CN109358329B - Method for establishing platform-mobile bistatic SAR echo model in pulse propagation time - Google Patents

Method for establishing platform-mobile bistatic SAR echo model in pulse propagation time Download PDF

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CN109358329B
CN109358329B CN201811310158.3A CN201811310158A CN109358329B CN 109358329 B CN109358329 B CN 109358329B CN 201811310158 A CN201811310158 A CN 201811310158A CN 109358329 B CN109358329 B CN 109358329B
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武俊杰
张强辉
张志高
李中余
黄钰林
杨建宇
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University of Electronic Science and Technology of China
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention discloses a method for establishing a platform maneuvering bistatic SAR echo model in pulse propagation time, which aims at solving the problems that all echo models used for maneuvering platforms single-base SAR and bistatic SAR are based on the assumption of 'stop-go-stop', and cause considerable propagation delay errors and azimuth secondary phase errors; the method takes the maneuvering of a platform in the pulse propagation process into consideration, modifies the traditional pulse propagation delay equation based on the assumption of 'stopping and stopping', thereby establishing an accurate pulse propagation delay equation, approximately solves a high-precision approximate analytical expression of the accurate pulse propagation delay equation solution by carrying out the historical high-order term of the distance of a receiving station, then carries out first-order Taylor expansion on the high-precision approximate analytical expression with respect to the fast time, and finally establishes a high-precision bistatic SAR echo model, so that the method can be suitable for various bistatic SAR conditions.

Description

Method for establishing platform-mobile bistatic SAR echo model in pulse propagation time
Technical Field
The invention belongs to the technical field of Synthetic Aperture Radar (SAR) imaging, and particularly relates to an echo model establishing technology.
Background
The SAR has special all-weather all-day-time high-resolution imaging capability, and more emerging High Mobility Platforms (HMPs) such as unmanned aerial vehicles and hypersonic flight vehicles are expected to improve the environmental perception capability by carrying the SAR. The echo model plays a key role in data processing of SAR.
The current "stop-and-go" assumption is widely adopted in echo modeling. But are ineffective in some types of systems, such as many emerging SAR systems with high resolution or high speed.
To solve this problem, some documents propose some improved echo models that do not rely on the "stop-and-go-stop" assumption. For example, based on the assumption of uniform linear motion, the documents "Echo models and imaging algorithm for high-resolution SAR on high-resolution platform, IEEE trans. geosci.remote sens, vol.50, No.3, pp.933-950, and mar.2012" propose an accurate Echo model based on linear-moving-reducing-prediction (LDP) within a pulse propagation time for Low Earth Orbit (LEO) SAR; based on a fourth-order doppler parameter model, documents "The acquisition focusing and resolution analysis method in geosynchronous SAR, IEEE trans. geosci. remote sens., vol.49, No.10, pp.3548-3563, oct.2011" propose an accurate echo model for Geosynchronous (GEO) SAR. However, due to their inherent assumptions, such as uniform linear or satellite orbital motion, these existing echo models cannot be applied to general cases with mobility (i.e., non-uniform linear motion, which is common in circular SAR, mobile platform SAR, etc.) and bistatic configuration; the documents "full polar high-resolution 3-D imaging with circular SAR at L-Band, IEEE trans. geosci. Remote sensors, vol.52, No.6, pp.3074-3090, jun.2014", the documents "Feature-independent adaptive estimator for the current SAR, IEEE geo. Remote sensors, let, vol.4, No.2, pp.191-195, ap.2007" and the documents "adaptation model algorithms and imaging for high density sensing antenna mode SAR light with manual sensors, IEEE j.s.relay, top pics application, high object server, search 3-D imaging with dynamic SAR mapping with large or small base station configuration (map 3-D imaging) are considered as configurations that can be adapted to the configuration of the geometric motion platform, such as the configuration of the double-base station (e.g. the configuration of the velocity of the circular SAR) and the configuration of the velocity of the circular base station. However, to our knowledge, all current echo models for mobile platform monostatic and bistatic SAR are based on the "stop-and-go" assumption.
Disclosure of Invention
In order to solve the technical problems, the invention provides a platform-maneuvering bistatic SAR echo model building method in pulse propagation time, which considers the linear motion and the nonlinear motion of a platform during pulse propagation, avoids the assumption of 'stop-go-stop' and the assumption of uniform-speed linear motion of the platform, and is suitable for various bistatic SAR conditions.
The technical scheme adopted by the invention is as follows: a platform maneuvering bistatic SAR echo model building method in pulse propagation time considers the maneuvering of a platform in the pulse propagation process according to the characteristics of a rapid maneuvering platform, modifies the traditional pulse propagation delay equation based on the assumption of 'stop and go', builds an accurate pulse propagation delay equation, approximately solves a high-precision approximate analytical expression of the accurate pulse propagation delay equation solution by carrying out approximate solution on a historical high-order term of a receiving station distance, then carries out first-order Taylor expansion on the high-precision approximate analytical expression with respect to the fast time, and finally builds a high-precision bistatic SAR echo model.
A. The method for establishing the accurate pulse propagation delay equation comprises the following steps:
a1, determining an impulse propagation delay equation under the assumption of 'stop and go':
Figure BDA0001854722890000021
a2, correcting the pulse propagation delay equation under the assumption of stopping and stopping in the step A1 in consideration of the maneuvering of the platform in the pulse propagation time to obtain an accurate pulse propagation delay equation;
Figure BDA0001854722890000022
wherein, taudFor precise pulse propagation delay, c is the electromagnetic wave propagation velocity, η denotes the slow time, tsIndicating the relative pulse transmission time (η + t)s) Represents the absolute pulse transmission time, and t represents the fast time;
B. solving the high-precision analytic expression of the accurate pulse propagation delay equation comprises the following steps:
b1, R in equation for accurate pulse propagation delayR(η + t) the following approximation is made:
Figure BDA0001854722890000031
b2, according to R in B1R(η + t), for precise pulseUpdating and simplifying the impulse propagation delay equation to obtain the following equation:
(c2-|vR|2)τd 2-2(c|rT|+vR·rR)τd＝|rR|2-|rT|2，
wherein the content of the first and second substances,
Figure BDA0001854722890000032
Figure BDA0001854722890000033
b3, solving the equation obtained in the step B2, and removing the root increment to obtain high-precision approximate time delay (marked as tau)HP) The expression is as follows:
Figure BDA0001854722890000034
C. and performing first-order Taylor expansion on the high-precision approximate analytical expression about the fast time, and specifically comprising the following steps:
c1, carrying out Taylor series expansion on the high-precision approximate analytical expression to obtain
τHP(η,ts)≈τa(η)+ξ(η)ts，
Wherein, taua(η) represents the pulse signal center propagation delay,
Figure BDA0001854722890000035
ξ (η) shows the rate of change of pulse propagation delay with pulse transmission time,
Figure BDA0001854722890000036
c2, solving the parameter tau in the Taylor expansion obtained in the step C1a(η) and ξ (η);
①
Figure BDA0001854722890000037
②
Figure BDA0001854722890000041
wherein
Order to
Figure BDA0001854722890000042
Figure BDA0001854722890000043
Order to
Figure BDA0001854722890000044
Figure BDA0001854722890000045
By
Figure BDA0001854722890000046
Figure BDA0001854722890000047
By
Figure BDA0001854722890000048
Figure BDA0001854722890000049
C3, parameter τ obtained in step C2a(η) and ξ (η), updating the taylor expansion of step C1, and obtaining the expression of the fast time t according to the taylor expansion updated in step C1;
t＝ts+τd
≈ts+τHP(η,ts)
≈ts+τa(η)+ξ(η)ts
＝(1+ξ(η))ts+τa(η)
c4, obtaining the high-precision time delay tau according to the Taylor expansion of the step C1 and the expression of the fast time t of the step C3HPFirst order Taylor expansion for t:
Figure BDA0001854722890000051
D. establishing a high-precision bistatic SAR echo model, which specifically comprises the following steps: obtaining the high-precision time delay tau according to the step C4HPAnd obtaining a high-precision bistatic SAR echo model by regarding the first-order Taylor expansion of t:
Figure BDA0001854722890000052
where σ denotes the radar cross-sectional area RCS, ωr(. and ω)a(. h) Window functions representing the distance and azimuth directions, respectively, KrRepresenting the chirp signal frequency modulation, fcRepresenting the frequency of the carrier frequency.
The invention has the beneficial effects that: the method of the invention considers the linear motion and the nonlinear motion of the platform during the pulse propagation period, and derives the high-precision analytic solution of the pulse propagation delay by approximating the high-order term of the accurate distance history of the receiving station; because the hypothesis of ' stop and go ' and stop ' and the hypothesis of uniform linear motion of the platform are avoided, the echo model established by the invention can be applied to various bistatic SAR conditions, including the conventional bistatic SAR of the slow uniform linear motion platform, the new bistatic SAR of the fast maneuvering platform and the like; the method of the invention has the following advantages:
1. compared with the traditional model which can cause quite large propagation delay errors and azimuth secondary phase errors, the method approximately derives the high-precision analytic solution of the pulse propagation delay by carrying out high-order terms of the accurate distance history of the receiving station; the established echo model is highly accurate;
2. the dynamic bistatic SAR echo model of the platform in the pulse propagation time does not simply make the assumption of stopping and stopping the motion of the platform, but fully considers the motion of the platform in the pulse propagation time, so that the model provided by the invention is more accurate, and simulation proves that the imaging algorithm based on the echo model established by the invention can well focus the target echo, while the traditional model cannot.
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FIG. 1 is a flow chart of a protocol of the present invention;
FIG. 2 is a bistatic SAR echo recording geometric model of a mobile platform;
FIG. 3 is a schematic diagram of an actual path of pulse propagation and an imaginary path under the assumption of "stop-go-stop" and a corresponding propagation delay model,
fig. 4 is a schematic diagram of pulse propagation delay errors of different echo models:
wherein, fig. 4(a) is a proposed intrapulse Maneuver (MDP) model; FIG. 4(b) is a uniform linear motion within a pulse (LDP) model; FIG. 4(c) is the "stop and go" (SAG) model;
fig. 5 is a schematic diagram of the variation of the azimuth secondary phase error of the receiving station with different parameters:
wherein, fig. 5(a) is the variation with the acceleration; FIG. 5(b) is a graph showing variation with jerk;
FIG. 6 is a geometric distribution of a simulation point target;
FIG. 7 shows the imaging results of the back-propagation (BP) algorithm based on different echo models:
wherein, fig. 7(a) is an intravascular Motor (MDP) model proposed by the present invention; FIG. 7(b) is a uniform linear motion within a pulse (LDP) model; FIG. 7(c) is a "stop and go" (SAG) model;
FIG. 8 is the impulse response of the BP algorithm;
wherein, FIG. 8(a) is target B; fig. 8(b) shows a target C.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
As shown in fig. 1, a scheme flow chart of the present invention, the technical scheme adopted by the present invention includes: according to the characteristics of a rapid maneuvering platform, the maneuvering of the platform in the pulse propagation process is considered, the traditional pulse propagation delay equation based on the assumption of 'stop-go-stop' is modified, the accurate pulse propagation delay equation is established, a high-precision analytical expression of the accurate pulse propagation delay equation is approximately solved by high-order terms of the accurate distance history of a receiving station, then first-order Taylor expansion is carried out on the accurate pulse propagation delay equation with respect to the fast time, and finally a high-precision bistatic SAR echo model is established.
The method for establishing the accurate pulse propagation delay equation comprises the following steps:
a1, determining an impulse propagation delay equation under the assumption of 'stop and go':
Figure BDA0001854722890000061
wherein η denotes the slow time, RT(η) shows the distance history of the transmitting station under the assumption of "stop and go", RR(η) shows the distance history of the receiving station under the "stop and go" assumption, vT(vR)、aT(aR)、jT(jR) Respectively representing the velocity, acceleration, jerk, r, of the movement of the transmitting station (receiving station)PA position vector representing a point target;
in the 'stop-and-go' model, a2, the transmitting station and the receiving station platform are assumed to be in a static state during the time when the pulse signal is propagated from the transmitting station to the receiving station; in fact, the transmitting station and the receiving station platform are not in a static state during the period of time when the pulse signal propagates from the transmitting station to the receiving station, and the assumption of 'stop-and-go-stop' as shown in fig. 3 can cause errors in the calculation of the pulse propagation delay;
in the step, the maneuvering of the platform in the pulse propagation time is considered, and the pulse propagation delay equation under the assumption of 'stop and go' in the step A1 is corrected to obtain the accurate pulse propagation delay equation
Figure BDA0001854722890000071
Wherein, taudTo be preciseC is the propagation speed of the electromagnetic wave, η denotes the slow time, tsIndicating the relative pulse transmission time (η + t)s) Represents the absolute pulse transmission time, and t represents the fast time;
solving the high-precision analytic expression of the accurate pulse propagation delay equation comprises the following steps:
b1, R in equation for accurate pulse propagation delayR(η + t) the following approximation is made:
Figure BDA0001854722890000072
b2, according to R in B1R(η + t), the exact pulse propagation delay equation is updated and simplified to yield the following equation:
(c2-|vR|2)τd 2-2(c|rT|+vR·rR)τd＝|rR|2-|rT|2，
wherein the content of the first and second substances,
Figure BDA0001854722890000073
Figure BDA0001854722890000074
b3, solving the equation obtained in the step B2, and removing the root, so as to obtain a high-precision time delay expression as follows:
Figure BDA0001854722890000081
the method for establishing the high-precision bistatic SAR echo model specifically comprises the following steps:
c1, performing Taylor series expansion on the high-precision time delay expression in the step B3, specifically:
for high-precision time delay tauHPWith respect to tsPerforming a first-order Taylor expansion to obtain
τHP(η,ts)≈τa(η)+ξ(η)ts，
Wherein the content of the first and second substances,
Figure BDA0001854722890000082
which represents the propagation delay at the center of the pulse signal,
Figure BDA0001854722890000083
representing the rate of change of the pulse propagation delay with the pulse transmission time;
c2, solving the parameter tau in the Taylor expansion obtained in the step C1a(η) and ξ (η);
① finding τa(η)：
Order to
Figure BDA0001854722890000084
Figure BDA0001854722890000085
Can obtain
Figure BDA0001854722890000086
② found ξ (η):
order to
Figure BDA0001854722890000087
Figure BDA0001854722890000091
Order to
Figure BDA0001854722890000092
Figure BDA0001854722890000093
By
Figure BDA0001854722890000094
Figure BDA0001854722890000095
By
Figure BDA0001854722890000096
Figure BDA0001854722890000097
In summary,
Figure BDA0001854722890000098
c3, parameter τ obtained in step C2a(η) and ξ (η), updating the taylor expansion of step C1, and obtaining the expression of the fast time t according to the taylor expansion updated in step C1;
t＝ts+τd
≈ts+τHP(η,ts)
≈ts+τa(η)+ξ(η)ts
＝(1+ξ(η))ts+τa(η)
c4, obtaining the high-precision time delay tau according to the Taylor expansion of the step C1 and the expression of the fast time t of the step C3HPFirst order Taylor expansion for t:
Figure BDA0001854722890000101
establishing a high-precision bistatic SAR echo model, which specifically comprises the following steps: obtaining the high-precision time delay tau according to the step C4HPAnd obtaining a high-precision bistatic SAR echo model by regarding the first-order Taylor expansion of t:
Figure BDA0001854722890000102
where σ denotes the radar cross-sectional area RCS, ωr(. and ω)a(. h) Window functions representing the distance and azimuth directions, respectively, KrRepresenting the chirp signal frequency modulation, fcRepresenting the frequency of the carrier frequency.
As shown in fig. 4, which is a schematic diagram of pulse propagation delay errors of different echo models, the pulse propagation delay error introduced by the echo model provided by the present invention is far smaller than a fast time sampling unit and can be ignored, while the pulse propagation delay error introduced by the existing two echo models can be non-negligible; the echo model of the invention is more accurate;
as shown in fig. 5, which is a schematic diagram of changes of azimuth secondary phase errors of a receiving station along with different parameters, the azimuth secondary phase errors introduced by the echo model provided by the present invention are far less than pi/4 and thus can be ignored, while the existing two echo models can introduce non-negligible azimuth secondary phase errors; it can be seen that the echo model proposed by the present invention is very accurate.
The technical effects of the present invention will be described below with reference to specific data.
Table 1 shows the simulation parameters used in the present embodiment, the geometric model of the echo obtained by the maneuvering BSAR of the present embodiment is shown in fig. 2, the geometric distribution of the simulation point target is shown in fig. 6, and the obtained simulation results are shown in fig. 7 and fig. 8.
As can be seen from fig. 7(a), the target can be well focused when using the MDP echo model proposed by the present invention. In contrast, when the intra-pulse straight-and-straight motion (LDP) model of fig. 7(b) and the "stop-and-go" (SAG) model of fig. 7(c) are used, the target cannot be focused; moreover, geometric distortion exists in the image; as shown in fig. 8, the BP algorithm based on the echo model proposed by the present invention can obtain good target impulse response, and the accuracy of the model is laterally verified. The effectiveness and the necessity of the method of the invention in the bistatic SAR imaging processing are shown by simulation results in figures 7 and 8.
TABLE 1 simulation parameters
Figure BDA0001854722890000111
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (5)

1. The platform maneuvering bistatic SAR echo model building method in the pulse propagation time is characterized in that the maneuvering of a platform in the pulse propagation process is considered, the traditional pulse propagation delay equation based on the assumption of 'stop and go' is modified, so that an accurate pulse propagation delay equation is built, a high-precision approximate analytical expression of the accurate pulse propagation delay equation solution is approximately solved by the distance history high-order term of a receiving station, then first-order Taylor expansion is carried out on the high-precision approximate analytical expression with respect to the fast time, and finally a high-precision bistatic SAR echo model is built;
the exact pulse propagation delay equation is:
Figure FDA0002489987200000011
wherein, taudFor precise pulse propagation delay, c is the electromagnetic wave propagation velocity, η denotes the slow time, tsIndicating the relative pulse transmission time (η + t)s) Representing the absolute pulse transmission instant, t representing the fast time,
Figure FDA0002489987200000012
Figure FDA0002489987200000013
。
2. the method for building the platform-maneuverable bistatic SAR echo model within the pulse transit time according to claim 1, wherein solving the high-precision analytical expression of the precise pulse transit time equation comprises the following steps:
b1, historical high-order term R for distance of receiving station in accurate pulse propagation delay equationR(η + t) the following approximation is made:
Figure FDA0002489987200000014
wherein, tauSAGMeaning the pulse propagation delay under the assumption of "stop-and-go-stop". vRIndicating the speed of movement of the receiving station, aRAcceleration representing movement of the receiving station, jRJerk, r, representing movement of the receiving stationPA position vector representing a point target; r isR0Indicating the initial position of the receiving station;
b2, R approximated according to step B1R(η + t), the exact pulse propagation delay equation is updated and simplified to yield the following equation:
(c2-|vR|2)τd 2-2(c|rT|+vR·rR)τd＝|rR|2-|rT|2，
wherein the content of the first and second substances,
Figure FDA0002489987200000015
Figure FDA0002489987200000021
rT0denotes the initial position of the transmitting station, aTAcceleration, v, representing movement of the transmitting stationTWhich is indicative of the speed at which the transmitting station is moving,
b3, solving the equation obtained in the step B2, and removing the added root, so that the high-precision approximate time delay expression is obtained as follows:
Figure FDA0002489987200000022
3. the method for building the platform-maneuverable bistatic SAR echo model within the pulse propagation time according to claim 2, wherein the traditional pulse propagation delay equation based on the "stop-go-stop" assumption is as follows:
Figure FDA0002489987200000023
wherein R isT(η) shows the distance history of the transmitting station under the assumption of "stop and go", RR(η) represents the distance history of the receiving station under the "stop-and-go-stop" assumption.
4. The method for building a platform-maneuverable bistatic SAR echo model within a pulse transit time according to claim 3, characterized in that the first order Taylor expansion of the high-precision approximate analytical expression with respect to fast time is performed, comprising the following steps:
c1, carrying out Taylor series expansion on the high-precision approximate analytical expression to obtain
τHP(η,ts)≈τa(η)+ξ(η)ts，
Wherein, taua(η) represents the pulse signal center propagation delay,
Figure FDA0002489987200000025
ξ (η) shows the rate of change of pulse propagation delay with pulse transmission time,
Figure FDA0002489987200000024
c2, solving the parameter tau in the Taylor expansion obtained in the step C1a(η) and ξ (η);
c3, parameter τ obtained in step C2a(η) and ξ (η), updating the taylor expansion of step C1, and obtaining the expression of the fast time t according to the taylor expansion updated in step C1;
t＝ts+τd
≈ts+τHP(η,ts)
≈ts+τa(η)+ξ(η)ts
＝(1+ξ(η))ts+τa(η)
c4, obtaining the high-precision time delay tau according to the Taylor expansion of the step C1 and the expression of the fast time t of the step C3HPFirst order Taylor expansion for t:
Figure FDA0002489987200000031
5. the method for establishing a platform-mobile bistatic SAR echo model within a pulse propagation time according to claim 4, characterized in that a high-precision bistatic SAR echo model is established, specifically: obtaining the high-precision time delay tau according to the step C4HPAnd obtaining a high-precision bistatic SAR echo model by regarding the first-order Taylor expansion of t:
Figure FDA0002489987200000032
where σ denotes the radar cross-sectional area RCS, ωr(. and ω)a(. h) Window functions representing the distance and azimuth directions, respectively, KrRepresenting the chirp signal frequency modulation, fcRepresenting the frequency of the carrier frequency.
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