Method and device for measuring difference in signal arrival time and in signal reception frequency

FIELD: radio engineering.

SUBSTANCE: proposed method and device can be used for measuring difference in signal arrival time from spaced receiving positions and in its reception frequency dispensing with a priori information about signal structure and about modulating message. Proposed device has two signal receiving means, device for defining arguments of signal two-dimensional digital cross-correlation function maximum , two analog-to-digital converters, three fast Fourier transform processors, cross-spectrum computer, and arithmetical unit. Proposed method depends on calculation of two-dimensional cross-correlation function using inverse fast Fourier transform of plurality of cross-spectrums, spectrum of one of signals being transformed for generating mentioned plurality of cross-spectrums by way of re-determining index variables.

EFFECT: enhanced computing efficiency, eliminated discreteness error.

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The invention relates to electrical engineering and can be used to measure the time difference of arrival and difference frequency signals with spaced receiving positions without the involvement of a priori information about the structure of the signal and modulating the message.

Measuring the time difference of arrival (ETA) and difference frequency reception (RCP) signals separated receiving positions is of great importance in systems for deep-space communications with the spacecraft (SC) type Mars Polarlander, Mars Pathfinder [1] or with the AC type Voyager and Galileo [2], including for determining motion parameters such KA.

A known number of analog measurements RWPs and RCP signals separated receiving positions [3-6], is based on finding arguments to a maximum of two-dimensional cross-correlation function, potentially giving a statistically optimal maximum likelihood estimates of differences of time and frequency of arrival of signals. However, the potential accuracy of the methods [3-6] unrealizable in practice due to the lack of adjustable standards of time and frequency [7, 8].

The known range of digital methods of measurement RWPs signals separated receiving positions [8], is based on finding the argument of the maximum of the cross-correlation function or the argument of the minimum of the differential cross-correlation functions to implement potentialyno the accuracy of methods [3-6] by eliminating errors discreteness by parabolic interpolation surroundings maximum or minimum of the corresponding functions. However, digital measurement techniques, RWPs signals separated receiving positions [8-9] are not applicable in the presence of motion of the source or receiving position, which is the case in systems for deep-space communications with the spacecraft. Another disadvantage of digital measurement methods presented in [8], is the low computational efficiency for large sample sizes the data because they are based on the direct calculation of cross-correlation functions (with this method of finding the cross-correlation function, the number of multiplications is proportional to the square of the length (n) data sampling, such proportionality is usually referred to as O(n2)).

In patents [10-12] presents a set of digital ways of joint measurement RWPs and RCP signals separated receiving position based on the presence of arguments to a maximum of two-dimensional discrete cross-correlation function (DCCF)that allow you to make measurements in the presence of motion of the source or receiving position. The main goal set by the author of patents [10-12], devoted to the reduction of data streams transmitted between the spaced receiving positions, and compensation of the systematic errors that occur when the correlation compressed and reference signals. However, in the ways change is possible RWPs and RCP [10-12] not solved the issues of exceptions error discreteness (correlation between RVP and RCP [13] does not allow the obvious way to distribute the joint measurement approaches described in [8]), and the issues of improving computational efficiency, since the cross-correlation function methods [10-12] does not come from a direct method through the convolution of the two sequences of data, as in [8], and due to the n-fold repetition (for search argument of the maximum in the frequency domain), the number of multiplications increases proportionally to the cube of length (n) data sample, i.e. O(n3).

Closest to the proposed method of measurement RWPs and RCP signals, collectively used actions on signal is method [14], is based on finding arguments to a maximum DCCF (computational significantly more effective than analogues)adopted for the prototype.

According to this method:

1. Receive signals on two separated receiving positions.

2. Convert the signal received from one of the selection positions, in the first digital data stream, which digitally represents the signal as a series of values of a function of time.

3. Convert the signal received from the other of the receiving position, the second digital data stream, which digitally represents the signal as a series of values of a function of time.

4. Transform using the fast Fourier transform (FFT) of the said first digital data stream on the adjacent periods of time in the value of the first range is, which represents the signal as a series of values of a function of frequency.

5. Transform using the FFT mentioned second digital data stream on the adjacent periods of time in the value of the second spectrum, which represents the signal as a series of values of a function of frequency.

6. Pointwisely mutually Peremohy values of the first and second spectra at adjacent points in time to generate the aggregate cross-spectra as a function of time.

7. Convert each frequency from the specified aggregate cross-spectra as a function of time, in many values RCP (to find the argument of the maximum RCP).

8. Choose from a specified set of values RCP those that correspond to the signal of interest.

9. Summarize the specified values of the cross-spectra for each of the selected values RCP through the calculation of the inverse FFT to find the RWPs as the argument of the maximum amounts found.

Essentially the method described above [14], implements a computationally efficient in comparison with analogues [10-12] finding arguments to a maximum DCCP using when calculating DCCF fast Fourier transform on the basis of theorem of Wiener-Khinchin [15], which determines the relationship between the spectrum and correlation function of the signal.

Considering the fact that the full data sample length (n) in the method prototype is divided into k to shift the segments to obtain permission in the area of uncertainty based on the Doppler shift, as stated in the third paragraph of the first column of the eighth page of the description of the prototype [14] with the subsequent calculation of the spectra and the corresponding cross-spectra for each shifted in time adjacent segments of the sample data, we can estimate the computational cost of finding the two-dimensional cross-correlation function in the method prototype.

Finding the Fourier image for one sample of data of length n requires to implement O(n·logn) multiplications [16-17]. Considering the fact that from each sample, data from the two receiving positions of the form k adjacent segments, each of which are Fourier transform, the total amount of multiplication operations required to find the Fourier images of the input data is A(2·k·n·logn). To find the corresponding cross-spectra requires O(k·n) multiplications. Calculation DCCF through inverse FFT of the received k cross-spectra requires O(k·n·logn) multiplications. Thus, in the method prototype for finding DCCF only requires About(3·k·n·logn+k·n) multiplications, which is much smaller than the counterparts. So, for example, to fetch data length n=1024 k=32 in the method prototype for finding DCCF will require only about one million Of(3·32·1024·log1024+32·1024)=O(3·32·1024·10+32·1024)=O(995072) operations in which norene. In the extreme case k=n the number of multiplications increases only up to 30 million. While in counterparts [10-12] will need about a billion (O(n3)) multiplications.

Despite a significant reduction in computational costs in comparison with analogues one of the drawbacks of the prototype method is the lack of computational efficiency. Another disadvantage of the prototype method is as analogues [10-12], the error of the discrete nature of the arguments of the maximum, since the correlation between RVP and RCP [13] does not allow the obvious way to distribute the joint measurement approaches for its exclusion set out in [8].

Device-prototype [14] contains the first tool receiving signals, connected to the determination device of the arguments of the maximum DCCF whose output is the output of the prototype, through the series-connected first analog-to-digital Converter (ADC), the first FFT processor, the transmitter, the cross-spectra and the second FFT processor. Between the second tool receiving signals and a second input of the transmitter of the cross-spectra of series-connected second ADC and the third FFT processor.

The drawback of the prototype is the lack of performance definition RCP and RWPs signals. Another drawback of the prototype t is aetsa insufficient accuracy RCP and RWPs, due to the presence of errors in the incremental definition of the arguments of the maximum DCCF.

The technical result of the invention is to improve the computational efficiency due to the use of the adjusted spectral properties of the discrete Fourier transform digital signal converted in frequency, eliminating the need for segmentation of the data on the adjacent subsets and calculating Fourier transforms of the images for the specified subsets of the signal.

The technical result is achieved by the fact that in the method of measuring the time difference of arrival and frequency signals, including a signal at two separated receiving positions, analog-to-digital conversion of the signal received from one of the selection positions, in the first digital data stream representing the signal in digital form as a series of values of a function of time, analog-to-digital conversion of the signal received from the other of the receiving position, the second digital data stream, converting the first digital data stream using a fast Fourier transform (FFT) in the value of the first spectrum representing the signal as a series of values of the frequency function S1(k), where k is an integer index variable, which varies the length of the data, converting the second digital data stream using the FFT in the meaning of the Oia second spectrum, representing the second signal as a series of values of the frequency function S2(k), mutual multiplication of the values of the spectrum of one of the signals with a complex conjugate values of the spectrum of another signal, generating a cross-spectrum calculation of the discrete two-dimensional cross-correlation function (DCCF) signal through inverse FFT of many cross-spectra, determining the time difference of arrival and frequency signals as arguments to a maximum DCCF signal, according to the invention, the spectrum of one of the signals Si(k), where i=1, 2 is the number of one of the two spectra, convert the frequency value of m chosen according to the requirements of resolution RCP from the integer range of values from one to (N-1), where N is the length of the processed digital data stream, creating a sequence converted by the frequency spectra of Si,m(k)obtained from the original spectral signal components according to the following rule:

the values of the spectra of Si,m(k) the converted frequency signals mutually Peremohy complex conjugate values of the spectrum of the second of the two input signals to generate a variety of cross-spectra.

Other technical result of the invention is the exception error discreteness due to the use of the fact that Plovdiv city suburbs is here the main maximum of two-dimensional cross-correlation function of the signal has the shape of an elliptic paraboloid [13, p.8-9], and through the development of optimal, in the mean square sense, the analytical method of estimating the parameters of the elliptic paraboloid and the arguments to its maximum, based on the projective transformation.

The technical result is achieved by the fact that in the method of measuring the time difference of arrival and frequency signals in the vicinity of the arguments of the maximum DCCF signal choose a nite set of points specified function, including the peak point and at least two points located on opposite sides relative to the argument of the maximum RVP, and two points located on opposite sides relative to the argument of the maximum RCP, values DCCF for the selected points are combined into a column vector z, of the units form the vector-column 1 of the same dimension as the vector z, combine the vectors 1 and z in the two-column matrix G, the first the column which put the unit vector 1, and the second is the vector z, pseudobradya matrix G, indicating a pseudo-inverse matrix as G+where Superscript+denotes the operation of pseudouridine matrices, multiply a matrix G right on her pseudo-inverse matrix G+form the projectoras the difference between the matrix is identical to the conversion and the result of the multiplication, the arguments corresponding to P Is P for selected points DCCF, ordered as components of a vector z, are combined into a column vector x, and the squares of the components of the vector x similarly combined into a column vector q, arguments, corresponding RCP for selected points DCCF ordered as components of a vector z, are combined into a column vector y, and the squares of the components of the vector y similarly combined into a column vector v, the vector-columns x, y, v in the order listed together in crestorbuy matrix F, find the least squares estimation of three-dimensional vector-columnwhere Superscripttdenotes transposition of a matrix, according to the following rule:half the value of the first vector componentdivided by the sampling rate of the signal Fsand get the updated value ofRVP signal, and half the value of the second vector componenttaken with the opposite sign, multiplied by the sampling rate of the signal and the value of the third components of the specified vector, divided by the size N of the processed digital data stream and receive the updated value ofRCP signal.

The method is implemented by a device for measuring time difference of arrival and frequency of the reception signals, terrasim the first tool receiving signals, connected to the determination device of the arguments of the maximum of the discrete two-dimensional cross-correlation function signal, the output of which is the output of the measuring device, sequentially through the first analog-to-digital Converter (ADC), the first FFT processor, the transmitter, the cross-spectra and the second FFT processor, between the second tool receiving signals and a second input of the transmitter of the cross-spectra of series-connected second ADC and the third FFT processor according to the invention, between the output of the first FFT processor and the third input of the transmitter of the cross-spectra included arithmetic unit (AU), which converts the values of Si(k) the spectrum of one of the two signals in frequency on the magnitude of m is chosen from an integer range of values from one to (N-1), and generates at the output a lot of spectra Si,m(k) by the following rule:

where Si,m(k) be the set of transformed frequency on the magnitude of m spectra of one of the signals, N is the length of the processed digital data flow, i is the number of one of the two received signals, k is an integer index variable, which varies the length of the data.

The drawing shows a structural diagram of a device that implements the proposed method.

According to the proposed method:

1. Taking the Ute signal on two separated receiving positions.

2. Convert the signal received from one of the selection positions, in the first digital data stream, which digitally represents the signal as a series of values of a function of time.

3. Convert the signal received from the other of the receiving position, the second digital data stream, which digitally represents the signal as a series of values of a function of time.

4. Transform using the fast Fourier transform (FFT) of the said first digital data stream in the value of the first spectrum, which represents the signal as a series of values of the frequency function S1(k), where k is an integer index variable, which varies the length of the data.

5. Transform using the FFT mentioned second digital data stream in the value of the second spectrum, which represents the signal as a series of values of the frequency function S2(k).

6. Mutually Peremohy spectrum values of one of the signals with a complex conjugate values of the spectrum another signal to generate the cross-spectrum.

7. Range of one of the signals Si(k), where i=1, 2 is the number of one of the two spectra, convert the frequency value of m chosen according to the requirements of resolution RCP from the integer range of values from one to (N-1), where N is the length of the processed digital data stream, creating a sequence converted to the frequency spectra of S i,m(k)obtained from the original spectral signal components according to the following rule:

where i is the number of one of the two received signals values.

8. The values of the spectra of Si,m(k) the converted frequency signals mutually Peremohy complex conjugate values of the spectrum of the second of the two input signals to generate a variety of cross-spectra.

9. Compute the discrete two-dimensional cross-correlation function (DCCF) signal using inverse FFT of many cross-spectra

10. Determine the time difference of arrival and frequency signals as arguments to the maximum DCCF signal.

In the known method, to build a discrete two-dimensional cross-correlation function of a signal using the set of shifted frequency spectra of one of the signals Si,m(k), these spectra get through multiple FFT shifted by the magnitude m of adjacent segments of the digital data obtained by analog-to-digital conversion of the received signal, that is, the direct application of known Fourier transform theorems about the delay of the signal in the time domain [15-16].

We show that the application of rule (1) also yields a set of shifted frequency spectra of a signal is in S i,m(k).

If in continuous time real signal s(t) is the frequency on the value of g Hz, the resulting signal

where(t)=HT(s(t)) is the Hilbert transform of s(t).

The Fourier transform (FT) to (2) due to linearity is

To simplify (3) take into account the known properties of the Fourier transform and Hilbert [15-16, 19]

whereand the function sgn(f) by definition [19] equal to

Then for the first term in (3), we obtain

as for the second term of expression (3)

substituting these into the expression (3), have

Taking into account the definition (5) expression (6) can be rewritten in the form

On the basis of the results received for a valid signal s(t) in continuous time to discrete sequencesin discrete time, below are similar spectral properties.

If discrete sequence s[n} corresponding periodically continued follower who must be described as its discrete Fourier transform is defined as

Let- discrete analogue of the analytical signal used inside the parentheses in the expression (2)then, following [18, 19],

where- a valid sequence, and.

This result can be used to get converted in frequency by the value ofsequence, defined as

Because of the definitions (8) in discrete time has the equality

which is similar to equations (4) for continuous time. Therefore, due to the properties of the discrete Hilbert transform [18, str.257], in the current notation

where the designation kmodN means the integer remainder of dividing the index variable k on the size of the processed digital data stream N, and considering the fact thatyou can record

The last expression on the basis of definition integer sign function sgnN(k)introduced in (12), easily converted to the form (1)that provides the get converted in frequency by the value of m spectra of the signal through Perevoznaya index of variables per rule (1) without segmentation data and without FFT for each data segment, as in the method prototype. This eliminates About(2·k·n·logn) multiplications, here k denotes the number of data segments, to improve computational efficiency and, in the extreme case k=n, to reduce about three times the number of required multiplications and, in comparison with the above example for the prototype method, reducing their number from 30 to 10 million operations.

According to the second variant of the proposed method, eliminating errors discreteness:

1. Receive signals on two separated receiving positions.

2. Convert the signal received from one of the selection positions, in the first digital data stream, which digitally represents the signal as a series of values of a function of time.

3. Convert the signal received from the other of the receiving position, the second digital data stream, which digitally represents the signal as a series of values of a function of time.

4. Transform using the fast Fourier transform (FFT) of the said first digital data stream in the value of the first spectrum, which represents the signal as a series of values of the frequency function S1(k), where k is an integer index variable, which varies the length of the data.

5. Transform using the FFT mentioned second digital data stream in value is of a second spectrum, which represents the signal as a series of values of the frequency function S2(k).

6. Mutually Peremohy spectrum values of one of the signals with a complex conjugate values of the spectrum another signal to generate the cross-spectrum.

7. Range of one of the signals Si(k), where i=1, 2 is the number of one of the two spectra, convert the frequency value of m chosen according to the requirements of resolution RCP from the integer range of values from one to (N-1), where N is the length of the processed digital data stream, creating a sequence converted by the frequency spectra of Si,m(k)obtained from the original spectral signal components according to the following rule:

where i is the number of one of the two received signals values.

8. The values of the spectra of Si,m(k) the converted frequency signals mutually Peremohy complex conjugate values of the spectrum of the second of the two input signals to generate a variety of cross-spectra.

9. Compute the discrete two-dimensional cross-correlation function (DCCF) signal using inverse FFT of many cross-spectra

10. Determine the time difference of arrival and frequency signals as arguments to the maximum DCCF signal.

11. In the vicinity of the arguments of the maximum DCCF signal select end m is these points specified function, including the peak point and at least two points located on opposite sides relative to the argument of the maximum RVP, and two points located on opposite sides relative to the argument of the maximum RCP.

12. Values DCCF for the selected points are combined into a column vector z.

13. Of the units to form a column vector 1 of the same dimensionality as the z vector.

14. Combine the vectors 1 and z in the two-column matrix G, the first column put the unit vector 1, and the second is the z vector.

15. Pseudobradya matrix G, indicating a pseudo-inverse matrix as With+where Superscript+denotes the operation of pseudouridine matrix.

16. Multiply the matrix G to the right on her pseudo-inverse matrix G+.

17. Form the projectoras the difference between the matrix is identical to the conversion and the result of the multiplication.

18. The arguments that are appropriate for the selected RWPs points DCCF ordered as components of a vector z, are combined into a column vector x.

19. The squares of the components of the vector x similarly combined into a column vector q.

20. Arguments corresponding RCP for selected points DCCF ordered as components of a vector z, are combined into a column vector y.

21. The squares of the components of the vector y similarly combined into a column vector v.

22. Vectors-columns x, y, v in the order listed together in crestorbuy matrix F.

23. Find the least squares estimation of three-dimensional vector-columnwhere Superscriptgdenotes transposition of a matrix, according to the following rule:

24. Half the value of the first vector componentdivided by the sampling rate of the signal Fsget the updated value ofRVP signal.

25. Half the value of the second vector componenttaken with the opposite sign, multiplied by the sampling rate of the signal and the value of the third components of the specified vector, divided by the size N of the processed digital data stream and receive the updated value ofRCP signal.

It is known [17-18], the discrete representation of continuous functions inevitably leads to quantization noise, creating errors discrete with error variancewhere b is the quantization step. A variant of the proposed method, eliminating errors of discretion in assessing the parameters of two-dimensional cross-correlation functions With the12(τ,fd), based on the fact that in the vicinity of maximumpoolsize 12(τ,fd) has the shape of an elliptic paraboloid [13] [21]estimated the parameters of which the solution of systems of linear equations, you can specify values RWPs and RCP received as arguments to the maximum DCCF because DCCP is a sample from the function With12(τ,fd).

The canonical equation of an elliptic paraboloid in the Cartesian coordinate system OXYZ [21, p.101]

describes the surface with a minimum at the point (0,0)Tso for our purposes (14) will be converted to the form

where C is the value of the paraboloid z-axis at the point of maximum τ - the argument of the maximum of the x-axis, corresponding in this case, the true value of RWPs, fd- the argument of the maximum on the y-axis, corresponding in this case the true value RCP.

The original equation (15) can be rewritten in a functional form

Here, the function z(x,y) is essentially a two-dimensional cross-correlation function in other notation.

Let us introduce the notation ρ=a/b and give the equations (15)-(16) are linear in the unknown parameters until paraboloid (16) τ, fd, A, B, C, mean

or in other words

Equation (18) can PE epicate in vector form as follows:

Let us introduce notations for vectors of the right-hand side of equation (19)

Let the selected point DCCP, which, in discrete time, the sampling function for a two-dimensional cross-correlation function C12(τ,fd), which in the region of maximum describes an elliptic paraboloid [13, p.8-9], then the vector-a line of the form hTand free of equation (19) are known values, and the vector-column- vector of unknown parameters. Therefore, if you select a sufficient number of such linearly independent rows of hTto create overridden the system of equations (19), it can be obtained the optimal least squares estimation five-dimensional vectorwhose components are associated with the unknown parameters of the elliptic paraboloid expressions (20).

For the formation of the required system of equations (19) are chosen at the point of maximum DCCF found in the first ten operations of the proposed method, and still at least four points DCCF (two points located on opposite sides relative to the argument of the maximum RVP, and two points located on opposite sides relative to the argument of the maximum RCP), then odesn is a rule solves the system of linear equations (19), allowing noiseless case, to find the true values of DDP τ and RCP fdand in the presence of noise to find their root-mean-square estimation.

Let the selected P points DCCF ordered random numberseach with coordinates (xp,yp,zp)Twhere, according to the above notation, xppoint p corresponds to its argument axis RWPs DCCF, ypher argument axis RCP DCCF and zpthe value DDCF for a point p, then their coordinates and the squares of their coordinates can be combined into a P-dimensional vectors-columns

which is similar to the vector hTare combined into a matrix N

.

Formed on the basis of the matrix H the system of equations has the following solution:

and allows, through the operation of pseudouridine matrix H [22-24] and multiplying the pseudo-inverse matrix H+on the right-hand column free members q, taking into account the relations (20), find updated estimates of the values of RVP τ and RCP fd. The value of the updated estimates of DDP τfor the transition from the field of discrete time in the region of a continuous time, it is necessary to divide the frequency of the sampling signal Fsand the value of the specified OC the NCI RCP f dmultiply by an amount equal to Fs/N. the Latter is obvious, since a discrete step between points DCCF axis RWPs is an amount equal to 1/Fsaxis RCP - an amount equal to the Fs/N.

Different ways to perform the operation of pseudouridine rectangular matrices are detailed in [22-27]. An example of practical implementation of the operation pseudouridine in a widespread software package MATLAB Release 13 described in its documentation [28, RR-91-2-93].

Despite the fact that the expression (22) allows you to find the updated estimates of the values of RVP τ and RCP fdthe high dimensionality of the vector (20) estimated parametersleads to greater conditionality matrix H [22], denoted by cond(H), and entails the reduction potentially achievable accuracy of estimation of the adjusted values of DDP τ and RCP fd.

One of the main features of the proposed method is an exception to the number of estimated parameters(20) the values of4,5which is not required to determine the coordinates of two-dimensional cross-correlation function With12(τ,fd). Reducing the dimension of the vector of estimated parameters reduces the dimensionality of the problem and allow you to plug the et to improve the conditioning of the system.

Unfortunately, there is no obvious solution to reduce the problem dimension. To reduce the dimensionality of the vector of estimated parameters will produce a series of transformations, systems of linear equations (19) and (23). This will divide pyatisetovuyu matrix H into two pieces and uses smaller dimension

Redefine the vector of estimated parameters as follows:

Let us introduce the definition of the vector of nuisance parameters

Then we can write the system of equations is identical to the system of linear equations (23)

If the system of equations (27) multiplied on the left on the projector [22, 23]

orthogonal space, stretched on the columns of the matrix G [22, 26, 27], such thatwhere I is the identical matrix transformation [23], from the system of equations (27) will result in the following system of equations:

Thus, as a result, the projective transformation (28) the system of equations (29) is a system with three unknowns instead of five and its conditionality significantly less [22] the conditioning of the system equations (23), which is confirmed by the results of computational experiments

So potentially achievable accuracy of estimation of the adjusted values of DDP τ and RCP fdbased on the solution of the system of equations (29) will be higher under the condition that the rank of the matrixequal to three

Then the least squares estimation of the vector-columnfrom the linear system of equations (28) has the form

Taking into account expressions (25) and taking into account the fact that, as for the system of equations (29), the value of the updated estimates of DDP τfor the transition from the field of discrete time in the region of a continuous time, it is necessary to divide the frequency of the sampling signal Fsand the value of the corrected estimates RCP fdmultiply by an amount equal to Fs/N, the final expression in these estimates have the form

Obtained on the basis of deduced here transformations on the signal sequence of actions and implements patented method.

A device that implements the proposed method of measuring the time difference of arrival and frequency of the reception signals (see drawing), contains the first tool receiving signals 1, connected to the determination device of the arguments of the maximum of the discrete two-dimensional cross-correlation function 2, through consistently included the e first ADC 3, the first FFT processor 4, the transmitter cross-spectra 5 and the second FFT processor 6. The output device 2 is the output of the measuring device. Between the second means of the reception signals 7 and a second input of the transmitter of the cross-spectra 5 cascaded second ADC 8 and the third FFT processor 9. Between the output of the first FFT processor 4 and the third input of the transmitter of the cross-spectra 5 includes the arithmetic unit 10.

The proposed device operates as follows. On one of the two separated receiving the position signal, the first means receiving signals 1, and on the other of the two separated receiving the position signal by the second means of the reception signals 7. From the output of the first means receiving signals 1 signal fed to the input of the first ADC 3 and convert the signal received from one of the selection positions, in the first digital data stream, which digitally represents the signal as a series of values of a function of time. From the output of the second means of the reception signals 7 received signal fed to the input of the second ADC 8 and convert the signal received from the other of the receiving position, the second digital data stream, which digitally represents the signal as a series of values of a function of time. In the first FFT processor 4 converts the first digital data stream received from the output of the first ADC 3, the value of the first SP is Ctra, which represents the signal as a series of values of the frequency function S1(k). In the third FFT processor 9 converts the second digital data stream received from the output of the second ADC 8, the value of the second spectrum, which represents the signal as a series of values of the frequency function S2(k). The evaluator cross-spectra 5 mutually Peremohy received on the first two inputs from the FFT processors 4 and 9 values of the spectrum of the first signal with a complex conjugate values of the spectrum another signal to generate the cross-spectrum without frequency conversion of signals. In addition, the evaluator cross-spectra 5 mutually Peremohy received at its third input from the output of the FFT processor 4 via AU 10 values of multiple spectra Si,m(k)obtained in AU 10 according to rule (1) of the values of the spectrum of the first signal with a complex conjugate values of the spectrum another signal to generate a variety of cross-spectra with frequency conversion of signals. After that, the second FFT processor 5 calculates DCCP using inverse FFT of many cross-spectra received at its input from the output of the transmitter cross-spectra 5. Finally, the device of the arguments of the maximum DCCF 2 received at its input from the output of the second FFT processor 5 function determines the time difference of arrival and frequency signals as argum the options maximum DCCF and displays the measured values on the output device.

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1. A method of measuring the time difference of arrival and frequency signals, including a signal at two separated receiving positions, analog-to-digital conversion of the signal received from one of the selection position in the first digital data stream representing the signal in digital form as a series of values of a function of time, analog-to-digital conversion of the signal received from the other of the selection position in the second digital data stream, converting the first digital data stream using a fast Fourier transform (FFT) in the value of the first spectrum representing the signal as a series of values of the frequency function S1(k), where k is an integer index variable, which varies the length of the data, converting the second digital data stream using the FFT in the value of the second spectrum representing the second signal as a series of values of the frequency function S2(k), mutual multiplication of the values of the spectrum of one of the signals with a complex conjugate values of the spectrum of another signal, generating a cross-spectrum calculation of the discrete two-dimensional cross-correlation function (DCCF) signal using inverse FFT of many cross-spectra, determining the time difference of arrival (ETA) and difference frequency reception (RCP) signals as arguments poppy is Imola DCCF signal, characterized in that the spectrum of one of the signals Si(k), where i=1, 2 is the number of one of the two spectra, convert the frequency value of m chosen according to the requirements of resolution RCP from the integer range of values from one to (N-1), where N is the size of the processed digital data stream, creating a sequence converted by the frequency spectra of Si,m(k)obtained from the original spectral signal components according to the following rule

the values of the spectra of Si,m(k) the converted frequency signals mutually Peremohy complex conjugate values of the spectrum of the second of the two input signals to generate a variety of cross-spectra.

2. A method of measuring the time difference of arrival and frequency signals according to claim 1, characterized in that in the vicinity of the arguments of the maximum DCCF signal choose a nite set of points specified function, including the peak point and at least two points located on opposite sides relative to the argument of the maximum RVP, and two points located on opposite sides relative to the argument of the maximum RCP, values DCCF for the selected points are combined into a column vector z, of the units to form a column vector l of the same dimension as the vector z, the combined vectors of l and z in Buchstaber matrix G, the first column put the unit vector l, and the second is the vector z, pseudobradya matrix G, indicating a pseudo-inverse matrix as G+where Superscript+denotes the operation of pseudouridine matrices, multiply a matrix G right on her pseudo-inverse matrix G+form the projector G, as the difference between the matrix is identical to the conversion and the result of the multiplication, the arguments that are appropriate for the selected RWPs points DCCF ordered as components of a vector z, are combined into a column vector x, and the squares of the components of the vector x similarly combined into a column vector q, arguments, corresponding RCP for selected points DCCF ordered as components of a vector z, are combined into a column vector y, and the squares of the components of the vector y similarly combined into a column vector v, the vector-columns x, y, v in the order listed unite in crestorbuy matrix F, find the least squares estimation of three-dimensional vector-columnwhere SuperscriptTdenotes transposition of a matrix, according to the following rule:

half the value of the first vector componentdivided by the sampling rate of the signal Fsand get the updated value of , RVP signal, and half the value of the second vector componenttaken with the opposite sign, multiplied by the sampling rate of the signal and the value of the third components of the specified vector, divided by the size N of the processed digital data stream and receive the updated value ofRCP signal.

3. The device for implementing the method according to claim 1, containing the first tool receiving signals, connected to the determination device of the arguments of the maximum of the discrete two-dimensional cross-correlation function signal, the output of which is the output of the measuring device through the series-connected first analog-to-digital Converter (ADC), the first FFT processor, the transmitter, the cross-spectra and the second FFT processor, between the second tool receiving signals and a second input of the transmitter of the cross-spectra of series-connected second ADC and the third FFT processor, characterized in that between the output of the first FFT processor and the third input of the transmitter of the cross-spectra included arithmetic unit (AU)converts the values of Si(k) the spectrum of one of the two signals in frequency on the magnitude of m is chosen according to the requirements of resolution RCP of integer number values from one to (N-1), and generates at the output a lot of spectra Si,m(k) what about the following rule

where Si,m(k) be the set of transformed frequency on the magnitude of m spectra of one of the signals, N is the length of the processed digital data flow, i is the number of one of the two received signals, k is an integer index variable, which varies the length of the data.



 

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