CN103792535A - Method for measuring TEC value of ionized layer by utilizing SAR satellite - Google Patents

Abstract

The invention discloses a method for measuring a TEC value of an ionized layer by utilizing an SAR satellite. After satellite-borne SAR transmission pulse signals penetrate through the ionized layer, the phase of the satellite-borne SAR transmission pulse signals contains complete TEC information of the ionized layer on the propagation path. By means of the method, multiple sub-bands are selected from the SAR signals with a certain band width, so that a freedom degree needed by phase ambiguity resolution is provided. Through the optimized design of parameters of the sub-bands and other technical means, the influence on phase position ambiguity resolution processing from an electromagnetic wave propagation distance phase is eliminated while the estimation accuracy of the TEC value is considered. Finally, a phase ambiguity resolution equation is built, and high-accuracy estimation of the TEC value of the ionized layer is achieved. The estimated TEC value of the ionized layer is utilized to supplement a satellite-borne SAR echo phase, and the satellite-borne SAR imaging quality and interferometry accuracy can be effectively improved.

Description

A kind of method of utilizing SAR satellite to measure ionized layer TEC value

Technical field

The present invention relates to a kind of method of measuring ionized layer TEC value, relate in particular to a kind of SAR of utilization satellite and realize the method for high-acruracy survey ionized layer TEC value, belong to geostationary orbit SAR system development field.

Background technology

Satellite-borne SAR transmitting and reception electromagnetic wave are passing through behind ionosphere, can there is the propagation effects such as group delay, phase drift, dispersion and faraday's polarized rotation, thereby the SAR image quality to low-frequency range impacts, for geostationary orbit SAR (GEO SAR), because its synthetic aperture time is long, the impact that imaging causes on GEO SAR of ionospheric change in time and space is further serious.At present domestic and international many research structures (as U.S. NASA JPL, Cranfield university of Britain, the Chinese Academy of Space Technology, Chinese Academy of Sciences electron institute, Beijing Institute of Technology) have been carried out the correlative study of GEO SAR.Point out the U.S. jet propulsion laboratory (JPL) that is subject to U.S. NASA subsidy to carry out GEO SAR research: accurately understanding atmospheric disturbance is the key issue that obtains meaningful conclusion on the impact of SAR signal.Britain's Cranfield (Cranfield) university has carried out passive double-basis GEO SAR systematic study, and points out that the impact of atmosphere is most important to GEO SAR imaging.

For ionosphere, the main method of GEO SAR effect correction is comprised both at home and abroad at present: phase gradient self-focusing (PGA) method from orientation to processing, weighted least require method and Minimum entropy method etc. based on; Look disposal route based on distance to the adaptive matched filter method of processing and distance more; Utilize existing measurement means to carry out the real-time method of measuring etc. to ionized layer TEC value.Can compensate ionosphere for orientation to the PGA method of processing and change the impact on azimuth focus, but it need to exist an isolated spy to show point on the one hand in image, the method can only be estimated the time dependent high-order term in ionosphere on the other hand, be unable to estimate ionized layer TEC value change constant term and once item, even if therefore realize the azimuth focus of image, but still cannot solve for positioning error and the follow-up interferometry error of image.Similar with PGA method, can compensate to a certain extent orientation to defocusing problem for weighted least require method and Minimum entropy method, but all be difficult to accurately estimate TEC value, thereby cannot carry out accurate phase compensation.The bandwidth simultaneously transmitting due to SAR is conventionally relatively little compared with its carrier frequency, for distance to adaptive matched filter method estimate that the precision of ionized layer TEC value is very low, be difficult to meet the requirement of high imaging quality.For the many vision methods of distance, it is by being divided into two parts by frequency spectrum, after imaging, estimate respectively the delay inequality between the two, and then estimation ionized layer TEC value, the method is subject to the restriction of SAR signal bandwidth equally, time delay estimation precision is lower, and (take carrier frequency as 1GHz, bandwidth is that 40M is example, and the delay inequality that 1TECU causes only has 10 ^-10second magnitude), be therefore difficult to accurately estimate the size of ionized layer TEC value.Due to ionosphere on the impact of Electromagnetic Wave Propagation on the one hand with space electronic density and distribute relevant, on the other hand with electromagnetic wave propagation path-dependent.And SAR transmitting is constantly to change with space with the pulse signal receiving in time, be difficult to guarantee identical with path and the time of SAR transmitting and receiving signal for ionospheric measurement, there is certain deviation in the TEC value of therefore measuring, thereby can not the impact of fine compensation ionosphere on SAR image quality.

All at the early-stage for the research of GEO SAR both at home and abroad at present, be that GEO SAR studies one of the most key and problem that must solve and overcome ionosphere for the impact of GEO SAR imaging.This problem has become at present the hot issue of SAR area research both at home and abroad.

Summary of the invention

The technical matters that the present invention solves is: overcome the deficiencies in the prior art, provide a kind of SAR of utilization satellite to measure the method for ionized layer TEC value, utilize satellite-borne SAR self signal to carry the feature of complete ionosphere information, extract the phase information of multiple selected sub-bands, estimate ionized layer TEC value by technological means such as multifrequency ambiguity solutions, thereby the impact of compensation ionosphere on Space-borne SAR Imaging and interferometry, improves image quality and interferometry precision.

Technical scheme of the present invention is: a kind of SAR of utilization satellite is measured the method for ionized layer TEC value, comprises the steps:

(1) at ground configuration SAR signal receiver for receiving the pulse signal of SAR satellite launch;

(2) the SAR satellite pulse signal receiving from step (1), choose three sub-frequency bands signals, be respectively sub-band 1, sub-band 2 and sub-band 3, sub-band 1, sub-band 2 are respectively f with the carrier frequency of sub-band 3 three sub-frequency bands signals ₁, f ₂, f ₃, the carrier frequency of three sub-frequency bands meets f ₃>f ₂>f ₁, and f ₂-f ₁=f ₃-f ₂=Δ f;

(3) frequency spectrum of the three sub-frequency bands signals of step (2) being chosen is moved respectively, make its frequency spectrum centre frequency all be positioned at zero-frequency, then utilize respectively matched filtering to carry out process of pulse-compression to three sub-frequency bands signals, obtain the phase place Φ at three sub-frequency bands signal peak value point places _n(n=1,2,3);

(4) the phase place Φ at the three sub-frequency bands signal peak value point places that obtain according to step (3) _n(n=1,2,3) calculate the interferometric phase of sub-band 1 and sub-band 2 signal peak value point, and computing formula is Φ ₁₂=angle[exp (j Φ ₁) × exp (j Φ ₂)]; The interferometric phase that calculates sub-band 2 and sub-band 3 signal peak value point, computing formula is Φ ₂₃=angle[exp (j Φ ₂) × exp (j Φ ₃)]; Wherein define angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

(5) the interferometric phase Φ that utilizes step (4) to obtain ₁₂and Φ ₂₃solve ionized layer TEC value, computing formula is as follows:

$\mathrm{TEC}=\frac{((f_2-f_1){\mathrm{\Φ}}_{23}-(f_3-f_2){\mathrm{\Φ}}_{12})c}{2\mathrm{\π}40.3((f_2-f_1)(\frac{1}{f_2}-\frac{1}{f_3})-(f_3-f_2)(\frac{1}{f_1}-\frac{1}{f_2}))}$

Wherein, c is the light velocity.

Utilize SAR satellite to measure a method for ionized layer TEC value, it is characterized in that comprising the steps:

(1) at ground configuration SAR signal receiver for receiving the pulse signal of SAR satellite launch;

(2) the SAR satellite pulse signal receiving from step (1), choose three sub-frequency bands signals, be respectively sub-band 1, sub-band 2 and sub-band 3, sub-band 1, sub-band 2 are respectively f with the carrier frequency of sub-band 3 three sub-frequency bands signals ₁, f ₂, f ₃, the carrier frequency of three sub-frequency bands meets f ₃>f ₂>f ₁, f ₂-f ₁≠ f ₃-f ₂;

(3) frequency spectrum of the three sub-frequency bands signals of step (2) being chosen is moved respectively, make its frequency spectrum centre frequency all be positioned at zero-frequency, then utilize respectively matched filtering to carry out process of pulse-compression to three sub-frequency bands signals, obtain the phase place Φ at three sub-frequency bands signal peak value point places _n(n=1,2,3);

(4) utilize relevant ephemeris information to obtain the rough estimate evaluation of the true propagation distance R of electromagnetic wave

utilize

the phase place Φ of the three sub-frequency bands signal peak value point that respectively step (3) obtained _n(n=1,2,3) compensate, the phase place of three sub-frequency bands signals after can being compensated:

${\mathrm{\Φ}}_n^{\′}=\mathrm{angle}\left[\exp \left(j({\mathrm{\Φ}}_n+\frac{2\mathrm{\π}\hat{R}{f}_n}{c})\right)\right],n=\mathrm{1,2,3};$

Wherein, definition angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

(5) whether the carrier frequency that judges three sub-frequency bands meets following constraint condition:

$\left\{\begin{array}{c}-\mathrm{\&pi;}<{\mathrm{\&Phi;}}_2^{\&prime;}+2\mathrm{\&pi;}\frac{\mathrm{\&Delta;R}}{c}(f_2-f_1)<\mathrm{\&pi;}\\ -\mathrm{\&pi;}<{\mathrm{\&Phi;}}_2^{\&prime;}+2\mathrm{\&pi;}\frac{\mathrm{\&Delta;R}}{c}(f_2-f_3)<\mathrm{\&pi;}\end{array}\right.$

If satisfied enter (6), otherwise re-execute step (2)-(5), wherein Δ R is the true propagation distance R of electromagnetic wave and its rough estimate evaluation

between evaluated error,

c is the light velocity;

(6) the phase place Φ ' at the three sub-frequency bands signal peak value point places that obtain according to step (4) _n(n=1,2,3) calculate the interferometric phase of sub-band 1 and sub-band 2 signal peak value point, and computing formula is Φ ₁₂=angle[exp (j Φ ' ₁) × exp (j Φ ' ₂)]; The interferometric phase that calculates sub-band 2 and sub-band 3 signal peak value point, computing formula is Φ ₂₃=angle[exp (j Φ ' ₂) × exp (j Φ ' ₃)]; Wherein define angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

(7) the interferometric phase Φ that utilizes step (6) to obtain ₁₂and Φ ₂₃solve ionized layer TEC value, computing formula is as follows:

$\mathrm{TEC}=\frac{((f_2-f_1){\mathrm{\&Phi;}}_{23}-(f_3-f_2){\mathrm{\&Phi;}}_{12})c}{2\mathrm{\&pi;}40.3((f_2-f_1)(\frac{1}{f_2}-\frac{1}{f_3})-(f_3-f_2)(\frac{1}{f_1}-\frac{1}{f_2}))}$

Wherein, c is the light velocity.

The present invention compared with prior art has following beneficial effect:

(1) the present invention proposes two kinds of solutions that overcome apart from phase effect, can take into account the estimated accuracy of TEC value, has effectively eliminated again the impact apart from phase place;

(2) the present invention, by the phase interference between multiple sub-band signals, has solved phase fuzzy problem, thereby can estimate accurately ionized layer TEC value;

(3) the measured ionized layer TEC value of the present invention is identical with the exomonental travel path of SAR and time, thereby can accurately compensate SAR phase of echo error, improves image quality and interferometry precision.

Accompanying drawing explanation

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

Fig. 2 is the processing flow chart of the inventive method scheme 2.

Embodiment

Satellite-borne SAR transponder pulse signal passes through behind ionosphere, comprises ionized layer TEC information complete on travel path in its phase place.The present invention chooses some sub-bands from have the SAR signal of certain bandwidth, to provide Used for Unwrapping Phase Ambiguity required degree of freedom.By technological means such as optimal design sub-band parameters, in taking into account TEC value estimated accuracy, eliminate the impact of electromagnetic wave propagation distance phase place on Used for Unwrapping Phase Ambiguity processing.Finally build Used for Unwrapping Phase Ambiguity equation, final realization estimated the high precision of ionized layer TEC value.Utilize estimated ionized layer TEC value to compensate satellite-borne SAR phase of echo, can effectively improve Space-borne SAR Imaging quality and interferometry precision.The present invention utilizes phase information to realize high-precision TEC value completely and measures, and as depicted in figs. 1 and 2, embodiment is as follows for realization flow figure:

The first step: at ground configuration SAR signal receiver, directly receive the pulse signal of SAR satellite launch, the impact of TEC value being estimated to eliminate ground scatter point.

Second step: choose three sub-frequency bands from the SAR echoed signal receiving.

Because the phase place that receives SAR signal is not only subject to ionosphere effect, and be subject to the impact of propagation distance R.Therefore choosing in sub-band process, overcome the impact apart from phase place by the method for choose reasonable sub-band centre frequency.Provide two seed mid-band frequency selection schemes below:

Scheme 1: the centre frequency of supposing three selected sub-frequency bands is respectively f ₁, f ₂, f ₃, and f ₃>f ₂>f ₁, while choosing three sub-frequency bands signals, between centre frequency, need to meet constraint condition and be: f ₂-f ₁=f ₃-f ₂=Δ f.

Scheme 2: while not selecting the constraint condition of scheme 1, i.e. f ₃>f ₂>f ₁, f ₂-f ₁≠ f ₃-f ₂time, can adopt following methods to eliminate the impact apart from phase place:

(1) utilize relevant ephemeris information to obtain the rough estimate evaluation of the true propagation distance R of electromagnetic wave

evaluated error $\mathrm{\&Delta;R}=R-\hat{R}.$

(2) frequency spectrum of the three sub-frequency bands signals of choosing is moved respectively, made its frequency spectrum centre frequency all be positioned at zero-frequency, then utilize respectively matched filtering to realize process of pulse-compression, can obtain the phase place Φ at three sub-frequency bands signal peak value point places _n(n=1,2,3), utilize

respectively the phase place of three sub-frequency bands signal peak value point is compensated, the distance phase place at compensated peak point place is the phase place of three sub-frequency bands signals after can being compensated:

${\mathrm{\&Phi;}}_n^{\&prime;}=\mathrm{angle}\left[\exp \left(j({\mathrm{\&Phi;}}_n+\frac{2\mathrm{\&pi;}\hat{R}{f}_n}{c})\right)\right],n=\mathrm{1,2,3}$

Wherein, definition angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

now the centre frequency of sub-band need to meet:

$\left\{\begin{array}{c}-\mathrm{\&pi;}<{\mathrm{\&Phi;}}_2^{\&prime;}+2\mathrm{\&pi;}\frac{\mathrm{\&Delta;R}}{c}(f_2-f_1)<\mathrm{\&pi;}\\ -\mathrm{\&pi;}<{\mathrm{\&Phi;}}_2^{\&prime;}+2\mathrm{\&pi;}\frac{\mathrm{\&Delta;R}}{c}(f_2-f_3)<\mathrm{\&pi;}\end{array}\right.$

Therefore this scheme needs constantly to adjust selected f ₁, f ₂, f ₃size, until meet above-mentioned constraint condition.Wherein Δ R is the true propagation distance R of electromagnetic wave and its rough estimate evaluation

between evaluated error, $\mathrm{\&Delta;R}=R-\hat{R}$ C is the light velocity.

The 3rd step: calculate the interferometric phase between sub-band signal.

(1) if adopt the constraint condition of scheme 1 in second step, the frequency spectrum of the three sub-frequency bands signals of choosing is moved respectively, make its frequency spectrum centre frequency all be positioned at zero-frequency, then utilize respectively matched filtering to realize process of pulse-compression, can obtain the phase place Φ at three sub-frequency bands signal peak value point places _n(n=1,2,3), then calculate the interferometric phase of sub-band 1 and sub-band 2 signal peak value point: Φ ₁₂=angle[exp (j Φ ₁) × exp (j Φ ₂)], the interferometric phase of sub-band 2 and sub-band 3 signal peak value point: Φ ₂₃=angle[exp (j Φ ₂) × exp (j Φ ₃)], wherein define angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

for the constraint condition in scheme 1, interferometric phase Φ ₁₂, Φ ₂₃meet respectively:

$\left\{\begin{array}{c}{\mathrm{\&Phi;}}_{12}+2\mathrm{M\&pi;}=2\mathrm{\&pi;}\frac{40.3\mathrm{TEC}}{c}(\frac{1}{f_2-\mathrm{\&Delta;f}}-\frac{1}{f_2})+\frac{2\mathrm{\&pi;R\&Delta;f}}{c}\\ {\mathrm{\&Phi;}}_{23}+2\mathrm{M\&pi;}=2\mathrm{\&pi;}\frac{40.3\mathrm{TEC}}{c}(\frac{1}{f_2}-\frac{1}{f_2+\mathrm{\&Delta;f}})+\frac{2\mathrm{\&pi;R\&Delta;f}}{c}\end{array}\right.---\left(1\right)$

Wherein M is an integer, represents fuzzy number.

(2) if adopt the constraint condition of scheme 2 in second step, through selected three sub-frequency bands signal spectrum centers being moved to zero-frequency, matched filtering and apart from after phase compensation, according to the Φ ' obtaining _n(n=1,2,3) calculate the interferometric phase of sub-band 1 and sub-band 2 signal peak value point: Φ ₁₂=angle[exp (j Φ ' ₁) × exp (j Φ ' ₂)], the interferometric phase of sub-band 2 and sub-band 3 signal peak value point: Φ ₂₃=angle[exp (j Φ ' ₂) × exp (j Φ ' ₃)], wherein define angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

for the constraint condition in scheme 2, interferometric phase Φ ₁₂, Φ ₂₃meet respectively:

$\left\{\begin{array}{c}{\mathrm{\&Phi;}}_{12}=2\mathrm{\&pi;}\frac{40.3\mathrm{TEC}}{c}(\frac{1}{f_1}-\frac{1}{f_2})-\frac{2\mathrm{\&pi;\&Delta;R}(f_1-f_2)}{c}\\ {\mathrm{\&Phi;}}_{23}=2\mathrm{\&pi;}\frac{40.3\mathrm{TEC}}{c}(\frac{1}{f_2}-\frac{1}{f_3})-\frac{2\mathrm{\&pi;\&Delta;R}(f_2-f_3)}{c}\end{array}\right.---\left(2\right)$

The 4th step: formula that can derived for solving ionized layer TEC value according to formula (1) or (2), as follows:

$\mathrm{TEC}=\frac{((f_2-f_1){\mathrm{\&Phi;}}_{23}-(f_3-f_2){\mathrm{\&Phi;}}_{12})c}{2\mathrm{\&pi;}40.3((f_2-f_1)(\frac{1}{f_2}-\frac{1}{f_3})-(f_3-f_2)(\frac{1}{f_1}-\frac{1}{f_2}))}$

The interferometric phase Φ that utilizes the 3rd step to obtain ₁₂and Φ ₂₃try to achieve ionized layer TEC value according to above formula, wherein c is the light velocity.

Because the interferometric phase calculated value between sub-band has certain error, so according to formula $\mathrm{TEC}=\frac{((f_2-f_1){\mathrm{\&Phi;}}_{23}-(f_3-f_2){\mathrm{\&Phi;}}_{12})c}{2\mathrm{\&pi;}40.3((f_2-f_1)(\frac{1}{f_2}-\frac{1}{f_3})-(f_3-f_2)(\frac{1}{f_1}-\frac{1}{f_2}))}$ The reality calculating is the estimated value of ionized layer TEC

but the two schemes that the present invention proposes has overcome the estimated accuracy that can take into account TEC value apart from the impact of phase place, effectively eliminate again the impact apart from phase place, by the phase interference between multiple sub-band signals, solve phase fuzzy problem, although interferometric phase has certain error, still can estimate accurately ionized layer TEC value.

Reach under the prerequisite of different guaranteeing between carrier frequency, the frequency spectrum of sub-band signal can be overlapping to increase the bandwidth of sub-band, is convenient to improve follow-up every sub-frequency bands is carried out to matched filtering output Y-PSNR after treatment.

The present invention not detailed description is known to the skilled person technology.

Claims (2)

1. utilize SAR satellite to measure a method for ionized layer TEC value, it is characterized in that comprising the steps:

(1) at ground configuration SAR signal receiver for receiving the pulse signal of SAR satellite launch;

(2) the SAR satellite pulse signal receiving from step (1), choose three sub-frequency bands signals, be respectively sub-band 1, sub-band 2 and sub-band 3, sub-band 1, sub-band 2 are respectively f with the carrier frequency of sub-band 3 three sub-frequency bands signals ₁, f ₂, f ₃, the carrier frequency of three sub-frequency bands meets f ₃>f ₂>f ₁, and f ₂-f ₁=f ₃-f ₂=Δ f;

(3) frequency spectrum of the three sub-frequency bands signals of step (2) being chosen is moved respectively, make its frequency spectrum centre frequency all be positioned at zero-frequency, then utilize respectively matched filtering to carry out process of pulse-compression to three sub-frequency bands signals, obtain the phase place Φ at three sub-frequency bands signal peak value point places _n(n=1,2,3);

(4) the phase place Φ at the three sub-frequency bands signal peak value point places that obtain according to step (3) _n(n=1,2,3) calculate the interferometric phase of sub-band 1 and sub-band 2 signal peak value point, and computing formula is Φ ₁₂=angle[exp (j Φ ₁) × exp (j Φ ₂)]; The interferometric phase that calculates sub-band 2 and sub-band 3 signal peak value point, computing formula is Φ ₂₃=angle[exp (j Φ ₂) × exp (j Φ ₃)]; Wherein define angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

(5) the interferometric phase Φ that utilizes step (4) to obtain ₁₂and Φ ₂₃solve ionized layer TEC value, computing formula is as follows:

$\mathrm{TEC}=\frac{((f_2-f_1){\mathrm{\&Phi;}}_{23}-(f_3-f_2){\mathrm{\&Phi;}}_{12})c}{2\mathrm{\&pi;}40.3((f_2-f_1)(\frac{1}{f_2}-\frac{1}{f_3})-(f_3-f_2)(\frac{1}{f_1}-\frac{1}{f_2}))}$

Wherein, c is the light velocity.

2. utilize SAR satellite to measure a method for ionized layer TEC value, it is characterized in that comprising the steps:

(1) at ground configuration SAR signal receiver for receiving the pulse signal of SAR satellite launch;

(2) the SAR satellite pulse signal receiving from step (1), choose three sub-frequency bands signals, be respectively sub-band 1, sub-band 2 and sub-band 3, sub-band 1, sub-band 2 are respectively f with the carrier frequency of sub-band 3 three sub-frequency bands signals ₁, f ₂, f ₃, the carrier frequency of three sub-frequency bands meets f ₃>f ₂>f ₁, f ₂-f ₁≠ f ₃-f ₂;

(3) frequency spectrum of the three sub-frequency bands signals of step (2) being chosen is moved respectively, make its frequency spectrum centre frequency all be positioned at zero-frequency, then utilize respectively matched filtering to carry out process of pulse-compression to three sub-frequency bands signals, obtain the phase place Φ at three sub-frequency bands signal peak value point places _n(n=1,2,3);

(4) utilize relevant ephemeris information to obtain the rough estimate evaluation of the true propagation distance R of electromagnetic wave

utilize

the phase place Φ of the three sub-frequency bands signal peak value point that respectively step (3) obtained _n(n=1,2,3) compensate, the phase place of three sub-frequency bands signals after can being compensated:

${\mathrm{\&Phi;}}_n^{\&prime;}=\mathrm{angle}\left[\exp \left(j({\mathrm{\&Phi;}}_n+\frac{2\mathrm{\&pi;}\hat{R}{f}_n}{c})\right)\right],n=\mathrm{1,2,3};$

Wherein, definition angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

(5) whether the carrier frequency that judges three sub-frequency bands meets following constraint condition:

$\left\{\begin{array}{c}-\mathrm{\&pi;}<{\mathrm{\&Phi;}}_2^{\&prime;}+2\mathrm{\&pi;}\frac{\mathrm{\&Delta;R}}{c}(f_2-f_1)<\mathrm{\&pi;}\\ -\mathrm{\&pi;}<{\mathrm{\&Phi;}}_2^{\&prime;}+2\mathrm{\&pi;}\frac{\mathrm{\&Delta;R}}{c}(f_2-f_3)<\mathrm{\&pi;}\end{array}\right.$

If satisfied enter (6), otherwise re-execute step (2)-(5), wherein Δ R is the true propagation distance R of electromagnetic wave and its rough estimate evaluation

between evaluated error, c is the light velocity;

(6) the phase place Φ ' at the three sub-frequency bands signal peak value point places that obtain according to step (4) _n(n=1,2,3) calculate the interferometric phase of sub-band 1 and sub-band 2 signal peak value point, and computing formula is Φ ₁₂=angle[exp (j Φ ' ₁) × exp (j Φ ' ₂)]; The interferometric phase that calculates sub-band 2 and sub-band 3 signal peak value point, computing formula is Φ ₂₃=angle[exp (j Φ ' ₂) × exp (j Φ ' ₃)]; Wherein define angle[exp (j (α+2k π))]=α, α ∈ [π, π], k is integer,

(7) the interferometric phase Φ that utilizes step (6) to obtain ₁₂and Φ ₂₃solve ionized layer TEC value, computing formula is as follows:

$\mathrm{TEC}=\frac{((f_2-f_1){\mathrm{\&Phi;}}_{23}-(f_3-f_2){\mathrm{\&Phi;}}_{12})c}{2\mathrm{\&pi;}40.3((f_2-f_1)(\frac{1}{f_2}-\frac{1}{f_3})-(f_3-f_2)(\frac{1}{f_1}-\frac{1}{f_2}))}$

Wherein, c is the light velocity.

Images