CN117851735A - Simplified time-delay fusion ranging method - Google Patents
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Abstract
The invention discloses a simplified time delay fusion ranging method, which belongs to the field of signal ranging and aims at the technical problems that in the prior art, positioning errors are increased along with the increase of use scenes when RSSI information is used, the performance of a Matrix Pencil algorithm is poor under the working conditions of long-distance multipath and low SNR, and the channel equalization and time delay estimation method for Chirp signals is poor under the conditions of multipath signals and low SNR; the invention estimates TOA integer delay through a correlation method, and uses the judgment of multipath distance and SNR to select the algorithm which is most suitable for the current scene to carry out distance measurement and positioning, thereby improving the distance measurement and positioning performance under the condition of long-distance multipath scene and low SNR and reducing the calculation complexity of distance measurement and positioning.
Description
Technical Field
The invention belongs to the technical field of signal ranging, and particularly relates to a simplified delay fusion ranging method.
Background
In wireless communication, positioning is receiving more and more attention as a basis for intelligent awareness. The positioning method comprises the steps of positioning by using angle measurement information, positioning by using delay information and positioning by using RSSI. The use of angle information for positioning requires high precision angle measuring equipment, however as the scene size becomes larger, the same angle error will cause a larger positioning error. When positioning using RSSI information, errors also increase as scene size increases. Both angular positioning and RSSI positioning are therefore more difficult to use for larger scenarios.
When the time delay information is used for ranging and positioning, the ranging and positioning precision is only related to the time delay estimation precision and the synchronization precision, and is irrelevant to the scene size.
In addition, compared with the RSSI scheme, the accuracy of ranging and positioning based on time delay is higher, and the performance of noise resistance and multipath is better. Delay-based positioning and ranging schemes have received great attention.
The ranging algorithm based on time delay comprises a MUSIC algorithm, a Matrix Pencil algorithm and the like, and the MUSIC algorithm has very good performance under the condition of medium and low SNR and under the condition of a long-distance multipath, however, the method has spectrum peak searching of a plurality of points, so the calculated amount is large. Compared with the MUSIC algorithm, the Matrix Pencil algorithm does not need to calculate an autocorrelation Matrix, and the calculated amount is very low, however, the Matrix Pencil algorithm is often not as satisfactory under the conditions of long-distance multipath and low SNR.
The paper Joint ESPIRIT for Time Delay Estimation of Chirp Spread Spectrum (2008), the authors NaYoung Kim propose a channel equalization and delay estimation method for Chirp signals, which firstly performs MMSE or ZF channel equalization, and then obtains delay estimation through matrix pencil algorithm with lower complexity. However, this method performs poorly in multipath signals and low SNR conditions, so a fused ranging and positioning method is needed to improve ranging and positioning performance in long-range multipath scenarios and low SNR conditions.
Disclosure of Invention
Aiming at the technical problems that the RSSI information positioning error in the prior art can be increased along with the increase of the use scene, the Matrix Pencil algorithm has poor performance under the working conditions of long-distance multipath and low SNR, and the channel equalization and delay estimation method for Chirp signals has poor performance under the conditions of multipath signals and low SNR, the invention provides a simplified delay fusion ranging method, which aims at: and the ranging precision under the multipath and low SNR conditions is improved, and the calculation complexity of the MUSIC algorithm is reduced.
The technical scheme adopted by the invention for achieving the purpose is as follows:
a simplified time delay fusion ranging method comprises the following steps;
s1, transmitting a Chirp signal, and performing delay estimation by using the transmitted signal to obtain integer delay data;
s2, calculating and judging according to the maximum value and the next maximum value of the integer part in the delay data, if the delay data is judged to be a far multipath scene, entering a step S3, and if the delay data is judged to be a near multipath scene, entering an SNR value judging process; calculating an SNR value, and entering a step S3 when the SNR value is smaller than a second threshold value, otherwise entering a step S4;
s3, firstly, carrying out channel estimation, then carrying out average calculation on a preamble part of a transmitting signal, then carrying out extraction, grouping and averaging on data of a code chip, then calculating an autocorrelation matrix and matrix eigenvalue decomposition, then calculating a guide vector, and finally carrying out ranging calculation to obtain distance data;
s4, firstly, carrying out channel estimation, then carrying out noise reduction treatment on part of transmitted signals, then carrying out extraction, grouping and averaging on data of a plurality of chips, then carrying out singular value decomposition on a Z matrix, and finally calculating a delay result and obtaining distance data;
s5, sorting and outputting the distance data obtained in the steps S3 and S4.
Further, in the step S1, a correlation method is adopted for delay estimation, and the specific steps are as follows:
s1.1: an integer part in the delay data is obtained, the preamble signals in the transmission signal and the reception signal are operated, the formula is as follows,
where fft represents the fast fourier transform,represents the conjugate of rx, ||represents the absolute value, |>Representing the preamble signal in the transmitted signal, is->Represents a preamble signal in the received signal, a>Representing an integer portion of the delay data;
s1.2: then finding the subscript corresponding to the maximum value of the integer part in the delay dataI.e. integer delay data, wherein +.>The formula is as follows,
this step is completed.
Further, in the step S2, the multipath distance is judged, the SNR is judged according to the value of the multipath distance, and the calculation is performed according to the judgment result selection algorithm, and the specific judgment steps are as follows:
s2.1, finding the maximum value and the next maximum value in the integer part in the delay data, if the maximum value minus the next maximum value is larger than a first threshold value, judging as a far multipath scene, otherwise judging as a near multipath scene, if the near multipath scene is the far multipath scene, entering a step S3, otherwise entering a step S4;
s2.2, calculating the signal energy in the integer part of the delay data, the formula is as follows,
wherein the method comprises the steps ofRepresents the maximum value of the integer part in the delay data, < >>A next largest value representing an integer part of the delay data,/->Is signal energy;
s2.3: the noise energy of the integer part of the delay data is calculated, as follows,
wherein the method comprises the steps ofIs noise energy, SF is a velocity factor;
s2.4, finally calculating the SNR value, the formula is as follows,
and comparing the obtained SNR value with a second threshold value, and if the SNR value is smaller than the second threshold value, proceeding to step S3, otherwise proceeding to step S4.
Further, step S3 uses a MUSIC algorithm with large steps and small steps.
Further, the specific flow of the MUSIC algorithm of the big step and the small step adopted in the step S3 is as follows:
s3.1, carrying out channel estimation, wherein the formula is as follows,
and S3.2, averaging a plurality of symbols in the preamble, wherein the formula is as follows,
where s represents the symbol number, SYM represents the number of symbols,represents a preamble average;
s3.3, extracting, grouping and averaging the data of the plurality of chips, making the extraction strength be L, and grouping the chips according to the extraction strength, wherein the chips of the first group are the same as the data of the second groupThe method comprises the following steps:
and S3.4, calculating the average value of the correlation results among a plurality of groups, wherein the formula is as follows,
wherein j is more than or equal to 1 and less than or equal to 2 SF/L,representing the value of the j-th element after the extraction average, is->Represents +.o after preamble averaging>The value of the individual chips;
s3.5: the autocorrelation matrix is calculated, the formula is as follows,
wherein H represents the conjugate transpose and Rhh represents the autocorrelationThe matrix is formed by a matrix of,represents a decimated average;
the autocorrelation matrix is then subjected to matrix eigenvalue decomposition,
wherein the characteristic values are arranged in the order from big to small, and the arrangement order of the characteristic vectors and the characteristic values is consistent;
s3.6, calculating a guiding vector, wherein the calculation formula is as follows,
wherein n represents the nth chip (0<n<2 SF and n is an integer), m represents a steering vector corresponding to the mth delay point, fc represents a carrier frequency, j represents an imaginary unit,is a guide vector;
s3.7, performing signal processing to search decimal delay, and adopting a method of combining big steps with small steps to enable the step length of the big steps to be stp_rough and the step length of the small steps to be stp_acc;
assuming that the number of multipaths in the space is Mut, then arranging the characteristic values in order from big to small, wherein the characteristic values after the sorting are as follows，
When the number of the pins is small,
，
then go to the next step and th3 represents a third threshold;
s3.8, obtaining MUSIC pseudo spectrum according to the calculation of the large step length, the formula is as follows,
the energy value of the MUSIC pseudo spectrum is the value range
The interval between two points in m1 is a step length of a large step, offset1 represents a delay search window value 1, and offset2 represents a delay search window value 2;
after the energy value of the MUSIC pseudo spectrum is obtained, the subscript corresponding to the maximum value of the energy value is the delay less than the minimum sampling interval,
a delay less than the minimum sampling interval;
s3.9, calculating MUSIC pseudo spectrum of small step length, the calculation formula is as follows,
wherein the method comprises the steps ofThe value range is as follows: />
And is also provided withThe interval between the middle 2 points is the step length of the small steps;
s3.10 findThe subscript corresponding to the maximum value in the range is the accurate search delay, the calculation formula is as follows,
representing the subscript corresponding to the maximum value in the MUSIC pseudo spectrum;
the final accurate TOA delay is expressed as:
the ranging result is expressed as,
wherein BW represents the bandwidth of the signal, and c represents the speed of light as the value，/>Representing the distance measurement.
Further, in step S4, a noise reduction Matrix decision algorithm is adopted.
Further, the specific flow of the noise reduction Matrix pecil algorithm adopted in the step S4 is as follows:
s4.1 the channel estimation is performed,
s4.2, the preamble of a plurality of symbols is noise reduced,
wherein s represents a symbol number;
s4.3, extracting, grouping and averaging the data of the plurality of chips,
let the extraction strength be L, then group the chips according to the extraction strength, wherein the firstGroup of chipsIn order to achieve this, the first and second,
the correlation results among the multiple groups are averaged, the calculation formula is as follows,
wherein the method comprises the steps ofWherein j represents the j-th group;
s4.4, extracting subarrays, wherein the calculation formula is as follows,
wherein LL is selected asA number between them, let c traverse 1 to LL+1, the calculated Z matrix dimension is LL row,>a column;
s4.5, singular value decomposition is carried out on the Z matrix, the calculation formula is as follows,
wherein V represents a right singular vector of the Z matrix, sigullar represents singular values of the Z matrix, the singular values are arranged in a mode from large to small, and the arrangement sequence of the right singular vector is consistent with the singular values;
s4.6, extracting the signal subspace from V, assuming the multipath number of the space is Mut2, then acquiring the multipath number,
the singular values are arranged in the order from big to small, and the ordered characteristic is that
，
When the number of the pins is small,
then the next step is entered, and,
th4 represents a fourth threshold, and the corresponding Mut2 is the dimension of the signal subspace;
after Mut2 is determined, the signal subspace is,
s4.7, constructing two phase rotation vectors, wherein the calculation formula is as follows,
calculation ofAnd->The phase rotation between them, the calculation formula is as follows,
wherein the method comprises the steps ofRepresenting matrix->Moore-pentase generalized inverse of (C);
s4.8, decomposing the characteristic value of the MM matrix, wherein the calculation formula is as follows,
，
wherein the method comprises the steps ofThe characteristic values are arranged in the order from big to small;
s4.9, modeling the characteristic value, calculating the following formula,
the maximum value after the modulus is calculatedAnd the value before the corresponding modulo is recorded as；
S4.10, calculating a delay result according to the maximum characteristic value, wherein a calculation formula is as follows,
where exp represents the natural logarithm, L represents the extraction strength,representing taking the imaginary part of the complex number, +.>Representing the circumference rate, ++>Representing logarithm>The result is the estimation result of decimal delay;
the final estimated distance is:
wherein BW represents the bandwidth of the signal and c represents the speed of light as，/>For the final estimated distance.
Further, the step S5 is as follows: and (3) sorting the calculated data obtained in the steps S3 and S4, and outputting the sorted calculated data to a display terminal.
The associated abbreviations are as follows:
SF：Spread factor;
BW：Bandwidth;
MUSIC：Multiple Signal Classification;
RSSI：Reference Signal Strength Indicator;
MMSE：Minimum Mean Square Error;
ZF：Zero Force;
1. the Matrix pencil algorithm and the MUSIC algorithm of large-step and small-step search used by the method improve the ranging precision under the conditions of multipath and low SNR, the ranging precision in the prior art is tens of meters, and the method improves the ranging precision to be within ten meters.
2. The method for combining big steps and small steps can reduce the calculation complexity of the MUSIC algorithm and reduce the calculation amount.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some examples of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of a simplified time-lapse fusion ranging method of the present invention.
Fig. 2 is a schematic step size diagram of a method used in an embodiment of the invention.
FIG. 3 is a flow chart of an embodiment of the present invention.
Detailed Description
To make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention. Accordingly, the detailed description of the embodiments of the invention provided below is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus, once an item is defined in one figure, it may not be further defined and explained in the following figures.
Example 1:
as shown in fig. 1, 2 and 3, a simplified delay-fusion ranging method includes the following steps;
s1, transmitting a Chirp signal, and performing delay estimation by using the transmitted signal to obtain integer delay data;
s2, calculating and judging according to the maximum value and the next maximum value of the integer part in the delay data, if the delay data is judged to be a far multipath scene, entering a step S3, and if the delay data is judged to be a near multipath scene, entering an SNR value judging process; calculating an SNR value, and when the SNR value is smaller than a second threshold value, entering a step S3, otherwise, entering a step S4;
s3, firstly, carrying out channel estimation, then carrying out average calculation on a preamble part of a transmitting signal, then carrying out extraction, grouping and averaging on data of a code chip, then calculating an autocorrelation matrix and matrix eigenvalue decomposition, then calculating a guide vector, and finally carrying out ranging calculation to obtain distance data;
s4, firstly, carrying out channel estimation, then carrying out noise reduction treatment on part of transmitted signals, then carrying out extraction, grouping and averaging on data of a plurality of chips, then carrying out singular value decomposition on a Z matrix, and finally calculating a delay result and obtaining distance data;
s5, sorting and outputting the distance data obtained in the steps S3 and S4.
In the step S1, a correlation method is adopted for delay estimation, and the specific steps are as follows:
s1.1: an integer part in the delay data is obtained, the preamble signals in the transmission signal and the reception signal are operated, the formula is as follows,
where fft represents the fast fourier transform,represents the conjugate of rx, ||represents the absolute value, |>Representing the preamble signal in the transmitted signal, is->Represents a preamble signal in the received signal, a>Representing an integer portion of the delay data;
s1.2: then finding the subscript corresponding to the maximum value of the integer part in the delay dataI.e. integer delay data, wherein +.>The formula is as follows,
，
this step is completed.
S2, carrying out multi-path distance judgment and SNR value judgment, and calculating according to a judgment result selection algorithm, wherein the specific judgment steps are as follows:
s2.1, finding the maximum value and the next maximum value in the integer part in the delay data, if the maximum value minus the next maximum value is larger than a first threshold value, judging as a far multipath scene, otherwise judging as a near multipath scene, if the near multipath scene is the far multipath scene, entering a step S3, otherwise entering a step S4;
s2.2, calculating the signal energy in the integer part of the delay data, the formula is as follows,
wherein the method comprises the steps ofRepresents the maximum value of the integer part in the delay data, < >>A next largest value representing an integer part of the delay data,/->Is signal energy;
s2.3: the noise energy of the integer part of the delay data is calculated, as follows,
wherein the method comprises the steps ofIs noise energy;
s2.4, finally calculating the SNR value, the formula is as follows,
and comparing the obtained SNR value with a second threshold value, and if the SNR value is smaller than the second threshold value, proceeding to step S3, otherwise proceeding to step S4.
The specific flow of the MUSIC algorithm of a big step and a small step adopted in the step S3 is as follows:
s3.1, carrying out channel estimation, wherein the formula is as follows,
and S3.2, averaging a plurality of symbols in the preamble, wherein the formula is as follows,
where s represents the symbol number, SYM represents the number of symbols,represents a preamble average;
s3.3, extracting, grouping and averaging the data of the plurality of chips, making the extraction strength be L, and grouping the chips according to the extraction strength, wherein the chips of the first group are the same as the data of the second groupThe method comprises the following steps:
and S3.4, averaging the correlation results among the multiple groups, wherein the formula is as follows,
wherein j is more than or equal to 1 and less than or equal to 2 SF/L,a value representing the j-th element after the extraction average; s3.5: the autocorrelation matrix is calculated, the formula is as follows,
wherein H represents a conjugate transpose, and Rhh represents an autocorrelation matrix;
the autocorrelation matrix is then subjected to matrix eigenvalue decomposition,
wherein the characteristic values are arranged in the order from big to small, and the arrangement order of the characteristic vectors and the characteristic values is consistent;
s3.6, calculating a guiding vector, wherein the calculation formula is as follows,
wherein n represents the nth chip (0<n<2 SF and n is an integer), m represents a steering vector corresponding to the mth delay point, fc represents a carrier frequency, j represents an imaginary unit,is a guide vector;
s3.7, performing signal processing to search decimal delay, and adopting a large-step and small-step combined method to enable the step length of the large step to be stp_rough and the step length of the small step to be stp_acc;
assuming that the number of multipaths in the space is Mut, then arranging the characteristic values in order from big to small, and the ordered characteristic is that
When (when),
The process proceeds to the next step of the process,
th3 represents the third threshold value and,
s3.8, obtaining MUSIC pseudo spectrum according to the calculation of the large step length, the formula is as follows,
is the energy value of the MUSIC pseudo spectrum, wherein +.>The range of the values is as follows
，/>The interval between the two points is the step length of a large step, offset1 represents a delay search window value 1, and offset2 represents a delay search window value 2;
then find the energy value of the MUSIC pseudo spectrum, the subscript corresponding to the maximum value of the energy value is the decimal delay,
a delay less than the minimum sampling interval;
s3.9, calculating MUSIC pseudo spectrum of small step length, the calculation formula is as follows,
wherein the method comprises the steps ofThe value range is +.> And->The interval between the middle 2 points is the step length of the small steps;
in the prior art, the window sizes of offset1 and offset2 near the integer delay need to be at least 1, because the value of the fractional delay cannot be determined, so that only all points around the integer delay can be searched in a traversing way; if the search step stp=0.005, we need to search 2/0.005=400 points and find the maximum to get an accurate fractional delay value;
in the present invention, as shown in fig. 2, a large-step-small-step combination method is employed. The step length of the big step is stp_rough, and the step length of the small step is stp_acc; also searching for 2 chips, using stp_rough=0.1, stp_acc=0.005. Then only 2/0.1+0.2/0.005=60 times of searching is needed to complete the searching, and the calculated amount is 15% of the calculated amount in the traditional mode.
S3.10 findThe subscript corresponding to the maximum value in the range is the accurate search delay, the calculation formula is as follows,
representing the subscript corresponding to the maximum value in the MUSIC pseudo spectrum;
the final accurate TOA delay is expressed as:
the ranging result is expressed as,
where BW represents the bandwidth of the signal,representing the distance measurement.
The specific flow of the noise reduction Matrix pecil algorithm adopted in the step S4 is as follows:
s4.1 the channel estimation is performed,
s4.2, the preamble of a plurality of symbols is noise reduced,
wherein s represents a symbol number, and the SNR can be remarkably improved by multi-symbol averaging;
s4.3, extracting, grouping and averaging the data of the plurality of chips,
let the extraction strength be L, then group the chips according to the extraction strength, wherein the firstGroup of chipsIn order to achieve this, the first and second,
the correlation results among the multiple groups are averaged, the calculation formula is as follows,
wherein the method comprises the steps of；
S4.4, extracting subarrays, wherein the calculation formula is as follows,
wherein LL is selected asA number between them, let c traverse 1 to LL+1, the calculated Z matrix dimension is LL row,>a column;
s4.5, singular value decomposition is carried out on the Z matrix, the calculation formula is as follows,
wherein V represents a right singular vector of the Z matrix, sigullar represents singular values of the Z matrix, the singular values are arranged in a mode from large to small, and the arrangement sequence of the right singular vector is consistent with the singular values;
s4.6, extracting the signal subspace from V, assuming the multipath number of the space is Mut2, then acquiring the multipath number,
the singular values are arranged in the order from big to small, and the ordered characteristic is that,
；
When the number of the pins is small,
，
the process proceeds to the next step of the process,
th4 represents a fourth threshold, and the corresponding Mut2 is the dimension of the signal subspace;
after Mut2 is determined, the signal subspace is,
s4.7, constructing two phase rotation vectors, wherein the calculation formula is as follows,
calculation ofAnd->The phase rotation between them, the calculation formula is as follows,
，
wherein the method comprises the steps ofRepresenting matrix->Moore-pentase generalized inverse of (C);
s4.8, decomposing the characteristic value of the MM matrix, wherein the calculation formula is as follows,
wherein the method comprises the steps ofThe characteristic values are arranged in the order from big to small;
s4.9, modeling the characteristic value, calculating the following formula,
the maximum value after the modulus is calculatedAnd the value before the corresponding modulo is recorded as；
S4.10, calculating a delay result according to the maximum characteristic value, wherein a calculation formula is as follows,
where exp represents the natural logarithm, L represents the extraction strength,representing taking the imaginary part of the complex number, +.>Representing the circumference rate, ++>Representing logarithm>The result is the estimation result of decimal delay;
the final estimated distance is:
wherein BW represents the bandwidth of the signal and c represents the speed of light as，/>For the final estimated distance.
S5, the step of: and (3) sorting the calculated data obtained in the steps S3 and S4, and outputting the sorted calculated data to a display terminal.
Example 2: as shown in fig. 3, first, obtaining integer delay part data, judging whether the integer delay part data is a long-distance multipath, if the integer delay part data is a long-distance multipath, performing channel estimation calculation on the integer delay part data, performing noise reduction operation on a plurality of symbols in a preamble, then extracting and averaging data of a plurality of chips in a frequency domain, calculating an autocorrelation matrix, completing eigenvalue decomposition of the autocorrelation matrix, calculating a guide vector, performing signal processing by adopting a large-step and small-step combination method to search for decimal delay, then calculating a pseudo spectrum of MUSIC, and finally finding estimated delay and distance;
if the integer delay part is not the long-distance multipath, judging whether the current scene is a low SNR scene, if so, completing the operation consistent with the operation, and if not, performing the following steps: and carrying out channel estimation calculation on the integer delay data, carrying out noise reduction operation on a plurality of symbols in the preamble, extracting and averaging data of a plurality of chips in a frequency domain, extracting subarrays, carrying out singular value decomposition, calculating the product of the pseudo inverse of the phase rotation vector V1 and the phase rotation vector V2, carrying out eigenvalue decomposition, and calculating the delay and the distance according to the eigenvalue.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that the above-mentioned preferred embodiment should not be construed as limiting the invention, and the scope of the invention should be defined by the appended claims. It will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the spirit and scope of the invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.
Claims (8)
1. A simplified time delay fusion ranging method is characterized by comprising the following steps of;
s1, transmitting a Chirp signal, and performing delay estimation by using the transmitted signal to obtain integer delay data;
s2, calculating and judging according to the maximum value and the next maximum value of the integer part in the delay data, if the delay data is judged to be a far multipath scene, entering a step S3, and if the delay data is judged to be a near multipath scene, entering an SNR value judging process; calculating an SNR value, and when the SNR value is smaller than a second threshold value, entering a step S3, otherwise, entering a step S4;
s3, firstly, carrying out channel estimation, then carrying out average calculation on a preamble part of a transmitting signal, then carrying out extraction, grouping and averaging on data of a code chip, then calculating an autocorrelation matrix and matrix eigenvalue decomposition, then calculating a guide vector, and finally carrying out ranging calculation to obtain distance data;
s4, firstly, carrying out channel estimation, then carrying out noise reduction treatment on part of transmitted signals, then carrying out extraction, grouping and averaging on data of a plurality of chips, then carrying out singular value decomposition on a Z matrix, and finally calculating a delay result and obtaining distance data;
s5, sorting and outputting the distance data obtained in the steps S3 and S4.
2. The simplified time-delay fusion ranging method according to claim 1, wherein the step S1 of performing time-delay estimation by using a correlation method comprises the following specific steps:
s1.1: an integer part in the delay data is obtained, the preamble signals in the transmission signal and the reception signal are operated, the formula is as follows,
where fft represents the fast fourier transform,represents the conjugate of rx, ||represents the absolute value, |>Representing the preamble signal in the transmitted signal, is->Represents a preamble signal in the received signal, a>Representing an integer portion of the delay data;
s1.2: then finding the subscript corresponding to the maximum value of the integer part in the delay dataNamely integer delay data, wherein +.>I represents the i-th chip, the formula is as follows,
arg represents an independent variable; SF spreading factor;
this step is completed.
3. The simplified time-lapse fusion ranging method according to claim 1, wherein the steps of S2 are performed for multi-path distance judgment and SNR value judgment, and calculation is performed according to a judgment result selection algorithm, and the specific judgment steps are as follows:
s2.1, finding the maximum value and the next maximum value in the integer part in the delay data, if the maximum value minus the next maximum value is larger than a first threshold value, judging as a far multipath scene, otherwise judging as a near multipath scene, if the near multipath scene is the far multipath scene, entering a step S3, otherwise entering a step S4;
s2.2, calculating the signal energy in the integer part of the delay data, the formula is as follows,
wherein the method comprises the steps ofRepresents the maximum value of the integer part in the delay data, < >>A next largest value representing an integer part of the delay data,/->Is signal energy;
s2.3: the noise energy of the integer part of the delay data is calculated, as follows,
wherein the method comprises the steps ofAs noise energy, SF is spreading factor;
s2.4, finally calculating the SNR value, the formula is as follows,
and comparing the obtained SNR value with a second threshold value, and if the SNR value is smaller than the second threshold value, proceeding to step S3, otherwise proceeding to step S4.
4. The simplified time-lapse fusion ranging method according to claim 1, wherein step S3 uses a MUSIC algorithm of big step and small step.
5. The simplified time-lapse fusion ranging method according to claim 4, wherein the step S3 adopts a MUSIC algorithm with large steps and small steps, and the specific flow is as follows:
s3.1, carrying out channel estimation, wherein the formula is as follows,
and S3.2, averaging a plurality of symbols in the preamble, wherein the formula is as follows,
where s represents the symbol number, SYM represents the number of symbols,represents a preamble average;
s3.3, extracting, grouping and averaging the data of the plurality of chips, making the extraction strength be L, and grouping the chips according to the extraction strength, wherein the chips of the first group are the same as the data of the second groupThe method comprises the following steps:
and S3.4, calculating the average value of the correlation results among a plurality of groups, wherein the formula is as follows,
wherein j is more than or equal to 1 and less than or equal to 2 SF/L,representing the value of the j-th element after the extraction average, is->Represents +.o after preamble averaging>The value of the individual chips;
s3.5: the autocorrelation matrix is calculated, the formula is as follows,
wherein H represents the conjugate transpose, rhh represents the autocorrelation matrix,represents a decimated average;
the autocorrelation matrix is then subjected to matrix eigenvalue decomposition,
wherein the characteristic values are arranged in the order from big to small, and the arrangement order of the characteristic vectors and the characteristic values is consistent;
s3.6, calculating a guiding vector, wherein the calculation formula is as follows,
wherein n represents the nth chip (0<n<2 SF and n is an integer), m represents a steering vector corresponding to the mth delay point, fc represents a carrier frequency, j represents an imaginary unit,is a guide vector;
s3.7, performing signal processing to search decimal delay, and adopting a large-step and small-step combined method to enable the step length of the large step to be stp_rough and the step length of the small step to be stp_acc;
assuming that the number of multipaths in the space is Mut, then arranging the eigenvalues in order from large to small, the eigenvalues after the sorting are,
，
when the number of the pins is small,
，
the process proceeds to the next step of the process,
th3 represents a third threshold;
s3.8, obtaining MUSIC pseudo spectrum according to the calculation of the large step length, the formula is as follows,
is the energy value of the MUSIC pseudo spectrum, wherein +.>The range of the values is as follows
And->The interval between the two points is the step length of a large step, offset1 represents a delay search window value 1, and offset2 represents a delay search window value 2;
after the energy value of the MUSIC pseudo spectrum is obtained, the subscript corresponding to the maximum value of the energy value is the delay less than the minimum sampling interval,
，
a delay less than the minimum sampling interval;
s3.9, calculating MUSIC pseudo spectrum of small step length, the calculation formula is as follows,
wherein the method comprises the steps ofThe value range is as follows:
and->The interval between the middle 2 points is the step length of the small steps;
s3.10 findThe subscript corresponding to the maximum value in the range is the accurate search delay, the calculation formula is as follows,
representing the subscript corresponding to the maximum value in the MUSIC pseudo spectrum;
the final accurate TOA delay is expressed as:
the ranging result is expressed as,
wherein BW represents the bandwidth of the signal, and c represents the speed of light as the value，/>Representing the distance measurement.
6. The simplified time-lapse fusion ranging method according to claim 1, wherein the step S4 employs a noise reduction Matrix pencil algorithm.
7. The simplified time-lapse fusion ranging method according to claim 1, wherein the specific procedure of the noise reduction Matrix pencil algorithm adopted in the step S4 is as follows:
s4.1 the channel estimation is performed,
s4.2, noise reduction is carried out on the lead codes of a plurality of symbols,
wherein s represents a symbol number;
s4.3, extracting, grouping and averaging the data of the plurality of chips,
let the extraction strength be L, then group the chips according to the extraction strength, wherein the firstGroup chip->In order to achieve this, the first and second,
the correlation results among the multiple groups are averaged, the calculation formula is as follows,
wherein the method comprises the steps of；
S4.4, extracting subarrays, wherein the calculation formula is as follows,
wherein LL is selected asA number between them, let c traverse 1 to LL+1, the calculated Z matrix dimension is LL row,>a column;
s4.5, singular value decomposition is carried out on the Z matrix, the calculation formula is as follows,
wherein V represents a right singular vector of the Z matrix, sigullar represents singular values of the Z matrix, the singular values are arranged in a mode from large to small, and the arrangement sequence of the right singular vector is consistent with the singular values;
s4.6, extracting the signal subspace from V, assuming the multipath number of the space is Mut2, then acquiring the multipath number,
the singular values are arranged in order from big to small, and the ordered features are,
，
when the number of the pins is small,
，
the process proceeds to the next step of the process,
th4 represents a fourth threshold, corresponding to Mut2, which is the dimension of the signal subspace;
when Mut2 determines, the signal subspace is,
s4.7, constructing two phase rotation vectors, wherein the calculation formula is as follows,
calculation ofAnd->The phase rotation between them, the calculation formula is as follows,
wherein the method comprises the steps ofRepresenting matrix->Moore-pentase generalized inverse of (C);
s4.8, decomposing the characteristic value of the MM matrix, wherein the calculation formula is as follows,
wherein the method comprises the steps ofThe characteristic values are arranged in the order from big to small;
s4.9, modeling the characteristic value, calculating the following formula,
the maximum value after the modulus is calculatedAnd the value before the corresponding modulo is recorded as；
S4.10, calculating a delay result according to the maximum characteristic value, wherein a calculation formula is as follows,
where exp represents the natural logarithm, L represents the extraction strength,representing taking the imaginary part of the complex number, +.>Representing the circumference rate, ++>Representing logarithm>The result is the estimation result of decimal delay;
the final estimated distance is:
wherein BW represents the bandwidth of the signal and c represents the speed of light as，/>For the final estimated distance.
8. The simplified time-lapse fusion ranging method according to claim 1, wherein the step S5 is: and (3) sorting the calculated data obtained in the steps S3 and S4, and outputting the sorted calculated data to a display terminal.
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