CN108427095B - A data missing snapshot number and array element detection method based on covariance matrix - Google Patents

Abstract

The invention proposes a method for detecting the number of snapshots of data loss and array elements based on covariance matrix, including calculating the covariance matrix of each base station, estimating the noise coefficient of each base station, constructing a curve equation, and estimating the snapshot of data loss of each base station. and the number of data-missing array elements, estimate the number of data-missing snapshots and data-missing array elements of each array element, and compare the two estimation results to determine the final estimation result. The invention overcomes the shortcomings and deficiencies of the prior art, and can better detect the time of data loss and the data loss array element.

Description

A data missing snapshot number and array element detection method based on covariance matrix

technical field

The invention belongs to the fields of array signal processing technology, information fusion technology, far-field signal processing technology and target detection and identification technology, in particular to a method for detecting data loss snapshot numbers and array elements based on covariance matrix.

Background technique

Multi-station passive positioning technology is an important branch in the field of array signal processing. However, in the process of array reception, one or several elements in the array may fail before the measurement is completed, that is, data loss will occur. If the moment of data loss and the array elements with data loss cannot be well detected, the subsequent positioning performance will be greatly affected.

The document "Direction of Arrival(DoA) Estimation Under Array Sensor FailuresUsing a Minimal Resource Allocation Neural Network" uses neural network to train a large number of measurement data without data loss, and extracts relevant characteristic parameters. , effectively estimate the time of data loss and data loss array elements through feature parameter matching; the literature "Rank constrained MLestimation of structured covariance matrices with applications in radartarget detection" proposes a target detection algorithm based on covariance matrix, which requires pre-estimation of interference and noise covariance matrix and target angle, even if it is extended to the case of data loss, it is necessary to predict the covariance matrix and the reference target angle information in the case of no data loss to form a whitening matrix.

SUMMARY OF THE INVENTION

On the basis of the multi-station passive positioning model, the present invention proposes a method for detecting the number of data missing snapshots and the array element based on the covariance matrix, aiming at the detection problems of the number of failed array elements, the failure time of the array element and the failure position of the array element. , to better detect the time of data loss and the data loss array element.

The object of the present invention is achieved through the following technical solutions: a kind of data loss snapshot number and array element detection method based on covariance matrix, comprising the following steps:

Step 1. Use the measurement data x _l (t)=A _l s(t)+n _l (t) obtained by each base station, where x _l (t) represents the measurement data of the lth base station at time t, and A _l =[ a _l (r ₁ ),..., _al (r _q )] is the M×q-dimensional positioning matrix of the lth base station, where M denotes the number of array elements of each base station, q denotes the number of signal sources, and a _l (r ₁ ) is the M×1-dimensional positioning vector from the first signal to the l-th base station, r ₁ is the 2×1-dimensional vector of the first signal, s(t)=[s ₁ (t),...,s _q ( t)] ^T is the q×1-dimensional signal vector at time t, n _l (t)=[n _l,1 (t),...,n _l,M (t)] ^T represents the signal vector of the lth base station at time t Additive noise vector, estimating the covariance matrix of each base station:

In the formula, T represents the number of snapshots, the symbol "T" represents the transpose symbol of the matrix, and "H" represents the conjugate transpose symbol of the matrix;

以及已知的信源数目q通过排列组合的方式遍历任意的q+1个阵元组合，计算各个阵元组合对应的协方差矩阵的迹，选择迹最大的组合对应的协方差矩阵估计噪声系数：Step 2. Use the covariance matrix of each base station

And the number of known sources q is traversed by any combination of q+1 array elements, the trace of the covariance matrix corresponding to each array element combination is calculated, and the covariance matrix corresponding to the combination with the largest trace is selected to estimate the noise coefficient. :

为迹最大的组合对应的协方差矩阵，eig{·}表示矩阵的特征值函数，min{·}表示向量中的最小值；in the formula

is the covariance matrix corresponding to the combination with the largest trace, eig{·} represents the eigenvalue function of the matrix, and min{·} represents the minimum value in the vector;

Step 3. Construct the curve fitting equation according to the change of the data missing covariance matrix trace:

表示前n个快拍估计的协方差矩阵，R_l表示理想的协方差矩阵，

表示快拍估计的协方差矩阵，

表示去除噪声项的协方差矩阵，trace{·}表示矩阵的迹；in the formula

represents the estimated covariance matrix of the first n snapshots, R _l represents the ideal covariance matrix,

represents the covariance matrix of the snapshot estimate,

Represents the covariance matrix for removing noise terms, and trace{·} represents the trace of the matrix;

若出现

情况，则可直接估计数据遗失阵元数：Step 4. Use the curve fitting equation to estimate the number of snapshots of data loss and the number of data loss array elements of each base station

if it appears

In this case, the number of missing array elements can be estimated directly:

表示邻近取整符号；若

则令

若

则令

即无数据遗失；Among them, the symbol

represents the adjacent rounding symbol; if

order

like

order

i.e. no data loss;

Step 5. For the base station with data loss, traverse each array element and estimate the number of snapshots of data loss for each array element:

和出现数据遗失的快拍数：Calculate the number of array elements with data loss in the lth base station by estimating one by one array element

and the number of snapshots with data loss:

In the formula, m represents the mth array element;

和

确定最终估计结果。Step 6. According to the estimation results of steps 4 and 5

and

Determine the final estimate.

Further, the step 6 is specifically as follows: if the estimated result of each array element matches the result of multi-array element estimation, the estimation is correct, and the estimated result is the estimated result of each array element; if the estimated result of each array element is If the result does not match the result of the multi-array element estimation, the estimation is wrong, and all the data of the entire base station is not enough to realize the positioning function, then the measurement data on the base station is eliminated:

Among them, the threshold T_threshold ₂ =κ ₂ T, and κ ₂ is an infinitesimal positive number;

The estimation of the position of the array element is expressed as:

Description of drawings

Fig. 1 is a flow chart of the data loss snapshot number and array element detection method based on covariance matrix of the present invention;

Figure 2 Multi-station positioning model diagram;

Figure 3. Simulation scene model diagram;

Fig. 4 curve fitting result graph;

Figure 5 is a graph of the variation of the detection probability of the number of missing array elements with the signal-to-noise ratio.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

1 and 2, the present invention proposes a method for detecting the number of missing snapshots and array elements based on a covariance matrix, which includes the following steps:

Step 1. Use the measurement data x _l (t)=A _l s(t)+n _l (t) obtained by each base station, where x _l (t) represents the measurement data of the lth base station at time t, and A _l =[ a _l (r ₁ ),..., _al (r _q )] is the M×q-dimensional positioning matrix of the lth base station, where M denotes the number of array elements of each base station, q denotes the number of signal sources, and a _l (r ₁ ) is the M×1-dimensional positioning vector from the first signal to the l-th base station, r ₁ is the 2×1-dimensional vector of the first signal, s(t)=[s ₁ (t),...,s _q ( t)] ^T is the q×1-dimensional signal vector at time t, n _l (t)=[n _l,1 (t),...,n _l,M (t)] ^T represents the signal vector of the lth base station at time t Additive noise vector, estimating the covariance matrix of each base station:

In the formula, T represents the number of snapshots, the symbol "T" represents the transpose symbol of the matrix, and "H" represents the conjugate transpose symbol of the matrix;

The step 1 is specifically:

1) Consider a probing network composed of L base stations, each of which is composed of M array elements. Assuming that there are q far-field narrowband signals with a known center frequency of ω ₀ , that is, the waveform received by each base station array element can be considered as a plane wave, as shown in Figure 2, then at the mth array element of the lth base station The receiving model can be expressed as:

Among them, s _k ( ) represents the kth signal source, τ _l,mk represents the propagation delay from the kth signal source to the mth array element of the lth base station, and a _l,k represents the kth signal to the The attenuation coefficient of the lth base station, the attenuation coefficient of each array element in the base station corresponding to the same signal source is considered to be the same, and n _l,m (t) represents the additive noise of the mth array element of the lth base station;

利用此关系，接收模型可以表示为:2) The narrowband assumption will have the following approximate representation for the kth signal and each array element:

Using this relationship, the receiving model can be expressed as:

3) The M array element receiving model of the lth base station is formed into an M×1-dimensional receiving vector, which can be obtained

where a _l (r _k ) is the M×1-dimensional positioning vector from the k-th signal to the l-th base station, which can be expressed as

where r _k is a 2 × 1-dimensional vector of the k-th signal, containing the two-dimensional spatial information of the x-axis and y-axis, namely:

r _k =[x _k ,y _k ] ^T

4) Re-express the receiving model in the form of a matrix as:

x _l (t)=A _l s(t)+n _l (t)

where A _l =[a _l (r ₁ ),…,a _l (r _q )] is an M×q-dimensional matrix, and s(t)=[s ₁ (t),…,s _q (t)] ^T is q×1 dimensional signal vector.

5) The entire array is sampled at time t ₁ , _t

where T represents the number of snapshots.

以及已知的信源数目q通过排列组合的方式遍历任意的q+1个阵元组合，计算各个阵元组合对应的协方差矩阵的迹，选择迹最大的组合对应的协方差矩阵估计噪声系数：Step 2. Use the covariance matrix of each base station

And the number of known sources q is traversed by any combination of q+1 array elements, the trace of the covariance matrix corresponding to each array element combination is calculated, and the covariance matrix corresponding to the combination with the largest trace is selected to estimate the noise coefficient. :

为迹最大的组合对应的协方差矩阵，eig{·}表示矩阵的特征值函数，min{·}表示向量中的最小值；in the formula

is the covariance matrix corresponding to the combination with the largest trace, eig{·} represents the eigenvalue function of the matrix, and min{·} represents the minimum value in the vector;

The step 2 is specifically:

时刻，所有阵元的接收数据都是未遗失的，即此时对于第l个基站的接收数据

可以表示为：1) For

At the moment, the received data of all the array elements are not lost, that is, the received data of the lth base station at this time

It can be expressed as:

表示

时刻的信号向量，

表示

的噪声向量。in,

express

signal vector at time,

express

noise vector.

个快拍采样数据的矩阵表达形式为：all

The matrix representation of the snapshot sampling data is:

分别表示

时刻的测量矩阵，信号矩阵和噪声矩阵。in,

Respectively

The measurement matrix, the signal matrix and the noise matrix at the moment.

时刻，第l个基站的协方差矩阵

可以表示为：for

time, the covariance matrix of the lth base station

It can be expressed as:

表示

时刻的信号协方差矩阵，

表示

时刻的噪声系数。in

express

The signal covariance matrix at time,

express

noise figure at time.

时刻，一个或者多个阵元存在数据遗失的情况，接收数据中只存在噪声项，对于第l个基站的接收数据

可以表示为：2) For

At the moment, one or more array elements have data loss, there is only noise term in the received data, for the received data of the lth base station

It can be expressed as:

表示

时刻的信号向量，

表示

时刻第l个基站第m个阵元的接收噪声，其中m＜M，Ω_l表示第l个基站无数据遗失的阵元集合，

表示第l个基站有数据遗失的阵元集合。Among them, A _l,m represents the positioning vector of the m-th array element of the l-th base station,

express

signal vector at time,

express

The received noise of the m-th array element of the l-th base station at time, where m<M, Ω _l represents the set of array elements without data loss at the l-th base station,

Indicates that the lth base station has a set of array elements with data loss.

时刻，引入M×M维的对角矩阵Q_l，即

可以表示为For the lth base station and

At the moment, an M×M-dimensional diagonal matrix Q _l is introduced, that is,

It can be expressed as

The received data of the lth base station can be re-expressed as:

个快拍采样数据

的矩阵表达形式为：3) All

snapshot sample data

The matrix representation of is:

表示

时刻的测量矩阵，

分别表示

时刻的信号矩阵和噪声矩阵。in,

express

the measurement matrix at the moment,

Respectively

Signal matrix and noise matrix at time.

时刻，第l个基站的协方差矩阵

可以表示为：for

time, the covariance matrix of the lth base station

It can be expressed as:

表示

时刻的信号协方差矩阵，

表示

时刻的噪声系数。in

express

The signal covariance matrix at time,

express

noise figure at time.

For the whole measurement time, the covariance matrix of the lth base station can be expressed as:

因此第l个基站的协方差矩阵可以进一步表示为：Using the ergodic and stationary properties of signal and noise, we can get

Therefore, the covariance matrix of the lth base station can be further expressed as:

4) For all the array elements of the lth base station, assuming that the number of sources q is known, traverse any combination of q+1 array elements, calculate the traces of their covariance matrices, and select the covariance matrix corresponding to the combination with the largest trace. Estimate the noise figure. Calculate all the permutations and combinations Υ, and make a look-up table after all the combinations are calculated, so as to facilitate future applications:

Υ=combntns{1:M,q+1}

即Υ为一个P×(q+1)维的矩阵，每行代表一种排列组合。Among them, the combntns{1:J,I} function indicates that all combinations of I data are selected from the 1:J data, and the number of all combinations

That is, Y is a P×(q+1)-dimensional matrix, and each row represents a permutation combination.

5) Calculate the covariance matrix and the trace of the covariance matrix under each combination mode:

表示第l个基站第p种组合下的协方差矩阵，p＝1,…,P，

是协方差矩阵

对应的迹，此过程协方差矩阵可由原始计算的协方差矩阵中抽取相关组合阵元对应的数据，计算量较小。in,

Represents the covariance matrix under the p-th combination of the l-th base station, p=1,...,P,

is the covariance matrix

Corresponding trace, the covariance matrix of this process can be extracted from the covariance matrix of the original calculation.

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 cannot be accurately known, and it is difficult to judge whether there is data loss through the threshold setting, so it is necessary to assume that at least one If there is a combination of missing data, then you only need to select the covariance matrix corresponding to the combination with the largest trace to estimate the noise coefficient:

7) Since there are q+1 eigenvalues corresponding to q+1 array elements, and the value with the smallest eigenvalue corresponds to the noise coefficient, we can obtain:

为迹最大的组合对应的协方差矩阵，eig{·}表示矩阵的特征值函数，min{·}表示向量中的最小值；in the formula

is the covariance matrix corresponding to the combination with the largest trace, eig{·} represents the eigenvalue function of the matrix, and min{·} represents the minimum value in the vector;

Step 3. Construct the curve fitting equation according to the change of the data missing covariance matrix trace:

表示前n个快拍估计的协方差矩阵，R_l表示理想的协方差矩阵，

表示快拍估计的协方差矩阵，

表示去除噪声项的协方差矩阵，trace{·}表示矩阵的迹；in the formula

represents the estimated covariance matrix of the first n snapshots, R _l represents the ideal covariance matrix,

represents the covariance matrix of the snapshot estimate,

Represents the covariance matrix for removing noise terms, and trace{·} represents the trace of the matrix;

The step 3 is specifically:

1) It is assumed that the various sources are uncorrelated, that is,

Among them, s _i and s _j represent the i-th and j-th rows of the signal matrix s, respectively,

So the signal covariance matrix S can be expressed as:

时刻和第l个基站的协方差矩阵主对角线上的第m个元素可以表示为：2) For

The moment and the mth element on the main diagonal of the covariance matrix of the lth base station can be expressed as:

That is, the elements on the diagonal are equal, and η _l ≥ 0.

时刻，协方差矩阵的迹可以表示为：for

time, the trace of the covariance matrix can be expressed as:

时刻，协方差矩阵的迹可以表示为：3) For

time, the trace of the covariance matrix can be expressed as:

表示Ω_l中元素的个数，

表示

中元素的个数。in,

represents the number of elements in Ω _l ,

express

The number of elements in .

4) For the whole measurement period, the trace of the covariance matrix can be expressed as

与

的信息：5) The trace of the covariance matrix contains the information of the data missing time and the number of data missing array elements to be estimated, but there are noise power terms and signal power terms in the covariance matrix, and it is difficult to directly extract the dual parameter information through the difference. Next, by constructing the following functional relationship, we extract about

and

Information:

近似表示，且需满足快拍数为大快拍数，经过仿真验证至少要1000个快拍，

表示利用前n个快拍估计的协方差矩阵，分别可表示为Among them, R _l represents the ideal covariance matrix, but limited by the number of snapshots, R _l can use the estimated covariance matrix of all snapshots

Approximate representation, and the number of snapshots needs to be a large number of snapshots. After simulation verification, at least 1000 snapshots are required.

Represents the covariance matrix estimated by the first n snapshots, which can be expressed as

表示去除噪声项的协方差矩阵，即in,

represents the covariance matrix of the removed noise term, i.e.

若出现

情况，则可直接估计数据遗失阵元数：Step 4. Use the curve fitting equation to estimate the number of snapshots of data loss and the number of data loss array elements of each base station

if it appears

In this case, the number of missing array elements can be estimated directly:

表示邻近取整符号；若

则令

若

则令

即无数据遗失；Among them, the symbol

represents the adjacent rounding symbol; if

order

like

order

i.e. no data loss;

The step 4 is specifically:

1) When the number of snapshots is large enough, the theoretical curve can be derived as

且

故分母不可能全为0，此曲线表明整个测量周期只会出现一次数据遗失的情况，也可推广到出现多次数据遗失的情况，在这里不做详细的阐述。It can be seen from the assumption that

and

Therefore, it is impossible for the denominator to be all 0. This curve shows that only one data loss occurs in the entire measurement period, and it can also be extended to the case of multiple data loss, which will not be described in detail here.

故可通过曲线拟合法估计这两个参数。在曲线拟合过程中可以采用曲线匹配的方法，即利用各个可能的

值以及

值建立字典Ψ，此字典建立完成后可做成查找表，降低计算复杂度。字典的维度为T×TM维，利用实际的曲线

与字典中的每一列做相关处理，但是相关处理计算复杂度较高，故本发明利用设定阈值统计拟合点数的方法去拟合曲线，即满足：2) The first section is a straight line, and the second section is a part of a hyperbola. For this section of the curve, there are only two unknowns T ₂ ^l and

Therefore, these two parameters can be estimated by the curve fitting method. In the process of curve fitting, the method of curve matching can be used, that is, using each possible

value and

value to establish a dictionary Ψ, which can be made into a lookup table after the establishment of the dictionary to reduce the computational complexity. The dimension of the dictionary is T×TM dimension, using the actual curve

Perform correlation processing with each column in the dictionary, but the computational complexity of the correlation processing is relatively high, so the present invention uses the method of setting the threshold statistical fitting points to fit the curve, that is, it satisfies:

where count{·} represents the counter, and threshold _l represents the curve fitting threshold of the lth base station.

还是

3) At this time, it is impossible to distinguish between two extreme cases, that is, there is no data loss and data loss occurs from the beginning. It needs to be judged again by the trace of the covariance matrix.

still

时，协方差矩阵的迹可以表示为：when

When , the trace of the covariance matrix can be expressed as:

时，协方差矩阵的迹可以表示为：when

When , the trace of the covariance matrix can be expressed as:

The above formula can be approximated by the trace of the covariance matrix obtained by the estimated q+1 array elements:

的估计得：Therefore, it can be obtained

is estimated to be:

表示对

的估计值。in,

express right

estimated value of .

Step 5. For the base station with data loss, traverse each array element and estimate the number of snapshots of data loss for each array element:

和出现数据遗失的快拍数：Calculate the number of array elements with data loss in the lth base station by estimating one by one array element

and the number of snapshots with data loss:

In the formula, m represents the mth array element;

The step 5 is specifically:

和

的估计后，接下来是转化为对阵元位置的估计，即已知数据遗失的阵元个数，但是并不知道数据遗失阵元的具体位置。故实现对各个基站是否有数据遗失的判断以及有数据遗失基站中数据遗失的快拍数

和数据遗失的阵元数

后，接下来是对各个阵元进行是否有数据遗失的判断。1) Realize the pair

and

After the estimation of , the next step is to convert it into the estimation of the position of the array element, that is, the number of array elements whose data is lost is known, but the specific position of the array element with which the data is lost is not known. Therefore, it is possible to judge whether each base station has data loss and the number of snapshots of data loss in the base station with data loss.

and the number of elements with missing data

After that, the next step is to judge whether there is data loss for each array element.

2) For the received data of the mth array element of the lth base station, its covariance matrix can be expressed as

R _l,m =R _l (m,m)

If there is no data missing, the trace of the covariance matrix can be expressed as

If data loss occurs from the beginning, the trace of the covariance matrix can be expressed as

快拍后才出现数据遗失，则协方差矩阵的迹可以表示为if from

If the data is lost after the snapshot, the trace of the covariance matrix can be expressed as

3) Therefore, the estimation of the moment when data loss occurs on each array element can be expressed as

的估计也需设定门限T_threshold₁＝κ₁T，κ₁是一个无穷小的正数，有以下关系式成立：for

The estimation of , also needs to set the threshold T_threshold ₁ =κ ₁ T, where κ ₁ is an infinitesimal positive number, and the following relationship holds:

和

确定最终估计结果。Step 6. According to the estimation results of steps 4 and 5

and

Determine the final estimate.

The step 6 is specifically as follows: if the estimated result of each array element matches the result of multi-array element estimation, the estimation is correct, and the estimated result is the result of each array element estimation; if the estimated result of each array element matches the multi-array element estimation result If the results of the array element estimation do not match, the estimation is wrong, and all the data of the entire base station is not enough to realize the positioning function, so the measurement data on the base station is eliminated:

Among them, the threshold T_threshold ₂ =κ ₂ T, and κ ₂ is an infinitesimal positive number;

The estimation of the position of the array element is expressed as:

Simulation condition 1: As shown in Figure 3, the four base stations are located at [-500m, 0m], [0m, -500m], [500m, 0m], [0m, 500m], and 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, arranged in a uniform linear array, and the array element interval is λ/2, 2 temporally and spatially independent target sources, the positions are [-100m, 100m], [200m, -100m], the number of snapshots is 10,000, and the fourth array element of the second base station is after the 5,000th snapshot. Data is missing, other array elements are normal, threshold=0.01, and the curve fitting results are shown in Figure 4.

Take the results of 10 Monte Carlo experiments, record the noise figure estimation results and the number of missing array elements and snapshots estimated by curve fitting.

Table 1 Curve fitting estimation results

As can be seen from Figure 4, the second base station has data loss, so it consists of a segmented curve. The turning point of the curve represents the number of snapshots with data loss, and the curves fitted by base stations 1, 3, and 4 are in near 0. Through the first curve fitting, a set of estimates of the number of array elements and the number of snapshots related to data loss can be obtained. As shown in Table 1, 10 sets of experimental results are given. The number of snapshots is estimated to be around 5000, but sometimes There will be a large deviation, so it is necessary to use a high-precision second estimation, and the results are shown in Table 2.

Take the results of 10 Monte Carlo experiments, and record the estimated results of the first data-missing snapshots and the second estimated data-missing snapshots.

Table 2 Estimated results of the number of snapshots for secondary data loss

Simulation condition 2: As shown in Figure 3, the four base stations are located at [-500m, 0m], [0m, -500m], [500m, 0m], [0m, 500m], and the orientations of the base stations are [90 °,0°,-90°,180°], the noise is Gaussian white noise, each base station has 4 array elements, arranged in a uniform linear array, the array element interval is λ/2, and the two are independent in time and space , the positions are [-100m, 100m], [200m, -100m], the number of snapshots is 10,000, the fourth array element of the second base station has data loss from the first snapshot, and other arrays The element is normal, the signal-to-noise ratio is from -10dB to 10dB, and the Monte Carlo experiment is 100 times. The curve of the detection probability of the number of missing data elements with the signal-to-noise ratio is shown in Figure 5.

It can be seen from Figure 5 that the detection of the number of data missing array elements after -5dB can reach a success probability of 100%, which is suitable for the detection of data loss above -5dB.

Simulation condition 3: As shown in Figure 3, the four base stations are located at [-500m, 0m], [0m, -500m], [500m, 0m], [0m, 500m], and 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, arranged in a uniform linear array, and the array element interval is λ/2, 2 A target source that is independent in time and space, the positions are [-100m, 100m], [200m, -100m], the number of snapshots is 10,000, and the second to fourth array elements of the second base station are taken from the first snapshot. When data loss occurs, other array elements are normal. Take 10 Monte Carlo experiments and record the estimated results of secondary data loss of the second base station. The results are shown in Table 3.

Table 3 Estimation results of secondary data missing

It can be seen from Table 3 that at this time, the second base station has 4 array elements, 3 of which have data loss, then the estimated noise coefficient and signal power are incorrect at this time, resulting in two estimated data loss. The number of array elements and the number of snapshots do not match. At this time, it can be considered that the entire base station has data loss and needs to be eliminated.

A method for detecting the number of missing snapshots and array elements based on a covariance matrix provided by the present invention has been described above in detail. In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The above embodiments The description is only used to help understand the method of the present invention and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation and application scope. However, the contents of this specification should not be construed as limiting the present invention.

Claims (2)

1. a data loss snapshot number and array element detection method based on covariance matrix, is characterized in that: comprise the following steps: Step 1. Use the measurement data x _l (t)=A _l s(t)+n _l (t) obtained by each base station, where x _l (t) represents the measurement data of the lth base station at time t, and A _l =[ a _l (r ₁ ),..., _al (r _q )] is the M×q-dimensional positioning matrix of the lth base station, where M denotes the number of array elements of each base station, q denotes the number of signal sources, and a _l (r ₁ ) is the M×1-dimensional positioning vector from the first signal to the l-th base station, r ₁ is the 2×1-dimensional vector of the first signal, s(t)=[s ₁ (t),...,s _q ( t)] ^T is the q×1-dimensional signal vector at time t, n _l (t)=[n _l,1 (t),...,n _l,M (t)] ^T represents the signal vector of the lth base station at time t Additive noise vector, estimating the covariance matrix of each base station:

In the formula, the parameter T represents the number of snapshots, the superscript symbol " ^T " represents the transpose symbol of the matrix, and the superscript symbol " ^H " represents the conjugate transpose symbol of the matrix; Step 2. Use the covariance matrix of each base station

And the number of known sources q traverses any q+1 array element combination by permutation and combination, calculates the trace of the covariance matrix corresponding to each array element combination, and selects the covariance matrix corresponding to the combination with the largest trace to estimate the noise coefficient. :

in the formula

is the covariance matrix corresponding to the combination with the largest trace, eig{·} represents the eigenvalue function of the matrix, and min{·} represents the minimum value in the vector; Step 3. Construct the curve fitting equation according to the change of the data missing covariance matrix trace:

in the formula

represents the estimated covariance matrix of the first n snapshots, R _l represents the ideal covariance matrix,

represents the covariance matrix of the snapshot estimate,

Represents the covariance matrix for removing noise terms, and trace{·} represents the trace of the matrix; Step 4. Use the curve fitting equation to estimate the number of snapshots of data loss and the number of data loss array elements of each base station

if it appears

In this case, the number of missing array elements can be estimated directly:

Among them, the symbol

represents the adjacent rounding symbol; if

order

like

order

i.e. no data loss; Step 5. For the base station with data loss, traverse each array element and estimate the number of snapshots of data loss for each array element:

Calculate the number of array elements with data loss in the lth base station by estimating one by one array element

and the number of snapshots with data loss:

In the formula, m represents the mth array element; Step 6. According to the estimation results of steps 4 and 5

and

Determine the final estimate. 2. The method according to claim 1, wherein: the step 6 is specifically: if the result of each array element estimation matches the result of the multi-array element estimation, the estimation is correct, and the estimation result is taken from each array element. The result of element estimation; if the estimated result of each array element does not match the result of multi-array element estimation, the estimation is wrong, and all the data of the entire base station is not enough to realize the positioning function, then the measurement data on the base station is eliminated:

Among them, the threshold T_threshold ₂ =κ ₂ T, and κ ₂ is an infinitesimal positive number; The estimation of the position of the array element is expressed as:

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