impact to image quality, i.e. determine distance that ionosphere causes to Maximum three phase errors, and then determine the 4th vertical total electron content value TEC₄；

(6) according to four the TEC values determined in step (2)～(5), vertical total electron content mean value TEC is calculated_Averagely；

(7) according to the TEC obtained in step (6)_Averagely, determine that the ionosphere zero degree in step (1) is to three phase errors；(concrete Embodiment illustrates TEC_AveragelySubstitute in step 1 formula)

(8) according to the ionosphere zero degree determined in step (7) to three phase errors, satellite-borne SAR image is compensated, obtains Remove the borne SAR image of ionosphere effect.

A kind of broad band low frequency Space-borne SAR Imaging ionosphere the most according to claim 1 phase error compensation method, its feature It is: in described step (1), the phase error of zero degree to three times is followed successively by Δ φ_0Le(f_τ)、Δφ_1Le(f_τ)、Δφ_2Le(f_τ)、 Δφ_3Le(f_τ), obtain especially by equation below:

${\mathrm{\Δ\φ}}_{0Le}\left(f_{\mathrm{\τ}}\right)=\frac{A_0\·TEC}{B}ln\left(\frac{2f_0+B}{2f_0-B}\right)$

${\mathrm{\Δ\φ}}_{1Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC\·f_{\mathrm{\τ}}(\frac{12}{B^2}-\frac{12f_0}{B^3}ln(\frac{2f_0+B}{2f_0-B}\left)\right)$

$\begin{array}{c}{\mathrm{\Δ\φ}}_{2Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC(\frac{30f_{\mathrm{\τ}}^2}{B^3}-\frac{5}{2B})\\ \·(-\frac{1}{2}\ln (\frac{2f_0+B}{2f_0-B})-\frac{6f_0}{B}+\frac{6f_0^2}{B^2}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\end{array}$

$\begin{array}{c}{\mathrm{\Δ\φ}}_{3Le}\left(f_{\mathrm{\τ}}\right)=A_0\·TEC(\frac{140f_{\mathrm{\τ}}^3}{B^4}-\frac{21f_{\mathrm{\τ}}}{B^2})\\ \·(-\frac{4}{3}+\frac{3f_0}{B}\ln (\frac{2f_0+B}{2f_0-B})+\frac{20f_0^2}{B^2}-\frac{20f_0^3}{B^3}\ln (\frac{2f_0+B}{2f_0-B}\left)\right)\end{array}$

Wherein, f₀For carrier frequency, B is transmitted bandwidth, A₀For constant, and A₀=40.28；f_τ∈ [-B/2, B/2] is SAR signal spectrum Scope, TEC is vertical total electron content value.

A kind of broad band low frequency Space-borne SAR Imaging ionosphere the most according to claim 1 phase error compensation method, its feature Be: described step (2) determines orientation that ionosphere zero degree phase error causes to maximum secondary phase error, and then really Fixed first vertical total electron content value TEC₁, particularly as follows:

Wherein L_sFor length of synthetic aperture, TEC₀Be defined as radar away from TEC value when target minimum oblique distance, TEC₀=TEC₁/ cos θ, θ are radar downwards angle of visibility, f₀For carrier frequency, B is transmitted bandwidth, and c is The light velocity, ΔΦ_a2LeFor orientation to maximum secondary phase error.

A kind of broad band low frequency Space-borne SAR Imaging ionosphere the most according to claim 1 phase error compensation method, its feature It is: described step (3) determines that image distance that one time, ionosphere phase error causes, to translational movement, and then determines that second is vertical Total electron content value TEC₂, particularly as follows:

Wherein, Δ L_rLeFor image distance to translation Amount.

A kind of broad band low frequency Space-borne SAR Imaging ionosphere the most according to claim 1 phase error compensation method, its feature It is: described step (4) determines that distance that ionosphere causes, to maximum secondary phase error, and then determines the 3rd vertical total electronics Content value TEC₃, particularly as follows:

Wherein, Δ Φ_r2LeFor distance to maximum secondary phase error.

A kind of broad band low frequency Space-borne SAR Imaging ionosphere the most according to claim 1 phase error compensation method, its feature It is: described step (5) determines that distance that ionosphere causes, to maximum three phase errors, and then determines the 4th vertical total electronics Content value TEC₄, particularly as follows:

${\mathrm{\Δ\Φ}}_{r3Le}=\frac{2255.68{\mathrm{\πTEC}}_4}{cB}\·(\frac{4}{3}-\frac{3f_0}{B}\ln (\frac{2f_0+B}{2f_0-B})-\frac{20{f_0}^2}{B^2}+\frac{20{f_0}^3}{B^3}\ln (\frac{2f_0+B}{2f_0-B}\left)\right),$

Wherein, ΔΦ_r3LeFor distance to maximum three phase errors.

A kind of broad band low frequency Space-borne SAR Imaging ionosphere the most according to claim 1 phase error compensation method, its feature It is: the TEC in step (6)_Averagely=(TEC₁+TEC₂+TEC₃+TEC₄)/4。