RU2537788C1 - Method of measuring radial velocity of reflector in side-looking synthetic aperture radar - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method of measuring radial velocity of a reflector in side-looking synthetic aperture radar relates to radar scanning of the Earth's surface from aircraft and can be used to simultaneously form brightness and velocity portraits of a surface with high resolution, precise referencing to coordinates of an area and noise-immunity. The invention employs a differential (differential-frequency) method of processing a series of coherent pulses which form an azimuthal image line in synthetic aperture radar. The method comprises use of two synthesizers, where a forward and a double-period delayed signal are transmitted to the inputs of said synthesizers. Both external signals, as well as a reference (synthesizing) signal, undergo differentiation before reaching the synthesizers. The synthesized complex-conjugated signals are correlated to form, at the output of a correlator, two signals which are calibrated on the radar cross section and radial velocity of the reflector.

EFFECT: providing geographic referencing of images of moving objects to a location and suppressing signals of fixed reflectors located in the region of azimuthal synthesis.

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Description

The invention relates to radar surface of the Earth from aircraft and can be used for the simultaneous formation of brightness (amplitude) and speed portraits of the surface, including small moving objects, with high spatial resolution, referenced to the coordinates of the area and noise immunity. A similar problem is typical when forming in SAR (side-scan radar with a synthesized aperture) images of sea currents against the background of an excited surface, river currents with strong reflections from coastal structures, and also when measuring speed and determining the location of local moving objects on the surface of land or ocean.

Known methods of signal processing in SAR, allowing to measure the speed of objects on the surface of the Earth. In [1, 2], processing methods are proposed that allow one to determine both (radial and tangential) components of the speed of the reflector from the aircraft - but only at high speeds sufficient to shift the reflector by dozens of longitudinal and transverse resolution elements during the synthesis. There is a processing method that allows you to restore the radial velocity of marine mesoscale currents by displacing the median of the Doppler spectrum, the shape of which is due to interference of elementary reflectors of a rough surface when moving the antenna and the random nature of sea waves [3, 4]. In this case, on the contrary, the measured speed is small, and for its measurement it is necessary to accumulate independent samples of the signal at sites that include several thousand resolution elements. Finally, the TerraSAR-X spacecraft was developed and put into operation, using an interferometer with a longitudinal antenna base to form high-speed portraits of the Earth’s surface [7, 8, 11].

In many works using the measuring properties of aerospace SAR, the processing method is taken as the basis in which the synthesizing (reference) signal compensates for the phase change of the received signal due to the moving radial reflector during tangential movement of the antenna [5]. Neglecting the effect of “range migration” in the ideal case of a single (point) reflector, the synthesis process is described by the convolution integral when forming the azimuth line U (x) of the radar image:

, $$U\left(x\right)=\frac{U_0}{D_x}{\displaystyle \underset{-L_x/2}{\overset{L_x/2}{\int }}\exp }\left\{-j\left[\Delta \Psi \left(x,u\right)\right]\right\}du$$

,

,Where $$\Delta \Psi \left(x,u\right)={\varphi }_0-\frac{2\pi f_{dy}}{W_x}\left(x-u\right)+\frac{k}{R_n}{\left(x-u\right)}^2-\frac{k{u}^2}{R_n}\left(\mathrm{one}\right)$$

,

- доплеровский сдвиг, вызываемый радиальной скоростью V_y отражателя, R_n и γ_n - наклонная дальность и угол визирования отражателя, D_x и L_x - размеры реального и синтезированного раскрывов антенны, k=2π/λ, λ - длина волны сигнала, u - аргумент функции свертки. В результате подобной операции для каждой строки дальности R_n получается азимутальный сигнальный отклик:U ₀ and φ ₀ - constant initial amplitude and phase of the reflector, $$f_{dy}=\frac{2V_y\sin {\gamma }_n}{\lambda }$$

is the Doppler shift caused by the radial velocity V _{y of the} reflector, R _n and γ _n are the slant range and angle of sight of the reflector, D _x and L _x are the dimensions of the real and synthesized antenna openings, k = 2π / λ, λ is the wavelength of the signal, u is an argument to the convolution function. As a result of a similar operation, for each row of the range R _n, an azimuthal signal response is obtained:

$$U\left(x\right)=U_0\frac{r_{x0}}{r_x}\exp \left[-\frac{\pi }{2r_x^2}{\left(x-x_V\right)}^2\right]\exp \left\{j\left[{\varphi }_{\Sigma }+\frac{2kx}{R_n}\left(x-x_V\right)\right]\right\}\left(2\right)$$

- сдвиг оси синтеза, обусловленный применяемым алгоритмом.where x is the azimuthal resolution of the real and synthesized apertures, $$x_V=\frac{V_y{R}_n\sin {\gamma }_n}{W_x}$$

- shift of the synthesis axis due to the applied algorithm.

Thus, the shift of the synthesis axis and the presence of an unpredictable phase φ ₀ excludes the possibility of measuring the velocity in the SAR from the phase of the signal at the center of the amplitude peak (x = x _V ). If to use a correlator, i.e. to compare the phases of the signals, one of which is delayed by two pulse repetition periods (2T _r ), then based on (2) the responses of each of the two channels are recorded in the form:

$$U_{\mathrm{one},2}\left(t\mp T_r\right)=U_0\frac{r_{x0}}{r_x}\exp \left[-\frac{\pi W_x^2}{2r_x^2}{\left(t\mp T_r-t_V\right)}^2\right]\exp \left\{j\left[{\mathrm{<figure-callout\; id="0"\; label="\phi "\; filenames="00000021.png,00000022.png"\; state="\{\{state\}\}">\varphi </figure-callout>}}_0+\frac{2k{W}_x^2}{R_n}\left(t\mp T_r\right)\left(x\mp T_r-x_V\right)\right]\right\}\left(3\right)$$

At the output of the correlator, we obtain the azimuthal response

, $$\begin{array}{l}{U}_{cor}\left(t\right)={\left[U_{\mathrm{one}}\left(t-T_r\right)\times {\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="00000022.png"\; state="\{\{state\}\}">U</figure-callout>}}_2^{*}\left(t+T_r\right)\right]}^{\mathrm{one}/2}=\\ =U_0\frac{r_{x0}}{r_x}\exp \left[-\frac{\pi W_x^2}{2r_x^2}{\left(t-t_V\right)}^2\right]\exp \left(-\frac{\pi W_x^2{\mathrm{<figure-callout\; id="2"\; label="T\; r"\; filenames="00000022.png"\; state="\{\{state\}\}">T\; </figure-callout>}}_r^{}}{2r_x^2}\right)\exp \left[-\mathrm{four}kj\frac{W_x^2{T}_r}{R_n}\left(2t-t_V\right)\right]\left(\mathrm{four}\right)\end{array}$$

,

. Таким образом, в отклике (4) исключена начальная фаза φ₀, и в центре амплитудного пика содержится информация о скорости отражателя, но сам пик сдвигается по азимутальной оси на величину $$t_V=\frac{x_V}{W_x}=\frac{V_y{R}_n\sin {\gamma }_n}{W_x^2}$$

.so in the center of the peak (t = t _V ) we have the phase $${\psi }_n=\frac{8\pi T_r{V}_y\sin {\gamma }_n}{\lambda }=\mathrm{four}\pi T_r{f}_{dy}$$

. Thus, in response (4), the initial phase φ _{0 is} excluded, and information on the speed of the reflector is contained in the center of the amplitude peak, but the peak itself is shifted along the azimuthal axis by $$t_V=\frac{x_V}{W_x}=\frac{V_y{R}_n\sin {\gamma }_n}{W_x^2}$$

.

, имеем ограничение на величину продольного разрешения РСА: r_x≥2W_xT_r, что соответствует возможности полной фокусировки апертуры. В центре амплитудного пика при полной фокусировке получим отклик $$U_{cor}=U_0\frac{r_{x0}}{r_x}\exp \left(-\frac{\pi }{8}\right)\exp \left(j4\pi T_r{f}_{dy}\right)$$

. Крутизна фазоскоростной характеристики составитAssuming a valid value for the modulus of the correlation coefficient $${\rho }_n=\exp \left(-\frac{\pi W_x^2{\mathrm{<figure-callout\; id="2"\; label="T\; r"\; filenames="00000022.png"\; state="\{\{state\}\}">T\; </figure-callout>}}_r^{}}{2r_x^2}\right)\ge \exp \left(-\frac{\pi }{8}\right)$$

, we have a restriction on the longitudinal resolution of the SAR: r _x ≥2W _x T _r, which corresponds to the possibility of full focusing of the aperture. In the center of the amplitude peak with full focus, we obtain a response $$U_{cor}=U_0\frac{r_{x0}}{r_x}\exp \left(-\frac{\pi }{8}\right)\exp \left(j\mathrm{four}\pi T_r{f}_{dy}\right)$$

. The steepness of the phase-speed characteristic is

, $$\frac{\partial {\Psi }_n}{\partial V_y}=\frac{8\pi T_r\sin {\gamma }_n}{\lambda }\left(5\right)$$

,

which, as we see, is determined by the wavelength, the pulse repetition period and the angle of sight and does not depend on the speed of the device.

Figure 1 shows the graphs plotted on the x axis for the modules and phases of the signals at the correlator output, built on the basis of expression (4) with the parameters of the space-based interference SAR of the TerraSAR-X apparatus (W _x = 8 · 10 ³ m / s, H = 6.5 · 10 ³ m, γ _n = 30 ⁰ , λ = 3-10 ^-2 m, D _x = 4 m, r _x0 = 6 · 10 ³ m). The distance l _x = 2 m between the phase centers of the antenna in this case is equivalent to the repetition period T _r = l _x / 2W _x = 0.125 ms. The calculations were made with a resolution of r _x = 4 m, setting V _y = 0 and 1 m / s. It is seen that in the presence of radial velocity, a phase shift appears in the center of the amplitude peak, but a tangential shift of the peak appears, reaching 50 m, or ~ 12 elements of longitudinal resolution r _x . A sea ship moving radially at a speed of 15 knots (~ 8 m / s) in the radar image should be shifted by half a kilometer along the axis of movement of the vehicle (i.e., by the value x _v >> r _x practically along the meridian when the ship moves along parallel) .

Thus, with this synthesis method in interference SAR (IRSA) it is possible to measure the speed of the reflector V _y by changing the phase of the reflected signal, as has long been used in radar systems SDS (selection of moving targets) operating without synthesis [9]. At the same time, it is known that deep suppression of signals from fixed reflectors in SDC systems is carried out by using a frequency-difference algorithm implemented by periodically subtracting the phases of the received and reference signals. As applied to SAR, this means that the synthesis algorithm must perform convolution with the reference signal not in phases, but in their derivatives, i.e., at current Doppler frequencies. Differentiating the initial phase difference (1) as a function of time t = x / W _x, we find a new algorithm in the form:

$$U\left(t\right)=U_0\frac{W_x}{D_x}{\displaystyle \underset{-{\tau }_x/2}{\overset{{\tau }_x/2}{\int }}\exp \left\{-jt\frac{\partial \Delta \Psi \left(t,\tau \right)}{\partial d}\right\}d\tau }=U_0\frac{W_x}{D_x}{\displaystyle \underset{-{\tau }_x/2}{\overset{{\tau }_x/2}{\int }}\exp \left\{-jt\left[\frac{2k{W}_x^2}{R_n}\left(t-\tau \right)-2\pi f_{dy}\right]\right\}d\tau }\left(6\right)$$

, $${\tau }_s=\frac{L_x}{W_x}$$

. Азимутальный отклик РСА на временной оси при этом составляетWhere $$f_{dy}=\frac{2V_y\sin {\gamma }_n}{\lambda }$$

, $${\tau }_s=\frac{L_x}{W_x}$$

. The azimuthal response of the SAR on the time axis in this case is

$$U\left(t\right)=U_0\frac{r_{x0}}{r_x}\exp \left(-\frac{\pi W_x^2{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="00000022.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}{2r_x^2}\right)\exp \left[-j\frac{\mathrm{four}\pi W_x^2}{\lambda R_n}t\left(t-t_v\right)\right]\left(7\right)$$

Thus, when synthesizing the aperture according to the difference-frequency algorithm, the azimuthal shift of the moving reflector mark on the luminance image in the SAR disappears, the phase in the center of the amplitude peak does not depend on φ ₀ , however, the determination of the velocity by phase remains impossible. Repeating the previous transformations for the two-channel method of measuring velocity, for the synthesized responses (7) we obtain the following response at the output of the correlator:

, $$U_{cor}\left(t\right)={\left[U_{\mathrm{one}}\left(t-T_r\right)\times {\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="00000022.png"\; state="\{\{state\}\}">U</figure-callout>}}_2^{*}\left(t+T_r\right)\right]}^{\mathrm{one}/2}=U_0\frac{r_{x0}}{r_x}\exp \left(-\frac{\pi W_x^2}{2r_x^2}\right)\exp \left(-\frac{\pi W_x^2{\mathrm{<figure-callout\; id="2"\; label="T\; r"\; filenames="00000022.png"\; state="\{\{state\}\}">T\; </figure-callout>}}_r^{}}{2r_x^2}\right)\exp \left[-j\frac{\mathrm{four}k{W}_x^2{T}_r}{R_n}\left(t-t_V\right)\right]\left(8\right)$$

,

those. in the center of the amplitude peak (t = 0) at the output of the correlator we get the same phase shift as in the synthesis according to the difference-phase algorithm (see expression (4)) - but without shifting the peak itself along the synthesis axis:

$${\psi }_n=\frac{8\pi T_r{V}_y\sin {\gamma }_n}{\lambda }=\mathrm{four}\pi T_r{f}_{dy}\left(9\right)$$

Corresponding graphs on the x axis are constructed in FIG. 2 and FIG. 3 for the same parameters of a space SAR as in FIG. 1. It is seen that, in the presence of speed V _y , a phase shift appears, but the amplitude peak does not shift.

Functional representation of the difference-frequency synthesis algorithm:

$$U\left(n\right)=\frac{{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="00000021.png,00000022.png"\; state="\{\{state\}\}">U</figure-callout>}}_0}{2}{\displaystyle \sum _{m=-M/2}^{m=M/2}\exp }\left\{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="00000022.png"\; state="\{\{state\}\}">j</figure-callout>}2\pi n\left[\Delta {\Psi }_x\left(n\right)-\Delta {\Psi }_u\left(m\right)\right]\right\}\left(10\right)$$

Here n and m are the ordinal numbers of pulses of the external and reference signals, ΔΨ _x and ΔΨ _u are the inter-pulse increments of their phases, T _r = D _x / 4W _x is the pulse repetition period, M = L _x / W _x T _r is the number of summed pulses . In accordance with expression (9), when convolving an external signal with a reference signal, it is necessary to multiply the phase difference of the external and reference signals obtained over the period by the current number n of synthesized pulses, because n = t / T _r . It can be seen that with such a replacement, the exponent turns into the difference between the interpulse frequency increments of the external and reference signals multiplied by the current synthesis time.

The above calculations show the following. First, the use of a correlator in the IRSA comparing the signals of two antennas with the spacing of their phase centers along the flight line [7, 8] - can be successfully replaced by a correlator that uses a signal delay of two pulse repetition periods. It is this method that is used in radar systems with selection of moving targets (SDC) for the deep suppression of signals from stationary reflectors falling into the antenna beam, including along its side lobes [9]. Secondly, the implementation of such a method in SAR means the transition from a difference-phase synthesis algorithm to a difference-frequency one. Its advantages are, in addition to compensating for the initial phase of the reflector signal, also in eliminating the azimuthal shift of the mark of the moving reflector in the brightness image of the area.

Thus, the proposed method for measuring the speed of the reflector in the SAR allows you to simultaneously generate high-speed and luminance images of the area with reference luminance images of the moving reflectors to the geographical coordinates of the area. Finally, the simultaneous (two-channel) formation of brightness and speed images should allow, by introducing a threshold value of the measured _pore speed (V _y ), to exclude from each (or both) images fixed reflectors located within the synthesis region (L _x ) and on the same range line (R _n ). This is achieved by introducing key (cut-off) cascades during the formation of the azimuthal line in the brightness and speed channels.

Comparison of the proposed method for forming high-speed images in SAR with the available patents of similar composition and purpose [10-13] shows the following. In the patent [10], which is the prototype, it is also proposed to use one antenna with subsequent separation into two channels, their independent synthesis and measurement of the Doppler frequency shift, which determines the phase difference at the output of the multiplier when sighting a radially moving reflector (see Fig 11, page 12 and Fig. 12, page 13). However, as indicated above, the necessary condition for the selection of a moving reflector, if there are stationary reflectors on the same range (and within the azimuthal synthesis region), is the use of a matched filter, which in this case should be the difference-frequency synthesis algorithm, which we offered. The patent [11] substantiates the principle of operation and composition of the currently operating TerraSAR-X radar space complex, in which, as it later became clear [8], the signal from fixed reflectors is not suppressed in the high-speed channel. The patent [12] substantiates the principle of operation and composition of the recently launched Tandem TerraSAR-X two-device space complex; patent [13] proposes the principle of operation of an interferometer specifically designed to measure the height of fast-moving sea waves.

The technical result consists in providing a geographic reference of the images of moving objects to the terrain and suppressing the signals of stationary reflectors located in the field of azimuthal synthesis.

A functional diagram of the method is presented in figure 4, where are indicated: 1 - PCA antenna; 2 - microwave receiver with a pulse signal at a carrier frequency f ₀ ; 3 - delay for the period of the pulses; 4 - delay for two periods; 5 - phase inverter; 6 - the generator of the reference radio signal at a frequency f ₀ modulated in accordance with the range R _n ; 7 - amplitude-frequency modulator and synchronizer; 8 - quadrature phase detector; 9 - synthesizer; 10 - drive with the introduction of the number of accumulated pulses m _x = L _x / W _x T _r ; 11 - correlator of synthesized azimuthal responses that are separated in time by calculating the amplitude and phase of the resulting response; 12 - calculator of the formation of the azimuthal line in the amplitude and speed images with a cut-off (if necessary) of signals from fixed reflectors; a - input oblique range; b - synchronization, c - input of the number of accumulated pulses; d - output to a two-channel display.

The measurements of the radial velocity of the reflector in the synthetic-aperture side-view radar are as follows. The signal from the antenna (1) enters the microwave receiver (2), from the output of which at the carrier frequency f ₀ it enters the inputs of two inter-period self-correlators, consisting of delay elements for the repetition period (3), phase inverters (5) and quadrature phase detectors ( 8), and at the input of the second autocorrelator, the signal enters through the delay element for two repetition periods (4). The reference (synthesizing) signal at the same frequency f ₀ is generated in element (6) with the corresponding amplitude and frequency modulation parameters provided by the synchronization modulator (7), fed to the interperiodic autocorrelator similar to the signal (3, 5, 8) and then to the inputs video frequency synthesizers (9). The direct and delayed signals from the outputs of the quadrature detectors (8) are fed to the same synthesizers (9), where the signal from the output of the reference quadrature detector (8) is supplied. From the outputs of the synthesizers (9), the signals arrive at the inputs of the coherent drives of a given number of pulses m _x (10), from the outputs of the drives the time-shifted synthesized signals are fed to the input of the correlator (11), which performs their complex conjugate multiplication and calculates the module and phase of the resulting signal , from the output of the correlator, signals calibrated in terms of intensity and speed are fed to a computer (12), which forms the azimuthal line of the radar image with access to a two-channel display and performs the cutoff epodvizhnyh reflectors in one or both channels.

Information sources

1. Objects of radar. Detection and recognition. Ed. A.V. Sokolova / M., Radio Engineering, 2007, Chapter 4: Radar image of the target during aperture synthesis with ultra-high resolution synthetic-aperture radar, pp. 117-128.

2. Pettersson M.I. Detection of Moving Targets in Wideband SAR // IEEE Trans. on Aerospace and Electronic Systems, 2004, v.40, No. 3, pp. 780-786.

3. Dostovalov M.Yu., Neronsky LB, Pereslegin S.V. The study of the velocity field of ocean currents according to the phasometric data obtained by the SAR of the ERS spacecraft // Oceanology, 2003, v. 43, No. 3, pp. 473-480.

4. Neronsky L. B., Dostovalov M. J., Pereslegin S. V. The extended algorithms for Doppler centroid estimation // Proc. EUSAR-2004, Ulm, Germany, May 2004, v. 2, pp. 709-712.

5. Nero LB Estimation of the resolving power of a synthesized aperture radar according to the transient characteristics and the correlation interval of the output signal // Radio Engineering and Electronics, 1975, No. 2, p.271-279.

6. Romeiser R., Runge H., Flament P. Towards an Operational Spacebome System for High Resolution Current Measurements in Coastal Areas // Oceans 2003 Proc., 2003, v. 3, pp. 1524-1530.

7. Gabele M., Brautigam B., Shuize D., Steinbrecher U., Nuria T., Youns M. Fore and Aft Channel Reconstruction in the TerraSAR-X Dual Receive Antenna Mode // IEEE Trans. on Geosciense Remote Sensing, 2010, v. 48. No. 2, pp. 795-806.

8. Romeiser R., Suchand S., Hartmut R., Steinbrecher U., Grimier S. First Analysis of TerraSAR-X Along-Track InSAR-Derived Current Fields // IEEE Trans. on Geoscience and Remote Sensing, v. 48. No. 2, pp. 820-829.

9. Willow B.C. Aviation complexes of radar patrol and guidance. Status and development trends. M., Radio Engineering, 2008, 432 p.

10. Takashi Fujimura. Along-track interferometric synthetic aperture radar / US Patent, Number 5.945.937, Data of patent Aug. 31, 1999.

11. Martin Suss, Werner Wiesbeck. Side-looking synthetic aperture radar system / ER Patent, Number 1.241.487. B1, Data of filing 03/15/2001.

12. Alberto Moreira, Gerhard Krieger, Josef Mittermayier. Satellite configuration for interferometric and / or tomographic remote sensing by means of synthetic aperture radar / US Patent, Number 6.667.884 B2, Date of Patent Jan. 13, 2004.

13. Paul Vincent. Using dynamic interferometric synthetic aperture radar (INSAR) to image fast-moving surface waves / US Patent, Number 6.911.931 B2, Data of patent Jun. 28, 2005.

Claims (1)

A method for measuring the radial velocity of a reflector in a synthetic aperture side-view radar using azimuthal synthesis of two signals received in series, characterized in that the first signal is delayed relative to the second by two pulse repetition periods, periodically subtracting phases (differentiation) of the first, second and reference signals in autocorrelators, the azimuthal synthesis of the differentiated first and second signals is carried out in synthesizers with differentiation applied to them of the reference signal, the complex-conjugated output signals of the synthesizers are fed to the correlator input, the square of the module and the phase of the signal at the correlator output are calibrated, proportional to the effective scattering surface (EPR) and the radial velocity of the reflector, calibrated signals are fed to the calculator, where the azimuthal amplitude and high-speed radar images of the area, and, if necessary, cut off the signals of the stationary reflectors or select the reflectors with a given orostyu.

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