CN103983970A

CN103983970A - Ground accelerating moving target imaging method based on equivalent range equation

Info

Publication number: CN103983970A
Application number: CN201410143272.7A
Authority: CN
Inventors: 王彤; 李永康; 鲁缘政; 任倩倩
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2014-04-10
Filing date: 2014-04-10
Publication date: 2014-08-13

Abstract

The invention belongs to the technical field of radar, and discloses a ground accelerating moving target imaging method based on an equivalent range equation. The method includes the steps that (1) quadratic fit is carried out on a square of a target range equation, the equivalent range equation is built, and a ground accelerating target is equivalent into a static target; (2) an original echo signal of the target is changed into a two-dimensional frequency domain; (3) according to the equivalent range equation, a signal model of a two-dimensional frequency domain ground accelerating target is built; (4) according to the signal model of the two-dimensional frequency domain ground accelerating target and by means of a static target imaging algorithm, the ground accelerating target is imaged. According to the method, people only need to know equivalent speed and do not need to know speed parameters, position parameters and the acceleration speed of the target to precisely image the ground accelerating moving target by means of the static target imaging algorithm, and accordingly a programming and system signal processing structure is greatly simplified.

Description

Ground accelerated motion target imaging method based on equivalent distances equation

Technical field

The invention belongs to Radar Technology field, a kind of ground accelerated motion target imaging method based on equivalent distances equation specifically, for the synthesis of aperture radar (Synthetic Aperture Radar, SAR) to ground acceleration motive target imaging.

Background technology

That synthetic-aperture radar (Synthetic Aperture Radar, SAR) is that grow up nineteen fifties a kind of has is round-the-clock, the microwave imaging radar of round-the-clock, high-penetration, high-resolution characteristic.Compare with traditional radar, SAR can obtain higher resolution and imaging precision.As the important breakthrough of modern radar technology, SAR has been widely used in the fields such as military investigation, geological exploration, the condition of a disaster assessment, remote sensing.Along with the competitively research of countries in the world to technique, SAR technology is fast-developing towards directions such as high-resolution, multiband, multi-mode, complete polarizations.

Tradition SAR is just used for surface feature background to carry out two-dimensional imaging, and does not relate to detection and the imaging for moving target.Because moving-target has kinetic characteristic, can cause after utilizing conventional imaging algorithm to moving-target imaging and defocus with orientation to skew, therefore need to, by imaging technique and moving target detection technique combination, can distinguish moving-target and quiet target.Along with the increase of military and civilian demand, ground moving object detects (Ground Moving Target Indication, GMTI) function and more and more comes into one's own, and SAR-GMTI technology is arisen at the historic moment.SAR-GMTI technology can, when obtaining static scene, detect moving target.In military affairs, SAR-GMTI system has great using value, and it can carry out large area investigation, supervision to ground or sea, moving target is detected, follows the tracks of, is located simultaneously, significant for military battle field information Real Time Observation and feedback.At civil area, the same tool of SAR-GMTI is of great significance, for example, the operation conditions of the vehicle on highway and the ship on sea is monitored, thereby provide necessary help for traffic administration.

In recent years, in order further to improve scouting and the monitoring capacity of SAR-GMTI system, SAR Ground moving target imaging becomes study hotspot.Yet existing SAR Ground moving target imaging technology, mostly for ground moving object at the uniform velocity, has no report for the technology of accelerating ground moving object.

Summary of the invention

The object of the invention is to propose a kind of ground accelerated motion target imaging method based on equivalent distances equation, without location parameter, speed parameter and the acceleration of knowing target, utilize the existing imaging algorithm for static target to ground accelerated motion target imaging, greatly simplified programming and system signal and processed structure; And can be accurate to ground accelerated motion target imaging, counting yield is high.

Technical thought of the present invention is: 1) to target range equation square carry out quadratic fit, set up equivalent distances equation, and target Equivalent is accelerated in ground become static target; 2) target original echoed signals is transformed to two-dimensional frequency, and according to equivalent distances equation, set up the signal model of two-dimensional frequency ground acceleration target; 3), according to the signal model of two-dimensional frequency ground acceleration target, utilize static target imaging algorithm to accelerate target imaging to ground.Utilize equivalent distances equation that ground accelerated motion target Equivalent is become to static target, then utilize the existing imaging algorithm for static target to ground accelerated motion target imaging.

In order to achieve the above object, the present invention is achieved by the following technical solutions.

A ground accelerated motion target imaging method based on equivalent distances equation, is characterized in that, comprises the following steps:

Step 1, to target range equation square carry out quadratic fit, set up equivalent distances equation, and target Equivalent is accelerated in ground become static target;

Wherein radar is operated under positive side-looking pattern, and Texas tower speed is v _a, t _afor the slow time; t _a=0 o'clock, target azimuth was respectively v to speed, distance to acceleration to acceleration, distance to speed, orientation _x, a _x, v _yand a _y, and now, radar is positioned at true origin, and target is positioned at (0, y ₀);

T _atarget to the instantaneous distance the Representation Equation of radar is constantly:

R (t_{a}) = \sqrt{{(y_{0} + v_{y} t_{a} + 0.5 a_{y} t_{a}^{2})}^{2} + {(v_{x} t_{a} + 0.5 a_{x} t_{a}^{2} - v_{a} t_{a})}^{2}}

The quadratic fit under minimum variance meaning of square carrying out to target range equation:

R^{2} (t_{a}) = a_{0} + a_{1} t_{a} + a_{2} t_{a}^{2} = {(\sqrt{a_{2}} t_{a} + \frac{a_{1}}{2 \sqrt{a_{2}}})}^{2} + a_{0} - \frac{a_{1}^{2}}{{4 a}_{2}}

Wherein, a ₀, a ₁and a ₂be respectively constant term, once and quadratic term coefficient;

Target range equation is carried out to equivalence, sets up equivalent distances equation:

Order

\sqrt{a_{2}} = v_{e}, - \frac{a_{1}^{2}}{2 \sqrt{a_{2}}} = x_{e}, \sqrt{a_{0} - \frac{a_{1}^{2}}{{4 a}_{2}}} = y_{e}

Can obtain equivalent distances equation:

R (t_{a}) = \sqrt{{(\sqrt{a_{2}} t_{a} + \frac{a_{1}}{2 \sqrt{a_{2}}})}^{2} + a_{0} - \frac{a_{1}^{2}}{{4 a}_{0}}} = \sqrt{{(v_{e} t_{a} - x_{e})}^{2} + y_{e}^{2}}

Wherein, v _e, x _ewith _yebe respectively speed, position, target azimuth and the target range of the rear radar of equivalence to position;

Step 2, by the expression formula of the original echoed signals of equivalent distances equation substitution ground acceleration moving target, then carries out distance successively to Fourier transform and orientation to Fourier transform, obtains the signal model of two-dimensional frequency ground acceleration target;

Step 3, according to the signal model of two-dimensional frequency ground acceleration target, utilizes static target imaging algorithm to accelerate target imaging to ground.

In technique scheme, the concrete sub-step of step 2 is:

2a) original echoed signals of ground acceleration target can be expressed as:

s (t_{a}, t_{r}) = w_{a} (t_{a}) w_{r} (t_{r} - \frac{2 R (t_{a})}{c}) \exp {- j 4 π f_{c} \frac{R (t_{a})}{c} + jπ K_{r} {(t_{r} - \frac{2 R (t_{a})}{c})}^{2}}

Wherein, t _rfor the fast time, c is the light velocity, w _a(t _a), w _r(t _r) be respectively the orientation envelope of target echo signal and apart from envelope, f _cfor the carrier frequency of radar emission signal, K _rfrequency modulation rate for the linear FM signal of radar emission;

2b) by the expression formula of the original echoed signals of equivalent distances equation substitution ground acceleration moving target, then carry out successively distance to Fourier transform and orientation to Fourier transform, to set up the signal model of two-dimensional frequency ground accelerated motion target:

\begin{matrix} S (f_{a}, f_{r}) = W_{r} (f_{r}) W_{a} (f_{a} - f_{ac}) \exp {- j [\frac{π f_{r}^{2}}{K_{m} (v_{e}, f_{a})} + \frac{4 π y_{e}}{λ} (D (f_{a}, v_{e}) + \frac{f_{r}}{f_{c} D (f_{a}, v_{e})}) + \frac{2 π f_{a} x_{e}}{v_{e}}]} \\ D (f_{a}, v_{e}) = \sqrt{1 - \frac{c^{2} f_{a}^{2}}{{4 v}_{e}^{2} f_{c}^{2}}} \\ K_{m} (v_{e}, f_{a}) = K_{r} + \frac{{2 v}_{e}^{2} K_{r}^{2} f_{c}^{3} D^{3} (f_{a}, v_{e})}{{cy}_{e} f_{a}^{2}} \end{matrix}

Wherein, W _r(f _r) be the envelope of range on target signal frequency spectrum, W _a(f _a) be the envelope of echo signal azimuth spectrum, f _rfor frequency of distance, λ is wavelength, f _aorientation frequency, f _acfor target doppler centroid.

The present invention compared with prior art has the following advantages: when a) the present invention carries out imaging to target, only need to know velocity equivalent v _e, and without location parameter, speed parameter and the acceleration of knowing target, be conducive to improve counting yield and engineering application; B) the present invention can, with static target imaging algorithm to ground accelerated motion target imaging, simplify programming and system signal and process structure greatly; C) the present invention is accurate to the imaging of ground accelerated motion target.

Accompanying drawing explanation

Below in conjunction with accompanying drawing explanation and embodiment, the present invention is described in further details.

Fig. 1 is realization flow schematic diagram of the present invention;

Fig. 2 oblique distance planar S AR-GMTI systematic observation geometric graph; Wherein horizontal ordinate represent orientation to, ordinate represent distance to;

Fig. 3 is the target trajectory figure before range migration correction; Wherein horizontal ordinate represents range unit, and ordinate represents Doppler unit;

Fig. 4 is with the target trajectory figure after the range migration correction of the inventive method; Wherein horizontal ordinate represents range unit, and ordinate represents Doppler unit;

Fig. 5 (a) is with the target imaging result figure after the Azimuth Compression of the inventive method; Wherein horizontal ordinate represents range unit, and ordinate represents localizer unit;

Fig. 5 (b) is the contour map after amplifying; Wherein horizontal ordinate represent distance to, ordinate represent orientation to.

Embodiment

With reference to Fig. 1, the ground accelerated motion target imaging method based on equivalent distances equation of the present invention is described, its specific implementation step is as follows:

Step 1, to target range equation square carry out quadratic fit, set up equivalent distances equation, and target Equivalent is accelerated in ground become static target.

1a) be illustrated in figure 2 oblique distance planar S AR-GMTI systematic observation geometric graph, wherein radar is operated under positive side-looking pattern, and Texas tower speed is v _a, t _afor the slow time.T _a=0 o'clock, target azimuth was respectively v to speed, distance to acceleration to acceleration, distance to speed, orientation _x, a _x, v _yand a _y, and now, radar is positioned at true origin, and target is positioned at (0, y ₀).

Therefore, t _atarget can be expressed as to the instantaneous distance equation of radar constantly:

R (t_{a}) = \sqrt{{(y_{0} + v_{y} t_{a} + 0.5 a_{y} t_{a}^{2})}^{2} + {(v_{x} t_{a} + 0.5 a_{x} t_{a}^{2} - v_{a} t_{a})}^{2}}

1b) the quadratic fit under minimum variance meaning of square carrying out to target range equation:

R^{2} (t_{a}) = a_{0} + a_{1} t_{a} + a_{2} t_{a}^{2} = {(\sqrt{a_{2}} t_{a} + \frac{a_{1}}{2 \sqrt{a_{2}}})}^{2} + a_{0} - \frac{a_{1}^{2}}{{4 a}_{2}}

Wherein, a ₀, a ₁and a ₂be respectively constant term, once and quadratic term coefficient.Above-mentioned matching can realize by the function ployfit in matlab.Above-mentioned matching meeting brings error, but this error will, much smaller than wavelength, can be ignored.Illustrate, SAR systematic parameter is in Table 1, and target component is: y ₀=12km, v _x=6m/s, v _y=6m/s, a _x=1m/s ², a _y=1m/s ², the error that above-mentioned matching brings is 0.00086m, much smaller than wavelength (0.0333m), therefore, error can be ignored.

1c) target range equation is carried out to equivalence, sets up equivalent distances equation:

Order

\sqrt{a_{2}} = v_{e}, - \frac{a_{1}^{2}}{2 \sqrt{a_{2}}} = x_{e}, \sqrt{a_{0} - \frac{a_{1}^{2}}{{4 a}_{2}}} = y_{e}

Can obtain equivalent distances equation:

R (t_{a}) = \sqrt{{(\sqrt{a_{2}} t_{a} + \frac{a_{1}}{2 \sqrt{a_{2}}})}^{2} + a_{0} - \frac{a_{1}^{2}}{{4 a}_{0}}} = \sqrt{{(v_{e} t_{a} - x_{e})}^{2} + y_{e}^{2}}

Wherein, v _e, x _eand y _ebe respectively speed, position, target azimuth and the target range of the rear radar of equivalence to position.

1d) by equivalent distances equation, can be found out, be positioned at (0, y ₀) ground accelerated motion target range equation be positioned at (x _e, y _e) the range equation of static target the same.Therefore, can (0, y will be positioned at ₀) ground accelerated motion target Equivalent for being positioned at (x _e, y _e) static target, equivalence after radar speed size become v _e, direction is constant.

Step 2, by the expression formula of the original echoed signals of equivalent distances equation substitution ground acceleration moving target, then carries out distance successively to Fourier transform and orientation to Fourier transform, obtains the signal model of two-dimensional frequency ground acceleration target.

2a) original echoed signals of ground acceleration target can be expressed as:

s (t_{a}, t_{r}) = w_{a} (t_{a}) w_{r} (t_{r} - \frac{2 R (t_{a})}{c}) \exp {- j 4 π f_{c} \frac{R (t_{a})}{c} + jπ K_{r} {(t_{r} - \frac{2 R (t_{a})}{c})}^{2}}

Wherein, t _rfor the fast time, c is the light velocity, w _a(t _a), w _r(t _r) be respectively the orientation envelope of target echo signal and apart from envelope, f _cfor the carrier frequency of radar emission signal, K _rfrequency modulation rate for the linear FM signal of radar emission.

\begin{matrix} S (f_{a}, f_{r}) = W_{r} (f_{r}) W_{a} (f_{a} - f_{ac}) \exp {- j [\frac{π f_{r}^{2}}{K_{m} (v_{e}, f_{a})} + \frac{4 π y_{e}}{λ} (D (f_{a}, v_{e}) + \frac{f_{r}}{f_{c} D (f_{a}, v_{e})}) + \frac{2 π f_{a} x_{e}}{v_{e}}]} \\ D (f_{a}, v_{e}) = \sqrt{1 - \frac{c^{2} f_{a}^{2}}{{4 v}_{e}^{2} f_{c}^{2}}} \end{matrix}

\begin{matrix} K_{m} (v_{e}, f_{a}) = K_{r} + \frac{{2 v}_{e}^{2} K_{r}^{2} f_{c}^{3} D^{3} (f_{a}, v_{e})}{{cy}_{e} f_{a}^{2}} \end{matrix}

Static target imaging algorithm has a lot, and all applicable.Take below simple, range Doppler algorithm illustrates imaging process as example efficiently.

The main process of SAR imaging is Range compress, range migration correction and Azimuth Compression.Range compress, can be configured to apart from matched filter by realizing apart from matched filtering in two-dimensional frequency:

H_{r} (f_{r}) = \exp {j \frac{π f_{r}^{2}}{K_{m} (v_{e}, f_{a})}}

Range migration correction can accurately be realized by sinc interpolation at range-Dopler domain, and the expression formula of the signal after range migration correction is:

S (f_{a}, t_{r}) = W_{a} ({f_{a} - f}_{ac}) p_{r} (t_{r} - \frac{2 y_{e}}{c}) \exp {- j [\frac{4 π y_{e}}{λ} D (f_{a}, v_{e}) + \frac{2 π f_{a} x_{e}}{v_{e}}]}

Wherein, p _r(t _r) be apart from impulse response function.

Azimuth Compression can be realized by orientation matched filtering at range-Dopler domain, and orientation matched filter can be configured to:

H_{a} (f_{a}) = \exp {j \frac{4 π y_{e}}{λ} D (f_{a}, v_{e})}

Signal after orientation matched filtering is carried out to orientation and to inverse Fourier transform, just can realize the imaging to ground accelerated motion target, after imaging, target SAR image area signal can be expressed as:

s (t_{a}, t_{r}) = p_{a} (t_{a} - \frac{x_{e}}{v_{e}}) p_{r} (t_{r} - \frac{2 y_{e}}{c}) \exp {j 2 π f_{ac} t_{a}}

Wherein, p _a(t _a) be orientation impulse response function.

Effect of the present invention further illustrates by following emulation experiment:

Emulation 1, the target trajectory after Range compress.

SAR systematic parameter is in Table 1, and target component is: y ₀=12km, v _x=6m/s, v _y=6m/s, a _x=1m/s ², a _y=1m/s ².In two-dimensional frequency, by phase multiplication, realize Range compress, then carry out distance and obtain the target trajectory after Range compress to inverse Fourier transform.Simulation result is shown in Fig. 3.By Fig. 3, can see that target trajectory exists obvious range migration.

Table 1SAR systematic parameter

Carrier frequency	9GHz	Radar speed	140m/s
				Apart from bandwidth	150MHz	Scene center distance	12km
Distance samples frequency	240MHz	Orientation bandwidth	140Hz
				Pulse repetition rate	1000Hz	Pulsewidth	20μs

Emulation 2, carries out the target trajectory after range migration correction with the present invention.

Parameter setting in this emulation is identical with arranging in emulation 1, has only used velocity equivalent v during emulation _e, and not using location parameter, speed parameter and the acceleration of target, simulation result is shown in Fig. 4.As seen from Figure 4, the track of target has become straight line, and its range migration has well been proofreaied and correct.This emulation experiment explanation the present invention can only know velocity equivalent v _eprerequisite under realize the range migration correction to ground acceleration moving target.

Emulation 3, Ground moving target imaging result of the present invention.

Parameter setting in this emulation is identical with arranging in emulation 1, has only used velocity equivalent v during emulation _e, and not using location parameter, speed parameter and the acceleration of target, simulation result is shown in Fig. 5.Fig. 5 (a) has provided the result after Azimuth Compression, and Fig. 5 (b) has provided the contour map after amplifying.By Fig. 5 (a), can be found out, target has well been focused on, and by Fig. 5 (b), can be found out, image quality is very high.This simulation results show the present invention can only know velocity equivalent v _eprerequisite under realize the accurately image to ground accelerated motion target.

Claims

1. the ground accelerated motion target imaging method based on equivalent distances equation, is characterized in that, comprises the following steps:

R (t_{a}) = \sqrt{{(y_{0} + v_{y} t_{a} + 0.5 a_{y} t_{a}^{2})}^{2} + {(v_{x} t_{a} + 0.5 a_{x} t_{a}^{2} - v_{a} t_{a})}^{2}}

R^{2} (t_{a}) = a_{0} + a_{1} t_{a} + a_{2} t_{a}^{2} = {(\sqrt{a_{2}} t_{a} + \frac{a_{1}}{2 \sqrt{a_{2}}})}^{2} + a_{0} - \frac{a_{1}^{2}}{{4 a}_{2}}

Order

\sqrt{a_{2}} = v_{e}, - \frac{a_{1}^{2}}{2 \sqrt{a_{2}}} = x_{e}, \sqrt{a_{0} - \frac{a_{1}^{2}}{{4 a}_{2}}} = y_{e}

Can obtain equivalent distances equation:

R (t_{a}) = \sqrt{{(\sqrt{a_{2}} t_{a} + \frac{a_{1}}{2 \sqrt{a_{2}}})}^{2} + a_{0} - \frac{a_{1}^{2}}{{4 a}_{0}}} = \sqrt{{(v_{e} t_{a} - x_{e})}^{2} + y_{e}^{2}}

Wherein, v _e, x _eand y _ebe respectively speed, position, target azimuth and the target range of the rear radar of equivalence to position;

2. the ground accelerated motion target imaging method based on equivalent distances equation according to claim 1, is characterized in that, the concrete sub-step of step 2 is:

2a) original echoed signals of ground acceleration target can be expressed as:

s (t_{a}, t_{r}) = w_{a} (t_{a}) w_{r} (t_{r} - \frac{2 R (t_{a})}{c}) \exp {- j 4 π f_{c} \frac{R (t_{a})}{c} + jπ K_{r} {(t_{r} - \frac{2 R (t_{a})}{c})}^{2}}

\begin{matrix} S (f_{a}, f_{r}) = W_{r} (f_{r}) W_{a} (f_{a} - f_{ac}) \exp {- j [\frac{π f_{r}^{2}}{K_{m} (v_{e}, f_{a})} + \frac{4 π y_{e}}{λ} (D (f_{a}, v_{e}) + \frac{f_{r}}{f_{c} D (f_{a}, v_{e})}) + \frac{2 π f_{a} x_{e}}{v_{e}}]} \\ D (f_{a}, v_{e}) = \sqrt{1 - \frac{c^{2} f_{a}^{2}}{{4 v}_{e}^{2} f_{c}^{2}}} \\ K_{m} (v_{e}, f_{a}) = K_{r} + \frac{{2 v}_{e}^{2} K_{r}^{2} f_{c}^{3} D^{3} (f_{a}, v_{e})}{{cy}_{e} f_{a}^{2}} \end{matrix}