CN108427095B - Covariance matrix-based data loss fast-beat number and array element detection method - Google Patents

Covariance matrix-based data loss fast-beat number and array element detection method Download PDF

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CN108427095B
CN108427095B CN201810073143.3A CN201810073143A CN108427095B CN 108427095 B CN108427095 B CN 108427095B CN 201810073143 A CN201810073143 A CN 201810073143A CN 108427095 B CN108427095 B CN 108427095B
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毛兴鹏
王亚梁
赵春雷
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Harbin Institute of Technology
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Abstract

The invention provides a covariance matrix-based data loss fast-beat number and array element detection method, which comprises the steps of calculating a covariance matrix of each base station, estimating a noise coefficient of each base station, constructing a curve equation, estimating the data loss fast-beat number and the data loss array element number of each base station, estimating the data loss fast-beat number and the data loss array element number of each array element, and comparing two estimation results to determine a final estimation result. The invention overcomes the defects of the prior art and better detects the data loss time and the data loss array element.

Description

Covariance matrix-based data loss fast-beat number and array element detection method
Technical Field
The invention belongs to the technical fields of array signal processing technology, information fusion technology, far-field signal processing technology and target detection and identification, and particularly relates to a data loss fast-beat number and array element detection method based on a covariance matrix.
Background
The multi-station passive positioning technology is an important branch of the array signal processing field, but in the array receiving process, a situation that one or more array elements in the array fail before the measurement is completed can be encountered, and a data loss phenomenon can occur. If the time of data loss and the array element with data loss cannot be detected well, the subsequent positioning performance will be greatly affected.
The document "Direction of Arrival Estimation Under Array sources Using a minimum Resource Allocation Neural Network" trains a large amount of measured data without data loss by Using a Neural Network, extracts related characteristic parameters, and effectively estimates the data loss time and data loss Array elements by matching the characteristic parameters for the measured data with data loss; the document Rank constrained ML estimation of structured covariance matrices with applications in radar target detection proposes a target detection algorithm based on covariance matrices, which needs to estimate covariance matrices of interference and noise and target angles in advance, and even if the algorithm is generalized to a data loss situation, it needs to predict covariance matrices without data loss situations and reference target angle information to form whitening matrices.
Disclosure of Invention
The invention provides a covariance matrix-based data loss fast beat number and array element detection method based on the detection problems of the number of failure array elements, the failure time of the array elements and the failure positions of the array elements on the basis of a multi-station passive positioning model, and the method can better detect the data loss time and the data loss array elements.
The purpose of the invention is realized by the following technical scheme: a data loss fast beat number and array element detection method based on covariance matrix comprises the following steps:
step 1, measuring data x obtained by each base stationl(t)＝Als(t)+nl(t) wherein xl(t) measurement data at time t of the ith base station, Al＝[al(r1),…,al(rq)]For the M × q dimension positioning matrix of the ith base station, M represents the array element number of each base station, q represents the information source number, al(r1) Is the M x 1-dimensional location vector, r, from the 1 st signal to the l base station1Is a 2 × 1 dimensional vector of the 1 st signal, s (t) ═ s1(t),…,sq(t)]TA q × 1 dimensional signal vector at time t, nl(t)＝[nl,1(t),…,nl,M(t)]TRepresenting an additive noise vector at the t moment of the ith base station, and estimating a covariance matrix of each base station:
Figure BDA0001558697060000021
where T represents the fast beat number, the symbol "T" represents the transposed symbol of the matrix, and "H" represents the conjugate transposed symbol of the matrix;
step 2, utilizing covariance matrixes of all base stations
Figure BDA0001558697060000022
And traversing any q +1 array element combinations by the known source number q in a permutation and combination mode, calculating the trace of a covariance matrix corresponding to each array element combination, and selecting the covariance matrix corresponding to the combination with the maximum trace to estimate the noise coefficient:
Figure BDA0001558697060000023
in the formula
Figure BDA0001558697060000024
The covariance matrix corresponding to the combination with the maximum trace is represented, eig {. is used for representing the eigenvalue function of the matrix, and min {. is used for representing the minimum value in the vector;
step 3, constructing a curve fitting equation according to the change of the data loss covariance matrix trace:
Figure BDA0001558697060000025
in the formula
Figure BDA0001558697060000026
Covariance matrix, R, representing the first n snapshot estimateslWhich represents an ideal covariance matrix,
Figure BDA0001558697060000027
a covariance matrix representing the snapshot estimate,
Figure BDA0001558697060000028
representation removalA covariance matrix of the noise term, trace {. cndot } represents the trace of the matrix;
step 4, estimating the data loss fast beat number and the data loss array element number of each base station by utilizing the curve fitting equation
Figure BDA0001558697060000029
If it occurs
Figure BDA00015586970600000210
In this case, the number of missing array elements can be directly estimated:
Figure BDA00015586970600000211
wherein, the symbol
Figure BDA00015586970600000212
Representing adjacent rounded symbols; if it is
Figure BDA00015586970600000213
Then order
Figure BDA00015586970600000214
If it is
Figure BDA00015586970600000215
Then order
Figure BDA00015586970600000216
Namely, no data is lost;
step 5, for the base station with data loss, traversing each array element, and estimating the data loss fast beat number of each array element:
Figure BDA0001558697060000031
calculating the number of array elements with data loss at the first base station by estimating one by one
Figure BDA0001558697060000032
And snapshot number with data loss:
Figure BDA0001558697060000033
wherein m represents the m-th array element;
step 6, according to the estimation results of the step 4 and the step 5
Figure BDA0001558697060000034
And
Figure BDA0001558697060000035
and determining a final estimation result.
Further, the step 6 specifically includes: if the result of each array element estimation is matched with the result of the multi-array element estimation, the estimation is correct, and the estimation result is the result of each array element estimation; if the result of each array element estimation is not matched with the result of the multi-array element estimation, the estimation is wrong, all data of the whole base station are not enough to realize the positioning function, and the measurement data on the base station are rejected:
Figure BDA0001558697060000036
wherein the threshold T _ threshold2＝κ2T，κ2Is an infinitely small positive number;
the estimate for the position of the array element is expressed as:
Figure BDA0001558697060000037
Figure BDA0001558697060000038
drawings
FIG. 1 is a flow chart of a method for detecting lost data fast beat and array elements based on covariance matrix according to the present invention;
FIG. 2 is a diagram of a multi-station positioning model;
FIG. 3 is a diagram of a simulation scene model;
FIG. 4 is a graph of the results of curve fitting;
fig. 5 is a diagram of the variation of the detection probability of the missing array element number with the signal-to-noise ratio.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
With reference to fig. 1 and fig. 2, the present invention provides a method for detecting data loss fast beat number and array element based on covariance matrix, which comprises the following steps:
step 1, measuring data x obtained by each base stationl(t)＝Als(t)+nl(t) wherein xl(t) measurement data at time t of the ith base station, Al＝[al(r1),…,al(rq)]For the M × q dimension positioning matrix of the ith base station, M represents the array element number of each base station, q represents the information source number, al(r1) Is the M x 1-dimensional location vector, r, from the 1 st signal to the l base station1Is a 2 × 1 dimensional vector of the 1 st signal, s (t) ═ s1(t),…,sq(t)]TA q × 1 dimensional signal vector at time t, nl(t)＝[nl,1(t),…,nl,M(t)]TRepresenting an additive noise vector at the t moment of the ith base station, and estimating a covariance matrix of each base station:
Figure BDA0001558697060000041
where T represents the fast beat number, the symbol "T" represents the transposed symbol of the matrix, and "H" represents the conjugate transposed symbol of the matrix;
the step 1 specifically comprises the following steps:
1) consider a sounding network consisting of L base stations, each consisting of M array elements. Suppose that there are q known center frequencies of ω0The received waveform of each base station array element can be regarded as a plane wave, as shown in fig. 2, then the receiving model of the m-th array element at the l-th base station can be expressed as:
Figure BDA0001558697060000042
wherein s isk(. denotes the kth source, τl,mkRepresenting the propagation delay, a, from the kth source to the mth element of the ith base stationl,kExpressing the attenuation coefficient from the kth signal to the l base station, considering the attenuation coefficient of each array element in the base station corresponding to the same information source as the same, and considering nl,m(t) additive noise representing the mth array element of the mth base station;
2) the narrowband hypothesis will have the following approximate representation for the kth signal and each array element:
Figure BDA0001558697060000051
with this relationship, the receive model can be expressed as:
Figure BDA0001558697060000052
3) forming M array element receiving models of the ith base station into an M multiplied by 1-dimensional receiving vector to obtain the receiving vector
Figure BDA0001558697060000053
Wherein a isl(rk) Is the M x 1-dimensional positioning vector of the kth signal to the l base station, which can be expressed as
Figure BDA0001558697060000054
Wherein r iskIs a 2 × 1-dimensional vector of the kth signal, containing two-dimensional spatial information of the x-axis and the y-axis, namely:
rk＝[xk,yk]T
4) the receiving model is re-represented in the form of a matrix as:
xl(t)＝Als(t)+nl(t)
wherein A isl＝[al(r1),…,al(rq)]Is an M × q dimensional matrix, s (t) ═ s1(t),…,sq(t)]TIs a q × 1 dimensional signal vector.
5) The whole array is at t1,…,tTSampling at a moment, that is, each array element obtains sampling data of T snapshots, and the covariance matrix of the ith base station can be expressed as:
Figure BDA0001558697060000055
wherein T represents the number of fast beats.
Step 2, utilizing covariance matrixes of all base stations
Figure BDA0001558697060000056
And traversing any q +1 array element combinations by the known source number q in a permutation and combination mode, calculating the trace of a covariance matrix corresponding to each array element combination, and selecting the covariance matrix corresponding to the combination with the maximum trace to estimate the noise coefficient:
Figure BDA0001558697060000057
in the formula
Figure BDA0001558697060000058
The covariance matrix corresponding to the combination with the maximum trace is represented, eig {. is used for representing the eigenvalue function of the matrix, and min {. is used for representing the minimum value in the vector;
the step 2 specifically comprises the following steps:
1) for the
Figure BDA0001558697060000059
At the moment, the received data of all array elements are not lost, namely the received data of the ith base station at the moment
Figure BDA00015586970600000510
Can be expressed as:
Figure BDA0001558697060000061
wherein,
Figure BDA0001558697060000062
to represent
Figure BDA0001558697060000063
The signal vector of the time of day,
Figure BDA0001558697060000064
to represent
Figure BDA0001558697060000065
The noise vector of (2).
All of
Figure BDA0001558697060000066
The matrix expression form of the snapshot sampling data is as follows:
Figure BDA0001558697060000067
wherein,
Figure BDA0001558697060000068
respectively represent
Figure BDA0001558697060000069
A measurement matrix of time instants, a signal matrix and a noise matrix.
For the
Figure BDA00015586970600000610
Time of day, covariance matrix of the ith base station
Figure BDA00015586970600000611
Can be expressed as:
Figure BDA00015586970600000612
wherein
Figure BDA00015586970600000613
To represent
Figure BDA00015586970600000614
The signal covariance matrix of the time of day,
Figure BDA00015586970600000615
to represent
Figure BDA00015586970600000616
The noise figure at the time of day.
2) For the
Figure BDA00015586970600000617
At the moment, one or more array elements have data loss, only noise items exist in the received data, and the data received by the ith base station
Figure BDA00015586970600000618
Can be expressed as:
Figure BDA00015586970600000619
wherein A isl,mA positioning vector representing the mth array element of the mth base station,
Figure BDA00015586970600000620
to represent
Figure BDA00015586970600000621
The signal vector of the time of day,
Figure BDA00015586970600000622
to represent
Figure BDA00015586970600000623
Receiving noise of mth array element of the ith base station at moment, wherein M is less than M and omegalThe array element set which indicates that the ith base station has no data loss,
Figure BDA00015586970600000624
and indicating the array element set with data loss of the ith base station.
For the l base station and
Figure BDA00015586970600000625
time of day, introducing a diagonal matrix Q of M × M dimensionslI.e. by
Figure BDA00015586970600000626
Figure BDA00015586970600000627
Can be expressed as
Figure BDA00015586970600000628
The received data of the ith base station can be re-expressed as:
Figure BDA00015586970600000629
3) all of
Figure BDA00015586970600000630
Snapshot sampling data
Figure BDA00015586970600000631
Is expressed in the form of:
Figure BDA00015586970600000632
wherein,
Figure BDA0001558697060000071
to represent
Figure BDA0001558697060000072
The measurement matrix of the time of day,
Figure BDA0001558697060000073
Figure BDA0001558697060000074
respectively represent
Figure BDA0001558697060000075
A signal matrix and a noise matrix at a time.
For the
Figure BDA0001558697060000076
Time of day, covariance matrix of the ith base station
Figure BDA0001558697060000077
Can be expressed as:
Figure BDA0001558697060000079
wherein
Figure BDA00015586970600000710
To represent
Figure BDA00015586970600000711
The signal covariance matrix of the time of day,
Figure BDA00015586970600000712
to represent
Figure BDA00015586970600000713
The noise figure at the time of day.
For the entire measurement time, the covariance matrix of the ith base station can be expressed as:
Figure BDA00015586970600000714
by using the traversal and stability characteristics of signal and noise, the method can obtain
Figure BDA00015586970600000715
The covariance matrix of the ith base station can therefore be further expressed as:
Figure BDA00015586970600000716
4) and for all array elements of the ith base station, assuming that the source number q is known, traversing any q +1 array element combinations, calculating the traces of the covariance matrixes of the array elements, and selecting the covariance matrix corresponding to the combination with the largest trace to estimate the noise coefficient. All the arrangement combinations were calculated and made into a look-up table after completion of all the combinations for later use:
Υ＝combntns{1:M,q+1}
wherein, the combnns {1: J, I } function represents that all combinations of I data are selected from the 1: J data, and the number of all combinations
Figure BDA00015586970600000722
I.e., γ is a matrix of dimension P × (q +1), with each row representing a permutation combination.
5) Calculating the covariance matrix and the trace of the covariance matrix under each combination mode:
Figure BDA00015586970600000717
Figure BDA00015586970600000718
wherein,
Figure BDA00015586970600000719
denotes the covariance matrix at the ith base station at the pth combination, P1, …, P,
Figure BDA00015586970600000720
is a covariance matrix
Figure BDA00015586970600000721
Corresponding to the trace, the covariance matrix in the process can extract data corresponding to the relevant combined array elements from the originally calculated covariance matrix, and the calculated amount is small.
6) For the combination with data loss, the trace of the covariance matrix is smaller than that of the combination without data loss, but the signal noise is not known accurately, and it is difficult to determine whether data loss occurs through threshold setting, so it is necessary to assume that there is at least one combination without data loss, and the covariance matrix corresponding to the combination with the largest trace is selected to estimate the noise coefficient:
Figure BDA0001558697060000081
Figure BDA0001558697060000082
7) because q +1 array elements have q +1 corresponding characteristic values, wherein the minimum value of the characteristic values corresponds to a noise coefficient, and the following can be obtained:
Figure BDA0001558697060000083
in the formula
Figure BDA0001558697060000084
The covariance matrix corresponding to the combination with the maximum trace is represented, eig {. is used for representing the eigenvalue function of the matrix, and min {. is used for representing the minimum value in the vector;
step 3, constructing a curve fitting equation according to the change of the data loss covariance matrix trace:
Figure BDA0001558697060000085
in the formula
Figure BDA0001558697060000086
Covariance matrix, R, representing the first n snapshot estimateslWhich represents an ideal covariance matrix,
Figure BDA0001558697060000087
Figure BDA00015586970600000814
a covariance matrix representing the snapshot estimate,
Figure BDA0001558697060000088
a covariance matrix representing the removed noise term, trace {. cndot.) represents the trace of the matrix;
the step 3 specifically comprises the following steps:
1) it is assumed that the sources are uncorrelated, i.e.
Figure BDA0001558697060000089
Wherein s isiAnd sjRespectively representing the ith and jth rows of the signal matrix s,
Figure BDA00015586970600000810
the signal covariance matrix S can therefore be expressed as:
Figure BDA00015586970600000811
2) for the
Figure BDA00015586970600000812
The mth element on the time and the major diagonal of the covariance matrix of the ith base station can be expressed as:
Figure BDA00015586970600000813
i.e. the elements on the diagonal are equal, and ηl≥0。
For the
Figure BDA0001558697060000091
At time, the trace of the covariance matrix may be expressed as:
Figure BDA0001558697060000092
3) for the
Figure BDA0001558697060000093
At time, the trace of the covariance matrix may be expressed as:
Figure BDA0001558697060000094
wherein,
Figure BDA0001558697060000095
represents omegalThe number of the elements in the Chinese character,
Figure BDA0001558697060000096
to represent
Figure BDA00015586970600000916
The number of the elements in (B).
4) For the entire measurement period, the trace of the covariance matrix can be expressed as
Figure BDA0001558697060000097
5) The trace of the covariance matrix contains information of data missing time to be estimated and information of data missing array element number, but noise power item and signal power item exist in the covariance matrix, and it is difficult to directly extract the two-parameter information through difference. Next, the following functional relation is constructed to extract
Figure BDA0001558697060000098
And
Figure BDA0001558697060000099
the information of (2):
Figure BDA00015586970600000910
wherein R islRepresenting an ideal covariance matrix, but limited by the number of snapshots, RlCovariance matrix that can be estimated with all snapshots
Figure BDA00015586970600000911
Approximately represents, and needs to satisfy the condition that the fast beat number is large, at least 1000 fast beats are needed after simulation verification,
Figure BDA00015586970600000912
the covariance matrix representing the estimate using the first n snapshots can be expressed as
Figure BDA00015586970600000913
Figure BDA00015586970600000914
Wherein,
Figure BDA00015586970600000915
representing covariance matrices with noise terms removed, i.e.
Figure BDA0001558697060000101
Step 4, estimating the data loss fast beat number and the data loss array element number of each base station by utilizing the curve fitting equation
Figure BDA0001558697060000102
If it occurs
Figure BDA0001558697060000103
In this case, the number of missing array elements can be directly estimated:
Figure BDA0001558697060000104
wherein, the symbol
Figure BDA0001558697060000105
Representing adjacent rounded symbols; if it is
Figure BDA0001558697060000106
Then order
Figure BDA0001558697060000107
If it is
Figure BDA0001558697060000108
Then order
Figure BDA0001558697060000109
Namely, no data is lost;
the step 4 specifically comprises the following steps:
1) when the number of snapshots is large enough, a theoretical curve can be deduced as
Figure BDA00015586970600001010
As can be seen from the assumption that,
Figure BDA00015586970600001011
and is
Figure BDA00015586970600001012
Therefore, the denominators cannot be all 0, and the curve shows that the data loss occurs only once in the whole measurement period, and can also be generalized to the situation that multiple times of data loss occur, which is not described in detail herein.
2) The front section is a straight line and the rear section is a part of a hyperbola, and only two unknowns T exist for the curve2 lAnd
Figure BDA00015586970600001013
both parameters can be estimated by curve fitting. In the curve fitting process, a curve matching method can be used, i.e. the method utilizes all the possibilities
Figure BDA00015586970600001014
Value and
Figure BDA00015586970600001015
and a dictionary psi is established by the values, and the dictionary can be made into a lookup table after being established, so that the computational complexity is reduced. The dimension of the dictionary is T multiplied by TM dimension, and the actual curve is utilized
Figure BDA00015586970600001016
And performing relevant processing on each column in the dictionary, but the calculation complexity of the relevant processing is higher, so the method disclosed by the invention utilizes a method for setting the threshold value to count the number of fitting points to fit a curve, namely the following requirements are met:
Figure BDA00015586970600001017
wherein count {. denotes a counter, threshold { } represents a counterlRepresenting the curve fitting threshold for the ith base station.
3) At this time, it is unable to distinguishIn two extreme cases, namely, no data loss occurs and data loss occurs from the beginning, the second judgment needs to be performed through the trace of the covariance matrix, and the judgment is that
Figure BDA00015586970600001018
Or also
Figure BDA00015586970600001019
When in use
Figure BDA00015586970600001020
The trace of the covariance matrix can be expressed as:
Figure BDA00015586970600001021
when in use
Figure BDA00015586970600001022
The trace of the covariance matrix can be expressed as:
Figure BDA0001558697060000111
the above equation can be approximated by the trace of the covariance matrix obtained by estimating q +1 array elements:
Figure BDA0001558697060000112
thus can obtain the pair
Figure BDA0001558697060000113
The estimation of (d) is:
Figure BDA0001558697060000114
wherein,
Figure BDA0001558697060000115
presentation pair
Figure BDA0001558697060000116
An estimate of (d).
Step 5, for the base station with data loss, traversing each array element, and estimating the data loss fast beat number of each array element:
Figure BDA0001558697060000117
calculating the number of array elements with data loss at the first base station by estimating one by one
Figure BDA0001558697060000118
And snapshot number with data loss:
Figure BDA0001558697060000119
wherein m represents the m-th array element;
the step 5 specifically comprises the following steps:
1) realize to
Figure BDA00015586970600001110
And
Figure BDA00015586970600001111
the estimation is then converted into the estimation of the array element position, namely the number of the array elements with data missing is known, but the specific position of the array elements with data missing is not known. Therefore, the judgment of whether each base station has data loss or not and the snapshot number of data loss in the base station with data loss are realized
Figure BDA00015586970600001112
And array element number of data loss
Figure BDA00015586970600001113
Then, the method is followed by the step of aligning each array elementAnd judging whether data are lost or not.
2) For the received data of the mth array element of the ith base station, the covariance matrix can be expressed as
Rl,m＝Rl(m,m)
If no data loss occurs, the trace of the covariance matrix can be represented as
Figure BDA00015586970600001114
If data loss occurs from the beginning, the trace of the covariance matrix can be represented as
Figure BDA0001558697060000121
If from
Figure BDA0001558697060000122
Data loss occurs only after snapshot, and then the trace of the covariance matrix can be expressed as
Figure BDA0001558697060000123
3) Thus, the estimate of the time at which a data loss occurs on each array element can be expressed as
Figure BDA0001558697060000124
For the
Figure BDA0001558697060000125
The estimation of (2) also sets a threshold T _ threshold1＝κ1T，κ1Is an infinitely small positive number, and the following relationship holds:
Figure BDA0001558697060000126
step 6, according to the estimation results of the step 4 and the step 5
Figure BDA0001558697060000127
And
Figure BDA0001558697060000128
and determining a final estimation result.
The step 6 specifically comprises the following steps: if the result of each array element estimation is matched with the result of the multi-array element estimation, the estimation is correct, and the estimation result is the result of each array element estimation; if the result of each array element estimation is not matched with the result of the multi-array element estimation, the estimation is wrong, all data of the whole base station are not enough to realize the positioning function, and the measurement data on the base station are rejected:
Figure BDA0001558697060000129
wherein the threshold T _ threshold2＝κ2T，κ2Is an infinitely small positive number;
the estimate for the position of the array element is expressed as:
Figure BDA00015586970600001210
Figure BDA00015586970600001211
simulation condition 1: as shown in fig. 3, the positions of the four base stations are [ -500m,0m ], [0m, -500m ], [500m,0m ], [0m,500m ], the orientations of the base stations are [90 °,0 °, [90 °,180 ° ], the noise is gaussian white noise with a signal-to-noise ratio of 10dB, each base station has 4 array elements, the array elements are arranged in a uniform linear array, the interval between the array elements is λ/2, 2 time and space independent target sources, the positions are [ -100m,100m ], [200m, -100m ], the snapshot number is 10000, the 4 th array element of the 2 nd base station has data loss after the 5000 th snapshot, other array elements are normal, the threshold is 0.01, and the curve fitting result is shown in fig. 4.
And taking the results of 10 Monte Carlo experiments, and recording the estimation result of the noise coefficient and the array element number and the fast beat number of data loss estimated by curve fitting.
TABLE 1 Curve fitting estimation results
Figure BDA0001558697060000131
As can be seen from fig. 4, the 2 nd base station has data loss, so it will be composed of a segmented curve, the turning point of the curve represents the fast beat number of the data loss, and the curve fitted to the 1, 3, and 4 base stations is around 0. A group of estimates of array element number and snapshot number related to data loss can be obtained through first-time curve fitting, as shown in Table 1, 10 groups of experimental results are given, the estimation of the snapshot number is about 5000, but large deviation sometimes occurs, so that high-precision second-time estimation is needed, and the results are shown in Table 2.
And taking the results of 10 Monte Carlo experiments, and recording the estimation result of the first data loss fast beat number and the estimation result of the second data loss fast beat number.
TABLE 2 evaluation results of the number of snapshots of secondary data loss
Figure BDA0001558697060000132
Simulation condition 2: as shown in fig. 3, the positions of the four base stations are [ -500m,0m ], [0m, -500m ], [500m,0m ], [0m,500m ], the orientations of the base stations are [90 °,0 °, [90 °,180 ° ], the noise is gaussian white noise, each base station has 4 array elements, the array elements are arranged according to a uniform linear array, the interval between the array elements is λ/2, 2 time and space independent target sources, the positions are [ -100m,100m ], [200m, -100m ], the snapshot number is 10000, the 4 th array element of the 2 nd base station has data loss from the 1 st snapshot, the other array elements are normal, the signal-to-noise ratio is from-10 dB to 10dB, the monte carlo experiment is 100 times, and a curve of the detection probability of the data loss array element number varying with the signal-to-noise ratio is shown in fig. 5.
From fig. 5, it can be seen that the detection of the number of data missing array elements after-5 dB can reach 100% success probability, and is suitable for data missing detection above-5 dB.
Simulation condition 3: as shown in fig. 3, the positions of the four base stations are [ -500m,0m ], [0m, -500m ], [500m,0m ], [0m,500m ], the orientations of the base stations are [90 °,0 °, [90 °,180 ° ], the noise is gaussian white noise with a signal-to-noise ratio of 10dB, each base station has 4 array elements, the array elements are arranged according to a uniform linear array, the interval between the array elements is λ/2, 2 time and space independent target sources, the positions are [ -100m,100m ], [200m, -100m ], the number of snapshots is 10000, the 2 nd to 4 th array elements of the 2 nd base station have data loss from the 1 st snapshot, other array elements are normal, 10 monte carlo experiments are taken, the estimation result of the 2 nd base station secondary data loss is recorded, and the result is shown in table 3.
TABLE 3 Secondary data loss estimation results
Figure BDA0001558697060000141
As can be seen from table 3, at this time, the 2 nd base station has 4 array elements, and 3 of the array elements have data loss, so the estimated noise coefficient and the signal power are incorrect, and the array element number and the snapshot number of the data loss estimated twice are not matched, and at this time, it can be considered that the data loss occurs in the entire base station, and all the data loss needs to be eliminated.
The method for detecting the data loss fast beat number and the array element based on the covariance matrix is described in detail, a specific example is applied in the text to explain the principle and the implementation mode of the invention, and the description of the embodiment is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.

Claims (2)

1. A data loss fast beat number and array element detection method based on covariance matrix is characterized in that: the method comprises the following steps:
step 1, measuring data x obtained by each base stationl(t)＝Als(t)+nl(t) wherein xl(t) measurement data at time t of the ith base station, Al＝[al(r1),…,al(rq)]For the M × q dimension positioning matrix of the ith base station, M represents the array element number of each base station, q represents the information source number, al(r1) Is the M x 1-dimensional location vector, r, from the 1 st signal to the l base station1Is a 2 × 1 dimensional vector of the 1 st signal, s (t) ═ s1(t),…,sq(t)]TA q × 1 dimensional signal vector at time t, nl(t)＝[nl,1(t),…,nl,M(t)]TRepresenting an additive noise vector at the t moment of the ith base station, and estimating a covariance matrix of each base station:
Figure FDA0002974990580000011
in the formula, the parameter T represents the number of fast beats and is marked with a symbol "T"transposed symbols, superscript symbols, representing a matrix"H"represents the conjugate transpose symbol of the matrix;
step 2, utilizing covariance matrixes of all base stations
Figure FDA0002974990580000012
And traversing any q +1 array element combinations by the known source number q in a permutation and combination mode, calculating the trace of a covariance matrix corresponding to each array element combination, and selecting the covariance matrix corresponding to the combination with the maximum trace to estimate the noise coefficient:
Figure FDA0002974990580000013
in the formula
Figure FDA0002974990580000014
The covariance matrix corresponding to the combination with the maximum trace is represented, eig {. is used for representing the eigenvalue function of the matrix, and min {. is used for representing the minimum value in the vector;
step 3, constructing a curve fitting equation according to the change of the data loss covariance matrix trace:
Figure FDA0002974990580000015
in the formula
Figure FDA0002974990580000016
Covariance matrix, R, representing the first n snapshot estimateslWhich represents an ideal covariance matrix,
Figure FDA0002974990580000017
Figure FDA00029749905800000112
a covariance matrix representing the snapshot estimate,
Figure FDA0002974990580000018
a covariance matrix representing the removed noise term, trace {. cndot.) represents the trace of the matrix;
step 4, estimating the data loss fast beat number and the data loss array element number of each base station by utilizing the curve fitting equation
Figure FDA0002974990580000019
If it occurs
Figure FDA00029749905800000110
In this case, the number of missing array elements can be directly estimated:
Figure FDA0002974990580000021
wherein, the symbol
Figure FDA0002974990580000022
Representing adjacent rounded symbols; if it is
Figure FDA0002974990580000023
Then order
Figure FDA0002974990580000024
If it is
Figure FDA0002974990580000025
Then order
Figure FDA0002974990580000026
Namely, no data is lost;
step 5, for the base station with data loss, traversing each array element, and estimating the data loss fast beat number of each array element:
Figure FDA0002974990580000027
calculating the number of array elements with data loss at the first base station by estimating one by one
Figure FDA0002974990580000028
And snapshot number with data loss:
Figure FDA0002974990580000029
wherein m represents the m-th array element;
step 6, according to the estimation results of the step 4 and the step 5
Figure FDA00029749905800000210
And
Figure FDA00029749905800000211
and determining a final estimation result.
2. The method of claim 1, wherein: the step 6 specifically comprises the following steps: if the result of each array element estimation is matched with the result of the multi-array element estimation, the estimation is correct, and the estimation result is the result of each array element estimation; if the result of each array element estimation is not matched with the result of the multi-array element estimation, the estimation is wrong, all data of the whole base station are not enough to realize the positioning function, and the measurement data on the base station are rejected:
Figure FDA00029749905800000212
wherein the threshold T _ threshold2＝κ2T，κ2Is an infinitely small positive number;
the estimate for the position of the array element is expressed as:
Figure FDA00029749905800000213
Figure FDA0002974990580000031
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