Circular curved trajectory imaging algorithm based on special Stolt interpolation

Abstract

The invention provides a circular curved trajectory imaging algorithm based on special Stolt interpolation, comprising the following steps: step 1, acquiring position information of a target ground area, and establishing a circular trajectory geometric model based on the position information of a radar target; step 2, based on the circular trajectory geometric model, performing range pulse compression and dechirp processing on a slope distance expression between the radar and a target point to obtain a first expression of range frequency domain and azimuth time domain signals; 3, constructing a two-bit frequency domain distance phase based on the imaging geometric model, and compensating the phase without distance and azimuth coupling to obtain a second expression; and step 4, compensating the coupling phase and performing Stolt interpolation compensation, and obtaining an imaging image of the circular trajectory SAR image based on a processing result. According to the method, the imaging quality can still be ensured under the conditions that the aircraft is interfered by the outside and the radar motion is unstable.

Description

Technical Field

[0001] The invention relates to the field of radar imaging technology, and in particular to an imaging algorithm of a circular curved trajectory based on a special Stolt interpolation. Background Art

[0002] Synthetic Aperture Radar (SAR) is an active ground observation technology that can be installed on aircraft, satellites or spacecraft and other flying platforms, with all-weather and all-time monitoring capabilities. It has shown unique advantages in disaster monitoring, environmental monitoring, marine research, resource exploration, crop estimation, surveying and mapping, and has therefore received increasing attention from the international community.

[0003] However, in practical applications, the flying platform is affected by airflow, which may cause the radar's motion to be unstable, causing the antenna phase center to deviate from the ideal position. This deviation will affect the received echo phase and thus reduce the imaging quality. Therefore, phase compensation for SAR imaging is an indispensable link. Summary of the invention

[0004] The purpose of the present invention is to propose an imaging algorithm of a circular curved trajectory based on a special Stolt interpolation, which can still ensure the imaging quality when the aircraft is disturbed by the outside world and the radar motion is unstable.

[0005] In order to solve the above technical problems, the technical solution of the present invention is:

[0006] An imaging algorithm for circular curved trajectories based on special Stolt interpolation includes the following steps:

[0007] Step 1: Obtain the location information of the target ground area and establish a circular trajectory geometric model based on the location information of the radar target;

[0008] Step 2: Based on the circular trajectory geometric model, the slant range expression between the radar and the target point is subjected to range pulse compression to obtain a first expression of the range frequency domain and azimuth time domain signal;

[0009] Step 3: Apply the slant range expression to transform it into the slant range parameter in the two-dimensional frequency domain, and then construct a two-dimensional frequency domain model, and perform distance compression on the echo in the two-dimensional frequency domain, so as to obtain the frequency f of the azimuth. a Multiply the frequency f by the distance r Coupling phase compensation;

[0010] Step 4: Compensate the coupling phase and perform Stolt interpolation compensation, and obtain an imaging image of the circular trajectory SAR image based on the processing results.

[0011] Preferably, the step 1 is specifically as follows:

[0012] A circular curved trajectory imaging geometric model is established with the ground scene center of the target ground area as the origin.

[0013] Preferably, the slope distance expression is specifically:

[0014]

[0015] where θ a R is the positive angle between the projection of the line connecting the far point and the target point on the XOY plane to the origin O and the line connecting the SAR radar to the origin O. n is the projection length of the line between the origin and the target point on the XOY plane after a period of time, R(t) is the slant distance between the radar and the target point, r is the radius of the circular curved trajectory, H is the initial height, and a h is the acceleration in height, v h is the altitude speed.

[0016]

[0017] Among them, f r is the distance frequency domain, t is the azimuth time domain, c is the speed of light, f c is the carrier frequency, k0 is the zero-order term after the slant distance R(t) series is expanded, k1 is the first-order term after the slant distance R(t) series is expanded, k2 is the second-order term after the slant distance R(t) series is expanded, k3 is the third-order term after the slant distance R(t) series is expanded, and k4 is the fourth-order term after the slant distance R(t) series is expanded.

[0018] Preferably, the step 3 specifically comprises:

[0019] The first expression is subjected to series inversion processing to obtain a second expression, which is specifically:

[0020]

[0021] Among them, f a is the azimuth frequency domain, is an intermediate variable used in the simplified formula. Further, the imaging image of the circular curved trajectory SAR obtained based on the second expression is specifically:

[0022]

[0023] Preferably, the second expression is subjected to removal of non-coupling terms to obtain a third expression, coupling term compensation is performed on the third expression, and Stolt interpolation is performed to obtain an imaging image of a circular curved trajectory SAR.

[0024] The present invention has the following characteristics and beneficial effects:

[0025] By adopting the above technical scheme, the present invention establishes a motion geometry imaging model, and integrates the height change and angle into the geometric model. Then, the model is used to perform range pulse compression and de-slant on the slant distance between the radar and the target point, and a preliminary expression of the range frequency domain and azimuth time domain signal is generated. Then, the range phase in the two-dimensional frequency domain is constructed, and the phase that does not have the distance and azimuth coupling is compensated. Finally, the coupled phase is compensated and Stolt interpolation is applied to generate a SAR imaging image based on a circular curved trajectory. The above scheme completes the imaging effect after the change of angle and height. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0027] Figure 1 A schematic flow chart of an imaging method of a circular curved trajectory based on special Stolt interpolation according to an embodiment of the present invention;

[0028] Figure 2 This is a c imaging geometric model diagram of an imaging method of a circular curved trajectory based on special Stolt interpolation according to an embodiment of the present invention;

[0029] Figure 3 A schematic diagram of the results of an imaging method for a circular curved trajectory based on special Stolt interpolation according to an embodiment of the present invention; DETAILED DESCRIPTION

[0030] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0031] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0032] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0033] The present invention provides an imaging method of a circular curved trajectory based on a special Stolt interpolation, such as Figure 1 As shown, the specific steps are as follows:

[0034] Step 1: Obtain the position information of the radar target ground area, and establish a circular trajectory geometry model based on the position information such as the tilt angle of the space platform, the initial distance, the speed and acceleration of the space platform, and the change of the center angle during the movement.

[0035] In this embodiment, the target ground area refers to the ground area of ​​circular imaging, which is the ground target to be observed. The target and its surrounding area are all ground scenes; the target point refers to a point in the circular imaging area. If the target point P can be imaged, then points at other positions in the area can also be imaged.

[0036] Furthermore, a circular trajectory geometric model is established, with the center of the ground scene of the target ground area as the origin.

[0037] Step 2: Calculate the slant range between the radar and the target based on the circular trajectory geometry model, and perform range pulse compression on the obtained slant range.

[0038] Specifically, Figure 2 As shown, the center of the scene is point O, the distance from the target point at the original position of the SAR radar to the center point O is R0, the radius of the circle is set to r, and the angle between the target point and the SAR radar to the center point is θ a , the initial angle between the target point and the SAR radar is θ, the horizontal velocity is V, the initial height is H, and the height acceleration is a h , the velocity in height is v h , after azimuth time t, R n is the angle between the new radar target and the center point O and the radar on the ground. The ground angle between the target point and the SAR radar is θ c , the height at this time is H c . Then the initial slant range between the radar and the target is:

[0039]

[0040] The slope distance R after time t is

[0041]

[0042] Wherein, formula (2) is the slant range expression under the imaging model.

[0043] Step 3: Construct an echo model based on the distance parameter and perform distance compression on the echo to obtain the azimuth frequency f. a Multiply by the distance frequency f r Specifically, let R(t) be written as an expression based on R, where R is a constant. Separating the variable from the constant can more clearly express the specific distance change, then:

[0044]

[0045] Among them, R n It can be expressed as k multiples of R0, k can be expressed as:

[0046]

[0047] After Taylor expansion of formula (3), we can get:

[0048] R(t)=k0+k1t+k2t+k3t+k4t

[0049] Specifically, k i (i=0,…,4) is expressed as:

[0050]

[0051]

[0052] Let the speed of light be c and the carrier frequency be f c , the frequency modulation is γ. The radar echo time domain phase can be obtained according to the above formula, and the expression is as follows:

[0053]

[0054] in, The formula is distance to time.

[0055] It should be noted that, for the sake of simplicity of calculation, the azimuth and range coefficients are not added, and only the phase is retained for operation.

[0056] Let f r is the distance frequency, and formula (9) performs distance Fourier transform, transforming the time domain signal into the distance frequency domain and azimuth time domain. By converting the time domain into the frequency domain, the phase error can be quickly compensated in batches, and the obtained phase expression is:

[0057]

[0058] Among them, γ is the frequency modulation slope.

[0059] In order to compress the phase in the range frequency domain, the phase of the first exp(·) formula in equation (10) is filtered to construct the phase filter H1 as follows:

[0060]

[0061] Multiplying the phase filter H1 with formula (10) can obtain the formula after range frequency domain compression, namely:

[0062]

[0063] Perform azimuth Fourier transform on formula (12) to convert the distance-time formula into azimuth-frequency formula so that it can be compensated in batches. Then transform it into the two-dimensional frequency domain to obtain:

[0064]

[0065] Among them, f a is the azimuth frequency, α i The term represents the coupling coefficient in the range and azimuth directions, t n The term is the time error and does not need to be processed. Then α i The coefficients are:

[0066] α2=1 / 4k2

[0067]

[0068] Then, replace f in formula (13) rand f a The coupling term is expanded. Since the coupling term contains f r With f a The multiplied coupling term directly compensates the coupling phase, but the compensation effect is not very ideal. By constructing the coupling phase expansion term, we get:

[0069]

[0071] in is the coefficient of the expanded phase, then the coefficient of the specific phase is:

[0072]

[0073] Then the coupled phase is expanded. The phase after the coupling term is expanded can be divided into uncoupled phase and coupled phase. Accurate compensation for these two phases can obtain a good focusing effect. The phase is expanded to obtain:

[0074]

[0075] Next, the f in the above phase r and f a The non-mixed terms are processed and the non-mixed phase is eliminated using the following function filter H2, which can remove the non-coupled phase in the phase. Since the phase has a coefficient, the filter H2 also changes, which can be obtained:

[0076]

[0077] After eliminating the phase, we get:

[0078]

[0079] Step 4: Perform Stolt interpolation compensation on the coupling phase, and obtain an imaging image of the circular trajectory SAR image according to the result of Stolt interpolation compensation.

[0080] Specifically, by constructing a special interpolation formula, we can get the following formula:

[0081]

[0082] Substituting the above generalized Stolt substitution into formula (17) yields:

[0083]

[0084] Directly use formula (20) to eliminate the distance error term error in formula (19):

[0085]

[0086] The phase term after compensation is

[0087]

[0088] where k 0ref , represents k0, reference value.

[0089] After the phase is compensated by the above formula, the two-bit frequency domain offset term is compensated. After the two-dimensional Fourier inverse transform is transformed to the time domain, it can be seen that the imaging result is good, the focusing effect is excellent, and it is not easily defocused. The time domain formula after the two-dimensional Fourier inverse transform is:

[0090]

[0091] in Represents the transformed time dimension after substitution.

[0092] In this embodiment, by establishing a circular motion trajectory geometric imaging model, the height change and angle transformation are integrated into the geometric model. Next, the model is used to perform range pulse compression on the slant distance between the radar and the target point to generate a preliminary expression of the distance frequency domain and azimuth time domain signal. Then, the distance phase in the two-dimensional frequency domain is constructed, and the phase that does not have distance and azimuth coupling is compensated. Finally, the coupled phase is compensated and Stolt interpolation is applied to generate a SAR imaging image based on a circular trajectory. The above scheme completes the imaging effect after the change of the tilt angle and height.

[0093] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments including components are made without departing from the principles and spirit of the present invention, and still fall within the scope of protection of the present invention.

Claims

1. An imaging algorithm for circular curved trajectories based on special Stolt interpolation, characterized in that: The steps include: Step 1: Obtain the location information of the radar target ground area, and establish a circular trajectory geometric model based on the location information; Step 2: Calculate the slant range between the radar and the target based on the circular trajectory geometry model, and perform range pulse compression on the obtained slant range by deslanting the slant range. The method is as follows: f r is the distance frequency domain, t is the azimuth time domain, c is the speed of light, f c is the carrier frequency, k0 is the zero-order term after the slant range series is expanded, k1 is the first-order term after the slant range series is expanded, k2 is the second-order term after the slant range series is expanded, k3 is the third-order term after the slant range series is expanded, and k4 is the fourth-order term after the slant range series is expanded; Step 3: Apply the slant range expression to transform it into the slant range parameter in the two-dimensional frequency domain, and then construct a two-dimensional frequency domain model, and perform distance compression on the echo in the two-dimensional frequency domain, so as to obtain the frequency f of the azimuth. a Multiply the frequency f by the distance r Coupling phase compensation; Step 4: Perform Stolt interpolation compensation on the coupling phase, and obtain an imaging image of the circular trajectory SAR image according to the result of Stolt interpolation compensation.

2. The imaging algorithm of a circular curved trajectory based on special Stolt interpolation according to claim 1, characterized in that: In the step 1, a circular trajectory geometric model is established, with the center of the ground scene of the target ground area as the origin.

3. The imaging algorithm of a circular curved trajectory based on special Stolt interpolation according to claim 1, characterized in that: In step 2, the center of the scene is defined as point O, the distance from the target point at the original position of the SAR radar to the center point O is R0, the radius of the circle is set to r, and the angle between the target point and the SAR radar to the center point is θ a , the initial angle between the target point and the SAR radar is θ, the horizontal velocity is V, the initial height is H, and the height acceleration is a h , the velocity in height is v h , then the initial slant range between the radar and the target is: After the azimuth time t, R n is the angle between the new radar target and the center point O and the radar on the ground. The ground angle between the target point and the SAR radar is θ c , the height at this time is H c , then the slope distance after time t is:

4. The imaging algorithm of a circular curved trajectory based on special Stolt interpolation according to claim 2, characterized in that: In step 2, the method for deslanting the slant distance after time t is as follows: First, convert the slope distance R(t) to R as the basis, the expression is as follows: Among them, R n It can be expressed as k multiples of R0, k can be expressed as: Taylor expansion of the expression of k yields: R(t)=k0+k1t+k2t+k3t+k4t Definition: Let the speed of light be c and the carrier frequency be f c , the modulation frequency is γ, then the fundamental frequency echo signal is expressed as follows: in, Distance to time; Let f r is the distance frequency, and the baseband echo signal is transformed by distance Fourier transform to obtain: Among them, γ is the frequency modulation slope.

5. The imaging algorithm of a circular curved trajectory based on special Stolt interpolation according to claim 4, characterized in that: In step 2, the method of distance pulse compression is: First, the range pulse compression function is defined as: Then, the expression of the baseband echo signal after the range Fourier transform is multiplied by the defined range pulse compression function to obtain:

6. The imaging algorithm of a circular curved trajectory based on special Stolt interpolation according to claim 5, characterized in that: In step 3, the echo model expression is constructed as follows: Among them, f a is the azimuth frequency, α i The term represents the coupling coefficient in the range and azimuth directions, t n The term is the time error.

7. The imaging algorithm of a circular curved trajectory based on special Stolt interpolation according to claim 6, characterized in that: In step 3, the phase compensation method is: First, expand the two-bit frequency domain distance phase to obtain: in is the coefficient of the phase after unwrapping; Unwrap the unwrapped phase again:

8. The imaging algorithm of a circular curved trajectory based on special Stolt interpolation according to claim 7, characterized in that: In the step 3, the non-coupling term is eliminated, and after elimination, the following is obtained:

9. The imaging algorithm of a circular curved trajectory based on special Stolt interpolation according to claim 8, characterized in that: The specific method of step 4 is: First, construct the Stolt interpolation formula: Then substitute the constructed Stolt interpolation formula into the phase to eliminate the uncoupled term, and we get: Eliminate the distance error term and obtain the compensated phase term: where k 0ref , represents k0, Reference value; Finally, the compensation is completed by performing a two-dimensional Fourier inverse transform in Represents the transformed time dimension after substitution.

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