An Improved Meteor Echo Recognition Algorithm for SuperDARN HF Radar

Abstract

The SuperDARN HF radars can be used for meteor observation and inversion of mid-upper atmosphere neutral wind using observed meteor echo Doppler velocities. Aiming at the problem that the extraction of meteor echo based on echo power, Doppler velocity and spectral width is rough and contains ionospheric echo, this paper optimizes the extraction algorithm of meteor echo. Based on the AgileDARN HF radar’s digital characteristics, the observation method of meteor echo was improved, and we designed a meteor observation mode without changing the hardware system: using a meteor observation with a 7.5 km range resolution and a 2 s integration time, we extracted the Doppler characteristics of different echo types at meteor echo ranges; according to these features, the extraction algorithm of meteor echo was optimized. By analyzing the measured data, the characteristics of diurnal variation, power distribution, Doppler velocity distribution and spectral width distribution of meteor echo extracted by the optimization algorithm were obtained. The meteor echo characteristics obtained by the improved algorithm are more consistent with the theoretical analysis; thus, the improved algorithm is better than the SuperDARN high frequency radar meteor echo extraction algorithm and has good performance. The meteor echo extraction algorithm presented in this paper can extract the meteor echo more accurately, so that the atmospheric neutral wind can be retrieved more accurately. At the same time, the proposed algorithm is not only applicable to AgileDARN HF radar meteor observation mode data, but also to AgileDARN and SuperDARN normal mode data, which is beneficial to expand the data application of SuperDARN radars.

1. Introduction

A large number of meteoroids enter the Earth’s atmosphere every day [1], and the meteoroids interact with the atmosphere to form ionized trails, called meteor trails; radar emitted signals encounter the meteor trails and produce reflected signals, which are received by the radar to form meteor echoes. Driven by the atmospheric neutral wind, the meteor trail drifts and generates Doppler velocity. Therefore, the meteor trail can be used for the inversion of the atmospheric neutral wind [2]. Very high frequency (VHF) meteor radar is a type of special equipment used for meteor observation, which can invert the neutral wind in the middle and upper atmosphere through the observed meteor echoes [3]. However, VHF radar can only obtain local neutral wind characteristics [4]. Therefore, many different remote sensing devices, such as ionosondes and satellites, have also carried out meteor observation studies in order to obtain more reliable neutral wind characteristics over a wider area [5].

Hall et al. first used the globally distributed Super Dual Auroral Radar Network (SuperDARN) high frequency radars to observe and study meteor echoes, and Hall first proposed using echo power, Doppler velocity and spectral width as the parameters for identifying meteor echoes [2]. Since then, many scholars have carried out research on meteor echo extraction methods based on the SuperDARN HF radars [6,7,8,9]. In summary, three methods for obtaining meteor echo are formed according to previous studies: the first is to detect meteor echoes based on data from the existing SuperDARN dataset, according to the statistical characteristics of meteors that are different from other echoes [2,6,9]; the second approach is to develop new code based on SuperDARN’s existing hardware system to detect meteor echoes using the method of raw time series analysis [10]; a third method is to adjust the hardware system of the SuperDARN radar to detect meteor echoes through the meteor echo profile [11]. The first method is suitable for all SuperDARN radars, but with a range resolution of 45 km, the resolution is too low, which leads to the problem that the neutral wind speed of a single range unit will usually have a large change relative to the altitude during the meteor’s fading [11]; using the current crude range resolution provided by SuperDARN will not make it possible to obtain neutral wind information during meteor extinction. The second method requires the modification of the SuperDARN radar system, its resolution is also low, and it requires the analysis of the raw time series of the received signal; the data processing process is more complex, and the operation is also more complex. The third method needs to change the hardware system of the SuperDARN radar, oversample the received signal and detect the profile of the meteor echo; this method needs to change the hardware system, and it is difficult to switch between the normal observation mode and the meteor observation mode, thus making the operation complicated.

In view of the problems of the above methods, based on the AgileDARN high-frequency radar system, the meteor observation method was designed on the premise of not changing the hardware system. This method improves the range resolution and time resolution, and obtains the meteor echo more accurately. At the same time, it is easy to switch between the normal observation mode and the meteor observation mode, and the operation is simple. Based on the observation data of the meteor observation mode, this paper improves the extraction algorithm of meteor echo. First, echo power greater than 10 dB is selected; second, the autocorrelation function is obtained through the autocorrelation calculation of the echo signal, and the phase of the autocorrelation function is fitted by the least squares fitting—if the root mean square error after fitting is less than the threshold value, it is considered as an effective echo, so as to further eliminate the influence of external interference; then, the phase change of effective echo is investigated, and the effective echo whose phase change is greater than the set threshold of phase change is considered as the potential meteor echo; finally, potential meteor echoes are screened according to the threshold of Doppler velocity and spectrum width as the final meteor echoes. The proposed algorithm improves the time resolution and range resolution of meteor observation, reduces the impact of external noise on meteor echo detection and improves the accuracy of meteor target detection. Data analysis shows that the proposed algorithm is superior to the traditional meteor echo detection algorithm and has excellent performance.

The rest of the paper is organized as follows. Section 2 introduces the calculation methods of meteor echo Doppler velocity, spectral width and other related parameters. Section 3 describes the observation method of meteor echo. Section 4 presents the improved meteor echo extraction algorithm. Section 5 presents the data analysis results. In Section 6 we conclude the paper.

2. Meteor Echo Parameter Calculation Method

Most meteor echoes detected by SuperDARN are undense meteor echoes [2]. Due to the spread of the meteor trail, the echo power P attenuates exponentially [12]:

$$P\left(t\right)=P_0{e}^{-\frac{t}{\tau }}$$

(1)

where $P\left(t\right)$ represents the meteor trail power at time t, $P_0$ is the initial power of the meteor trail and τ is the attenuation coefficient. The attenuation coefficient can be obtained by the meteor diffusion coefficient, i.e.,

$$\tau =\frac{{\lambda }^2}{32{\pi }^{2}D}$$

(2)

In the formula: $D$ is the diffusion coefficient, the unit is m/s, and $\lambda$ is the working wavelength of the radar.

The AgileDARN radar periodically transmits sequences of pulses that are separated unevenly in time by integer multipliers of an elementary lag time [13], and the echo signal processing follows the data processing method of SuperDARN [14]. First, the autocorrelation calculation is performed on the sampled signal, and then the Doppler velocity and spectral width of the detected target are analyzed by the autocorrelation function. The calculation method of Doppler velocity and spectral width is explained below.

Assuming that the phase after autocorrelation is Ψ and the phase delay time is t, the Doppler velocity is:

$$v_d=\frac{\lambda }{4\pi }\frac{\partial \mathsf{\Psi }}{\partial t}$$

(3)

The calculation of the spectral width is related to the profile of the echo power the Formula (1). Generally, it is assumed that the spectraum of an underdense meteor echo is Lorentzian [9], and the slope of the fit is obtained by taking the logarithm of the echo power, and then performing the least square fitting ς, the spectrum width is:

$$\omega =\frac{\lambda }{\left(4\pi \right)\varsigma }$$

(4)

3. Observation Method

AgileDARN is a digital phased array radar, composed of a 16-element main antenna array and a 4-element sub-antenna array. The main antenna array sends and receives signals, while the sub-antenna array only receives signals. The main antenna array and the sub-antenna array implement an interferometric measurements elevation angle [15].

In the normal observation mode, the working parameters of AgileDARN are as follows [16]: the working frequency is the dot frequency within 8–20 MHz (generally 10.4 MHz), the transmitting pulse width is 300 μs (the corresponding range resolution is 45 km), the initial sampling time of AD is 1200 μs (corresponding to the initial sampling distance of 180 km), the maximum range unit is 100 (that is, the maximum detection range is 4500 km), 3.25° is taken as the stepping interval to scan 24 beams (the field of view range is (0°,78°), the duration of an observation period is 1 min, and the parameters in the normal observation mode are shown in

Table 1. AgileDARN working parameters in normal observation mode.

Parameters	Value
Frequency band	$8~20 \mathrm{MHz} \left(\mathrm{default} \mathrm{value}:10.4 \mathrm{MHz}\right)$
Pulse width	$300 \mathsf{\mu }\mathrm{s}$
AD start sampling time	$1200 \mathsf{\mu }\mathrm{s}$
Number of gates	$\ge 75 \left(\mathrm{default} \mathrm{value}:100\right)$
Field of overview	$78°$
Number of beams	$24$
Beam width	$3.25°$
Temporal resolution	$\le 2 \min \left(\mathrm{default} \mathrm{value}:1 \min \right)$
Integration time	$2.5 \mathrm{s}$
Range resolution	$45 \mathrm{km}$
AD sampling range	$180~4500 \mathrm{km}$

.

When the meteoroid enters the Earth’s atmosphere, the ablation produces an approximately cylindrical ionized meteor trail; the diameter of the cylindrical trail is about 0.5~4.5 m, the length of the trail is about 10~25 km (very few meteors have a length of 30~50 m) and the duration is about 0.1 to 10 s [17,18,19]. In conclusion, in the normal observation mode, the range resolution and integration time are both low, and it is difficult to obtain more meteor targets with short duration in the normal mode, which reduces the accuracy of wind field inversion. Therefore, the operating mode of AgileDARN radar needs to be adjusted to adapt to meteor target observation.

The AgileDARN high-frequency radar digital system is designed based on FPGA. Different observation modes can be switched by configuring different parameters in the control software and delivering them to the FPGA register. Therefore, different parameters can be configured to switch between different observation modes of AgileDARN radar without changing the hardware system [15]. The observation parameters of meteor targets are designed in this paper based on the flexible and adjustable parameters of the AgileDARN high frequency radar. According to Ref. [4], working at lower frequency bands, the SuperDARN high-frequency radar can detect more meteor echoes, and at the low frequency band, it can detect about 10 meteor echoes at most within 2 s of integration. Therefore, we set the operating frequency at 10.4 MHz, the range resolution at 7.5 km, and the integration time at 2 s. The parameters of the AgileDARN HF radar for meteor detection are shown in

Table 2. Working parameters of AgileDARN for observing meteor targets.

Parameters	Value
Frequency band	$10.4 \mathrm{MHz}$
Pulse width	$50 \mathsf{\mu }\mathrm{s}$
AD start sampling time	$500 \mathsf{\mu }\mathrm{s}$
Number of gates	$100$
Field of overview	$78°$
Number of beams	$24$
Beam width	$3.25°$
Temporal resolution	$1 \min$
Integration time	$2 \mathrm{s}$
Range resolution	$7.5 \mathrm{km}$
AD sampling range	$75~450 \mathrm{km}$

.

4. Meteor Echo Extraction Algorithm

Accurate extraction of meteor echo from radar observation data is the basis of neutral wind inversion. Hall et al. first proposed the meteor echo extraction algorithm [2]. After that, through the research of different scholars, it can be concluded that meteor echo has the following characteristics [4,8,9]: first, it is located at the height of the ionosphere D and E layers; second, meteor echoes from SuperDARN observations are characterized by smaller LOS Doppler velocity and smaller spectral widths. The characteristics of meteor echoes of the SuperDARN HF radar are shown in

Table 3. The characteristic values of meteor echo as extracted by the traditional algorithm.

Meteor Extraction Parameters	Nominal Values
Power (dB)	$\ge 3$
LOS Doppler velocity (m/s)	$\pm 50$
Spectral width (m/s)	$>1 \mathrm{and}<50$
Slant range (km)	$<500$

. The echoes screened according to the parameters in Table 3 are considered to be meteor echoes; it should be pointed out that these echoes still contain some ionospheric echoes [4]. For the convenience of later discussion, the method of extracting meteor echo according to the parameters in Table 3 is called the traditional algorithm in this paper.

The method of extracting meteor echo using Table 3 is not fully applicable to the AgileDARN high-frequency radar. First, the electromagnetic environment of AgileDARN is complex, and the echo threshold of 3 dB is small. Second, although the power threshold is set, there is still some interference noise in the echo extracted by using Table 3. Finally, the echo extracted by the traditional algorithm will be affected by ionospheric echo. To solve the problems existing in the traditional meteor echo recognition algorithm, this paper improves the meteor recognition method, and the specific analysis is as follows.

In order to further suppress the influence of noise on the identification of meteor echo, the autocorrelation function was obtained by calculating the autocorrelation of the echo signal; the phase of the autocorrelation function was fitted by least squares fitting, and then the root mean square error (RMSE) after fitting was calculated. The data with large fitting errors were eliminated by using RMSE as the threshold, so as to reduce the influence of noise and improve the accuracy of meteor echo recognition. We take the root mean square error after the autocorrelation phase fitting as the parameter to extract the meteor echo, which is called the root mean square threshold. The calculation method of RMSE is as follows.

Assuming that the phase after autocorrelation is $P_{obs}$, the phase after least-squares fitting is $P_{fit}$, and the number of phase points after autocorrelation is N, then the root mean square error is:

$$RMSE=\sqrt{\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(P_{fit}-P_{obs}\right)}^2}$$

(5)

We set that when RMSE ≥ 0.3, the data will be eliminated, because at the operating frequency of 10.4 MHz, the Doppler velocity generated by the phase shift of 0.3 is 16 m/s, which is already greater than the minimum velocity of the meteor target [18], which shows that the fluctuation of the autocorrelation function is larger and the interference is larger. Figure 1 shows the change curve of the phase of observed values and fitted values of the autocorrelation function of measured data of the AgileDARN high-frequency radar. Since the signal emitted by the AgileDARN radar is a seven-pulse non-equally spaced multi-pulse train, there is delay loss after autocorrelation calculation [13]. Therefore, to avoid uncertainty caused by delay loss, the first 16 lags were selected for fitting here. RMSE in the left figure is 0.12, less than the set threshold of 0.3, which is considered to be a potential meteor echo. RMSE in the right figure is 0.5, and the fitting error is large. It is considered as a non-meteor echo, and such data were excluded from subsequent processing.

However, only the root mean square error of the phase fitting of the autocorrelation function was considered, which can only reduce the influence of noise. It was found that the echo below the RMSE threshold is not necessarily the meteor echo. Figure 2 shows that the phase fitting root mean square error was satisfied, but it is not a meteor echo, which is discussed below. According to the parameter calculation method in Section 2, the echo power, Doppler velocity and spectral width shown in Figure 2 were respectively calculated to be 12.88 dB, −3.01 m/s and −5.58 m/s. According to the traditional method in Table 1, the echo should be listed as meteor echo. We investigated the RMSE of this echo, and calculated the ACF phase fitting error RMSE of this echo to be 0.11, which is less than the threshold value; thus, it should be judged as a meteor echo. However, as shown in Figure 2, the phase changes are chaotic, which does not conform to the feature that the meteor target moves at a uniform speed in the radar field of view with a linear phase change [20]; it is thus not a meteor echo. Observe the change of the phase value of the target in Figure 2: within 6.4 ms, the phase changes between 0.17 radian and −0.29 radian, the fitting phase change value is 0.2 radian, and the measured phase value is small, which leads to a smaller value when calculating the root mean square error of the measured phase value and the fitting phase value. The method of extracting meteor echo based on echo power, Doppler velocity, spectral width and phase fitting root mean square error is invalid.

According to the analysis of the velocity of the meteoroid, the velocity of the meteoroid entering the Earth’s atmosphere was about 11~72 km/s, and there was almost no deceleration in the process of the meteoroid ablating [1,20,21]. Thus, according to the velocity of the meteoroid combined with Equation (3), the phase slope of the ACF was between 4.8 and 32.1. assuming that the initial phase is 0, the phase change was between 28.8 and 192.6 degrees, that is, between 0.5 and 3.4 radians. Considering that the Doppler velocity of the meteor target observed by radar is the meteor velocity component, combined with the velocity characteristics of the meteor target observed by SuperDARN [21], the phase change value of less than 0.3 radian after selecting the phase fitting of the autocorrelation function was considered not to be the meteor echo, and the data were eliminated without subsequent processing. For the convenience of later discussion, this threshold is called the phase change, that is, data with a phase change of less than 0.3 radian are regarded as non-meteor echoes. Combined with the above analysis, the improved meteor target recognition parameters are summarized in

Table 4. Improved meteor echo recognition parameters.

Meteor Extraction Parameters	Value
Power (dB)	$\ge 10$
LOS Doppler velocity (m/s)	$\pm 50$
Spectral width (m/s)	$>1 \mathrm{and} <50$
Slant range (km)	$<500$
RMSE threshold	$\le 0.3$
Phase variety threshold	$\ge 0.3$

. In this paper, the method to extract the meteor echo based on Table 4 is called the improved algorithm.

5. Data Analysis

Figure 3 shows the typical variation characteristics of meteor echo power observed by the AgileDARN radar. From the variation of echo power in the figure, the process in which the meteor target enters the radar field of view and gradually disappears can be seen. Figure 3a shows a short-duration meteor echo with a duration of about 0.5 s, Figure 3b shows a long-duration meteor echo with a duration of about 2 s, Figure 3c shows the echo characteristics of meteors when the life process of meteors is completely seen in the field of view, and Figure 3d shows two meteor echoes seen at different slant ranges.

In order to determine the overall characteristics of the echo extracted by each parameter and obtain a dataset of meteor echoes, we analyzed the measured data of the AgileDARN radar with a slant range of 75 to 450 km. In order to reduce the impact of external interference, the echo power in Table 3 was changed to 10 dB, and the three main thresholds of Doppler velocity, spectral width and power in the traditional algorithm in Table 3 were used to filter the echo to extract the meteor echo. The statistical histogram of the echo was obtained, as shown in Figure 4. Figure 4a–c respectively show the distribution histograms of echo power, Doppler velocity and spectral width within 24 h; the blue line represents the effective echo obtained after data preprocessing, such as noise elimination; the red line represents echoes with echo power greater than 10 dB; the yellow line represents echoes with echo power greater than 10 dB and Doppler speeds between −50 and 50 m/s; the purple line represents the echoes of meteors with power greater than 10 dB, Doppler speeds between −50 and 50 m/s, and spectral widths between 1 and 50 m/s, namely meteor echoes. Figure 4d shows the statistical histogram of the time distribution of the number of meteor echoes extracted every hour within 24 h. It can be seen from the figure that the number of meteor echoes was the largest in the early morning of local time, and the number was small in the evening of local time, which is consistent with the typical distribution pattern of meteor targets over time [10]; however, there is a small spike around 18 o’clock in the evening, which may be part of the ionospheric echo as meteor echo [22].

Figure 5 shows the statistical characteristic histogram of the echo quantity of each parameter when the parameters in Table 4 were used to extract the meteor echo. The processed data were the same as the data in Figure 4. Figure 5a shows the histogram of the variation of echo quantity with power; the blue line represents the distribution characteristics of the echo quantity obtained after data preprocessing, such as noise elimination and effective echo extraction; the red line shows the distribution characteristics of echo quantity for power greater than 10 dB; the yellow line shows the echo quantity distribution characteristics with power greater than 10 dB and Doppler speed between −50 and 50 m/s; the purple line represents the number distribution characteristics of echoes with power greater than 10 dB, Doppler speeds between −50 and 50 m/s, and spectral widths between 1 and 50 m/s; the green line represents the distribution characteristics of meteor echo quantity after filtering all parameters in Table 4, namely meteor echoes. The meanings of the different color curves in Figure 5b, c are the same as the threshold values represented by the corresponding color curves in Figure 5a, except that they correspond to the distribution characteristics of echo number with Doppler velocity and echo number with spectral width. Figure 5d shows the histogram of meteor echo with time distribution extracted by the method in this paper; it can be seen from the figure that the maximum number of meteor echoes was observed in the early morning of local time, and the minimum number of meteor echoes was observed in the evening of local time, which is in good consistency with the distribution law of meteor targets. By comparing Figure 5d and Figure 4d, it can be found that in Figure 4d, a small peak of meteor echo was observed around 18 o’clock in the evening. Figure 5d shows the meteor echo extracted by the algorithm in this paper, and there is no peak around 18 o’clock in the evening, which is more consistent with the distribution characteristics of meteor echo within 24 h than the traditional algorithm.

Figure 6 shows the comparison distribution histogram of meteor echoes extracted by the traditional algorithm and the proposed algorithm. Figure 6(a1–a3) shows the histograms of statistical characteristic distribution of echo power, Doppler velocity and spectral width; the blue line represents the distribution characteristics of meteor echo extracted by the traditional algorithm and the red line represents the distribution characteristics of meteor echo extracted by the proposed method. Figure 6b is the same as Figure 6a, but the difference lies in the normalization. As can be seen from Figure 6(b1), the meteor echo extracted by the algorithm in this paper has a large echo power and a maximum incidence of meteor echo at 20 dB. It can be seen from Figure 6(b2) that the Doppler velocity of meteor echo extracted by the method in this paper has a better normal distribution feature, which is in good agreement with the Doppler velocity distribution feature of meteor echo [17]. Figure 6(b3) shows that the meteor echoes extracted by this method have better low-spectral width features, and the spectral width of most of the meteor echoes extracted is within 20 m/s, which can effectively eliminate some ionospheric echoes with low-spectral width features [23].

For the data shown in Figure 6, we took the power of 20 dB, a median Doppler velocity of ±25 m/s and a median spectral width of 25 m/s as boundaries to calculate the percentage of meteor echo, which is called the incidence of meteor echo. It was found that the incidence of meteor echo with echo powers greater than 20 dB of the algorithm in this paper was 0.7611, and that of the traditional algorithm was 0.4906, indicating that the echo extracted by the algorithm in this paper has greater echo power. The incidence of meteor echo of the proposed algorithm was 0.8423 when the Doppler velocity was between −25 and 25 m/s, while that of the traditional algorithm was 0.5946, indicating that the proposed algorithm has better characteristics of low Doppler velocity. The incidence of meteor echo of the proposed algorithm with spectral width less than 25 m/s was 0.7629, and that of the traditional algorithm was 0.6043, indicating that the proposed algorithm has better low Doppler spectral width. The results are shown in

Table 5. Comparison of the incidence of meteor echo between the traditional algorithm and the proposed algorithm under different parameter thresholds.

	Parameters	Power (dB)		Doppler Velocity (m/s)		Spectral Width (m/s)
Algorithm		$\ge 10 and <20$	$\ge 20$	$>25 and <-25$	$\le 25 and \ge -25$	$>25$	$\le 25$
Traditional Algorithm		0.5094	0.4906	0.4054	0.5946	0.3957	0.6043
Proposed Algorithm		0.2309	0.7611	0.1577	0.8423	0.2374	0.7629

.

Through the above analysis, it can be seen that the meteor echo extraction method proposed in this paper can effectively eliminate part of the ionospheric echoes, the statistical distribution characteristics of the meteor echo extracted are in good agreement with the distribution law of meteors, and the obtained meteor echo has a high signal-to-noise ratio; thus, the proposed method shows good performance of meteor echo extraction.

6. Conclusions

In this paper, a meteor observation method was designed by using the digital feature of the AgileDARN high frequency radar, an observation experiment of the meteor target was carried out, and the meteor echo extraction algorithm was optimized. Data analysis showed that the designed meteor observation model can obtain power variation characteristics of meteor echoes. The time distribution characteristics of meteor echo extracted by the improved meteor echo extraction algorithm are more consistent with the theoretical meteor target time distribution. The meteor echo obtained by the algorithm in this paper has higher SNR, lower Doppler velocity and lower spectral width characteristics, which can effectively eliminate part of the ionospheric echo, improve the identification accuracy of meteor echo, and has good performance. Although the algorithm presented in this paper has good performance, there are still some uncertainties in the extraction of meteor echoes based on statistical features, which will be the focus of future work. At the same time, a more reliable meteor extraction algorithm will be developed, and a neutral wind inversion algorithm will be studied based on meteor echo Doppler velocity.