A method for obtaining RCS characteristics of unmanned aerial vehicles using controllable step-frequency pulse signals

Abstract

The present invention belongs to the field of radar target cross-sectional area RCS measurement and processing, and provides a method for obtaining the RCS characteristics of a drone using a controllable step-frequency pulse signal, the method comprising: step 1, setting the transmission parameters of the coherent step-frequency signal according to the drone parameters, flight status and test background; step 2, using a direct digital frequency synthesizer DDS+phase-locked loop PLL to generate a step-frequency signal; step 3, based on a background cancellation and calibration processing method, processing the acquired data to obtain a one-dimensional range image of the target to be measured; step 4, using a one-dimensional image inversion method to process the data after background cancellation and calibration to obtain the RCS of each frequency point of the target to be measured. Using the method and system of the present invention, in the process of obtaining the RCS of the drone, the ability to resist background clutter interference is strong, and the accuracy of the acquired RCS value is high.

Description

Technical Field

[0001] The invention relates to the field of radar target cross-sectional area RCS measurement and processing, and in particular to a method for obtaining RCS characteristics of an unmanned aerial vehicle by using a controllable step-frequency pulse signal. Background Art

[0002] Since the drone target is small, it is difficult to accurately obtain its radar target cross-sectional area RCS characteristics. Traditional single pulse radar is difficult to achieve both high power and high resolution at the same time. In order to solve the above problems, a coherent accumulation stepped frequency (SF) test system is used.

[0003] In order to obtain the true RCS value of the drone, on the one hand, the target needs to be calibrated. The calibration body can be a calibration sphere or a trihedral angle inversion, but the calibration sphere is an isotropic calibration body, so the same set of calibration data can be used when the polarization mode of the antenna is changed during the test. When using the trihedral angle inversion as the calibration body, recalibration is required after changing the polarization mode. On the other hand, since the results tested by the system are not only about the RCS of the drone, the area where the target is to be tested needs to be extracted during data processing, and the RCS of some small drones is very low, so when testing, it is necessary to increase the signal-to-noise ratio as much as possible while eliminating the influence of other background clutter. Summary of the invention

[0004] In view of the above problems, the present invention is proposed to provide a technical solution to overcome the above problems or at least partially solve the above problems. Therefore, one aspect of the present invention provides a method for obtaining the RCS characteristics of the target cross-sectional area of ​​a UAV radar using a controllable step-frequency pulse signal, the method specifically comprising the steps of:

[0005] Step 1: Set the transmission parameters of the coherent stepped frequency signal according to the UAV parameters, flight status and test background;

[0006] Step 2: Use direct digital frequency synthesizer DDS + phase-locked loop PLL to generate a step frequency signal;

[0007] Step 3: Based on the background cancellation and calibration processing method, the acquired data is processed to obtain a one-dimensional range image of the target to be measured;

[0008] Step 4: Use the one-dimensional image inversion method to process the data after background cancellation and calibration to obtain the RCS of each frequency point of the target to be measured.

[0009] Furthermore, the transmission parameters are pulse parameters of a device that sends a coherent stepped frequency signal, specifically including the number of pulses, pulse width, pulse period and pulse power.

[0010] Furthermore, the background cancellation technology is a vector background subtraction technology, and the vector background subtraction technology mainly includes the following steps:

[0011] Step 3.1: Measure the empty background in the measured area to obtain the empty background echo B at this time. C ;

[0012] Step 3.2, place the calibration body in the measured area to perform measurement, and obtain the calibration body data at this time;

[0013] Step 3.3, move the calibration object out of the measured area, test the empty background at this time, and measure the empty background second echo B T ;

[0014] Step 3.4, placing the target to be measured in the measured area for measurement, and obtaining the target data T at this time;

[0015] Step 3.5: After frequency mixing and orthogonal phase discrimination, the secondary intermediate frequency signals S of the empty background 1, empty background 2, calibration object and target to be measured are obtained respectively. BC (t), S BT (t), S C (t) and S T (t);

[0016] Step 3.6: Calibrate the secondary intermediate frequency signal to obtain the calibrated S BC (t), S BT (t), S C (t) and S T (t);

[0017] Step 3.7: Use one-dimensional inverse fast Fourier transform to process the calibrated secondary intermediate frequency signal to obtain a one-dimensional range image of the target to be measured.

[0018] Further, step 3.5 is specifically as follows: first, the data of the empty background 1, the empty background 2, the calibration object and the target to be measured are mixed to obtain mixed echo data; then, secondary mixing is performed, and orthogonal phase detection is performed to obtain a secondary intermediate frequency signal S BC (t), S BT (t), S C (t) and S T (t).

[0019] Furthermore, step 4 is specifically as follows: multiply the processed one-dimensional range image g(l) of the target to be measured by the window function ω(l), perform filtering processing, extract the target area, and obtain the filtered signal y(l)=g(l)×ω(l), and then perform fast Fourier transform on the filtered signal to obtain the true RCS value of the target to be measured.

[0020] Furthermore, the calibration process in step 3.6 uses the following formula:

[0021]

[0022] in is the RCS of the target to be measured, is the RCS of the calibration body, and A is the calibration coefficient.

[0023] Further, the following formula is used in step 3.7:

[0024] g(l)=IFFT(S T (t)-S BT (t)-(S C (t)-S BC (t))) obtains the one-dimensional range image g(l) of the target to be measured after calibration.

[0025] The present invention also provides a system for obtaining the RCS characteristics of the target cross-sectional area of ​​a UAV radar using a controllable step-frequency pulse signal, the system comprising: a parameter setting unit, a signal generating unit, a data processing unit and a computing unit;

[0026] The parameter setting unit is used to set the transmission parameters of the coherent stepped frequency signal according to the UAV parameters, flight status and test background;

[0027] The signal generating unit is used to generate a step frequency signal using a direct digital frequency synthesizer DDS+phase locked loop PLL:

[0028] The processing unit is used to process the acquired data based on the background cancellation and calibration processing method to obtain a one-dimensional range image of the target to be measured;

[0029] The calculation unit is used to process the data after background cancellation and calibration by using a one-dimensional image inversion method to obtain the RCS of each frequency point of the target to be measured.

[0030] The technical solution provided in the embodiments of the present application has at least the following technical effects or advantages:

[0031] In the process of obtaining the UAV RCS, the ability to resist background clutter interference is strong, and the accuracy of the obtained RCS value is high.

[0032] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented according to the contents of the specification. In order to make the above technical solution of the present invention and its objectives, features and advantages more obvious and easy to understand, the specific implementation methods of the present invention are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0034] Figure 1 A flow chart of a method for obtaining RCS characteristics of a drone according to the present invention is shown;

[0035] Figure 2 A schematic diagram of a system for obtaining RCS characteristics of a drone according to the present invention is shown;

[0036] Figure 3 It is the one-dimensional image of the W-band VV polarization background in a darkroom environment;

[0037] Figure 4 It is the RCS of each frequency point of W band VV polarization angle in darkroom environment;

[0038] Figure 5 It is the one-dimensional image of the W-band VV polarization angle in the darkroom environment;

[0039] Figure 6 The RCS of each frequency point of W-band VV polarization quad-wing drone in darkroom environment;

[0040] Figure 7 This is a one-dimensional image of a W-band VV-polarized quad-wing drone in a darkroom environment;

[0041] Figure 8 This is a one-dimensional image of a four-wing UAV with X-band VV polarization in a darkroom environment;

[0042] Fig. 9 This is a one-dimensional image of a Ku-band VV-polarized quad-wing drone in a darkroom environment;

[0043] Fig.10 This is a one-dimensional image of a 8-18GHz VV polarization quad-wing drone in an outdoor environment. DETAILED DESCRIPTION

[0044] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0045] The purpose of the present invention is to propose a method for obtaining the RCS characteristics of UAVs based on coherently accumulated stepped frequency signals, because the target cross-sectional area RCS of UAV radar is small and the signal-to-noise ratio is low, so the test results are easily interfered by other background clutter.

[0046] In one aspect of the present invention, a neural path display method based on projection surface reconstruction is provided. The method is based on a coherent stepped frequency radar test system, and background cancellation and one-dimensional image inversion of radar target cross-sectional area RCS are performed on the intermediate frequency signal data of multiple parameters to obtain the RCS value of the target to be measured, such as Figure 1 As shown, the method specifically comprises the steps of:

[0047] Step 1: Set the transmission parameters of the coherent stepped frequency signal according to the UAV parameters, flight status and test background.

[0048] The transmission parameters are the pulse parameters of the device that sends the coherent stepped frequency signal, including the number of pulses, pulse width, pulse period and pulse power.

[0049] Among them, the stepped frequency pulse is used, and the number of pulses is set according to the flight stability of the UAV, and coherent accumulation is performed to improve the signal-to-noise ratio. After 1000 accumulations, the signal-to-noise ratio is improved by 30dB.

[0050] Use stepped frequency pulses and set the pulse width τ according to the size of the drone;

[0051] Use step frequency pulse, set the pulse period T according to the speed of the drone r ;

[0052] Use step frequency pulse, set the pulse power P according to the altitude of the drone T .

[0053] Then, a direct digital frequency synthesizer (DDS) is used to excite the phase-locked loop (PLL) to achieve stepped frequency output.

[0054] Step 2: Use DDS+PLL to generate a step frequency signal.

[0055] First, determine the starting frequency f0 and the ending frequency f end , and calculate the number of step frequency points N, the frequency hopping interval Δf, and the scanning time T respectively scan and pulse width τ, where the relationship between the parameters is: T scan =Nτ.

[0056] Secondly, write the starting frequency into the FTW0 register of the DDS, the ending frequency into the FTW1 register, the frequency hopping interval into the lower 32 bits of NLSCW and RLSCW, and the holding time of each frequency into the upper 8 bits of NLSCW and RLSCW.

[0057] Then, set the linear frequency sweep mode in the CFR1 register, set the PS0 pin to a high level, connect the DDS signal to the PLL, and write the frequency division ratio in the corresponding register of the PLL.

[0058] Finally, add a radio frequency switch after the PLL output, calculate the frequency hopping time, turn on the radio frequency switch in the second clock cycle after the frequency point is changed, and turn it off after a certain period of time. At this time, a step frequency pulse signal with the corresponding frequency point, pulse period, pulse width, and frequency hopping interval can be obtained at the output end, making the step frequency signal controllable.

[0059] Step 3: Based on the background cancellation and calibration processing method, the acquired data is processed to obtain a one-dimensional range image of the target to be measured.

[0060] Background cancellation technology is a vector background subtraction technology, because eliminating the influence of background clutter requires not only the amplitude of the background but also the phase of the background. Vector background subtraction technology mainly includes the following steps:

[0061] Step 3.1: Measure the empty background in the measured area to obtain the empty background echo B at this time. C .

[0062] First, the transmission signal of the coherent stepped frequency radar is in the form of:

[0063]

[0064] Where f0 is the starting frequency, Δf is the step size of the frequency step, T r is the pulse repetition time, θ n is the initial phase of the nth pulse carrier frequency, τ is the pulse width, j is the imaginary unit, n is the nth frequency point, and N is the total number of frequency points of the step frequency.

[0065] Then, the above formula corresponding to s(t) is used to calculate the empty background echo B C , B C The signal form is:

[0066]

[0067] Step 3.2: Place the calibration body in the measured area to perform measurement, and obtain the calibration body data C at this time.

[0068] Using the above formula corresponding to s(t), the calibration volume data C is calculated. The signal form of C is:

[0069]

[0070] Step 3.3, move the calibration object out of the measured area, test the empty background at this time, and measure the empty background second echo B T .

[0071] Using the above formula corresponding to s(t), calculate the echo data B T , B T The signal form is:

[0072]

[0073] Step 3.4: Place the target to be measured in the measured area for measurement, and obtain the target data T at this time.

[0074] Using the above formula corresponding to s(t), the target data T to be measured is calculated. The signal form of T is:

[0075]

[0076] Step 3.5: After frequency mixing and orthogonal phase discrimination, the secondary intermediate frequency signals S of the empty background 1, empty background 2, calibration object and target to be measured are obtained respectively. BC (t), S BT (t), S C (t) and S T (t).

[0077] First, using the formula

[0078]

[0079] Among them, s0(t) and s(t) are coherent signals generated by the same frequency source, so here we can let θ n -θ 0n =0.

[0080] The data of empty background 1, empty background 2, calibration object and target to be measured are mixed to obtain mixed echo data. Then, secondary mixing is performed and orthogonal phase detection is performed to obtain the secondary intermediate frequency signal S BC (t), S BT (t), S C (t) and S T (t).

[0081] Step 3.6: Calibrate the secondary intermediate frequency signal to obtain the calibrated S BC (t), S BT (t), S C (t) and S T (t).

[0082] According to the following formula

[0083]

[0084] in is the RCS of the target to be measured, is the RCS of the calibration body, and A is the calibration coefficient.

[0085] Step 3.7: Use one-dimensional inverse fast Fourier transform to process the calibrated secondary intermediate frequency signal to obtain a one-dimensional range image of the target to be measured.

[0086] Using the following formula:

[0087] g(l)=IFFT(S T (t)-S BT (t)-(S C (t)-S BC (t)))

[0088] The one-dimensional range image g(l) of the target to be measured is obtained after calibration.

[0089] Step 4: Use the one-dimensional image inversion method to process the data after background cancellation and calibration to obtain the RCS of each frequency point of the target to be measured.

[0090] The one-dimensional image inversion method is to perform inverse fast Fourier transform on the test data to obtain a one-dimensional range image of the target to be measured, and then perform time domain windowing and filtering to extract the target to be measured separately, and then perform fast Fourier transform on the area. The result is the RCS value only about the target to be measured.

[0091] Specifically, the processed one-dimensional range image g(l) of the target to be measured is multiplied by the window function ω(l), filtered, and the target area is extracted to obtain the filtered signal y(l)=g(l)×ω(l). The window function can be the most basic rectangular window or Hamming window or Hanning window. Then the filtered signal is fast Fourier transformed to obtain the true RCS value of the target to be measured.

[0092] The present invention also provides a neural path display system based on projection surface reconstruction, such as Figure 2 As shown, the system includes: a parameter setting unit, a signal generating unit, a data processing unit and a computing unit.

[0093] The parameter setting unit is used to set the transmission parameters of the coherent stepped frequency signal according to the UAV parameters, flight status and test background.

[0094] The transmission parameters are the pulse parameters of the device that sends the coherent stepped frequency signal, including the number of pulses, pulse width, pulse period and pulse power.

[0095] The parameter setting unit adopts step frequency pulses, sets the number of pulses according to the flight stability of the UAV, performs coherent accumulation to improve the signal-to-noise ratio, and accumulates 1000 times to improve 30dB;

[0096] The parameter setting unit adopts a step frequency pulse and sets the pulse width according to the size of the drone;

[0097] The parameter setting unit adopts a step frequency pulse and sets the pulse period according to the speed of the drone;

[0098] The parameter setting unit adopts a step frequency pulse and sets the pulse power according to the altitude of the UAV.

[0099] Direct digital frequency synthesizer (DDS) is used to excite the phase-locked loop (PLL) to achieve stepped frequency output.

[0100] The signal generating unit is used to generate a step frequency signal using DDS+PLL.

[0101] First, the signal generation unit determines the starting frequency and the ending frequency, and calculates the number of step frequency points, the frequency hopping interval, and the scanning time T respectively. scan and pulse width τ, where the relationship between the parameters is: T scan =Nτ.

[0102] Secondly, the signal generating unit writes the starting frequency into the FTW0 register of the DDS, the ending frequency into the FTW1 register, the frequency hopping interval into the lower 32 bits of NLSCW and RLSCW, and the holding time of each frequency into the upper 8 bits of NLSCW and RLSCW.

[0103] Subsequently, the signal generating unit sets the linear frequency sweep mode in the CFR1 register, sets the PS0 pin to a high level, connects the DDS signal to the PLL, and writes the frequency division ratio into the corresponding register of the PLL.

[0104] Finally, the signal generation unit adds a radio frequency switch after the PLL output terminal, calculates the frequency hopping time, turns on the radio frequency switch in the second clock cycle after the frequency point is changed, and turns it off after a certain period of time. At this time, a step frequency pulse signal with the corresponding frequency point, pulse period, pulse width, and frequency hopping interval can be obtained at the output terminal, realizing controllable step frequency signal.

[0105] The processing unit is used to process the acquired data based on the background cancellation and calibration processing method to obtain a one-dimensional range image of the target to be measured.

[0106] Background cancellation technology is a vector background subtraction technology, because eliminating the influence of background clutter requires not only the amplitude of the background but also the phase influence of the background.

[0107] The processing unit is specifically used to measure the empty background in the measured area to obtain the empty background echo B at this time. C .

[0108] The processing unit is also specifically used to place the calibration body in the measured area for measurement to obtain the calibration body data C at this time; move the calibration body out of the measured area, test the empty background at this time, and measure the empty background second echo B at this time. T ; Place the target to be measured in the measured area for measurement, and obtain the target data T at this time.

[0109] The processing unit is also used to obtain the secondary intermediate frequency signals S of the empty background 1, the empty background 2, the calibration body and the target to be measured respectively through mixing and orthogonal phase detection. BC (t), S BT (t), S C (t) and S T (t).

[0110] The processing unit is also specifically used to calibrate the secondary intermediate frequency signal to obtain the calibrated S BC (t), S BT (t), S C (t) and S T (t).

[0111] The processing unit is also specifically used to process the calibrated secondary intermediate frequency signal using a one-dimensional inverse fast Fourier transform to obtain a one-dimensional range image of the target to be measured.

[0112] The calculation unit is used to process the data after background cancellation and calibration by using a one-dimensional image inversion method to obtain the RCS of each frequency point of the target to be measured.

[0113] The one-dimensional image inversion method is to perform inverse fast Fourier transform on the test data to obtain a one-dimensional range image of the target to be measured, and then perform time domain windowing and filtering to extract the target to be measured separately, and then perform fast Fourier transform on the area. The result is the RCS value only about the target to be measured.

[0114] The calculation unit is specifically used to: multiply the processed one-dimensional range image g(l) of the target to be measured by the window function ω(l), perform filtering processing, extract the target area, and obtain the filtered signal y(l)=g(l)×ω(l). The window function can select the most basic rectangular window or Hamming window or Hanning window. Then, the filtered signal is fast Fourier transformed to obtain the real RCS value of the target to be measured.

[0115] The method of the present invention is carried out under three test conditions, namely, under three frequency bands (X, Ku, W) and two test environments (darkroom and outdoor field), but all of them are based on the test results of coherent step-frequency signals. For specific test results, see Figure 3-10 .

[0116] In the description provided herein, a large number of specific details are described. However, it is understood that embodiments of the present invention can be practiced without these specific details. In some instances, well-known methods, structures and techniques are not shown in detail so as not to obscure the understanding of this description.

[0117] Similarly, it should be understood that in order to streamline the present disclosure and aid in understanding one or more of the various inventive aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes grouped together into a single embodiment, figure, or description thereof. However, this disclosed method should not be interpreted as reflecting the intention that the claimed invention requires more features than those explicitly recited in each claim. More specifically, as reflected in the claims below, inventive aspects lie in less than all the features of the individual embodiments disclosed above. Therefore, the claims that follow the specific embodiment are hereby expressly incorporated into the specific embodiment, with each claim itself serving as a separate embodiment of the present invention.

[0118] It should be noted that the above embodiments illustrate the present invention rather than limit the present invention, and those skilled in the art may design alternative embodiments without departing from the scope of the appended claims. In the claims, any reference symbol between brackets shall not be construed as a limitation to the claims.

Claims

1. A method for obtaining the RCS characteristics of a target cross-sectional area of ​​a UAV radar using a controllable step-frequency pulse signal, characterized in that: The method specifically comprises the following steps: Step 1: Set the transmission parameters of the coherent stepped frequency signal according to the UAV parameters, flight status and test background; Step 2: Use direct digital frequency synthesizer DDS + phase-locked loop PLL to generate a step frequency signal; Step 3: Based on the background cancellation and calibration processing method, the acquired data is processed to obtain a one-dimensional range image of the target to be measured, wherein step 3 specifically includes: Step 3.1: Measure the empty background in the measured area to obtain the empty background echo B at this time. C ; Step 3.2, place the calibration body in the measured area to perform measurement, and obtain the calibration body data C at this time; Step 3.3, move the calibration object out of the measured area, test the empty background at this time, and measure the empty background second echo B T ; Step 3.4, placing the target to be measured in the measured area for measurement, and obtaining the target data T at this time; Step 3.5: After frequency mixing and orthogonal phase discrimination, the secondary intermediate frequency signals S of the empty background 1, empty background 2, calibration object and target to be measured are obtained respectively. BC (t), S BT (t), S C (t) and S T (t); Step 3.6: Calibrate the secondary intermediate frequency signal to obtain the calibrated S BC (t), S BT (t), S C (t) and S T (t); Step 3.7, using one-dimensional inverse fast Fourier transform to process the calibrated secondary intermediate frequency signal to obtain a one-dimensional range image of the target to be measured; Step 4: Use the one-dimensional image inversion method to process the data after background cancellation and calibration to obtain the RCS of each frequency point of the target to be measured.

2. The method according to claim 1, characterized in that The transmission parameters are pulse parameters of a device that sends a coherent stepped frequency signal, specifically including the number of pulses, pulse width, pulse period and pulse power.

3. The method according to claim 1, characterized in that Step 3.5 is as follows: first, the data of the empty background 1, the empty background 2, the calibration object and the target to be measured are mixed to obtain mixed echo data; Then, secondary mixing is performed and orthogonal phase detection is performed to obtain the secondary intermediate frequency signal S BC (t), S BT (t), S C (t) and S T (t).

4. The method according to claim 1, characterized in that: Step 4 is as follows: multiply the processed one-dimensional range image g(l) of the target to be measured by the window function ω(l), perform filtering, extract the target area, and obtain the filtered signal y(l)=g(l)×ω(l), and then perform fast Fourier transform on the filtered signal to obtain the true RCS value of the target to be measured.

5. The method according to claim 1, characterized in that: The calibration process in step 3.6 uses the following formula: in is the RCS of the target to be measured, is the RCS of the calibration body, and A is the calibration coefficient.

6. The method according to claim 1, characterized in that In step 3.7, the following formula is used: g(l) = IFFT(S T (t)-S BT (t)-(S C (t)-S BC (t))) obtains the one-dimensional range image g(l) of the target to be measured after calibration.

7. A system for obtaining the RCS characteristics of a target cross-sectional area of ​​a UAV radar using a controllable step-frequency pulse signal, characterized in that: The system utilizes the method of claim 1, and the system comprises: a parameter setting unit, a signal generating unit, a data processing unit and a computing unit; The parameter setting unit is used to set the transmission parameters of the coherent stepped frequency signal according to the UAV parameters, flight status and test background; The signal generating unit is used to generate a step frequency signal using a direct digital frequency synthesizer DDS+phase locked loop PLL: The processing unit is used to process the acquired data based on the background cancellation and calibration processing method to obtain a one-dimensional range image of the target to be measured; The calculation unit is used to process the data after background cancellation and calibration by using a one-dimensional image inversion method to obtain the RCS of each frequency point of the target to be measured.

8. The system according to claim 7, characterized in that The parameter setting unit adopts step frequency pulses and sets the number of pulses according to the flight stability state of the UAV; The parameter setting unit adopts a step frequency pulse and sets the pulse width according to the size of the drone; The parameter setting unit adopts a step frequency pulse and sets the pulse period according to the speed of the drone; The parameter setting unit adopts a step frequency pulse and sets the pulse power according to the altitude of the UAV.

9. The system according to claim 7, characterized in that The calculation unit is specifically used to: multiply the processed one-dimensional range image g(l) of the target to be measured by the window function ω(l), perform filtering processing, extract the target area, and obtain the filtered signal y(l)=g(l)×ω(l), and then perform fast Fourier transform on the filtered signal to obtain the true RCS value of the target to be measured.

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