CN104569913A - High-precision full-lightning positioning method - Google Patents

Abstract

The invention relates to a high-precision full lightning positioning method. This method can be used for three-dimensional positioning of lightning, not only for high-precision positioning of the spatial position and height of lightning between clouds and within clouds, but also for high-precision positioning of ground lightning. This method uses a five-station three-dimensional positioning algorithm, and transforms the nonlinear equations into a linear matrix equation to obtain a unique solution. It uses the time window, waveform cross-correlation extraction time difference method and Levenberg–Marquardt (LM) least squares optimization algorithm to solve the problem. The automatic matching of data waveforms of different detection stations, the accurate extraction of time difference, and the optimization of three-dimensional positioning of non-equal plane detection stations are solved, and the accurate three-dimensional geographical information and time information of lightning are obtained.

Description

A high-precision full lightning location method

technical field

The invention belongs to the electrical field, and in particular relates to a high-precision full lightning positioning method.

Background technique

In the "International Decade for Disaster Reduction" established by the United Nations in 1987, lightning was one of the ten most harmful disasters to human beings. For a long time, lightning has posed a great threat to the natural resources that human beings depend on for survival and the material civilization created by human beings. Especially today, with the widespread use of microelectronic devices, the direct and indirect disasters caused by lightning are becoming more and more serious. Therefore, the research on lightning is becoming more and more serious. More and more attention has been paid to it. The lightning location network LLS operated in my country covers most areas of our country and can monitor ground lightning very well. However, it cannot provide cloud flash information and cannot observe the development process of early lightning electromagnetic radiation such as cloud flash, which affects and limits the understanding of the richness of thunderstorm activities. In order to better study the occurrence and development mechanism of lightning, it is necessary to carry out research on three-dimensional detection technology of lightning.

The key technology of lightning three-dimensional detection technology research is the research of high-precision full lightning location method. This patent proposes a high-precision three-dimensional full lightning positioning method, which can be used for three-dimensional positioning of lightning, can locate traditional ground lightning, and can also locate cloud lightning. This method adopts the five-station three-dimensional positioning algorithm, and transforms the nonlinear equations into linear matrix equations to obtain a unique solution. The time window, waveform cross-correlation extraction time difference method and Levenberg–Marquardt (L-M) least squares optimization algorithm are proposed to solve the problem. The automatic matching of data waveforms of different detection stations, the accurate extraction of time difference, and the optimization of three-dimensional positioning of non-equal plane detection stations are solved, and the accurate three-dimensional geographical information and time information of lightning are obtained.

Contents of the invention

The present invention mainly solves the problems of automatic matching of data waveforms of different detection stations, accurate extraction of time difference, and optimization of three-dimensional positioning of non-equal plane detection stations existing in the prior art; it provides a three-dimensional positioning for lightning, which can not only detect lightning between clouds It is a high-precision full lightning positioning method that can perform high-precision positioning of the spatial position and height of the lightning in the cloud and the lightning in the cloud, and can also perform high-precision positioning of the ground position of the ground lightning.

Above-mentioned technical problem of the present invention is mainly solved by following technical scheme:

A high-precision full lightning positioning method is characterized in that it comprises the following steps:

Step 1: Digitize the radiated electric field waveforms of all lightning location and detection stations, and use the waveform cross-correlation algorithm to accurately extract the time difference of each station for the same lightning discharge event at each station. The specific method is as follows:

Step 1.1: Use the time window to identify the real response of the waveform to the same radiation event in time. Only the waveforms of all stations in the time window at the same time may be the response to the same radiation signal.

Step 1.2: The original electric field waveform is quickly changed into a normalized power waveform by Hilbert, which eliminates the differences in waveform polarity and amplitude caused by the different distances from the radiation source at each site

Step 1.3: Calculate the linear correlation coefficient of the available site power waveform within the allowable window, take the waveform with a correlation coefficient greater than the specified value as the threshold for the same event response, and take the combination with the best similarity and the most standards as the preliminary response to the same lightning event waveform matching results.

Step 1.4: Use the cross-correlation method to extract the waveform time difference of each station. Cross-correlation is the relative time function between signals. The average time delay reflected from the waveform characteristics is not the absolute time difference of a specific pulse, thus eliminating the environment and propagation of different stations. pathways resulting in small differences in the waveform.

Step 1.5: After obtaining the time difference of each station, use the geometric model to check whether the obtained time difference sequence is reasonable.

Step 2: Transform the nonlinear positioning distance algorithm equations into linear matrix equations to obtain the initial solution, the specific method is as follows:

Step 2.1: According to the waveform transmission equation, list the waveform transmission equation for each site.

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Where c is the speed of light in vacuum, (xi _, y _i , zi ₎ is the coordinates of the i-th positioning station, and t _i is the time when the lightning arrives at the i-th detection station.

Step 2.2: Transpose the transmission equation in step 2.1, and then subtract the transmission equations of different stations to obtain a linear equation.

c ² (t ² +t _i ² -2tt _i )＝x ² +xi ₂ ^-2xx _i +y ² +y _i ² -2yy _i +z ² +z _i ² -2zz _i

which defines:

r _i ² =x _i ² +y _i ² +z _i ²

r ² =x ² +y ² +z ²

Can get: c ² t ² +c ² t _i ² -r _i ² ＝r ² -2(xx _i +yy _i +zz _i -c ² tt _i )

At the jth station, the following equation can also be obtained:

c ² t ² +c ² t _j ² -r _j ² ＝r ² -2(xx _j +yy _j +zz _j -c ² tt _j )

Subtract the two equations to get:

c ² (t _i ² -t _j ² )-(r _i ² -r _j ² )＝-2(x( _xi -x _j )+y(y _i -y _j )+z(z _i -z _j )-c ² t(t _i -t _j ))

Also define:

t _ij =t _i -t _j ,x _ij =xi _{-x j} ,y _ij =y _i -y _j ,z _ij =z _i -z _j ,

${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Get the linear equation xx _ij +yy _ij +zz _ij -c ² tt _ij = b _ij

tij is the time difference between the two stations i and j

Step 2.3: For observations of any 5 or more stations, subtract 1 of them from the remaining 4 stations to obtain a matrix composed of 4 independent linear equations similar to step 2.2, where tij is obtained by using cross-correlation in step 1.4 Obtained by extracting the waveform time difference tij of each site by using the method;

$\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}\end{array}\right]<span\; class="notranslate">\; \&Center\; Dot;</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}\\ \mathrm{<span\; class="notranslate">\; z</span>}\\ \mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}\end{array}\right]$

Step 2.4: Take Calculate the three-dimensional position and time of the radiation source in the matrix equation formed by the linear combination of any 5 stations.

Step 3: According to the obtained initial solution, use the L-M least square method optimization algorithm to calculate the precise positioning point, the specific method is:

Step 3.1: Through the three-dimensional position and time of the radiation source calculated in step 2, invert the time when the lightning discharge event reaches each site, based on the following formula:

${\mathrm{<span\; class="notranslate">\; TOA</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

is the fitted arrival time of the inversion lightning discharge event at the inversion position (x ^fit , y ^fit , z ^fit ) to site i after the simple path transmission.

Step 3.2: Determine and measure the optimal calculation factor χ ² , the 5 stations use step 2 to obtain possible initial estimated analytical solutions, redundant stations are used to obtain numerical solutions with nonlinear iteration constraints, and finally the solution vector with the smallest χ ² value as the only exact solution vector.

${\mathrm{<span\; class="notranslate">\; \&chi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 5</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; TOA</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; obs</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; TOA</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Among them, N is the total number of currently available stations, σ is the standard deviation of the data of each detection station, which is a fixed value, is the arrival time observed at station i.

Therefore, the present invention has the following advantages: it can be used for three-dimensional positioning of lightning, and can not only perform high-precision positioning of spatial position and height of lightning between clouds and within clouds, but also perform high-precision positioning of ground position for ground lightning.

Description of drawings

Fig. 1 is a schematic flow chart of the method of the present invention.

FIG. 2 is a schematic flowchart of a method for extracting time differences by a cross-correlation algorithm involved in the present invention.

FIG. 3 is a schematic diagram of rapidly changing the original electric field waveform into a normalized power waveform through Hilbert involved in the present invention.

FIG. 4 is a schematic diagram of a detection method for detecting whether a time difference sequence obtained by using a geometric model detection is reasonable in the present invention.

Detailed ways

The technical solutions of the present invention will be further specifically described below through the embodiments and in conjunction with the accompanying drawings.

Example:

As shown in Figure 1, the high-precision full lightning location method first uses the waveform cross-correlation algorithm to accurately extract the record differences of each station for the same lightning discharge event at each station; Finally, according to the obtained initial solution, the exact solution is obtained by using the L-M least squares optimization algorithm.

The cross-correlation algorithm to extract the time difference method is shown in Figure 2:

Step 1: Time windows are used to identify the real response of the waveform to the same radiation event in time. Only the waveforms of all stations in the time window at the same time may be the response to the same radiation signal.

The second step: the original electric field waveform is quickly changed into a normalized power waveform by Hilbert, eliminating the differences in the polarity and amplitude of the waveform caused by the distance between each site and the radiation source, as shown in Figure 3.

Step 3: Calculate the linear correlation coefficient of the available site power waveform within the allowable window, and use the waveform with a correlation coefficient greater than the specified value as the threshold value belonging to the same event response, and take the combination with the best similarity and the most standards as the response to the same lightning event waveform Preliminary matching results.

Step 4: Use the cross-correlation method to extract the waveform time difference of each station. The cross-correlation is the relative time function between signals. The average time delay reflected from the waveform characteristics is not the absolute time difference of a specific pulse, thus eliminating the differences between different station environments and Propagation paths cause small differences in waveforms.

Step 5: After obtaining the time difference of each station, use the geometric model to check whether the obtained time difference sequence is reasonable. As shown in Figure 4, d ₁ is the distance from the lightning time to the site S _i , d ₂ is the distance from the lightning time to the S _j site, and d ₃ is the distance between the two sites S _i and S _j . Obviously, d ₁ -d ₂ <d ₃ , divide both ends by the speed of light c at the same time, we can get t _i -t _j <d ₃ /c, that is, DTOA _ij <d ₃ /c, so the time difference between all stations is less than the corresponding Inter-station propagation delay.

Using equation conversion to convert the nonlinear equation system into a linear matrix equation system to obtain the initial solution includes the following steps:

Step 1: List the waveform transmission equations for each site.

${\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

(where c is the speed of light in vacuum, (xi _, y _i , zi ₎ is the coordinates of the i-th positioning station, and t _i is the time when the lightning arrives at the i-th detection station).

Step 2: Transpose the transmission equation in step 1, and then subtract the transmission equations of different sites in pairs to obtain a linear equation.

c ² (t ² +t _i ² -2tt _i )＝x ² +xi ₂ ^-2xx _i +y ² +y _i ² -2yy _i +z ² +z _i ² -2zz _i

which defines:

r _i ² =x _i ² +y _i ² +z _i ²

r ² =x ² +y ² +z ²

Can get: c ² t ² +c ² t _i ² -r _i ² ＝r ² -2(xx _i +yy _i +zz _i -c ² tt _i )

At the jth station, the following equation can also be obtained:

c ² t ² +c ² t _j ² -r _j ² ＝r ² -2(xx _j +yy _j +zz _j -c ² tt _j )

Subtract the two equations to get:

c ² (t _i ² -t _j ² )-(r _i ² -r _j ² )＝-2(x( _xi -x _j )+y(y _i -y _j )+z(z _i -z _j )-c ² t(t _i -t _j ))

Also define:

t _ij =t _i -t _j ,x _ij =xi _{-x j} ,y _ij =y _i -y _j ,z _ij =z _i -z _j ,

${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Get the linear equation xx _ij +yy _ij +zz _ij -c ² tt _ij = b _ij

tij is the time difference between the two stations i and j

Step 3: For the observation values of any 5 or more stations, subtract 1 of them from the remaining 4 stations to obtain a matrix composed of 4 independent linear equations similar to step 2, wherein tij passes through the steps corresponding to claim 2 available.

$\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}\end{array}\right]<span\; class="notranslate">\; \&CenterDot;</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}\\ \mathrm{<span\; class="notranslate">\; z</span>}\\ \mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; ik</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; il</span>}}\\ {\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; im</span>}}\end{array}\right]$

Step 4: Take Calculate the three-dimensional position and time of the radiation source in the matrix equation formed by the linear combination of any 5 stations.

The exact solution is obtained by using the L-M least squares optimization algorithm, including the following steps:

Step 1: The three-dimensional position and time of the radiation source obtained through the calculation in claim 3. Retrieve the arrival times of lightning discharge events at various sites.

${\mathrm{<span\; class="notranslate">\; TOA</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

is the fitted arrival time of the inversion lightning discharge event at the inversion position (x ^fit , y ^fit , z ^fit ) to site i after the simple path transmission.

Step 2: Determine and measure the optimal calculation factor χ ² , use claim 3 in 5 stations to obtain a possible initial estimated analytical solution, redundant stations are used to cooperate with nonlinear iteration constraints to obtain a numerical solution, and finally use the solution with the smallest χ ² value vector as the only exact solution vector.

${\mathrm{<span\; class="notranslate">\; \&chi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 5</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; [</span>\frac{{\mathrm{<span\; class="notranslate">\; TOA</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; obs</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; TOA</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; fit</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Among them, N is the total number of currently available stations, σ is the standard deviation of the data of each detection station, which is a fixed value, is the arrival time observed at station i.

The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which the present invention belongs can make various modifications or supplements to the described specific embodiments or adopt similar methods to replace them, but they will not deviate from the spirit of the present invention or go beyond the definition of the appended claims range. 9 -->

Claims (1)

1. the full lightning positioning method of high precision, is characterized in that, comprise the steps:

Step 1: by the radiated electric field waveform digitization of full lightning location detection site, adopt waveform cross correlation algorithm accurately to extract each website to each website waveform poor in the writing time at each station for identical lightning discharge event, concrete grammar is as follows:

Step 1.1: adopt time window to screen waveform to the true response of identical radiation event from the time, each station waveform be simultaneously in time window is likely just the response to same radiation signal;

Step 1.2: be normalized power waveform by Hilbert Rapid Variable Design by original electric field waveform, eliminates the difference of polarity of wave that each website causes due to the difference of distance radiation source distance and amplitude

Step 1.3: calculate the linearly dependent coefficient of allowing stations available power waveform in window, waveform related coefficient being greater than setting, as the threshold value belonging to similar events response, gets best, the up to standard combination at most of similarity as the preliminary matches result to identical lightning event waveform;

Step 1.4: adopt cross-correlation method to extract each website waveform time poor, cross-correlation is relative time function between signal is not the absolute time difference of certain pulse concrete from time delay averaging time that waveform character reflects, thus eliminates different website environment and route of transmission causes waveform small differences;

Whether step 1.5: after the mistiming obtaining each website, use geometric model to detect the mistiming sequence obtained reasonable;

Step 2: non-linear orientation distance algorithm system of equations is converted to linear matrix equation group and tries to achieve just solution, concrete grammar is as follows:

Step 2.1: according to waveform transfer equation, lists each website waveform transfer equation;

$t_i=t+\frac{1}{c}\sqrt{{(x_i-x)}^2+{(y_i-y)}^2+{(z_i-z)}^2}$

Wherein c is the light velocity in vacuum, (x _i, y _i, z _i) be i-th localizer station point coordinate, t _ifor lightning arrives the time of i-th acquisition station;

Step 2.2: the transmission equation of step 2.1 is carried out transposition process, afterwards the transmission equation of different website is subtracted each other between two, obtain linear equation;

c ²(t ²+t _i ²-2tt _i)＝x ²+x _i ²-2xx _i+y ²+y _i ²-2yy _i+z ²+z _i ²-2zz _i

Wherein define:

r _i ²＝x _i ²+y _i ²+z _i ²

r ²＝x ²+y ²+z ²

Can obtain: c ²t ²+ c ²t _i ²-r _i ²=r ²-2 (xx _i+ yy _i+ zz _i-c ²tt _i)

In a jth website, following equation can be obtained equally:

c ²t ²+c ²t _j ²-r _j ²＝r ²-2(xx _j+yy _j+zz _j-c ²tt _j)

Two formulas are subtracted each other and can be obtained:

c ²(t _i ²-t _j ²)-(r _i ²-r _j ²)＝-2(x(x _i-x _j)+y(y _i-y _j)+z(z _i-z _j)-c ²t(t _i-t _j))

Same definition:

t _ij＝t _i-t _j,x _ij＝x _i-x _j,y _ij＝y _i-y _j,z _ij＝z _i-z _j,

$b_{\mathrm{ij}}=\frac{({r_i}^2-{r_j}^2)-c^2({t_i}^2-{t_j}^2)}{2}$

Obtain linear equation xx _ij+ yy _ij+ zz _ij-c ²tt _ij=b _ij

Tij is the mistiming that i, j two websites reach

Step 2.3: for station, any 5 stations or more observed reading, subtract each other with all the other 4 stations and wherein 1 station, can obtain the matrix be made up of the independent linearity equation of 4 similar steps 2.2, wherein tij obtains by adopting cross-correlation method to extract each website waveform time difference tij in step 1.4;

$\left[\begin{array}{cccc}{x}_{\mathrm{ij}}& y_{\mathrm{ij}}& z_{\mathrm{ij}}& {-c}^2{t}_{\mathrm{ij}}\\ x_{\mathrm{ik}}& y_{\mathrm{ik}}& z_{\mathrm{ik}}& {-c}^2{t}_{\mathrm{ik}}\\ x_{\mathrm{il}}& y_{\mathrm{il}}& z_{\mathrm{il}}& {-c}^2{t}_{\mathrm{il}}\\ x_{\mathrm{im}}& y_{\mathrm{im}}& z_{\mathrm{im}}& {-c}^2{t}_{\mathrm{im}}\end{array}\right].\left[\begin{array}{c}x\\ y\\ z\\ t\end{array}\right]=\left[\begin{array}{c}{b}_{\mathrm{ij}}\\ b_{\mathrm{ik}}\\ b_{\mathrm{il}}\\ b_{\mathrm{im}}\end{array}\right]$

Step 2.4: get radiation source three-dimensional position and time is calculated in the matrix equation of the formation of any 5 station linear combinations;

Step 3: according to the first solution obtained, adopt L-M least square method optimized algorithm to calculate accurate anchor point, concrete grammar is:

Step 3.1: the radiation source three-dimensional position calculated by step 2 and time, inverting lightning discharge event reaches the time of each website, based on following formula:

${\mathrm{TOA}}_i^{\mathrm{fit}}=\frac{1}{c}\sqrt{{(x^{\mathrm{fit}}-x_i)}^2+{(y^{\mathrm{fit}}-y_i)}^2+{(z^{\mathrm{fit}}-z_i)}^2}$

that inverting is at inverting position (x ^fit, y ^fit, z ^fit) the transmission of lightning discharge course of event simple path after arrive matching time of arrival of website i;

Step 3.2: determine to weigh Optimal calculation factor χ ², obtain possible initial estimation analytic solution in 5 station steps 2, redundant sites obtains numerical solution, χ the most at last for coordinating nonlinear iteration to retrain ²be worth minimum solution vector as unique accurate solution vector;

${\mathrm{\&chi;}}^2=\underset{N-5}{\overset{N}{\mathrm{\&Sigma;}}}{\left[\frac{{\mathrm{TOA}}_i^{\mathrm{obs}}-{\mathrm{TOA}}_i^{\mathrm{fit}}}{{\mathrm{\&sigma;}}_t^2}\right]}^2$

Wherein, N is current stations available sum, and σ is the standard deviation of each acquisition station data, is a fixed value, for the time of arrival that website i observes.