# The method for determining two-dimensional positions and frequency emitters

(57) Abstract:

The invention relates to electrical engineering and can be used for combined search and direction finding in azimuth and elevation with high precision multiple short-term operating transmitters at the same time fall within the current band reception. The method is based on direct two-dimensional Fourier transformation in time and space of the ensemble of signals received by a ring lattice of N antenna elements. At each temporal frequency, with fixed values pointing in elevation, each formed by converting a spatial frequency component of q times multiplied by the Fourier transform of the functions of guidance, depending on the frequency, elevation angle, the parameters of the antenna array and the azimuthal rotation 2q/m Produce q inverse spatial Fourier transformation of the received aggregate adjusted spatial frequency components, detect the presence of signal and obtain estimates of azimuth and elevation of its source at each frequency by the square of the module of the complex two-dimensional angular spectrum. The technical result is to increase the accuracy of determination of bearing on the source,referring to the radio and can be used for monitoring while solving the problem secretive determine the characteristics (frequency, azimuth and elevation) of many short-term operating transmitters at the same time fall within the current band reception.With the advent and improvement of communication systems, location, identification, and other using signals with a low probability of intercept, i.e. with high temporal stealth (short packet, the stepwise change of frequency) problems related to their search and direction finding with high accuracy.The known method wideband direction finding /1/ in which of the output signals of each element of the antenna array are allocated to digital signals characterizing the spectra of the received signals, and for each selected frequency band of the reception using the phase signals is a direct calculation of the spatial Fourier series, discrete describing the angular power spectrum at the selected frequency. After recovery of the angular spectrum at all frequencies is determined by the bearing of any source, emitting signals on any frequency within the current band reception. This way the maximum possible amplitude and phase information uses only the phase of the signal and has poor performance when determining the azimuthal p the attachment of the bearing as possible, amplitude and phase information, but also has poor performance when determining the azimuth bearing.Known more effective method of determining the azimuth bearing and frequency of the transmitters /3/ using symmetry properties of the ring antenna array based on fast convolution complex spectral signals from each antenna element with the reference signals of the amplitude-phase distribution calculated in advance, and adopted for the prototype.According to this method:1. Perform two-dimensional Fourier transform of the ensemble of signals x

_{n}(i) taken from the source ring lattice of N antenna elements, where n is the number of antenna element, a i is the number of the time reference signal:

time - , where F

_{t}{...} - operator Fourier transform in time,

in space , where F { ... } operator Fourier transform in space at each temporal frequency f.2. For each frequency f generated by the transformation of the spatial frequency component adjusted by multiplying by the correction function , where corrective function or Fourier-image of the environment of the function (in the simplest form, the

< / BR>

where

_{n}( ... ) is the radiation pattern of a single element of the lattice;

n= 0. ..N-1 to the current number, a N - number of nodes of a uniform grid in azimuth, which restored the angular spectrum at the frequency f;

R is the radius of the lattice;

- wave length at the frequency f.3. Performing inverse spatial Fourier transformation of the received aggregate adjusted frequency components to restore the complex angular range in azimuth at each frequency f by the formula:

< / BR>

where F

^{-1}{ ... } is the operator inverse Fourier transform in space;

azimuthal directions in which the frequency f is restored complex angular range increments

4. Obtain estimates of azimuth of the source signal at each frequency f by finding the maximum of the squared magnitude of a complex angular spectrum

In this way, after receiving signals temporal spectrum in the band of the reception, for the recovery of signals that describe the angular range in azimuth at each of the frequencies f, instead of requiring a large number of multiplications and summations of signals, direct way to perform circular convolution described by the formula

< / BR>

essentially implemented sposetti with formula (2). How fast calculation provides a substantial reduction in the required number of multiplications and summations of signals . It is particularly effective when implemented using the fast Fourier transform (FFT).In turn, the feature of the FFT, and hence the convolution (2), such that the number of values of the spectrum at the output is equal to the number of samples of the source distribution at the entrance. In this case, the length of sequences of signals are the same and equal to the number N. In this angular range in azimuth will be restored with resolution 360

^{o}/N, and the accuracy of direction finding is approximately equal to 360

^{o}/2N.It follows that for precision direction finding, 0.5

^{o}must be composed of an antenna array 360 antennas. System with the same number of antennas are unique and difficult to perform.In practice, as a rule, primarily for economic reasons the number of antennas N varies from 5 to 32. In this case, the method of the prototype, following (2), will be recovered only from 5 to 32 points azimuthal angular spectrum or in other terms - will be formed in a fan pattern grid at a frequency of f containing from 5 to 32 channels of reception. It is clear that the fan charts is Nala with a maximum signal level.Thus, the prototype method does not provide high accuracy azimuth direction finding with the most often implemented in practice annular configurations of antenna arrays with a small number of elements.Moreover, as follows from formula (1), environment function of the prototype method does not contain components that are dependent on the elevation angle. This means that the prototype method is always phase received signals at zero elevation and, therefore, does not provide a measurement of the elevation angle of the signal sources.As a consequence, the lack of phasing in elevation further reduces the accuracy of the azimuthal bearing of the signal sources with elevation angles different from zero. For example, when the direction finding from the surface sources of the signals that are placed on aircraft or satellites, as well as when solving the inverse problem of finding the ground source from an airplane or satellite.Improving the accuracy of estimating the angle of arrival of signals received circular antenna array with a small number of elements, when using the prototype method can provide several known ways [4]:

1. To clarify a rough estimate of the angle of arrival by comparing the amplitude of signal angle of arrival, applying in the vicinity of the estimated maximum approximation least-squares two-dimensional second order polynomial.3. To complement the sequence of complex signals of length N with zeros to artificially extend the length up to M and transformations in the sequence (where m = 0...M - 1 to the current number, and M is the number of nodes of a uniform grid in azimuth in which you want to restore the angular spectrum at frequency f) and restore complex angular range in azimuth at each frequency f by the formula (2) by replacing the index n on the index m.The first and second path does not radically solve the problem, so as to retain the dependence of the achievable accuracy depends on the number of antennas are narrowband with a fixed number of antennas in the array.The third way of increasing the accuracy of direction finding using the prototype method allows to obtain any desired accuracy direction finding price increase in the number of operations on signals, including non-productive operations. So it is also not acceptable, as it significantly reduces the speed of the azimuthal direction finding.The objective of the proposed method is the determination with high accuracy two-dimensional (azimuth and elevation) Islom elements.The problem is solved by the fact that in the method of determining a two-dimensional bearing and frequency emitters, based on a two-dimensional Fourier transform (in time and space) of the ensemble of signals received by a ring lattice of N antenna elements, according to the invention at each temporal frequency, with fixed values pointing in elevation, each formed by converting a spatial frequency component of q times multiplied by the Fourier transform of the functions of guidance, depending on the frequency, elevation angle, the parameters of the antenna array and the azimuthal rotation 2q/M, produce q inverse spatial Fourier transformation of the received aggregate adjusted spatial frequency components, detect the presence of signal and obtain estimates of azimuth and elevation of its source at each frequency by the square of the module of the complex two-dimensional angular spectrum.The drawing shows a structural diagram of a device that implements the proposed method.According to the proposed method:

1. Perform two-dimensional Fourier transform of the ensemble of signals x

_{n}(i) taken from the source ring lattice of N antenna elements..} - the operator of the Fourier transform in time,

in space , where F {...} operator Fourier transform in space at each temporal frequency f.2. At each temporal frequency f, for a fixed value of the angle pointing (phasing) in elevation h, formed in the result of the transformation of the spatial frequency component (correct q time by multiplying by the correction function , where corrective function or Fourier transform functions aiming at a frequency f, which has the following form:

< / BR>

where h= 0. . .H - 1 - the current number of mesh guidance lattice in elevation and H is the number of nodes in elevation, in which the restored cut of the azimuthal angular spectrum at frequency f;

where q = m(mod(M/N));

m= 0. . . M-1, M - the number of nodes of a uniform grid in azimuth, which restored the angular spectrum at the frequency f;

n=0...N-1 is the number of the antenna element, N is the number of antennas in the array;

R is the radius of the lattice;

- wave length at the frequency f;

_{n}( ... ) the pattern of the individual element in the array.From the formula (3), it follows that it is more General than the formula (1), and coincides with it when the following index values q=0 and h=0. Corrective functo shift 2q/M . At the same time, it allows at any frequency f to put the bars in elevation by changing the index h and to ensure the effect of the cyclic rotation of the grating in the azimuthal plane in increments of 2/M when the change of the index q.3. Perform q inverse spatial Fourier transformation of the received aggregate adjusted frequency components to restore the M complex values of the angular spectrum at the frequency f, when the value of the pointing angle space h by the formula:

< / BR>

where F

^{-1}{ ... } is the operator inverse Fourier transform in space.4. Repeat steps 2 and 3 for all values pointing in elevation h = 0...H - 1.5. Determine for each frequency f the unit square complex two-dimensional angular spectrum .6. Use the unit square to determine the presence of signal and provide an estimate of the azimuth and elevation of its source at each frequency f.Improving the accuracy of two-dimensional (azimuth and elevation) of the bearing signals received circular antenna array, is achieved by recovery at each temporal frequency f is substantially more complex values of the angular spectrum M than the number of antennas nA device that implements the proposed method contains connected in series circular antenna grid 1, the N-channel frequency Converter 2, N-channel, analog-to-digital Converter (ADC) 3, the transmitter is a two-dimensional Fourier transform 4, multi-channel parallel to the transmitter 5, the device of the computing unit square complex two-dimensional angular spectrum and display 6. In turn, the transmitter 5 contains a matrix solvers, the elements of which depend on two indices f = 1...K and h=1...H, where K is the number of increments in the time-dependent frequency, and H is the number of increments in elevation. Each evaluator matrix 5(K, N) includes a storage device 7 for storing pre-calculated correction functions for each of the combinations of indices K and H, serially connected to the output michelgrove accumulation 10.Signals received by the antenna 1 is converted to a lower frequency in the Converter 2 is converted by the ADC Converter 3 into digital signals x

_{n}(i), and the transmitter 4 is two-dimensional spectrum in time and frequency space . If the speed of the ADC is sufficient for direct analog-to-digital conversion of the input signals, as, for example, when building the image in the KB range, the inverter 2 can be excluded.The transmitter 5 is restored complex two-dimensional angular spectrum at each frequency f, for all values of the angle pointing in elevation h by the formula (4).With fixed values of wavelength or frequency f and the elevation h of the expression (4) provides for the implementation of each of the multipliers 8(1)...8(q) of the corresponding transmitter 5(K,N) complex multiplication of signals Fourier image stored in the storage device 7, the signals Fourier image and the inverse Fourier transform of the signals received works in computers 9(1)...9(q). That is, the signal is multiplied by q times on the correction function for dierent values of the index q. Results q the inverse transformation, which represents the M values of the angular spectrum in animatedstudios evaluator 5(K,N). All solvers matrix 5(K,N) similarly, at the same time restores the two-dimensional (azimuth and elevation) integrated angular spectrum at all frequencies f.Device 6 determines the presence of a signal, and obtains estimates of the azimuth and elevation of its source at each frequency f from the maxima of the square of the module of the complex two-dimensional angular spectrum .The physical meaning of the proposed method consists in the following. Cyclic, q times, the repetition of the fast convolution, whose length is equal to the number of antennas N with multiplication of the original signal on the phase multipliers dependent cyclic shift 2q/M. This is equivalent to adding to the input signal phase, changing the law of cosine (see formula (3)), which causes the rotation of the grating about its phase center or rotation of its chart. This ensures recovery at each temporal frequency f, for a fixed value of elevation is significantly more complex values of the azimuthal angular spectrum (pattern) M than the number of antennas N, which, in turn, provides increased accuracy in M/N times. For typical values of M and N, which is characteristic for modern and advanced bearing the t, 4 626 859, CL G 01 S 5/04, 19862. RU, patent, 2096797, CL G 01 S 3/14, 19963. US patent 4 641 143, CL G 01 S 5/04, 3/16, G 06 G 7 / 19th, 19874. Solomentsev centuries Quick processing of signals in the HEADLIGHTS stations. theory and practice of application and improvement of electronic systems. MEIGA, 1987. The method for determining two-dimensional positions and frequency emitters, including direct two-dimensional time and space in the azimuthal plane of the Fourier transform of the ensemble of signals received by a ring lattice of N antenna elements, wherein each temporal frequency, for a fixed value guidance in elevation, each formed by converting a spatial frequency component of q times multiplied by the Fourier transform of the functions of guidance, depending on the frequency, elevation angle, parameters of the antenna array and the azimuthal rotation 2q/M produce q inverse one-dimensional spatial in the azimuthal plane of the Fourier transformation of the received aggregate adjusted spatial frequency components, repeat the multiplication and inverse Fourier transformation for all values pointing in elevation, opredelyayuschego complex angular spectrum.

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