CN116679277A - Minimum L based on time-frequency domain 1 Double-channel SAR multi-jammer positioning method based on norm - Google Patents

Abstract

The invention discloses a method based on time-frequency domain minimumA dual-channel SAR multi-jammer positioning method of norm relates to the field of dual-channel synthetic aperture radar multi-jammer positioning algorithm, comprising: performing short-time Fourier transform (STFT) on the received pulse, and transforming the signal into a time-frequency domain; separating and extracting each interference signal component by using a ridge path detection and recombination algorithm; accumulating energy of each interference signal component pulse by pulse, and constructing minimum of double-channel interference cancellation according to energy accumulated energyAnd the norm, thereby obtaining the high-precision azimuth position of the jammer. The invention can realize accurate positioning when a plurality of interference sources exist in a scene.

Description

Minimum L based on time-frequency domain 1 Double-channel SAR multi-jammer positioning method based on norm

Technical Field

The invention relates to the field of a double-channel synthetic aperture radar (Synthetic Aperture Radar, SAR) multi-jammer positioning algorithm, in particular to a time-frequency domain-based minimumA dual-channel SAR multi-jammer positioning method of norm.

Background

Synthetic aperture radar (Synthetic Aperture Radar, SAR) has the capacity of all-day, all-weather and all-direction earth observation as an active microwave sensor, and has become an important means for modern civil mapping through development and evolution for half a century. With the increasing complexity of electromagnetic environment, SAR is susceptible to various active electromagnetic interference signals in the same wave band as SAR in daily work, such as radiation devices like ground radars. Under the condition that the position of an interference source is known, a beam forming technology can be adopted to form nulls in the interference incoming wave direction, so that interference signals are effectively restrained. Therefore, the high-precision interference source positioning method is a key technology for realizing the spatial filtering of the SAR system.

For the existing interference source positioning method of the SAR system, two methods, namely a method based on the conjugate cross correlation of the double-channel SAR echo signals and a method based on DOA (direction of arrival), are mainly used. The former requires that the interference signal energy is far greater than the SAR echo signal energy, and only a single jammer can be positioned, and the positioning accuracy is not high. The latter is to obtain the change relation of the angle between SAR and the interference source along with time by using DOA method, so as to obtain the two-dimensional coordinate estimated value of the interference source in the scene. However, DOA estimation is mainly aimed at the wavelength of the array antenna, the distance between adjacent array elements is required to be not more than 1/2, and for multi-channel SAR, the distance between channel phase centers is obviously impossible to meet the condition limit, so that under the condition of larger distance, the method is easy to cause fuzzy estimation angles, and the true estimation angles are difficult to distinguish. And for a dual-channel SAR system, the DOA method can also only obtain the angle of a single interferer. Therefore, both positioning methods are not applicable when there are multiple sources of interference in the scene.

Disclosure of Invention

To solve the above problems, a primary objective of the present invention is to provide a method for minimizing the frequency domain based on timeThe method comprises the steps of transforming signals to a time-frequency domain through short-time Fourier transform (STFT), and then separating and extracting interference signals by using a ridge path detection and recombination algorithm to obtain components of each interference signal in the time-frequency domain; finally, energy accumulation is carried out on each interference signal pulse by pulse, and the minimum +.>And obtaining the high-precision azimuth positions of a plurality of jammers after solving the norms.

In order to achieve the above purpose, the invention adopts the following technical scheme:

time-frequency domain-based minimumA dual-channel SAR multi-jammer positioning method of norm comprises the following steps:

step 1, carrying out short-time Fourier transform on SAR echo data containing interference, and transforming signals to a time-frequency domain;

step 2, separating and extracting each interference signal by using a ridge path detection and recombination method;

step 3, accumulating energy of each interference signal pulse by pulse, and constructing minimum of double-channel interference cancellationAnd the norm, thereby obtaining the high-precision azimuth position of the jammer.

Further, the step 2 includes:

detecting an instantaneous frequency value of an interference signal in a time-frequency domain according to a maximum value method, and taking the instantaneous frequency value as a ridge path of the interference signal; the ridge paths are subjected to cross detection, if the ridge paths are crossed, the ridge paths are cut off at the crossing positions, and recombination is carried out according to the continuity of slopes at the cutting points, so that the correct ridge paths of all interference signals are obtained; and then designing a mask according to the correct ridge path, thereby realizing separation and extraction of each interference signal.

The beneficial effects are that:

aiming at the limitations of the existing two-channel SAR system jammer positioning method (only a single jammer can be positioned and the precision is not high), the invention provides a multi-jammer positioning method for the two-channel SAR system innovation. The separation and extraction of a plurality of interference signals is achieved by transforming the interference signals into the time-frequency domain and utilizing a ridge path detection and recombination algorithm. Constructing minima in time-frequency domain from phase differences between channelsAnd solving the norm model by using an interior point method to obtain high-precision azimuth positions of a plurality of jammers. The effectiveness of the positioning algorithm is proved by the actual measurement data of the third high-resolution data.

Drawings

FIG. 1 is a time-frequency domain based minimum of the present inventionA flow chart of a dual-channel SAR multi-jammer positioning method of norm;

FIG. 2 is a schematic diagram of a front side view working model of a space-borne dual-channel SAR;

FIG. 3A is a schematic diagram of a selected high-resolution three-data scenario;

FIG. 3B is a schematic diagram of initial positions of 3 jammers;

FIG. 4A is a diagram of a single pulse time frequency diagram with interference;

FIG. 4B is a graph showing the first interference signal extraction result of FIG. 4A;

FIG. 4C is a graph showing the second interference signal extraction result of FIG. 4A;

FIG. 4D is a diagram of the third interference signal extraction result of FIG. 4A;

fig. 5 is a graph of the results of monte carlo experiments with three jammers positioned.

Detailed Description

The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by those skilled in the art without the inventive effort based on the embodiments of the present invention are within the scope of protection of the present invention.

According to an embodiment of the invention, a time-frequency domain-based minimum is providedThe dual-channel SAR multi-jammer positioning method of the norm comprises the following steps as shown in figure 1:

step 101: and performing STFT conversion on the data containing the interference echo received by the SAR system, and converting the signal into a time-frequency domain.

For the firstDirection of channel received n pulse signal receiving pulse +.>STFT transformation is carried out, and the result is:

(1)

wherein ,for distance to slow time, < >>、/>Time and frequency components in the time-frequency domain, respectively, < >>For analysis of window functions, +.>For receiving pulses +.>J is an imaginary unit. After transforming to time-frequency domain, the energy of interference signal is concentrated according toThis allows the interference signal to be separated and extracted.

Step 102: and separating and extracting each interference signal by using a ridge path detection and recombination algorithm.

The ridge path of the interfering signal is considered to be the location of the maximum of the interfering signal in the time-frequency diagram, and can be expressed as:

(2)

wherein ,，/>indicating the number of disturbances->Is estimated->Ridge path of individual interfering signals->Is a set of frequencies.

Order theFor the bandwidth occupied by the interference signal in the time-frequency domain, the detection steps of the interference signal ridge path are as follows:

1) For receiving pulsesThe maximum value is retrieved by the time-frequency diagram of (a): />Obtain->Instantaneous frequency estimate of time-of-day interference signal +.>：/>M represents the time sampling number of the maximum value.Representation->At maximum, the argument +.>、/>Is a value of (2);

2) Retrieving the instantaneous frequency of the interfering signal to the right, namely:order-makingObtain->Instantaneous frequency estimate of time-of-day interference signal: />And so on untilOr->, wherein />A threshold value set according to the interference characteristics;

3) Retrieving the instantaneous frequency of the interfering signal to the left, namely:order-makingObtain->Instantaneous frequency estimate of time-of-day interference signal: />And so on, until +.>Or->, wherein />The initial time of the time sampling;

4) Thus, the 1 st estimated ridge path of the interference signal is obtainedAlong the direction of the ridge pathSetting zero in the range, namely: />And then, continuing to search the ridge path of the next interference signal, and repeating the steps until the ridge path of the complete interference signal is extracted.

The ridge path obtained by the detection method is only a stronger energy trend of the interference signal, when the interference signal has a cross in a time-frequency domain, the detected ridge path may have erroneous judgment, and at the moment, the ridge path needs to be subjected to cross detection and separation recombination, and the specific steps are as follows:

1) Judging whether crossing points exist between ridge paths, if so:then it can be considered as the firstAnd->The crossing points exist in the ridge paths, and at this time, the crossing ridge paths need to be separated and recombined;

2) To minimize the impact of the crossover energy on the positioning results, one would:removing the ridge path value at the position, wherein the ridge path is +.>And->Then two segments are separated at the intersection point;

3) The continuity of the slope of the interference signal at the break point is utilized to recombine the four sections of ridge paths separated at the break point, so that the correct ridge path trend of the interference signal can be obtained;

4) Repeating the above steps until detection, separation and recombination of all ridge path crossing points are completed, and obtaining the correct ridge path of the interference signal。

Extracting each interference signal according to the ridge path design mask of the interference signal obtained by the steps, the firstIndividual interfering signalsThe extraction is as follows:

(3)

thus, the separation and extraction of each interference signal are realized in the time-frequency domain, and the components of the interference signal in the time-frequency domain are obtained:。

step 103: energy accumulating each extracted interference signal and constructing minimum of double-channel interference cancellation according to energy accumulatingAnd the norm, thereby obtaining the high-precision azimuth position of the jammer.

The dual-channel SAR front side view working model is shown in fig. 2, with reference to the channel transmit signal, and both channels are simultaneously received. Ground surface settingThe position of each jammer in the imaging scene isThe continuously transmitted interference signal is directly received by each sub-aperture through single-pass propagation. For the firstPulse signal (1)Jammer to the firstDistance of receiving channelThe method comprises the following steps:

(4)

in the formula ,for this pulse time SAR antenna center position location coordinates in the scene, +.>For the azimuth position of the jammer, +.>For the shortest skew of jammers, +.>Represents->Receive channel (reference channel) and->Phase center distance of receiving channel, < >>The SAR antenna sub-aperture length is the phase center distance between two adjacent receiving channels. For a space-borne SAR system, the track height is usually in the order of hundreds of kilometers, so that the change of an jammer in the distance direction does not greatly influence the pitch, and therefore, the space-borne SAR system can be considered +.>，/>Is the shortest skew distance of the scene center.

According to the linear property of short-time Fourier transform, for the firstChannel->First pulse->Individual interfering signalsThe method comprises the following steps: /> (5)

wherein ,represents the envelope of the interfering signal, and is determined by the waveform of the interfering signal, the signal gain and the antenna pattern.Is->The interference unit is to the antenna->Skew of channel, ">For signal wavelength, +.>Representing an exponential function. It can be seen that the main difference between the interference signals received by different channels in the time-frequency domain is the difference of the phase of the distance term, and because the time-frequency analysis method is processed pulse by pulse, the same pulse echoes received by two channels are only different by a fixed phase +.>：

(6)

Performing second-order Taylor expansion and simplification on the phase compensation factor (6) to obtain a phase compensation factor：

(7)

Phase difference of visible double-channel SAR receiving interference signals is mainly equal to azimuth position of jammerIn connection therewith, a minimum +.>And a norm model, and the azimuth position of the jammer is obtained by searching the minimum value of the energy after cancellation. To make the estimation result more accurate, a plurality of pulse data can be selected for processing, so the minimum +.>The norm optimization model may be built as:

(8)

wherein ,representing +.>Norms, i.e. the sum of the absolute values of the elements of the matrix,/->Namely +.>And estimating the result of the azimuth position of each jammer. />For the number of pulses selected, +.>Indicating the upper limit of the prescribed positional location of the jammer in the imaged scene. />Is indicated at->At minimum, the argument +.>Is a value of (a). Minimum->The norm model has no analytic solution, and the invention solves the numerical solution of the nonlinear constraint by using an interior point method, and has better performance in terms of speed and precision. For extracting->The interference signals use the minimum +.>And positioning the norm model, so that the high-precision azimuth positions of a plurality of jammers can be obtained in sequence.

From the periodicity of the trigonometric function, for the firstFor the jammer, the phase compensation factor +.>Is->Meaning that the actual jammer position may be:

(9)

indicating that the azimuth position of the jammer cannot be exactly positioned, and a series of fuzzy values exist in the estimated value. In practice, however, for a satellite-borne SAR, the ambiguity period may reach tens of kilometers, and at this time, the azimuth position of the jammer can be specifically determined according to the position of the jammer in the scene。

Example 1

In the embodiment, high-resolution third-size satellite-borne actual measurement data are selected for processing.

Fig. 3A shows the selected scene information, fig. 3B is a schematic diagram of initial positions of 3 jammers in the scene, 3 jammers, i.e., the first jammer 1, the second jammer 2 and the third jammer 3, each transmit chirp interference signals with a signal-to-noise ratio of-20 dB, and coordinates of 3 jammers in the scene are (-5000 m,2000 m), (5000 m,1000 m) and (3000 m, -2000 m), respectively.

Fig. 4A is a result of the first pulse of the SAR first channel transformed to the time-frequency domain. Therefore, since the received interference signals of the first jammer 1 and the second jammer 2 have the cross in the time-frequency domain, in order to avoid the influence of the interference signals, the interference signals at the cross position are cut off and the ridge paths of the interference signals are extracted by recombination according to the continuity of the slopes at the cross position, and then the mask is designed according to the ridge paths so as to extract the interference signals. The extraction results of the 3 interference signals are shown in fig. 4B, fig. 4C and fig. 4D, respectively. Utilizing minimum of extracted interference signalsThe norm models were subjected to positioning processing, and the results are shown in table 1. The azimuth positioning error of the method is in the order of ten meters, and extremely high positioning precision is achieved.

TABLE 1

In order to better illustrate the robustness of the proposed positioning method, the present invention designs a monte carlo experiment to observe the influence of Signal-to-interference Ratio (SIR) on the position estimation. The SIR range is set to between-30 dB and 10dB with a step change of 1dB. For each SIR, 20 Monte Carlo experiments are designed, the azimuth position of 3 jammers in each experiment is set randomly, and the random values are uniformly distributed within the range of [ -5000m, 5000m ]. Root-Mean-Square-Error (RMSE) is used to evaluate the accuracy of the interferer location estimate, which is defined as follows:

(10)

in the formula ,for the number of experiments>And->Respectively +.>The estimated and actual positions of the experiments.

Fig. 5 shows the transformation relation between RMSE and SIR of 3 jammer azimuth position estimation, and it can be seen that, although the positioning error starts to increase after 0dB, when SIR is 10dB, the positioning error is still in the order of ten meters, which indicates that the positioning method can still obtain a positioning result with higher accuracy when the signal-to-interference ratio is higher, and also verifies the effectiveness of the positioning method.

The foregoing is merely a few examples of the present invention, and the present invention is applicable in other situations and is not intended to limit the scope of the present invention.

Claims (2)

1. Time-frequency domain-based minimumThe dual-channel SAR multi-jammer positioning method of the norm is characterized by comprising the following steps of:

step 1, carrying out short-time Fourier transform on SAR echo data containing interference, and transforming signals to a time-frequency domain;

step 2, separating and extracting each interference signal by using a ridge path detection and recombination method;

and step 3, accumulating energy of each interference signal pulse by pulse, and constructing the minimum norm of the double-channel interference cancellation, so as to obtain the high-precision azimuth position of the jammer.

2. A time-frequency domain based minimum according to claim 1The dual-channel SAR multi-jammer positioning method of the norm is characterized in that the step 2 comprises the following steps:

detecting an instantaneous frequency value of an interference signal in a time-frequency domain according to a maximum value method, and taking the instantaneous frequency value as a ridge path of the interference signal; the ridge paths are subjected to cross detection, if the ridge paths are crossed, the ridge paths are cut off at the crossing positions, and recombination is carried out according to the continuity of slopes at the cutting points, so that the correct ridge paths of all interference signals are obtained; and then designing a mask according to the correct ridge path, thereby realizing separation and extraction of each interference signal.