CN102262222A - Inverse synthetic aperture radar range alignment method based on adaptive error elimination - Google Patents

Abstract

The invention discloses an inverse synthetic aperture radar envelope alignment method based on adaptive error elimination. It mainly solves the problems of large amount of computation and low alignment accuracy in the prior art, and its realization process is as follows: the estimated value of the adjacent walking distance and the estimated value of the absolute walking distance are obtained by the adjacent correlation method; the least squares fitting of the estimated value of the absolute walking distance Calculate the first-order difference to obtain the fitting value of the adjacent walking amount, and obtain the fitting error of the adjacent walking amount from the difference between the fitting value and the estimated value, and calculate its standard deviation, and define a fitting error greater than 3 times the standard deviation as a sudden jump error, and replace the corresponding estimated value of the adjacent walking distance with the fitted value, and accumulate it to obtain a new estimated value of the absolute walking distance. A least squares fit of the estimated values completes the envelope alignment. The invention has the advantages of small calculation amount and high precision of envelope alignment, and is used for estimating and compensating the translation component of the inverse synthetic aperture radar echo under the condition of low signal-to-noise ratio.

Description

Inverse synthetic aperture radar (ISAR) envelope alignment method based on the adaptive error rejecting

Technical field

The invention belongs to the radar imagery technical field, relating to the radar return envelope handles, the inverse synthetic aperture radar (ISAR) envelope alignment method that adopts least square polynomial fit under specifically a kind of low signal-to-noise ratio condition and reject based on adaptive error is used under the low signal-to-noise ratio condition estimating with degree of precision and the translation component of each time of compensation inverse synthetic aperture radar (ISAR) echo.

Background technology

Inverse synthetic aperture radar (ISAR) ISAR utilizes the relative motion of radar and target to obtain the orientation to high resolving power, be radar imagery give priority to one of direction, in strategic defensive, anti-satellite, tactical weapon and radar astronomy, have important use to be worth.Motion compensation is the committed step in the ISAR imaging technique, is divided into envelope alignment and first phase and proofreaies and correct for two steps.If the precision of envelope alignment is relatively poor, follow-up first phase will be proofreaied and correct be difficult to obtain gratifying result.Because traditional first phase bearing calibration, for example the performance of strong scattering point method, Doppler center tracing and phase gradient self-focusing method is subjected to the influence of envelope alignment precision very big, all require the precision of envelope alignment to reach in 0.5～1 resolution element, otherwise can have a strong impact on the performance that first phase is proofreaied and correct.Yet, for the low signal-to-noise ratio situation, often there is the kick error, accurate envelope alignment can have difficulties.Therefore, study the envelope alignment method that the kick error is had strong robustness, have important practical value.

At present, the sane envelope alignment method of kick error is mainly contained following two classes:

1. based on the envelope alignment method of echo envelope correlativity.In the article " A novel range alignment algorithm for real time ISAR imaging " that people such as M Liu deliver in signal Processing international conference in 2007, the relevant envelope alignment algorithm of a kind of improved accumulation is proposed, utilize the weighted sum of the echo that alignd to carry out envelope alignment for reference, can suppress the propagation of kick error, estimated accuracy is lower but single is walked momentum; In the article that people such as Xing Mengdao deliver " realizing the envelope alignment of ISAR imaging with the total optimization criterion ", propose the notion of mean distance picture on the electronic letters, vol of calendar year 2001, and utilize the mean distance picture to carry out envelope alignment for reference.Said method is all underused the kinetic characteristic of target, and is lower in low signal-to-noise ratio condition lower envelope alignment accuracy.

2. the envelope alignment method of based target kinetic characteristic.In fact, target has the easy motion characteristic usually in short viewing duration, adopts the fitting of a polynomial echo envelope to walk momentum and can effectively improve alignment accuracy.In the article that people such as Wang Junfeng deliver on IEEE Trans.on AES in 2007 " Improved Global Range Alignment for ISAR ", a kind of whole envelope alignment (Global Range Alignment is proposed, GRA) algorithm, definitely walk momentum owing to adopt the polynomial repressentation echo envelope, and by weigh alignd echo envelope and sharpening degree iteration correction multinomial coefficient, can under the low signal-to-noise ratio condition, obtain envelope alignment result preferably, but this method needs repeatedly iteration correction and optimizing among a small circle, and operand is big; In the article that people such as S.B.Peng deliver on IET Radar Sonar Navigation in 2011 " Parametric inverse synthetic aperture radar manoeuvring target motion compensation based on particle swarm optimizer ", adopt particle cluster algorithm (Particle Swarm Optimization, PSO) find the solution the polynomial fitting coefficient, avoid parameter estimation to be absorbed in local optimum, but need local and whole optimizing, the algorithm complex height.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned prior art, a kind of inverse synthetic aperture radar (ISAR) envelope alignment method of rejecting based on adaptive error is provided, reducing calculated amount, improve under the low signal-to-noise ratio condition estimation and compensation precision to each time of inverse synthetic aperture radar (ISAR) echo translation component.

Realize the object of the invention technical scheme, comprise the steps:

(1) calculates successively to walk momentum between adjacent radar return and get adjacent echo and walk momentum estimated value δ with adjacent relevant envelope alignment algorithm, the momentum estimated value of definitely walking that the data among the δ of adding up obtain each time echo is D, and initialization error reject the back new definitely walk momentum estimated value D '=D;

(2) adopt least square polynomial fit definitely to walk momentum estimated value D, obtain corresponding match value

(3) to match value

Ask first order difference, obtain the corresponding adjacent echo of radar and walk the momentum match value

Calculate adjacent echo and walk momentum estimated value δ and match value

Difference can get error of fitting Δ δ;

(4) establish δ _{K (k+1)},

With Δ δ _{K (k+1)}Be respectively described δ, With k data value among the Δ δ, k=1 wherein, L, N-1, N are the echo-pulse number in the observation time; According to the standard deviation std (Δ δ) of data among the standard deviation formula calculating error of fitting Δ δ, if | Δ δ _{K (k+1)}|＞3std (Δ δ), then think δ _{K (k+1)}There is the kick error, uses

Replace δ _{K (k+1)}Reject to realize error, and walk the middle data of momentum estimated value δ ' and add up rejecting adjacent echo after all kick errors, obtain the new momentum estimated value D ' that definitely walks, make D=D ' and repeated execution of steps (2), detect until no kick error to step (4);

(5) error is rejected the new momentum estimated value D ' that definitely walks in back and carry out least square polynomial fit, obtain corresponding match value

According to

The target translation component is carried out high-accuracy compensation, finish envelope alignment.

The present invention compared with prior art has the following advantages:

(1) adopts least square polynomial fit, make full use of the easy motion characteristic of target, compare based on the envelope alignment method result of echo envelope correlativity more accurate;

(2) adopt least square polynomial fit to reject the iterative operation that combines with error, iterations is low, and can self-adaptation adjust decision threshold, avoids repeatedly iteration correction and global optimizing, significantly reduces operand;

(3) reject operation by the adaptive iteration error, under the low signal-to-noise ratio condition, suppress the kick error effect, can obtain higher envelope alignment precision.

Can describe in detail by following accompanying drawing and example purpose of the present invention, feature, advantage.

Description of drawings

Fig. 1 is a process flow diagram of the present invention;

The rectilinear motion target geometric representation that Fig. 2 adopts when being emulation of the present invention;

Fig. 3 is the error change curve that adopts distinct methods emulation envelope alignment;

Fig. 4 is the envelope alignment result who adopts distinct methods emulation;

Fig. 5 is the imaging results that adopts distinct methods emulation correspondence;

Fig. 6 be emulation envelope alignment error root-mean-square value with pulse pressure after the signal to noise ratio (S/N ratio) change curve.

Embodiment

With reference to Fig. 1, performing step of the present invention is as follows:

Step 1. is definitely walked momentum estimated value D according to adjacent relevant each time of envelope alignment algorithm computation echo, and initialization error reject the back new definitely walk momentum estimated value D '=D.

1a), calculate k the data value δ that adjacent echo is walked momentum estimated value δ so that adjacent echo envelope correlation function value is criterion to the maximum _{K (k+1)}:

${\mathrm{\δ}}_{k(k+1)}=\arg \underset{{\mathrm{\δ}}_{k(k+1)}}{\max }\left|s_k\left(t\right)\right|\left|s_{k+1}(t-{\mathrm{\δ}}_{k(k+1)})\right|$

S in the formula _k(t) and s _K+1(t) be respectively the k time echoed signal and the k+1 time echoed signal, k=1, L, N-1, N are the echo-pulse number in the observation time;

1b) according to data value δ _{K (k+1)}, k=1, L, N-1 obtains adjacent echo and walks momentum estimated value δ expression formula and be:

δ＝[δ ₁₂，δ ₂₃，L，δ _(N-1)N] ^T

Wherein subscript T represents matrix transpose operation, and subscript i (i+1) represents this data value corresponding the i time and the i+1 time echoed signal, i=1 wherein, L, N-1;

Be reference with the 1st echo 1c), the adjacent echo that adds up is successively walked the data among the momentum estimated value δ, and the momentum estimated value of definitely walking that obtains each time echo is D=[D ₁, D ₂..., D _N] ^T, wherein

N=1, L, N-1, and D ₁=0, subscript T represents matrix transpose operation;

1d) initialization error reject the back new definitely walk momentum estimated value D '=D.

Step 2. utilizes the easy motion characteristic of the relative radar of target to carry out least square polynomial fit to walking the momentum data.

2a) establish t _m=[t ₁..., t _N] ^TBe slow time arrow, wherein t _k=kPRI is the slow time of radar transmitted pulse correspondence, and k=1, L, N, N are the echo-pulse number in the observation time, and PRI is the pulse repetition time, and subscript T represents matrix transpose operation; If $C=\left[\begin{array}{cccc}{t}_m^M& t_m^{M-1}& L& e\end{array}\right]$ Be corresponding slow time matrix, wherein M is the polynomial fitting exponent number,

L=1, L, M, e=[1 ..., 1] ^TBe unit vector; If ${\widehat{\mathrm{\θ}}}_{\mathrm{LS}}={[{\widehat{\mathrm{\θ}}}_M,{\widehat{\mathrm{\θ}}}_{M-1},L,{\widehat{\mathrm{\θ}}}_1,{\widehat{\mathrm{\θ}}}_0]}^T$ Be the least-squares estimation value of polynomial fitting coefficient vector, wherein

Corresponding

Coefficient, l=1, L, M, The coefficient of corresponding unit vector e;

2b) according to the least square theory, utilize following formula to calculate the least-squares estimation value of polynomial fitting coefficient vector

${\widehat{\mathrm{\θ}}}_{\mathrm{LS}}={\left(C^{T}C\right)}^{-1}{C}^{T}D$

And then the match value of momentum estimated value D is definitely walked in calculating

For:

${\hat{D}}_{\mathrm{LS}}=C\·{\widehat{\mathrm{\θ}}}_{\mathrm{LS}}.$

Step 3. is calculated error of fitting.

To match value

Ask first order difference, obtain the corresponding adjacent echo of radar and walk the momentum match value $\widehat{\mathrm{\δ}}={[{\widehat{\mathrm{\δ}}}_{12},{\widehat{\mathrm{\δ}}}_{23}L,{\widehat{\mathrm{\δ}}}_{(N-1)N}]}^T,$ Subscript T represents matrix transpose operation, calculates adjacent echo and walks momentum estimated value δ and match value

Difference can get error of fitting Δ δ=[Δ δ ₁₂, Δ δ ₂₃L, Δ δ _{(N-1) N}] ^T, wherein ${\mathrm{\Δ\δ}}_{k(k+1)}={\mathrm{\δ}}_{k(k+1)}-{\widehat{\mathrm{\δ}}}_{k(k+1)},$ K=1, L, N-1, N are the echo-pulse number in the observation time.

Step 4. adaptive iteration error is rejected.

It is gradual that the adjacent echo of easy motion target is walked momentum, the variable quantity of walking momentum is concentrated near average and distributed, and is far away if variable quantity departs from average, and may there be the kick error in the corresponding momentum estimated value of walking, adaptive iteration error based on this principle is rejected operation, carries out as follows:

4a) establish δ _{K (k+1)}For adjacent echo is walked k the data value of momentum estimated value δ,

For adjacent echo is walked the momentum match value K data value, Δ δ _{K (k+1)}Be k the data value of error of fitting Δ δ, k=1 wherein, L, N-1, N are the echo-pulse number in the observation time;

4b) calculate the standard deviation of data among the error of fitting Δ δ according to the standard deviation formula $\mathrm{std}\left(\mathrm{\Δ\δ}\right)=\sqrt{\frac{1}{N-2}\underset{i=1}{\overset{N-1}{\mathrm{\Σ}}}{(\mathrm{\Δ}{\mathrm{\δ}}_{i(i+1)}-\mathrm{\Δ}\stackrel{\‾}{\mathrm{\δ}})}^2},$ Δ δ in the formula _{I (i+1)}Be i data value among the described error of fitting Δ δ, i=1 wherein, L, N-1, $\mathrm{\Δ}\stackrel{\‾}{\mathrm{\δ}}=\frac{1}{N-1}\underset{i=1}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{\Δ}{\mathrm{\δ}}_{i(i+1)}$ Average for data among the error of fitting Δ δ;

4c) if | Δ δ _{K (k+1)}|＞3std (Δ δ), then think δ _{K (k+1)}There is the kick error, and uses

Replace δ _{K (k+1)}To realize the error rejecting, to k=1, L, each data value δ of N-1 _{K (k+1)}Carry out error and reject, obtain rejecting adjacent echo after all kick errors walk momentum estimated value δ '=[δ ' ₁₂, δ ' ₂₃L, δ ' _{(N-1) N}] ^T

4d) data that the adjacent echo of rejecting after all kick errors is walked among the momentum estimated value δ ' add up, obtain new definitely walk momentum estimated value D '=[D ' ₁, D ' ₂..., D ' _N] ^T, wherein N=1, L, N-1, and D ' ₁=0, subscript T represents matrix transpose operation;

4e) make D=D ' and repeated execution of steps (2), detect until no kick error to step (4).

Step 5. pair error is rejected the new momentum estimated value D ' that definitely walks in back and is carried out least square polynomial fit, and according to corresponding match value

Finish envelope alignment.

5a) according to the least square theory, utilize following formula to calculate and reject the new least-squares estimation value of definitely walking the corresponding polynomial fitting coefficient vector of momentum estimated value D ' in back with error

${\widehat{\mathrm{\θ}}}_{\mathrm{LS}}^{\′}={\left(C^{T}C\right)}^{-1}{C}^T{D}^{\′}$

Wherein subscript T represents matrix transpose operation, and C is slow time matrix;

5b) error of calculation is rejected the new match value of definitely walking momentum estimated value D ' in back

For:

${\hat{D}}_{\mathrm{LS}}^{\′}=C\·{\widehat{\mathrm{\θ}}}_{\mathrm{LS}}^{\′};$

5c) basis

Each echo envelope is carried out translation,, finish envelope alignment so that the target translation component is carried out high-accuracy compensation.

Effect of the present invention can further specify by following simulation result.

1. emulated data:

With space based radar monitored space target is simulation context, adopts certain dummy satellite as simulation object, and the rectilinear motion target geometric representation that adopts during emulation as shown in Figure 2.The motion of easy motion target relative radar in observation time can be approximated to be rectilinear motion, if the relative radar of target is made the orientation to translation, speed of related movement is 10km/s, point target and distance by radar are 200km in the simulation time, imaging 1s integration time, radar carrier frequency 10GHz, signal bandwidth 600MHz, pulse repetition rate 1kHz.To the translation target, polynomial fitting exponent number M gets 2～3 and gets final product, and gets M=2 in this emulation for the orientation, with classic method and the inventive method pulse pressure back echo signal is carried out motion compensation and imaging respectively.

2. emulation content and result

Signal to noise ratio snr=5dB after the echoed signal pulse pressure is established in emulation 1, respectively the envelope alignment error of adjacent correlation method, accumulation correlation method and the inventive method is carried out simulation analysis, obtains corresponding error change curve, as shown in Figure 3.Wherein:

Fig. 3 (a) is the error change curve that adopts existing adjacent correlation method emulation envelope alignment, Fig. 3 (b) is the error change curve that adopts existing accumulation correlation method emulation envelope alignment, Fig. 3 (c) is the error change curve that adopts the inventive method emulation envelope alignment, wherein LS is the result when only adopting step of the present invention (1) and step (2), be called the LS method, ICLS is the inventive method.

By Fig. 3 (a) as seen, there is tangible kick error in adjacent correlation method envelope alignment result, knows that easily adjacent correlation method can't overcome the influence of kick error under the low signal-to-noise ratio condition.

By Fig. 3 (b) as seen, the accumulation correlation method has effectively suppressed the propagation of kick error, but for complex target, multiple scattering point skip distance is walked about from the unit and is caused the target scattering dot structure with the observation visual angle change, make the correlativity of single pulse and pulse weighted sum reduce, and then it is lower to cause single to walk the momentum estimated accuracy.

By Fig. 3 (c) as seen, be subjected to the kick error effect, the envelope alignment error of LS method enlarges markedly, and can't finish envelope alignment, thereby and institute of the present invention extracting method can effectively detect the deterioration that kick is alleviated the parameter estimation precision.

Signal to noise ratio snr=5dB after the echoed signal pulse pressure is established in emulation 2, and the envelope alignment result to adjacent correlation method, accumulation correlation method and the inventive method carries out simulation analysis respectively, and simulation result as shown in Figure 4.Wherein:

Fig. 4 (a) is the envelope alignment result who adopts existing adjacent correlation method emulation, and Fig. 4 (b) is the envelope alignment result who adopts the emulation of existing accumulation correlation method, and Fig. 4 (c) is the envelope alignment result who adopts the inventive method emulation.

By Fig. 4 (a) as seen, there is tangible kick error in adjacent correlation method envelope alignment result, by Fig. 4 (b) as seen, the accumulation correlation method has effectively overcome the propagation of kick error, but alignment accuracy is lower, by Fig. 4 (c) as seen, the inventive method has higher alignment accuracy when overcoming kick error propagation.

Emulation 3 is carried out simulation analysis to the imaging results of adjacent correlation method, accumulation correlation method and the inventive method respectively, and simulation result as shown in Figure 5.Wherein:

Fig. 5 (a) is the imaging results that adopts existing adjacent correlation method emulation correspondence, and Fig. 5 (b) is the imaging results that adopts existing accumulation correlation method emulation correspondence, and Fig. 5 (c) is the imaging results that adopts the inventive method emulation correspondence.

By Fig. 5 (a) as seen, the kick error can cause serious distance images to defocus, cause to obtain correct imaging results, by Fig. 5 (b) as seen, alignment accuracy is low can to cause imaging results fuzzy, has a strong impact on image quality, by Fig. 5 (c) as seen, the inventive method gained imaging results is comparatively clear, and image quality is higher.

Fig. 3 to Fig. 5 shows that further under the low signal-to-noise ratio condition, there is tangible kick error in adjacent correlation method envelope alignment result, can't obtain correct imaging results; The accumulation correlation method can suppress the kick error effect on the basis of adjacent correlation method, but to walk the momentum estimated accuracy low excessively owing to single, and imaging effect is unsatisfactory; Directly adopt least square polynomial fit can be subjected to the kick error effect, cause the parameter estimation precision seriously to descend; Institute of the present invention extracting method can overcome the influence of kick error, and obtains higher envelope alignment precision by least square polynomial fit.

Emulation 4 has been carried out simulation analysis to the envelope alignment error of described LS method and the inventive method respectively, with envelope alignment error mean square root

Weigh its global error level, obtain the envelope alignment error mean square root that is obtained through 1000 Monte Carlo experiments With the change curve of signal to noise ratio (S/N ratio) after the pulse pressure, as shown in Figure 6.Wherein $\stackrel{\‾}{\mathrm{\Δ}}=\sqrt{E\left[{\mathrm{\Δ}}^2\right]},$ $E\left[{\mathrm{\Δ}}^2\right]=\frac{1}{N}\underset{i-1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\Δ}}_i^2,$ Δ=[Δ ₁, L, Δ _N] ^TBe the envelope alignment error, N is the echo-pulse number in the observation time.

As seen from Figure 6: when signal to noise ratio (S/N ratio) was lower than 4dB after pulse pressure, the envelope alignment error of LS method enlarged markedly, and can't finish envelope alignment; Compare the LS method, the inventive method can be rejected the deterioration that step is effectively alleviated the parameter estimation precision by adaptive error under the low signal-to-noise ratio condition, obtains comparatively stable envelope alignment performance; When signal to noise ratio (S/N ratio) is higher, there is the kick error hardly, the inventive method and LS method have close envelope alignment error.

Claims (5)

1. A reverse synthetic aperture radar envelope alignment method based on adaptive error elimination, comprising the steps: (1) Use the adjacent correlation envelope alignment algorithm to sequentially calculate the walking distance between adjacent radar echoes to obtain the estimated value δ of the walking distance of adjacent echoes, and accumulate the data in δ to obtain the estimated value of the absolute walking distance of each echo D, And initialize the new estimated value of absolute walking distance D'=D after the error is eliminated; (2) Use the least squares polynomial to fit the estimated absolute walking distance D to obtain the corresponding fitting value

(3) For the fitted value

Calculate the first-order difference to obtain the corresponding radar adjacent echo movement value fitting value Calculate the estimated value δ and the fitted value of the adjacent echo walking amount

The difference can be fitted error Δδ; (4) Let δ _k(k+1) 、

and Δδ _k(k+1) are the δ,

and the kth data value in Δδ, where k=1, L, N-1, N is the number of echo pulses within the observation time; calculate the standard deviation std(Δδ) of the data in the fitting error Δδ according to the standard deviation formula , if |Δδ _k(k+1) |＞3std(Δδ), then it is considered that there is a jump error in δ _k(k+1) , use

Replace δ _k(k+1) to achieve error elimination, and accumulate the data in the adjacent echo walking distance estimation value δ′ after removing all jump errors to obtain a new absolute walking distance estimation value D′, let D =D' and repeat step (2) to step (4), until no jump error is detected; (5) Carry out least squares polynomial fitting on the new estimated value of absolute walking distance D′ after the error is eliminated, and obtain the corresponding fitting value according to

Perform high-precision compensation on the target translation component to complete envelope alignment. 2. the inverse SAR envelope alignment method according to claim 1, wherein the calculation of adjacent echo walking amount estimated value δ described in step (1) is carried out as follows: 1a) Calculate the kth data value δ _k(k+1) of δ according to the adjacent correlation envelope alignment algorithm: ${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>$ In the formula, s _k (t) and s _k+1 (t) are the kth echo signal and the k+1th echo signal respectively, k=1, L, N-1, N is the echo pulse within the observation time number; 1b) According to the data value δ _k(k+1) , k=1, L, N-1, the expression of the estimated value δ of adjacent echo movement is obtained as: δ=[δ ₁₂ , δ ₂₃ L, δ _(N-1)N ] ^T where the superscript T represents the transpose operation. 3. the inverse synthetic aperture radar envelope alignment method according to claim 1, is characterized in that adopting the least squares polynomial fitting absolute moving amount estimated value D described in step (2), obtains corresponding fitting value Proceed as follows: 2a) Let t _m =[t ₁ ,...,t _N ] ^T be the slow time vector, where t _k =k·PRI is the slow time corresponding to the radar transmission pulse, k=1, L, N, N is the observation The number of echo pulses within the time period, PRI is the pulse repetition period, and the superscript T represents the transpose operation; set $C=\left[\begin{array}{cccc}{t}_m^m& t_m^{m-1}& L& e\end{array}\right]$ is the corresponding slow time matrix, where M is the order of the fitted polynomial,

l=1, L, M, e=[1,...,1] ^T is a unit vector; set ${\widehat{\mathrm{\&theta;}}}_{\mathrm{LS}}={[{\widehat{\mathrm{\&theta;}}}_m,{\widehat{\mathrm{\&theta;}}}_{m-1},L,{\widehat{\mathrm{\&theta;}}}_1,{\widehat{\mathrm{\&theta;}}}_0]}^T$ is the least squares estimate of the fitted polynomial coefficient vector, where

correspond The coefficient of l=1, L, M, Corresponds to the coefficients of the unit vector e. 2b) According to the least squares theory, use the following formula to calculate the least squares estimated value of the fitted polynomial coefficient vector

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LS</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; D.</span>}$ Then calculate the fitting value of the estimated absolute walking distance D for: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}}_{\mathrm{<span\; class="notranslate">\; LS</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LS</span>}}<span\; class="notranslate">\; .</span>$ 4. the inverse SAR envelope alignment method according to claim 1, wherein the standard deviation formula described in step (4) is: $\mathrm{<span\; class="notranslate">\; std</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;\&delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ In the formula, Δδ _i(i+1) is the i-th data value in the fitting error Δδ, wherein i=1, L, N-1, N is the number of echo pulses in the observation time, $\mathrm{\&Delta;}\stackrel{\&OverBar;}{\mathrm{\&delta;}}=\frac{1}{N-1}\underset{i=1}{\overset{N-1}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{\mathrm{\&delta;}}_{i(i+1)}$ is the mean value of the data in the fitting error Δδ. 5. the inverse SAR envelope alignment method according to claim 1, is characterized in that in the described step (5), the new absolute walking distance estimated value D ' after the error is eliminated carries out least squares polynomial fitting, Proceed as follows: 5a) According to the least squares theory, use the following formula to calculate the least squares estimated value of the fitted polynomial coefficient vector corresponding to the D'

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LS</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{<span\; class="notranslate">\; \&prime;</span>}$ where the superscript T represents the transpose operation. 5b) Calculate the fitting value of the new estimated absolute walking distance D′ after the error is eliminated

for: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}}_{\mathrm{<span\; class="notranslate">\; LS</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LS</span>}}^{<span\; class="notranslate">\; \&prime;</span>}$ where C is the slow time matrix.

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