CN102082618B - A Method for Analyzing Time Randomness of Received Point Group Path - Google Patents

Abstract

The invention discloses a method for analyzing the time randomness of receiving-point group paths, which comprises the following seven steps: 1, determining the longitudes and latitudes as well as forecasting time of a launching point and a receiving point so as to construct a dissemination environment; 2, calculating the great circle distance and the value range of a launching elevation angle according to geographic information; 3, solving a ray equation so as to obtain an estimated value of the launching elevation angle; 4, carrying out linear interpolation calculation, and solving an accurate value of the elevation angle; 5, repeating the steps 1 to 4 so as to obtain a value sequence of the group path in different time; 6, processing the sequence of the group path, and calculating a self-correlation coefficient; and 7, obtaining the correlation time of the group path according to the calculation result obtained in the step 6. The method disclosed by the invention has good practical value and a broad application prospect in the technical field of short-wave communication.

Description

A Method for Analyzing Time Randomness of Received Point Group Path

(1) Technical field

The invention relates to a method for analyzing the time randomness of a receiving point group path based on ray tracing technology, and belongs to the technical field of short-wave communication.

(2) Background technology

Short-wave communication is the main way of long-distance communication at present. Its frequency range is 3-30MHz, and it mainly relies on ionospheric reflection for propagation. In the process of short-wave propagation, the electron concentration in the ionosphere has a great influence on its operating frequency. When the concentration is high, the reflection frequency is high, and when the concentration is low, the reflection frequency is low. Because the height and electron concentration of the ionosphere change with the change of factors such as regions, seasons, time, and sunspot activities, they have certain randomness. Therefore, the radio wave parameters received at the receiving point will also change accordingly with the change of the ionosphere state, such as group path, time delay, coverage, etc. will change with time. In order to improve the reliability of short-wave communication, it is necessary to analyze and study the correlation between radio waves received at different times and locations.

The current commonly used methods for analyzing the time correlation of radio waves are mainly based on experimental tests. Experimental tests need to be carried out on the actual ionospheric link, and the basic characteristics of the ionosphere will change with time, seasons and other natural factors, requiring multiple measurements. Obtaining an exact solution makes the cost of the experimental test method very high, so under general conditions, the method of channel simulation is usually selected. The channel simulation method refers to the theoretical analysis of the channel characteristics, the establishment of a channel model, and the simulation of the actual channel in the laboratory environment. It can easily create various typical channel characteristic environments and electromagnetic environments, and the regions that can be simulated It is very broad, not limited by climatic conditions, and repeated experiments can be carried out at any time, and the test cost is low, which can shorten the development cycle of communication equipment. Among various typical shortwave channel models, the Watterson model is recommended and widely used by the International Radio Consultative Committee (CCIR) because it can simulate the characteristics of shortwave channels in most cases and has low complexity. However, the limitation of this model is that the accuracy is not high, and the user needs to have a certain prediction and understanding of the ionosphere and geomagnetic characteristics in a specific area. It is very inconvenient to operate, and it can only simulate typical environments. It is universal not tall.

Using ray tracing technology to predict some characteristic parameters in short-wave communication applications, as long as the model used can be as close to reality as possible, it can match the actual situation to a relatively accurate degree. Ray tracing technology refers to the approximation of electromagnetic waves as rays in the case of high frequency, and the calculation of electromagnetic wave trajectories according to the environmental conditions where the rays propagate. Therefore, using this technique, we can calculate all the rays from the transmitting point to the receiving point, and, according to the ray trajectory, we can calculate all the basic characteristics of each ray (such as field strength at the receiving point, time delay, group path, etc.), in Based on the simulation data, the time randomness of the group path can be obtained by introducing the corresponding algorithm. Usually, the quasi-parabolic model is mainly used in the application of ray tracing. The model is introduced as follows:

Generally, a simple parabolic curve is used to approximate the change of electron concentration with height in the layer, which is called a parabolic layer, and its mathematical expression is:

${\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; em</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>& <span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.$

In the formula, N _em is the maximum value of the electron concentration, h _m is the height where the electron concentration takes the maximum value, and Y _m is the half-thickness of the parabolic layer. Because this mathematical expression is relatively simple, it is often used.

For ray tracing technology, two-dimensional calculations are generally used, and the displayed situation is generally only the great-circle distance between the two places of communication. Therefore, the introduction of the ionospheric model and the introduction of the geomagnetic field are mostly simple approximate models. The use of the method can only use the average form, and the environment model cannot be reconstructed step by step, so there is a large error in the accuracy of the use. Models of the Earth's magnetic field are generally not introduced. But in reality, the earth's magnetic field has a greater influence on the rays. The use of the quasi-parabolic ionosphere model as the basis of ray tracing technology is not widely recognized. In addition, in the process of using the model, there are problems in obtaining the shape parameters of the model, and the ionosphere is constantly changing according to time and place, and according to the local time There will be stratification, which is difficult to reflect when using the quasi-parabolic model, and the credibility and practicality of the model are greatly reduced. The geomagnetic field model is rarely introduced in general applications, and the introduction of the geomagnetic field model is seldom explained. In addition, the use of two-dimensional display and calculation methods does not have high availability of calculated parameters (such as the arrival angle of rays, etc.). Therefore, the existing technology is not high in calculation accuracy and in line with the actual situation, and it is difficult to further apply the calculated parameters.

(3) Contents of the invention

(1) purpose of the invention: the purpose of the invention is to provide a method for analyzing the time randomness of the receiving point group path, the method overcomes the deficiencies in the prior art, and it adopts the international reference ionosphere (IRI) and the international geomagnetic field reference ( IGRF) constructs a propagation environment, uses three-dimensional ray tracing technology to simulate radio wave propagation, and obtains data that is more in line with the actual situation. Based on the simulation data, the time randomness of the group path is analyzed by using the serial time correlation algorithm and the correlation time is calculated. Therefore, based on the ray tracing technology, analyzing the time correlation of the receiving point signal group path in short-wave communication can guide the application of short-wave communication.

(2) Technical solution:

As shown in Figure 1, a kind of method of the present invention analyzes receiving point group path time randomness, the specific steps of this method are as follows:

Step 1: Determine the geographic latitude and longitude coordinates and prediction time of the transmitting point and receiving point, and construct the ionospheric electron concentration distribution and geomagnetic field distribution based on this, and further determine the spatial distribution of the refractive index according to the magnetic ion theory.

Step 2: According to the geographical location information of the transmitting point and the receiving point, the great-circle distance between the transmitting point and the receiving point along the earth's surface can be obtained, and the possible value range of the transmitting elevation angle can be roughly estimated.

)下的射线方程，并对发射仰角进行线性插值计算，即：在仰角的可能取值范围内，仰角值从某一初始值开始，每次计算后增加1°后重复计算，直至达到终止值；Step 3: For a certain emission frequency, solve the spherical coordinate system (r, θ,

) under the ray equation, and perform linear interpolation calculation on the launch elevation angle, that is: within the possible value range of the elevation angle, the elevation angle value starts from a certain initial value, increases by 1° after each calculation, and then repeats the calculation until it reaches the end value ;

In spherical coordinates, the ray equation can be written in component form:

为波矢量在球坐标系中的三个分量，c为光速，H为哈密尔顿算符。H与波矢量k、相折射指数n的关系为：Among them, P′ is the group path, k _r , k _θ ,

are the three components of the wave vector in the spherical coordinate system, c is the speed of light, and H is the Hamiltonian operator. The relationship between H, wave vector k and phase refraction index n is:

其中，Re代表取实部；w为角频率。

Among them, Re represents the real part; w is the angular frequency.

Step 4: Through the calculation in the previous step, the approximate elevation angle value at which the ray can just reach the receiving point can be obtained; under normal circumstances, this value is unique, but when the ionosphere distribution is relatively uneven, multiple elevation angle values may be obtained, That is the so-called high-angle wave and low-angle wave; the obtained elevation angle value is further interpolated to obtain a relatively accurate elevation angle value, so that the ray emitted at the elevation angle just reaches the receiving point and the obtained group path value is stored.

Step 5: Repeat the above steps 1 to 4, set the forecast time to different times, and keep other conditions unchanged, you can get group path values at different forecast times, and these values form a discrete time series.

Step 6: Process the group path sequence and calculate the autocorrelation coefficient

For a stationary random process, the autocorrelation coefficient

Among them, R(τ) is the autocorrelation function of x(t), and m is the time average of x(t).

For discrete time series, the calculation formula of correlation coefficient can be obtained:

$\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

为x(n)的平均值，N指x(n)的长度。利用上述公式，调用MATLAB工具中XCORR函数计算相关系数。here,

is the average value of x(n), and N refers to the length of x(n). Using the above formula, call the XCORR function in the MATLAB tool to calculate the correlation coefficient.

Step 7: In order to further illustrate the significance of the randomness of the group path time, the group path correlation time is further calculated according to the calculation result of step 7. In engineering, when the correlation coefficient is lower than 0.05, it is considered irrelevant. According to the calculation results, when the correlation coefficient is 0.05, the corresponding time value is the correlation time of the group path.

(3) Advantages and effects:

The invention establishes the ray propagation environment on the basis of the international ionosphere reference IRI, which greatly improves the accuracy and reliability. The analysis of the time randomness of the receiving point group path makes up for the current deficiency and can guide the application of short-wave communication.

In terms of use, users only need to predict the time randomness and related time of the group path near the receiving point by parameters such as the corresponding geographical location of the transmitting and receiving points, the time of use, and the antenna directionality. Sexual breakthroughs. In addition, as a three-dimensional ray tracing technology, it has great advantages in visualization, and it is more intuitive to use this method.

(4) Description of drawings

Fig. 1 is a block diagram of a method for analyzing the temporal randomness of receiving point group paths in the present invention

Figure 2 Schematic diagram of ionospheric electron density distribution under certain conditions

Figure 3 Schematic diagram of group path autocorrelation coefficient distribution near the receiving point

Figure 4 Schematic diagram of group path correlation time near the receiving point

(5) Specific implementation methods

See Fig. 1, a kind of method of analyzing the time randomness of receiving point group path of the present invention, the concrete steps of this method are as follows:

Step 1: Determine the geographic coordinates of the transmitting point and receiving point and the forecast time period, and construct the spatial distribution of the refractive index.

The launch point coordinates are located in Zhengzhou, its coordinates are (E113.63°, N34.80°), the receiving point coordinates are located in Qingdao, its coordinates are (E120.30°, N36.10°), and the forecast time is selected as 2009 20:00 on October 1st. Using the international reference ionosphere IRI and the international geomagnetic field reference IGRF to predict and calculate the environmental conditions of ray propagation under the current conditions. The ionospheric electron concentration distribution of the two centers at 20:00 is shown in Figure 2.

Step 2: According to the geographical location information of the transmitting point and the receiving point, the great-circle distance between the transmitting point and the receiving point along the earth's surface can be obtained, and the possible value range of the transmitting elevation angle can be roughly estimated.

The formula for calculating the great-circle distance is: D=R×φ where: D is the great-circle distance, R is the radius of the earth, which is taken as 6370km, and φ is the corresponding radian determined by the latitude and longitude, and D=620.992km can be calculated. It is roughly estimated that the elevation angle is between 5° and 45°, which is used as the launch elevation angle range.

)下的射线方程，并对发射仰角进行线性插值计算。在球坐标系中，射线方程可写成分量的形式：Step 3: Set the emission frequency to 8MHz, and solve the spherical coordinate system (r, θ

) under the ray equation, and perform linear interpolation calculation on the launching elevation angle. In spherical coordinates, the ray equation can be written in component form:

为地理经度(0-360) $k_r=\frac{\mathrm{\&omega;}}{c}\cos \mathrm{\&beta;}$ $k_{\mathrm{\&theta;}}=-\frac{\mathrm{\&omega;}}{c}\cos \mathrm{\&beta;}\cos \mathrm{\&alpha;},$

式中β为发射倾角，α为发射偏角，具体由发射点与接收点两地的经纬度来计算获取。k_r，k_θ，

为波矢量在球坐标系中的三个分量，c为光速，H为哈密尔顿算符。H与波矢量k、相折射指数n的关系为：Where P′ is the group path, in general, r is the radius of the earth, θ is pi/2-geographical latitude,

is the geographic longitude (0-360) $k_r=\frac{\mathrm{\&omega;}}{c}\cos \mathrm{\&beta;}$ $k_{\mathrm{\&theta;}}=-\frac{\mathrm{\&omega;}}{c}\cos \mathrm{\&beta;}\cos \mathrm{\&alpha;},$

In the formula, β is the launch inclination angle, and α is the launch deflection angle, which is calculated and obtained by the latitude and longitude of the launch point and the receiving point. k _r , k _θ ,

are the three components of the wave vector in the spherical coordinate system, c is the speed of light, and H is the Hamiltonian operator. The relationship between H, wave vector k and phase refraction index n is:

Among them, Re represents the real part; w is the angular frequency.

Set the initial value to:

r is 6370, θ is pi/2-36.1*pi/180, is 120.3*pi/180,

$k_r=\frac{\mathrm{\&omega;}}{c}\cos \mathrm{\&beta;}$ $k_{\mathrm{\&theta;}}=-\frac{\mathrm{\&omega;}}{c}\cos \mathrm{\&beta;}\cos \mathrm{\&alpha;},$

When the fixed elevation angle value is set to 5°, the initial value of the variable is substituted into the right end of the equation to obtain a new variable value, which is brought into the right end of the equation again, and so on, and finally the ray trajectory is obtained when the elevation angle is 5°. Then, increase the elevation angle value by 1°, recalculate the ray trajectory, and so on, until reaching the maximum value of 45° in the elevation angle range. Process the obtained ray trajectory data, compare the obtained great circle distance with the actual great circle distance, judge whether it can reach the receiving point, and save the data. Some calculation results can be obtained as follows:

serial number Transmit frequency (MHz) Launch elevation angle (degrees) Spherical distance (km) 1 8 43.00 683.26 2 8 44.00 663.90 3 8 45.00 642.49 4 8 46.00 621.46 5 8 47.00 601.26 6 8 48.00 582.15 7 8 49.00 567.57

By comparing with the actual great circle distance, we can see that the receiving point can be reached when the elevation angle is about 46°.

Step 4: Perform further interpolation calculation on the obtained elevation angle value, repeat the calculation process of the previous step with 0.01 degree as the step size, and obtain a relatively accurate elevation angle value, so that the rays emitted at this elevation angle just reach the receiving point. Some calculation results are as follows:

serial number Launch elevation angle (degrees) Group path (km) Spherical distance (km) serial number Launch elevation angle (degrees) Group path (km) Spherical distance (km) 1 45.39 931.02 621.88 6 45.44 930.12 620.69 2 45.40 930.42 621.36 7 45.45 927.22 618.60 3 45.41 930.42 621.25 8 45.46 929.92 620.33 4 45.42 930.42 621.13 9 45.47 929.92 620.22 5 45.43 930.22 620.98 10 45.48 929.82 620.04

After calculation, we can get that when the elevation angle is 45.43°, it just arrives at the receiving point. At this time, the corresponding group path is 930.22km. Record and save the value of the group path.

Step 5: Repeat the above steps 1 to 4, set the prediction time from 20:00 to 20:30, calculate the group path every 15 seconds, a total of 121 times, and keep other conditions unchanged. Group path values at different prediction times can be obtained, and these values form a discrete time series.

Step 6: Process the group path sequence and calculate the autocorrelation coefficient.

Bring the data in step 5 into the correlation coefficient calculation formula, as follows:

$\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

The group path autocorrelation coefficient ρ(m) can be obtained, as shown in FIG. 3 .

Step 7: Obtain the group path relative time according to the calculation result of step 7.

In engineering, when the correlation coefficient is lower than 0.05, it is considered irrelevant. According to the calculation results, when the correlation coefficient is 0.05, the corresponding time value is about 10 minutes, that is, the group path correlation time is about 10 minutes, as shown in FIG. 4 .

Claims (1)

1. a method of analyzing acceptance point group path time randomness, is characterized in that: the method concrete steps are as follows:

Step 1: determine geographical latitude and longitude coordinates and the predicted time of launch point and acceptance point, build accordingly ionospheric electron density distribution and earth magnetic field and distribute, and according to magneto-ionic theory, further determine the spatial distribution of refractive index;

Step 2: according to the geographical location information of launch point and acceptance point, obtain between launch point and acceptance point the great-circle distance along earth surface, and estimate the span of launching elevation;

Step 3: for a certain tranmitting frequency, under the ray propagates space environment having built, solve spherical coordinate system (r, θ,

) under ray equation, and launching elevation is carried out to linear interpolation calculating; That is: in the span at the elevation angle, elevation value is from a certain initial value, and double counting after each calculating increases by 1 ° afterwards, until reach stop value;

In spherical coordinate system, ray equation is write as the form of component:

Wherein, P' is group path, k _r, k _θ,

for three components of wave vector in spherical coordinate system, c is the light velocity, and H is Hamiltonian, and the pass of H and wave vector k, phase refractive index n is:

wherein, real part is got in Re representative; W is angular frequency;

Step 4: by the calculating of step 3, obtain ray and can just get at the approximate elevation value that reaches acceptance point place; Under normal conditions, this value is unique, but when ionosphere distribution is relatively inhomogeneous; The elevation value obtaining is further carried out to interpolation calculation, obtain relatively accurate elevation value, make the ray of launching at this elevation angle just in time arrive acceptance point;

Step 5: repeat above-mentioned steps one to step 4, predicted time is set to different time, and other condition is constant, obtains the group path value under different predicted times, these values form a discrete-time series;

Step 6: group path sequence is processed, and calculated auto-correlation coefficient;

For stationary random process x (t), auto-correlation coefficient $\mathrm{\&rho;}\left(\mathrm{\&tau;}\right)=\frac{R\left(\mathrm{\&tau;}\right)}{R\left(0\right)}=\frac{E\left\{\right[x(t+\mathrm{\&tau;})-m\left]\right[x\left(t\right)-m\left]\right\}}{E\left({[x\left(t\right)-m]}^2\right)}$

Wherein, R (τ) is the auto-correlation function of x (t), and m is the time average of x (t);

For discrete-time series, utilize Calculation of correlation factor formula to obtain:

$\mathrm{\&rho;}\left(m\right)=\frac{\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}(x_{n+m}-\stackrel{\&OverBar;}{x})(x_n-\stackrel{\&OverBar;}{x})}{\underset{n=0}{\overset{N}{\mathrm{\&Sigma;}}}{(x_n-\stackrel{\&OverBar;}{x})}^2}$

Utilize above-mentioned formula, in Calling MATLAB instrument, XCORR function calculates coefficient correlation;

Step 7: obtain group path correlation time according to the result of calculation of step 6; In engineering, when coefficient correlation is lower than 0.05 time, think uncorrelated; According to result of calculation, when coefficient correlation is 0.05, corresponding time value is the correlation time of group path.

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