WO2022174486A1 - Ultra-short baseline lightning three-dimensional positioning method based on broadband very high frequency radiation signal detection - Google Patents

Abstract

The present invention relates to the technical field of lightning positioning, and in particular, to an ultra-short baseline lightning three-dimensional positioning method based on broadband very high frequency radiation signal detection. The present invention combines the ultra-short baseline advantage of an interferometer and the three-dimensional positioning capability of multi-station time difference of arrival technique, and an ultra-short baseline multi-station lightning observation layout is designed; a traditional "centroid method" technical route is abandoned; an original signal is upsampled; an ensemble empirical mode decomposition technique is introduced to analyze and optimize the upsampled signal; a cross-correlation signal matching technique based on the combination of a main window and an auxiliary window is used to fully match and extract pulse information in a very high frequency radiation signal; three-dimensional positioning is performed using the time difference of arrival technique. According to the present invention, the ultra-high resolution three-dimensional positioning of a lightning discharge process can be realized; the time resolution at which a lightning discharge event is positioned can reach the nanosecond magnitude; the theoretical resolution of a spatial error is increased to the decimeter magnitude.

Description

Ultra-short baseline lightning three-dimensional localization method based on broadband VHF radiation signal detection technical field

The invention belongs to the technical field of lightning positioning, and in particular relates to a three-dimensional positioning method for ultra-short baseline lightning based on broadband very high frequency radiation signal detection.

Background technique

Electromagnetic signals of different frequency bands emitted when lightning occurs can be used for lightning localization. According to the differences of detection systems and different positioning methods, lightning positioning methods are mainly divided into three categories: Magnetic Direction Finding (MDF), Time of Arrival (TOA) and Interferometry.

The positioning technology of the time difference of arrival is to calculate the location information of the radiation source by measuring the time difference between the electromagnetic signals radiated by lightning in a specific frequency band reaching different radiation receiving antennas. tens to hundreds of meters), (2) short baselines (several kilometers to tens of kilometers), (3) long baselines (tens to hundreds of kilometers). The short baseline detection system receives lightning VHF band (30-300MHz) signals; the long baseline system receives lightning VLF and LF band (3-300KHz) signals. At present, the most widely used and influential TOA radiation positioning system operating in the VHF frequency band is the Lightning VHF radiation source positioning system (Lightning Mapping Array, LMA) developed by the United States (New Mexico Institute of Mining and Technology) (Thomasand Ronald, 2004), is usually observed by a network of about 10 radiation receiving antennas working at 60-66MHz. The time resolution of lightning radiation source positioning is in the order of tens of microseconds, and the spatial positioning error is tens of meters. The long-baseline positioning system is similar to the positioning principle of LMA, and is characterized by a wider coverage of the station network, but the spatial and temporal resolution is usually not high (Shao et al., 2006).

With the rapid development of various technical levels, especially electronic and computer technology, the development of lightning detection systems based on interferometry has been promoted. The broadband interferometer technology and lightning localization method based on broadband VHF signal detection were first introduced into the field of lightning observation and research by Shao et al. (1996). At present, the antenna layout of the common broadband interferometer inherits the orthogonal baseline structure of the narrow-band interferometer system, which is vertical between the baselines, that is, two orthogonal baselines are formed by three VHF radiation receiving antennas, and the baseline length is generally tens of meters to hundreds of meters. The working frequency of the antenna is wide, usually between tens of MHz and hundreds of MHz. The two-dimensional localization of the lightning discharge process is realized by detecting the time difference between the lightning radio frequency signal reaching the antenna. Due to the very short baseline of this type of system, a single high-performance acquisition card is usually used to simultaneously collect data from three antennas. The sampling rate is as high as several hundred megabytes. The time resolution of the sampling point is as high as nanoseconds. The rate can reach the sub-microsecond level (Stock et al., 2014).

However, both the current mainstream Time Difference of Arrival (TOA) method and the interferometer lightning positioning system have their own advantages and disadvantages: the baseline of the interferometer is very short, and the signals between different antennas are very easy to be matched to obtain the time difference, so the positioning results are not accurate. The time resolution is very high, which can reach the sub-microsecond level under the existing technology. The disadvantage is that the interferometer can only obtain the two-dimensional information (azimuth and elevation) of the lightning discharge event, and due to the plane wave approximation, its positioning The theory itself has very significant systematic errors; although the lightning location system similar to LMA based on TOA can obtain three-dimensional information of the lightning discharge process, due to the relatively long baseline length, the signals on different antennas will be very different, so the signals are not matched. The difficulty is relatively high and the accuracy rate is low. The time resolution that this type of system can currently achieve for lightning discharge events is in the order of tens of microseconds, and the spatial error is tens of meters. In addition, the current mainstream interferometers and three-dimensional lightning The positioning system generally adopts the "centroid method" to match the signal to obtain the time difference, which actually limits the full exploitation of the potential of the VHF observation signal.

With the continuous deepening of lightning physics research, the requirements for the spatial and temporal resolution of the positioning information obtained by the lightning positioning system are constantly increasing. Based on practical requirements and analysis of the advantages and disadvantages of various existing lightning positioning systems, the present invention proposes a three-dimensional positioning method and system for ultra-short baseline lightning based on broadband VHF radiation signals, that is, an ultra-short baseline combined with an interferometer. The advantages and the three-dimensional positioning capability of multi-station TOA technology, an ultra-short baseline multi-station observation layout is proposed, abandoning the traditional "centroid method" technical route, by up-sampling the original signal, and introducing the ensemble empirical mode decomposition technology to increase the sampling. The signal is analyzed and optimized, and the cross-correlation signal matching technology based on the combination of the main window and the auxiliary window is used to realize the full matching and extraction of the pulse information in the VHF radiation signal, and the TOA technology is used for three-dimensional positioning. This technology can achieve ultra-high-resolution three-dimensional localization of the lightning discharge process. The time resolution of localization events can reach the order of nanoseconds, and the theoretical resolution of spatial errors can be improved to the order of decimeters.

references

Shao, X. M., Stanley, M., Regan, A., Harlin, J., Pongratz, M., & Stock, M. (2006). Total lightning observations with the new and improved Los Alamos sferic array (LASA). Journal of Atmospheric&Oceanic Technology, 23(23), 1273, doi: 10.1175/JTECH1908.1.

Stock, M.G., Akita, M., Krehbiel, P.R., Rison, W., Edens, H.E., Kawazaki, Z., & Stanley, M.A. (2014). Continuous broadband digital interferometry of lighting using a generalized cross-correlation algorithm. Journal of Geophysical Research: Atmospheres, 119, 3134–3165. https://doi.org/10.1002/2013JD020217

Stock, M.G., P.R.Krehbiel, J.Lapierre, T.Wu, M.A.Stanley and H.E.Edens (2017), Fast positive breakdown in lightning, Journal of Geophysical Research: Atmospheres, 122, 15, 8135-8152.

Thomas, & Ronald, J.. (2004). Accuracy of the lightning mapping array. Journal of Geophysical Research, 109(D14), D14207.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a three-dimensional positioning method of ultra-short baseline lightning based on broadband VHF radiation signal with high temporal and spatial resolution.

The ultra-short baseline lightning three-dimensional positioning method based on the broadband VHF radiation signal provided by the invention combines the ultra-short baseline positioning advantage of the interferometer and the three-dimensional positioning capability of the multi-station arrival time difference technology, and adopts the ultra-short baseline multi-station observation layout; The traditional "centroid method" technical route, by up-sampling the original signal; introducing the collective empirical mode decomposition technology to analyze and optimize the up-sampled signal; using the cross-correlation signal matching technology based on the combination of the main window and the auxiliary window; Full matching and extraction of pulse information in VHF radiation signals; 3D positioning using time difference of arrival technology. The invention can realize the ultra-high-resolution three-dimensional positioning of the lightning discharge process, the time resolution of locating the lightning discharge event can reach the order of nanoseconds, and the theoretical resolution of the spatial error can be improved to the order of decimeters. Specific steps are as follows.

(1) Multi-station synchronous observation layout of ultra-short baseline VHF antennas

In the present invention, a total of seven very high frequency (VHF) radiation detection antennas commonly used in lightning broadband interferometers (INTF) are arranged in a symmetrical hexagonal layout, that is, antenna A is used as the central station and coordinate origin, and another six are the same. The antennas are denoted as antennas B-G in turn, and are arranged around antenna A. The distance between two adjacent antennas in antennas B-G is L (called the baseline), and the distance between antennas B-G and antenna A is also L. In this way, 7 antennas form a highly symmetrical hexagon, as shown in Figure 1.

(2) Signal characteristic analysis

The DBM_EEMD (DBM_EEMD algorithm based on the ensemble empirical mode decomposition algorithm (EEMD), which is a double-sided bidirectional mirror (DBM) continuation of the signal to be decomposed) is introduced into the VHF radiation generated by lightning. signal analysis. Analyze the background noise signal and the main components of the noisy lightning VHF radiation signal.

(3) Upsampling of the signal

The original signal is pre-processed by high-rate up-sampling, that is, the polyphase filter is used to realize the resampling of the original signal by more than 10 times (which can be adjusted according to the purpose of the positioning research). The upsampling of the signal helps to improve the time accuracy of the signal, change the non-conductive characteristics of the original signal, improve the accuracy of the DBM_EEMD decomposition and reconstruction of the signal, and improve the accuracy of the cross-correlation of signals on different antennas.

(4) DBM_EEMD noise reduction of the signal

A band-pass filter is constructed using DBM_EEMD to retain the signal component of 40-80MHz in the detection signal. This can effectively improve the accuracy of waveform matching, and also help to obtain a more accurate pulse peak time, which is used to obtain the time difference of the same pulse signal between different antennas, thereby realizing the precise positioning of the radiation source.

(5) Cross-correlation matching of signals

Use generalized cross-correlation technology to match signals on different antennas to prepare for further pulse signal identification and matching. The signals to be matched at each station are composed of a main window (mainwindow) and two auxiliary windows (auxiliary windows). accuracy. Take a signal with 192 sampling points as an example: a main window with a length of 64 sampling points located in the middle of the signal, and an auxiliary window with a length of 64 sampling points located on both sides of the main window. Specifically, antenna A (chA) is used as the central station, 64 sampling points are intercepted each time as the main window, and an auxiliary window with a value of 0 is constructed on both sides of the main window, while the antenna B-G (chX, X =B...G) on the main window intercepts the real signal of the same segment as chA, the difference is that their auxiliary windows are also the real signal extended to both sides with a length of 64 sampling points. The length of the auxiliary window depends on the length of the longest baseline formed by the INTF antenna, and the present invention takes 64 as the length of the auxiliary window. In the algorithm, the main window should maintain a similar weight to the auxiliary window, so the length of the main window is also set to 64 sampling points.

(6) Pulse extraction under the microscale window

In the window after the preliminary matching in step 5, a micro-scale window with a width of 11ns (which can be adjusted according to the signal characteristics) is traversed, and the combination of the number of pulse peaks greater than or equal to 5 in the micro-window is found. The time to extract the pulse peak.

(7) Three-dimensional positioning of radiation source based on nonlinear least squares algorithm

The solution method including the initial solution uses the initial solution to bring the nonlinear least squares method to obtain the exact solution, which can accurately obtain the three-dimensional position and the time of occurrence of the lightning radiation signal.

The advantages of the present invention are as follows.

The invention adopts the radiation signal receiving antenna with the same parameters as the interferometer, and the time resolution of the detected lightning discharge event is very high, which can reach the nanosecond level. Combined with the signal processing and matching technology, the nanosecond level resolution of the lightning discharge process can be obtained. Rate of hyperfine 3D channel and developmental characterization.

The antenna layout of the ultra-short baseline proposed by the invention can accurately obtain the three-dimensional space position and time of the occurrence of the lightning VHF radiation signal by using the arrival time difference positioning technology.

The invention performs high-rate up-sampling on the original observation signal, and then uses DBM_EEMD technology to optimize and band-pass filter the up-sampled signal, which further improves the time resolution of the VHF radiation signal and the accuracy of cross-correlation matching of waveforms.

The invention abandons the centroid method commonly used in the previous lightning positioning technology, and can realize the precise positioning of pulse events one by one in the lightning VHF radiation signal.

Description of drawings

Figure 1 shows the antenna erection layout of the ultra-short baseline lightning three-dimensional positioning system.

Figure 2 shows (a) the background noise and its (b) spectrum of a length of 1700 sampling points, (c) is a partial magnification of the part marked by the horizontal red box in (b), (d) is the vertical red box in (b) Partial magnification of the box.

Figure 3 shows (a) a signal with a length of 1700 sampling points and its (b) spectrum, and (c) is a partial magnification of the part marked by the red box in (b).

FIG. 4 is a schematic diagram of signal upsampling.

Figure 5 shows the filtered part (Fig.5a) and the retained part (Fig.5c) of the background noise signal in Figure 2a after passing through the band-pass filter and their respective frequency spectra.

Figure 6 shows the filtered part (Fig.6a) and the retained part (Fig.6c) of the lightning VHF radiation signal in Figure 3a after passing through the bandpass filter, and their respective frequency spectra.

Figure 7 shows the generalized cross-correlation waveform matching method based on the combination of the main window and the auxiliary window: with chA as the central station, a waveform (64 sampling points) with a duration of 352 ns is extracted as the main window of chA, and on both sides of the main window Construct an auxiliary window with the same length but value 0 respectively; extract the same-segment signal on the antenna B-G (chX, X=B...G) to obtain the generalized cross-correlation coefficient with chA.

Figure 8 shows the matching of pulse peaks within a microscale window (11 ns) for VHF waveforms matched together by generalized cross-correlation.

Figure 9 is a schematic diagram of an antenna array detecting lightning events (Thomas et al., 2004).

Figure 10 shows the successful matching and positioning of the pulses within the 0.355 μs duration window. Among them, (a) is the pulse matching result after the signal passes through the 40-80M bandpass filter, a total of 21 groups of pulses have been successfully matched and positioned; (b) is the pulse matching result after the signal passes through the 20-80M bandpass filter. 14 sets of pulses were successfully matched and located.

Detailed ways

(1) Multi-station synchronous observation layout of ultra-short baseline VHF antennas

In the present invention, a very high frequency (VHF) radiation detection antenna commonly used in a lightning broadband interferometer (INTF) is erected according to the layout scheme shown in FIG. 1 . In this observation plan, antenna A is used as the central station and the origin of coordinates, and 6 identical antennas (numbered B-G) are arranged around antenna A. The distance between two adjacent antennas in B-G is L, and the distance between antennas B-G and antenna A is L. The distance is also L. In this way, 7 antennas form a highly symmetrical hexagon. In order to ensure the accuracy of signal matching and the feasibility of antenna erection, the baseline length L is controlled at about 100 meters (such as 90-110 meters, L=100m in the example), which is an ultra-short baseline observation system. It is far smaller than the existing three-dimensional lightning positioning system in the world. Since the detection antenna of the interferometer is used, the present invention still refers to the antenna array as an INTF array for the convenience of expression. The seven detection antennas of the INTF array have the same performance indicators, and use a broadband VHF (16-88MHz) flat panel receiving antenna (the antenna layout is shown in Figure 1). The time series waveform of each receiver is recorded synchronously at a sampling rate of 180MHz/s and a sampling accuracy of 16 bits. The initial time resolution is 5.5ns, which can be further upgraded to a sampling rate of 500MHz/s and a sampling accuracy of 16 bits. Brings the initial time resolution of the signal to 2ns.

In addition, there is a fast electric field change measuring instrument, called fast antenna (FA), which is networked together with INTF. It measures the change of the vertical electric field on the ground with an attenuation constant of 100μs. The FA antenna is sensitive in the range of 3kHz to>20MHz, and is similar to the INTF array. The antenna is synchronously recorded by the acquisition card with the same sampling rate and sampling accuracy. This observation scheme is very helpful for the accurate matching of the VHF radiation signal generated in the physical process of lightning discharge and the low-frequency electric field waveform (usually called 'sferic'), especially It is of great significance for analyzing the development details of microsecond-scale discharge events. This device is used to identify the physical process of lightning discharge and does not participate in lightning localization.

(2) Signal characteristic analysis

Similar to what Fan et al. (2018, 2020) did in the improvement of the location capability of the low-frequency lightning detection system, the improvement of the location capability of the lightning location system always revolves around the accuracy of the characteristics of the detection system and the characteristics of the detected electric field signals. based on analysis. According to the characteristics of lightning electric field signals, the empirical mode decomposition (EMD) method (together with Hilbert transform is called Hilbert-Huang Transform, HHT) method is introduced into the analysis of lightning electric field signals (low frequency/very low frequency signals) (Fan et al. al., 2018), and then proposed the DBM_EEMD algorithm based on the ensemble empirical mode decomposition algorithm (EEMD), that is, the double-sided bidirectional mirror (DBM) extension of the signal to be decomposed to optimize the signal characteristics and improve the The noise reduction performance of the algorithm can greatly improve the accuracy of weak pulse signal extraction (Fan et al., 2020).

Here, the present invention introduces DBM_EEMD into the analysis of VHF radiation signals generated by lightning. As shown in Figures 2 and 3, the VHF waveform detected by 2-segment INTF is given as an example of signal characteristic analysis using HHT based on DBM_EEMD as the kernel. The first thing to understand is the background noise acquired by the detection system. Figure 2 shows a background noise (Figure 2a) and its spectrum (Figure 2b) with a length of 1700 sampling points (9.44μs). From the spectral band analysis of the background noise shown in Figure 2b, it can be seen that the sources of the background noise are the following aspects: 0-line drift of the signal (noise signal with ultra-low frequency); white noise in the acquisition frequency band (Figure 2c , possibly superimposed with weak noise from other sources); broadcast signals with strong power in multiple channels around 89MHz (Fig. 2d). These three types of noise signals will have a serious impact on the time difference based on generalized cross-correlation technique for positioning.

As shown in Figure 3a, it is a VHF radiation signal with the same length of 1700 sampling points (9.44μs), the overall radiation signal is weak (the amplitude is less than ±1500, compared with the maximum amplitude of the detection signal is ±2 ¹⁵ ) . From the spectrum analysis in Figure 3b, it can be seen that two strong noise sources in the background noise: 0-line drift and broadcast signal noise exist stably, and the background noise has not changed much in the analysis and comparison of a large number of detection signals. . Figure 3c shows the spectral distribution characteristics of the VHF radiation signal in the acquisition frequency band, which includes a weak white noise signal covering the entire frequency band (there may be other sources of noise with weak amplitude). In addition, comparing Fig. 3c, it can be seen that there are relatively low frequency signals and noises with relatively large amplitudes below 40 MHz (ie, relatively low frequency bands within the detection frequency band). In the process of pulse signal matching and pulse peak time difference calculation, the relative low frequency fluctuations in the detection frequency band have great interference to the accurate extraction of pulse signal information.

(3) Upsampling of the signal

Since the INTF antenna works in the VHF frequency band, the sampling rate of the acquisition card used is only 180M, and the ratio of the sampling rate to the cutoff frequency is barely greater than 2. Even if the acquisition card with a higher sampling rate is adopted in the future, this ratio will be reduced in a short time. It is difficult to reach more than 10, so the detected radiation signal is shown as the black scatter in Figure 4, which is a broken line composed of a scatter every 5.5 nanoseconds. This kind of broken line waveform cannot be directly optimized and filtered by DBM_EEMD because it is not steerable everywhere; this kind of broken line waveform has very limited measurement values in a narrow window due to its dispersion, and the cross-correlation method is used to calculate the correlation coefficient of the window waveform on different antennas. It is difficult to achieve the expected signal matching effect; in addition, although the time resolution of the waveform has reached 5.5 nanoseconds, this time resolution is still insufficient in order to obtain 3D positioning results with a spatial resolution of decimeters or even higher.

In order to solve the above problems, the present invention proposes a preprocessing method for high-rate up-sampling on the original signal, that is, using a polyphase filter to realize the resampling of the original signal by more than 10 times (which can be adjusted according to the purpose of positioning research) . For the convenience of showing the effect, Figure 4 shows an example of 10-fold sampling of the analog signal, and the algorithm implementation in Figure 5 and later uses the signal after 50-fold sampling of the real lightning VHF radiation signal.

(4) DBM_EEMD noise reduction of the signal

Through the analysis of the above signal characteristics, after mastering the main characteristics of the detection signal, we use DBM_EEMD (Fanet al., 2020) to construct a band-pass filter, which only retains the signal component of 40-80MHz in the detection signal, which can effectively improve the waveform The matching accuracy also helps to obtain a more accurate pulse peak time, which is used to obtain the time difference of the same pulse signal between different antennas, thereby realizing the precise positioning of the radiation source.

Fig. 5 shows the filtered part (Fig. 5a) and the retained portion (Fig. 5c) of the background noise signal in Fig. 2a after passing through the band-pass filter and their respective frequency spectra. Figure 5a includes the 0-line drift in the background noise, the broadcast signal and the white noise components below 40MHz. From the simple shape comparison with the original waveform in Figure 2a, it can be seen that the band-pass filter constructed with DBM_EEMD can effectively remove the noise. most of the quantity. The absolute component of the 40-80MHz background noise after the band pass is already very small (as shown in Figure 5c), and the range of the background noise (the difference between the maximum value and the minimum value) is less than 250 (the range of the collected signal is 2 ¹⁶ ).

For the noisy VHF detection signal, after passing through the band-pass filter, although part of the real signal component will be lost (as shown in Figure 6a), this abandonment of part of the signal component is very important for the accurate localization of lightning discharge events. Valuable: only a very small amount of noise signal components remain in the signal, which can minimize the impact of noise signals; the signal components after bandpass filtering are relatively simple and have a narrow bandwidth, which can effectively improve the accuracy of signal matching; Helps to significantly improve the richness and accuracy of pulse information extraction from waveforms.

(5) Cross-correlation matching of signals

After completing the analysis of the original signal characteristics and using DBM_EEMD to construct a band-pass filter to perform quality control and signal reconstruction on the original signal, this paper uses the generalized cross-correlation (Stock et al., 2014) technique to match the signals on different antennas, in order to further The pulse signal identification and matching are prepared.

Different from the window matching method of Stock et al. (2014), the technical route proposed and adopted in the present invention introduces the concept of auxiliary window. As shown in Figure 7, a signal of 192 samples is divided into 3 parts: a main window (mainwindow) of length 64 samples located in the middle of the signal, and a length of 64 samples located on both sides of the main window Auxiliary window of the point. Specifically, antenna A (chA) is used as the central station, 64 sampling points are intercepted each time as the main window, and an auxiliary window with a value of 0 is constructed on both sides of the main window, while the antenna B-G (chX, X =B...G) on the main window intercepts the real signal of the same segment as chA, the difference is that their auxiliary windows are also the real signal extended to both sides with a length of 64 sampling points. The length of the auxiliary window depends on the length of the longest baseline formed by the INTF antenna. Taking the layout shown in Figure 1 as an example, the baseline length L=100m. When the radiated signal generated by lightning is received by the INTF antenna, the generated time difference will not be greater than The time required for the speed of light to propagate 100m, that is, 330ns, corresponds to a deviation of about 60 sampling points at a sampling rate of 180M (time resolution 5.5ns). For the fault tolerance and generality of the algorithm, the present invention uses 64 as the length of the auxiliary window . In the algorithm, the main window should maintain a similar weight to the auxiliary window, so the length of the main window is also set to 64 sampling points.

This setting of the main window and the auxiliary window has many advantages. First, the signal does not repeatedly participate in positioning. This is because, on the time axis of the central station (chA), the signal is traversed with 64 sampling points (352ns), and in the signals of other antennas (the main window and the 2-segment auxiliary window), the generalized cross-correlation method is used to find a segment with The signals in the main window of chA are completely consistent for the subsequent pulse waveform matching and positioning calculation. The signals on chA will not be reused, so there will not be repeated positioning information; on the other hand, scholars usually expect that by further Reduce the size of the window to obtain more information about the radiation source, but the baseline length of the INTF usually limits the maximum time difference between different antennas for the same discharge event, which also limits the window matching (Stock et al., 2014) algorithm. The minimum window width that can be used, and the combination of the main window and the auxiliary window proposed in this paper actually breaks through the above restrictions; more importantly, the setting of only the main window and no auxiliary window on chA can Significantly improves the accuracy of window matching for generalized cross-correlation, and further improves the accuracy of matching and information extraction for pulse signals on a smaller time scale in the next step.

(6) Pulse extraction under the microscale window

As shown in Fig. 7, the maximum correlation coefficient between chX (X=B...G) and chA appears after shifting chX to Δt _AX respectively, and window pairing is realized (the result is shown in Fig. 8). In the previous interference This time difference Δt _AX is used to obtain the direction or location information of the "radiation source" in the positioning scheme of the instrument positioning technology Stock et al. However, in the window-based positioning technology, the correlation of the time series in the window on the two antennas mainly depends on one or even several strong pulse signals, and due to the influence of other signals in the window, the generalized cross-correlation between the antennas is used to calculate The resulting time delay will usually also deviate from the peak moment of the strongest pulse within the window.

In this way, in order to accurately pair the pulse signals on different antennas in the main window, more steps and constraints are needed to achieve:

(a) First find out the moment of all pulse peaks whose peaks (local maxima) are greater than the threshold (as shown by the horizontal dashed line in Fig. 8 ) in the main window of the central station chA (as shown in Fig. 8 on chA Take the strongest pulse as an example, its peak time is T _p );

(b) Taking T _p as the center, construct a microscale window with a width of 11ns and cover chA, chX (X=B...G) at the same time, and detect whether there is a pulse peak in the window range on chX (X=B...G) Within the 11ns window, when there are pulses detected on the signals of at least 5 antennas at the same time, continue to the next step;

(c) Judging the similarity of all the pulses preliminarily paired in step b, that is, _taking the respective peak times (T _pA , T _pB , . Waveform, calculate the correlation coefficient between pulse waveforms, only when the correlation coefficient between them is greater than 0.8, it is considered that all the above pulse signals come from the same "discharge"event;

(d) The peak times of the successfully paired pulses are respectively T _pA , T _pB , . . . , T _pG . Taking chA and chB as examples, the time difference between the arrival of the same pulse signal to the antennas of A and B is Δt _AB =T _pA -T _pB , the antenna array composed of n antennas has

The group time difference τ _ij , where n is the number of stations, m=2, when the number of antennas is greater than or equal to 5, the three-dimensional positioning result of the pulse radiation source can be obtained by the time difference of arrival technique.

(7) Three-dimensional positioning of radiation source based on nonlinear least squares algorithm

In the process of locating the lightning discharge event, it is necessary to calculate the location (x, y, z) and time (t) of the lightning discharge event according to the time difference between the lightning VHF radiation signal reaching each station, a total of 4 unknown parameters. When solving by the nonlinear least squares method, the equation group is required to be super-solved (the number of equations is greater than the number of unknowns, that is, the number of stations is greater than the number of unknowns), so when there are 5 or more stations, the same one is successfully matched. When a lightning discharge event occurs, the time difference between the pulse peak arriving at the station can be calculated, and the time difference of arrival (TOA) method can be used to calculate the occurrence position and time of the lightning discharge event to achieve three-dimensional positioning.

As shown in Figure 9, at time t ₀ , when the lightning discharge event occurs at (x, y, z), the lightning radiation signal propagates at the speed of light c, then, the measurement at (x _i , y _i , z _i ) The time when station i receives this event signal is:

For a nonlinear equation such as formula (1), it is very difficult to directly solve it by means of simultaneous equations, and it needs to be converted into a linear equation system and then solved.

First, the formula (1) is converted into the following form:

make:

r ² ≡x ² +y ² +z ² (4)

Bringing the above two equations into (2), it can be transformed into the following form:

After further merging similar items, we can get:

Similarly, the time equation for the arrival of the lightning discharge signal to the jth station can be given. After subtracting the equations of station i and station j, we can get:

make:

t _ij ≡t _i -t _j x _ij ≡x _i -x _j y _ij ≡y _i -y _j z _ij ≡z _i -z _j (8)

Transform the form of equation (7) into:

Further define the operator:

Then there are:

xx _ij +yy _ij +zz _ij -c ² tt _ij ≡q _ij (11)

At this time, equation (11) is a linear equation system about (x, y, z, t), which defines multiple planes in the four-dimensional space (x, y, z, t), and the solutions of the equation system are these super The intersection of planes. For such a system of linear equations, the analytical solution for (x, y, z, t) is:

It should be noted here that in actual observations, due to the short baseline of the station network, the coefficient of the height item z is generally small, and the coefficients of the x and y items relative to the horizontal position usually have a large magnitude difference, and the time item The coefficient of t includes the product of the speed of light, which is usually a value of a large magnitude, so that the height value z obtained by the method of solving the hyperplane equation system usually has a large error. Therefore, the solution given by the method of solving the hyperplane equation system can only be used as the initial solution of some optimization methods for solving the nonlinear equation system.

Equation (12) will be solved, the initial solution will be obtained, and it will be used as the initial estimated value of nonlinear least squares iterative calculation, which is conducive to obtaining a more reasonable numerical analytical solution (x, y, z, t), and effectively improves the Convergence rate of the iterative process. Similar to some similar lightning location systems abroad, this system also uses the Levenberg-Marquardt algorithm to iteratively solve the numerical solution of the equation system. For the optimal solution obtained by nonlinear least squares iteration, the quality of the positioning result is measured by the size of χ ² , where χ ² is defined as:

Among them, N represents the number of stations participating in the positioning, that is, there are N stations that successfully match the same lightning discharge event,

Represents the error level of pulse peak time extraction. The initial error of the system time measurement of the present invention is 5.5ns. After up-sampling and band-pass filtering, the time error level is significantly reduced. For the convenience of calculation and evaluation, it is set here. is 1ns.

represents the time when the i-th station actually received the lightning discharge event,

is the time when the lightning VHF radiation signal calculated by the least-squares iteration is transmitted from the occurrence position (x ^fit , y ^fit , z ^fit ) to the i-th station.

After the above steps, according to the data (1) obtained by the ultra-short baseline multi-station VHF radiation signal acquisition system proposed by the present invention, the characteristics of the detection signal are analyzed in detail (2), and the original signal is upsampled by using the DBM_EEMD method (3). Carry out quality control (4); combine the main window with the auxiliary window (5), and use the generalized cross-correlation method to achieve waveform matching of different antenna signals (6); under the micro-scale window (11ns) through the threshold constraint on the pulse signal , similarity constraints, etc. to achieve accurate pairing of pulse signals and extraction of time difference of arrival (7); finally, the nonlinear least squares method is used to obtain the spatial two-dimensional coordinates of the matched pulse radiation source (8), which can be compared to window-based interference. The two-dimensional localization method (Stock et al., 2014) and the long-baseline lightning localization system LMA (Thomas and Ronald, 2004) have more abundant lightning discharge information. Taking the main window waveform of chA with a length of 64 sampling points (0.355 μs) as shown in Figure 7 as an example, the window-based positioning method can only obtain 2 radiation sources when 32 sampling points are used as the step length. As for the positioning result, when the step length is 64 sampling points, only one radiation source positioning result can be obtained. However, using the localization method based on full pulse matching proposed in this paper, the richness of localization results is greatly improved, especially the band-pass filter constructed by the DBM_EEMD method introduced in this paper plays an important role in the extraction of pulse signals. As shown in Figure 10a, when the signal is called a relatively narrowband signal after 40-80M band-pass filtering, the pulse characteristics in the signal are highlighted, and a total of 21 groups of pulses that meet the screening threshold are successfully matched and located within the 0.355μs duration window; When the signal passes through a 20-80M bandpass filter, the upper limit frequency of the signal is 4 times the lower limit frequency. The superposition of the relatively low frequency signal and the relatively high frequency signal makes the characteristics of the VHF radiation signal more complex. There are only 14 groups of pulses. It meets the screening threshold and is successfully matched and located. This is because when signals of different frequency bands arrive at different antennas, due to the difference in arrival time, the superimposed signals may come from different radiation sources or the same radiation source but the phases of the superposition are different. Generate different signal amplification or cancellation effects, making the signal characteristics more complex. The noise signal outside the signal acquisition frequency band (the signal amplitude is much higher than the white noise signal) has a serious impact on the waveform matching and the extraction of the peak time of the pulse signal. Without the quality control of the original signal, the example signal in Figure 10 only There are 2 pulses that are matched and positioned.

Claims (6)

1. A three-dimensional positioning method of ultra-short baseline lightning based on broadband VHF radiation signal is characterized in that, combining the advantages of ultra-short baseline positioning of interferometers and the three-dimensional positioning capability of multi-station time difference of arrival technology, an ultra-short baseline multi-station observation layout is adopted. ; by up-sampling the original signal; introducing the ensemble empirical mode decomposition technology to analyze and optimize the up-sampling signal; adopting the cross-correlation signal matching technology based on the combination of the main window and the auxiliary window to realize the pulse detection in the VHF radiation signal. Full matching and extraction of information; three-dimensional positioning using time difference of arrival technology; specific steps are:

   (1) Multi-station synchronous observation layout of ultra-short baseline VHF antennas

   A total of seven VHF radiation detection antennas commonly used in lightning broadband interferometers (INTF) are arranged in a symmetrical hexagonal layout, that is, antenna A is used as the central station and coordinate origin, and the other 6 same antennas are used. Denoted as antennas B-G in turn, arranged around antenna A, the distance between two adjacent antennas in antennas B-G is L, and the distance between antennas B-G and antenna A is also L; in this way, 7 antennas form a highly symmetrical hexagon; Call L the baseline;

   (2) Signal characteristic analysis

   The DBM_EEMD algorithm is used to analyze the VHF radiation signal generated by lightning, and the main components of the background noise signal and the noise-containing lightning VHF radiation signal are obtained; here, the DBM_EEMD algorithm refers to the ensemble empirical mode decomposition algorithm (EEMD), And the signal to be decomposed is extended by two-way double-sided mirror (DBM);

   (3) Upsampling of the signal

   Preprocessing the original signal with high-rate upsampling, that is, using a polyphase filter to resample the original signal by more than 10 times, to improve the time accuracy of the signal, change the non-conductive characteristics of the original signal, and improve the use of DBM_EEMD for the signal. The accuracy of decomposition and reconstruction improves the accuracy of cross-correlation of signals on different antennas;

   (4) DBM_EEMD noise reduction of the signal

   DBM_EEMD is used to construct a band-pass filter, which retains the signal component of 40-80MHz in the detection signal, so as to effectively improve the accuracy of waveform matching and obtain a more accurate pulse peak time, which is used to obtain the same pulse signal between different antennas. time difference, so as to achieve precise positioning of the radiation source;

   (5) Cross-correlation matching of signals

   The generalized cross-correlation technology is used to match the signals on different antennas to prepare for further pulse signal identification and matching; the signals to be matched at each station are composed of a main window and two auxiliary windows. Auxiliary windows are assigned as 0 to improve the accuracy of window signal matching;

   (6) Pulse extraction under the microscale window

   In the window after preliminary matching in step (5), a micro-scale window with a width of 11ns is used to traverse, and the combination of the number of pulse peaks greater than or equal to 5 in the micro-window is found, so as to accurately extract the time of the pulse peak;

   (7) Three-dimensional positioning of radiation source based on nonlinear least squares algorithm

   Including the solution of the initial solution, the initial solution is used to bring the nonlinear least squares method to obtain an accurate solution, so as to accurately obtain the three-dimensional position and time of occurrence of the lightning radiation signal.
2. The ultra-short baseline lightning three-dimensional positioning method according to claim 1, wherein, in step (1), the length of the baseline L is controlled at about 100 meters; the performance indicators of the seven detection antennas of the INTF array are the same, and the broadband High-frequency flat panel receiving antenna; the time series waveform of each receiver is synchronously recorded at a sampling rate of 180MHz/s to 500MHz/s and a sampling accuracy of 16 bits, with an initial time resolution of 5.5ns to 2ns.
3. The ultra-short baseline lightning three-dimensional positioning method according to claim 2, characterized in that, co-networked observation with INTF array antenna also includes a fast electric field change measuring instrument, called fast antenna (FA), and the fast antenna (FA) takes 100 μs The attenuation constant measures the change of the vertical electric field on the ground. The FA antenna is sensitive in the range of 3kHz to >20MHz. It is recorded by the acquisition card synchronously with the same sampling rate and sampling accuracy as the INTF array antenna, which is convenient for VHF radiation generated in the physical process of lightning discharge. Precise matching of signals to low frequency electric field waveforms.
4. The ultra-short baseline lightning three-dimensional positioning method according to claim 3, is characterized in that, in step (5), the to-be-matched signal of each station is formed by the main window and two auxiliary windows, specifically, a section of 192 The signal of each sampling point is divided into 3 parts: the main window with a length of 64 sampling points located in the middle of the signal, and the auxiliary windows with a length of 64 sampling points located on both sides of the main window; that is, with antenna A as the central station, Taking 64 sampling points each time as the main window, and constructing an auxiliary window with a value of 0 on both sides of the main window, while the main window on the antenna B-G intercepts the real signal of the same period as the antenna A, the difference is Their auxiliary windows are also true signals extended to both sides by a length of 64 samples; the length of the auxiliary windows depends on the length of the longest baseline formed by the INTF antenna.
5. The ultra-short baseline lightning three-dimensional positioning method according to claim 4, wherein, in step (6), in order to accurately pair the pulse signals on different antennas in the main window, the specific process of extracting the time of the pulse peak is as follows: :

   (a) First, find out all the peaks in the main window of the central station antenna A, that is, the moment of the pulse peak whose local maximum value is greater than the threshold, and denote the peak moment as T _p ;

   (b) Taking T _p as the center, construct a micro-scale window with a width of 11ns covering antenna A, antenna B, ..., antenna G at the same time, and detect whether there is a pulse peak appearing in the window range on antenna B--antenna G, In the 11ns window, when there are pulses detected on the signals of at least 5 antennas at the same time, continue to the next step;

   (c) Judging the similarity of all the pulses preliminarily paired in step b, that is, _taking the respective peak times T _pA , T _pB , . Calculate the correlation coefficient between the pulse waveforms. Only when the correlation coefficient between them is greater than 0.8, can all the above pulse signals come from the same "discharge"event;

   (d) The peak times of the successfully paired pulses are respectively T _pA , T _pB , . . . , T _pG . Taking antenna A and antenna B as examples, the time difference between the arrival of the same pulse signal to the antennas of A and B is Δt _AB =T _pA − T _pB , the antenna array composed of n antennas has

   

   The group time difference τ _ij , where n is the number of stations, m=2, when the number of antennas is greater than or equal to 5, the three-dimensional positioning result of the pulse radiation source can be obtained by the time difference of arrival technique.
6. The ultra-short baseline lightning three-dimensional positioning method according to claim 5, is characterized in that, in step (7), the concrete flow of the radiation source three-dimensional positioning based on nonlinear least squares algorithm is:

   In the process of locating the lightning discharge event, it is necessary to calculate the location (x, y, z) and time (t) of the lightning discharge event according to the time difference between the lightning VHF radiation signal reaching each station, a total of 4 unknown parameters; When solving the nonlinear least squares method, the equation group is required to be over-solved. Therefore, when 5 or more stations are successfully matched to the same lightning discharge event, the time difference between the pulse peak arriving at the station can be calculated, and the arrival time difference method can be used. (TOA) Calculate the location and timing of lightning discharge events to achieve three-dimensional positioning;

   Assuming that at time t ₀ , when the lightning discharge event occurs at (x, y, z), the lightning radiation signal propagates at the speed of light c, then the station i at (x _i , y _i , z _i ) receives this The timing of the event signal is:

   

   Formula (1) is a nonlinear equation, which is converted into a linear equation system, and then solved;

   First, the formula (1) is converted into the following form:

   

   make:

   

   r ² ≡x ² +y ² +z ² (4)

   The above two equations are brought into (2) and converted into the following form:

   

   After further merging similar items, we get:

   

   Similarly, the time equation for the arrival of the lightning discharge signal to the jth station can be given, and the equation of station i and station j can be subtracted to obtain:

   

   make:

   t _ij ≡t _i -t _j x _ij ≡x _i -x _j y _ij ≡y _i -y _j z _ij ≡z _i -z _j (8)

   Transform the form of equation (7) into:

   

   Further define the operator:

   

   Then there are:

   xx _ij +yy _ij +zz _ij -c ² tt _ij ≡q _ij (11)

   At this time, equation (11) is a linear equation system about (x, y, z, t), which defines multiple planes in the four-dimensional space (x, y, z, t), and the solutions of the equation system are these super The intersection of the planes; for such a system of linear equations, the analytical solution for (x, y, z, t) is:

   

   In order to avoid large errors, the solution given by the method of solving the hyperplane equation system can only be used as the initial solution of some optimization methods for solving the nonlinear equation system; namely:

   Equation (12) will be solved, the initial solution will be obtained, and it will be used as the initial estimated value of nonlinear least squares iterative calculation, which is conducive to obtaining a more reasonable numerical analytical solution (x, y, z, t), and effectively improves the The convergence speed of the iterative process; for the optimal solution obtained by nonlinear least squares iteration, the quality of the positioning result is measured by the size of χ ² , where χ ² is defined as:

   

   Among them, N represents the number of stations participating in the positioning, that is, there are N stations that successfully match the same lightning discharge event,

   

   Indicates the error level of pulse peak time extraction. Since the initial error of time measurement is 5.5ns-2ns, after up-sampling and band-pass filtering, the time error level is significantly reduced. For the convenience of calculation and evaluation, it is set to 1ns here. ;

   

   represents the time when the i-th station actually received the lightning discharge event,

   

   is the time when the lightning VHF radiation signal calculated by the least-squares iteration is transmitted from the occurrence position (x ^fit , y ^fit , z ^fit ) to the i-th station.

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