Improved High-Order Cumulant TDE Parameter Accumulation Algorithm for Locating UHF Signals of Pulsed Electromagnetic Source

Abstract

Ultra-high frequency (UHF) signal detection is one of the most effective methods for spatial orientation and partial discharge fault diagnosis. However, when the background noise, especially Gaussian white noise and narrow-band interference, is very high, or the detection region is remote, location accuracy may decrease. To improve this, a location system based on the improved higher-order cumulant time delay estimation (TDE) method combined with energy accumulation is proposed. In the system, the UHF waves are received by a four-antenna array. Improved fourth-order cumulants with a smoothed coherence transform (SCOT) window are used in the TDE, by which Gaussian white noise and narrow-band interference can be efficiently suppressed. The energy accumulation algorithm is applied to the cross-correlation results, by which the accuracy of TDE can be enhanced. The applicability of the proposed localization algorithm is evaluated by simulation and experiment. The simulation results show that the improved fourth-order cumulant TDE-parameter accumulation algorithm is superior in accuracy to traditional location methods. In the experimental measurements, two partial discharge measurement points located in a complex electromagnetic environment are tested. The results illustrate that the proposed method can effectively suppress Gaussian white and narrow-band noise, and the location results can satisfy accuracy requirements when the measurement point is within 70 m.

1. Introduction

Pulsed electromagnetic waves generally radiate from a partial discharge (PD) source, which is in the broadband ultra-high frequency (UHF) range. They are anti-interference, highly sensitive, and stable in their propagation [1]. Therefore, the application of pulsed electromagnetic source detection based on UHF methods to spatial orientation and PD fault diagnosis will be interesting. The application of UHF methods in PD source location of high-voltage insulation systems, especially for substations and high-voltage transmission lines, is currently a research topic [2,3,4,5,6,7]. With power systems becoming larger and more complicated, unconnected and continuous monitoring technologies provide an effective and economical solution. In the aerospace field, precipitation static generated on aircraft leads to corona and spark discharges [8]. The detection of strong pulsed electromagnetic radiation can be used as a location method for aircraft, which may provide a new technique for target detection, ranging, and failure diagnosis in aircraft [9,10].

Traditionally, PD discharge faults have been detected by electrical connection tests [4,5,11] or non-electric detection, for example, ultraviolet and visible light (UV) imaging devices [12]. However, some insulation deterioration in electrical systems can trigger PD over several minutes, which can increase the cost of electric energy or cause faults in the power equipment. This kind of discharge is difficult to detect during site inspection; consequently, continuous detection would be a viable solution [13]. Iago Búa-Núñez designed an acoustic detection system for a PD source based on piezoelectric transducers and optical fiber sensors [14], which could be installed on the walls of a transformer tank or other high-voltage service. These sensors can detect acoustic signals online and are suitable for weak signals, due to their major advantage of being immune to electromagnetic interference. Nevertheless, for large-scale power systems, this approach requires more sensors for every service and is inefficient because of the increased installation, inspection, and maintenance costs.

Recently, many studies have been carried out on unconnected source localization, which is designed for early warning or PD spots in remote locations. Methods based on time delay estimation (TDE) or the direction of arrival (DOA) between the waveforms received by an antenna or microphone array have been applied to locate the PD source [15,16,17,18]. Philip J. Moore proposed a PD early-warning system for an air-insulated substation based on the TDE method [19,20]. The location site can be obtained by solving the localization equations of the time difference of arrival (TDOA). This approach is more accurate than the DOA method. To apply source location in a multipath environment, Ye Tian proposed an advanced TDOA estimation method with an L-shaped antenna array [21], and Hyunuk presented a PD fault-detection method using a microphone array and thermal imaging charge-coupled device (CCD). This approach can locate the position of the PD source with high accuracy and a high signal-to-noise ratio (SNR). However, under strong interference or a distant detection region, the SNR will be extremely low, such that the signal is covered by noise. To improve the abilities of field noise interference suppression and effective extraction of signal characteristics, a novel algorithm for locating UHF signals based on TDE combined with spectrum reconstruction and higher-order cumulants is presented by Huijuan Hou [22,23]. The reconstructed spectra show good performance in selecting the characteristic frequencies, and Gaussian noise and narrow-band periodical interference can be effectively suppressed for SNRs up to 10 dB.

For large substations and transmission lines, the span will be up to 100 m. To avoid influence between the location system and power equipment, it is better to place the locating system outside the substations. Hence, the required detection distance should be up to 100 m. In this case, the SNR of the UHF signal will decrease to below −20 dB, which may lead to insolvability or incorrect solution of the location equations. In this paper, an improved TDE method based on windowing fourth-order cumulants and an energy-accumulation algorithm is proposed. Because the fourth-order cumulants of the Gaussian white noise are equal to zero and the smoothed coherence transform window can smooth the cross-correlation results of a periodic signal, Gaussian white noise and narrow-band interference can be suppressed efficiently. The accumulation algorithm can enhance the detecting distance—in the experimental measurements, when the detecting distance is about 70 m, the localization error is less than 0.93 m, which satisfies accuracy requirements.

The rest of the paper is organized as follows. In Section 2, the proposed location system is introduced in detail. In Section 3, numerical simulation results are provided to demonstrate the validity of the algorithm. The concluding remarks are summarized in Section 4.

2. Improved Locating System

2.1. Location Algorithm

A locating platform is developed to locate a pulsed electromagnetic source. It is composed of a four-antenna array with amplifiers, a high-speed acquisition module to record the UHF waves, and a data-processing unit to estimate the time delay of the four antennas and confirm the location of the pulsed electromagnetic source.

The location is calculated by solving localization equations based on the time delay array. The localization equations are acquired as follows. Assuming that x(t) and y(t), listed below, are two signals received by two antennas in the array that radiate from the same source, as shown in Figure 1 and given by

$$\left\{\begin{array}{c}x\left(t\right)=A_{1}s\left(t+{\tau }_1\right)+w_1\left(t\right)+v_1\left(t\right)\\ y\left(t\right)=A_{2}s\left(t+{\tau }_2\right)+w_2\left(t\right)+v_2\left(t\right)\end{array}\right.$$

(1)

where s(t) represents the target signal, A₁ and A₂ are the amplitudes, τ₁ and τ₂ are the times at which the signals reach the two antennas, the time delay of the two signals is τ₁₂ = τ₂ − τ_1, w₁(t) and w₂(t) are Gaussian white noise, independent of s(t), and v₁(t) and v₂(t) are the narrow-band interference of the two antennas.

Assuming that the coordinates of the radiation source S and the ith antenna are (x₀, y₀, z₀) and (x_i, y_i, z_i), respectively, the localization equations can be written as follows:

$$\left\{\begin{array}{cc}{\tau }_{12}=\frac{1}{c}(L_1-L_2)\hspace{1em}& L_1=\sqrt{{(x_1-x_0)}^2+{(y_1-y_0)}^2+{(z_1-z_0)}^2}\\ {\tau }_{13}=\frac{1}{c}(L_2-L_3)\hspace{1em}& \begin{array}{l}{L}_2=\sqrt{{(x_2-x_0)}^2+{(y_2-y_0)}^2+{(z_2-z_0)}^2}\\ L_3=\sqrt{{(x_3-x_0)}^2+{(y_3-y_0)}^2+{(z_3-z_0)}^2}\end{array}\\ {\tau }_{14}=\frac{1}{c}(L_3-L_4)& L_4=\sqrt{{(x_4-x_0)}^2+{(y_4-y_0)}^2+{(z_4-z_0)}^2}\end{array}\right.$$

(2)

where L_i denotes the distance between the radiation source and the ith antenna, and τ₁₂, τ₁₃, and τ₁₄ are the time delay of the signals received by the first antenna and the ith antenna. By solving Equation (2), the location coordinates can be acquired. Therefore, the key to accurately locating the radiation source is to acquire the time delay between the preferred antenna and the other antennas in the array precisely. The accuracy can be enhanced by improving synchronization between the antennas and acquisition channels, increasing the sampling rate of the acquisition module, and optimizing the solving method of the localization equations. However, when the SNR is low and the signal is covered by noise, the time delay estimation error will be considerably large, which will lead to insolvability or incorrect results of the location equations. Therefore, the task of this study is to develop an approach to improve the abilities of noise-interference suppression and effective extraction of the time delay. The higher-order cumulants of the signal are equal to the higher-order non-Gaussian signals. In other words, they are insensitive to Gaussian noise because the higher-order cumulants of the Gaussian process are zero [20,21,22]. Moreover, detection is improved by adding a smoothed coherence transform window to the high-order cumulant results to suppress the narrow-band interference.

2.2. Improved Higher-Order Cumulants Algorithm to Estimate Time Delay

For an n-dimension time domain signal X = [x₁, x₂, …, x_n], the kth-order union cumulant C is defined as [24,25]:

$$\begin{gathered} C_{k_1+k_2+\dots k_n}=\mathit{cum}\left(x_1{,\mathrm{x}}_2,\dots {,\mathrm{x}}_n\right) \\ \hspace{1em}={(-i)}^k\left[\frac{{\partial }^k\psi \left(V\right)}{\partial v_1^{k_1}\partial v_2^{k_2}\dots \partial v_n^{k_n}}\right]\left|v_1=v_2=\dots =v_n=0|\right. \end{gathered}$$

(3)

where k₁, k₂, …, k_n are the orders of each sequence, and k = k₁ + k₂ + … + k_n. V = [v₁, v₂, …, v_n] are the angular frequency vectors. $\psi \left(V\right)$ is the second union characteristic function of X, which is the logarithm of the first union characteristic function $\varphi \left(v\right)$. The mathematical definition of $\psi \left(V\right)$ can be expressed as:

$$\psi (v)=\ln \varphi (v)=\ln [{\displaystyle {\int }_{-\infty }^{+\infty }f(x_i)e^{ivx}}d{x}_i],\hspace{1em}i\in \left[1,n\right]$$

(4)

where $f\left(x_i\right)$ is the probability density of $x_i$. The third- and fourth-order cumulants are generally used in the signal process because the higher-order cumulants calculation is complex and time-consuming. The third- and fourth-order cumulants can meet accuracy requirements. Considering the robustness of the location algorithm, we choose the fourth-order cumulants to process the received signals. The auto-fourth-order cumulants of a signal x(t) can be expressed as:

$$\begin{array}{ll}{C}_{4,x}\stackrel{\Delta }{=}& cum[x(t),x^{*}(t+D_1),x(t+D_2),x^{*}(t+D_3)]\\ \hfill =& {\left|A_1\right|}^{4}cum[s(t)+v_{11}(t),s^{*}(t+D_1)+\\ & v_{12}{}^{*}(t),s(t+D_2)+v_{13}(t),s^{*}(t+D_3)+v_{14}(t)]\end{array}$$

(5)

where * denotes the conjugate operation, D = (D₁, D₂, D₃) is the relative time delay, and v_1j(t) (j = 1, 2, 3, 4) is the narrow-band interference. The higher-order cumulants of the Gaussian process are zero. Gaussian white noise and narrow-band interference can be efficiently suppressed. Thus, there is no Gaussian noise component in Equation (5). For x(t) and y(t) received from the antenna array, the cross-fourth cumulants can be written as:

$$\begin{array}{ll}{C}_{xxyy}\stackrel{\Delta }{=}& cum(x(t),x^{*}(t+D_1),y(t+D_2),y^{*}(t+D_3))\\ \hfill =& {\left|A_1\right|}^2{\left|A_2\right|}^{2}cum[s(t)+v_{11}(t),s^{*}(t+D_1)+v_{12}{}^{*}(t)\\ & s(t+D_2+\tau )+v_{13}(t+{\tau }^{\prime }),s^{*}(t+D_3+\tau )+v_{14}{}^{*}(t+{\tau }^{\prime })]\end{array}$$

(6)

where τ denotes the time delay of the target signal s(t) between the two antennas, and τ’ is the time delay of the narrow-band interference. If the narrow-band interference is ignored, τ can be acquired by calculating the cross-correlation function between C_4,x, and C_xxyy. The three-dimensional cross-correlation function is defined as:

$$H_{xy}(D)={\displaystyle \underset{D_1,D_2,D_3}{\iiint }{C}_{4,x}(D_1,D_2,D_3)C^{*}{}_{xxyy}}(D_1,D_2+\tau ,D_3+\tau )d{D}_{1}d{D}_{2}d{D}_3$$

(7)

Therefore, the time delay τ = D is obtained when H_xy(D) is maximum:

$$\widehat{\tau }=\arg \underset{D}{\max } H_{xy}(D)$$

(8)

However, in the actual measurements, narrow-band interference cannot be ignored. In this case, Equation (6) is not applicable, which should, therefore, be rewritten as:

$$H_{xy}(D)={\displaystyle \underset{D_1,D_2,D_3}{\iiint }C(s(t),v(t))C^{*}}(s(t),s(t+\tau ),v(t),v(t+{\tau }^{\prime }))d{D}_{1}d{D}_{2}d{D}_3$$

(9)

where C denotes the fourth-order cumulation operation. It can be seen from Equation (9) that, when the correlation of narrow-band interference is higher than that of the target signal, the peak value of its cross-correlation results is higher than that of the target signals. It is described as:

$$\widehat{\tau }=\arg \underset{D}{\max } H_{xy}(D)=\left\{\begin{array}{c}\tau ,\hspace{1em}if\hspace{1em}{H}_{xy}(\tau )>H_{xy}(\tau \prime )\\ \tau \prime ,\hspace{1em}if\hspace{1em}{H}_{xy}(\tau \prime )>H_{xy}(\tau )\end{array}\right.$$

(10)

The influence of narrow-band interference can be weakened by adding a smoothed coherence transform (SCOT) window to the higher-order cumulants results. The smoothed coherence transform is defined as:

$$B_{SCOT}(\omega )=\frac{1}{\sqrt{G_{4,x}(\omega )G_{4,y}(\omega )}}$$

(11)

where G_4,x (ω) and G_4,y (ω) are the auto-power-spectra of C_4,x and C_4,y respectively. They are given by:

$$\left\{\begin{array}{c}{G}_{4,x}(\omega )=F(C_{4,x})\\ G_{4,y}(\omega )=F(C_{4,y})\end{array}\right.$$

(12)

where F denotes the Fourier transform. Therefore, the cross-correlation function of the cumulants results with the SCOT window can be expressed as:

$$H_{xxyy}(t)=F^{-1}[B_{SCOT}(\omega )G_{xxyy}(\omega )]$$

(13)

where G_xxyy(ω) is the cross-power spectrum of C_4,x and C_4,y, and F⁻¹ is the inverse Fourier transform operation. Consequently, an accurate time delay τ is acquired by extracting the coordinate of $\underset{D}{\max } H_{xxyy}\left(t\right)$:

$$\widehat{\tau }=\arg \underset{D}{\max } H_{xxyy}(t)$$

(14)

2.3. Time Delay Estimation Based on Energy Accumulation

The presence of background noise or random signals similar to the target signals may result in the time delay estimation becoming inaccurate or an unrealistic value, which may be caused by the time delay of certain random pulsed signals. An energy-accumulation technique of cross-correlation results is proposed to improve the estimation accuracy. The recorded data of the signal are divided into several subsequences with length n. We assume that the two subsequences from two different antennas are X_j = [x₁, x₂, …, x_n] and Y_j = [y₁, y₂,…, y_n] (j = 1, 2, 3, …, M), where M is the accumulation number. According to Equation (13), the cross-correlation function of the jth subsequence’s fourth-order cumulants is:

$$H_{j,xxyy}(t)=F^{-1}[B_{j,SCOT}(\omega )G_{j,xxyy}(\omega )]$$

(15)

To accumulate the cross-correlation results from 1 to M, the peak value of cross-correlation results caused by the target signal will be strengthened. In contrast, the cross-correlation results of random noise will be weakened or close to zero. Therefore, the accurate time delay τ is:

$$\widehat{\tau }=\arg \underset{D}{\max }\frac{1}{M}{\displaystyle \sum _{i=1}^M{H}_{j,xxyy}(t)}$$

(16)

Overall, the realization steps of locating a pulsed electromagnetic source are as follows:

Step 1: Discrete series x(t), y(t), z(t), and r(t) are collected simultaneously by the antenna array. They are respectively divided into M subsequences: X_j = [x₁, x₂, …, x_n], Y_j = [y₁, y₂,…, y_n], Z_j = [z₁, z₂, …, z_n], and R_j = [r₁, r₂, …, r_n] with length n, where i = 1, 2, …, M.

Step 2: Calculate the auto-forth-order cumulants and cross-forth-order cumulants of the subsequence of the reference antenna and the other three groups of subsequences. According to Equations (5) and (6), the auto-forth-order cumulants C_4,x, C_4,y, C_4,z, and C_4,r and cross-forth-order cumulants C_xxyy, C_xxzz, and C_xxrr are obtained.

Step 3: Calculate the cross-correlation results of the cumulants results with the SCOT window by Equations (11), (12), and (15). H_j,xxyy, H_j,xxzz, and H_j,xxrr are consequently acquired.

Step 4: Accumulate H_j,xxyy, H_j,xxzz, and H_j,xxrr from j = 1 to j = M, and extract the TDEs τ₁₂, τ₁₃, and τ₁₄ by Equation (16). Substitute τ₁₂, τ₁₃, and τ₁₄ into Equation (2). Iteration or search-optimization methods are used to solve the location equation. Consequently, the radiation source coordinate (x₀, y₀, z₀) is obtained.

3. Numerical Simulations

To confirm the applicability of the proposed localization algorithm for the UHF signals from electromagnetic sources, PD signals simulated by Matlab are processed and analyzed by simulation.

The coordinates of the antennas are set as in Figure 2 of Ref. [1], which are #1 (0.5, 0.5, 1), #2 (3.5, 0.5, 1), #3 (3.5, 4.5, 1), and #4 (0, 4.5, 1) in meters. The coordinates of the PD source are (3, 6, 3). PD signals are simulated by the double-exponent attenuation oscillation function:

$$s(t)=A(e^{m(t-t_0)/\xi }-e^{k(t-t_0)/\xi })\sin (2\pi f_{0}t)$$

(17)

where A is the amplitude of the PD waveform, and m, k, and ξ are attenuation coefficients. Parameter t₀ is the starting time and f₀ denotes the center oscillation frequency of the discharge spectrum. In the simulation, A is set to 1.1, and m and k are −5.27 and −2.58, respectively. ξ is assumed to be 1 ns. f₀ is set as 1 GHz. Antenna #1 is set as the reference antenna. According to the coordinates of the antennas and the PD source, the time delay differences between the reference antenna and the other three antennas are Δt₁₂ = 1.63 ns, Δt₁₃ = 12.71 ns, and Δt₁₄ = 8.2 ns.

To simulate the real situation, the starting time t₀₁ of the PD waveform received by antenna #1 is generated randomly. The time-domain waveform received by the antenna array is shown in Figure 3a. The simulated signals are mixed with Gaussian white noise under different SNRs and narrow-band noise with three different frequencies. The frequencies are 80 MHz, 100 MHz, and 150 MHz, and the corresponding amplitudes are 0.05 V, 0.2 V, and 0.5 V, respectively. Figure 3b shows the received PD signals with −20 dB Gaussian white noise and narrow-band noise. Frequency analyses of the simulated PD signal with and without noise are shown in Figure 4a,b, respectively.

For comparison, the location results are conducted by the improved TDE method based on windowing fourth-order cumulants and energy accumulation, the traditional fourth-order cumulant TDE without accumulation, and the typical TDE method [19,20]. For brevity, the three methods are called Method 1, Method 2, and Method 3 in the following section. A comparison of time delay results between Antennas #1 and #3 using the three methods is illustrated in Figure 5, Figure 6 and Figure 7.

Figure 5 shows the comparison results in the case that the number of accumulations of Method 1 is 10, and the background noise is Gaussian noise, giving an SNR = 10 dB. There is no narrow-band interference. The time delay values are extracted as described by Step 4 in Section 2. The maximum normalized amplitude is at 12.71 ns in Figure 5a,b, and 13.09 ns in Figure 5c The time delay values calculated by Methods 1 and 2 are equal to the true value $\mathsf{\Delta }{t}_{13}$, and the time delay value of Method 3 has an error of 0.38 ns.

Figure 6 shows the case for 100 accumulations in Method 1 and an SNR with Gaussian noise reduced to −20 dB. In addition, the three different frequencies of narrow-band noise mentioned in Figure 3b are mixed with the simulated PD signal. The time delay errors calculated by the three methods are 0.42 ns, 0.77 ns, and 114.25 ns respectively. The accuracy of Method 1 is 0.25 ns higher than that of Method 2, representing a difference of 0.56 m in location errors. The result of Method 3 is a false value. Therefore, the fourth-order cumulant processing is capable of suppressing Gaussian noise, even with low SNR.

The SNR is further decreased to −30 dB. To obtain a more accurate result, the number of accumulations of Method 1 is increased to 1000. The time delay errors calculated by the three methods are 1.04 ns, 106.57 ns, and 34.1 ns, as shown in Figure 7. Under this background noise, Method 1 can calculate the time delay value within the allowed error. However, the results of the other two methods are false values. It also can be seen that the waveforms of Figure 6c and Figure 7b,c show obvious periodic oscillations, while those of Figure 6a and Figure 7a do not. It is concluded that adding the smoothed coherence transform window to improve the high-order cumulant algorithm is effective in restraining narrow-band noise.

To evaluate the locating applicability of the three methods, location results, including the TDE value between antenna #1 and #3, TDE errors, coordinates of the PD source, and location errors, are listed in

Table 1. Comparison of location results among the three methods.

Noise Conditions	Locating Method	Time Delay Estimation(between #1 and #3)	TDE Errors (ns)	Coordinates (m)	Location Errors (m)
Gaussian noise with SNR = 10 dB	Method 1 (N = 10)	12.71	0	(3, 6, 3)	0
	Method 2	12.71	0	(3, 6, 3)	0
	Method 3	13.09	0.38	(2.96, 5.82, 2.62)	0.42
Gaussian noise (SNR = −20 dB) added narrow-band interference	Method 1 (N = 100)	13.13	0.42	(3.1, 6.48, 3.1)	0.5
	Method 2	13.48	0.77	(2.86, 5.32, 2)	1.06
	Method 3	126.96	114.25	—	—
Gaussian noise (SNR = −30 dB) added narrow-band interference	Method 1(N = 1000)	13.1	1.04	(2.8, 5.44, 2.14)	0.93
	Method 2	−93.86	106.57	—	—
	Method 3	46.81	34.1	—	—

. Location error is defined as $\sqrt{{(x_0-x_0^{’})}^2+{(y_0-y_0^{’})}^2+{(z_0-z_0^{’})}^2}$, where (x’₀, y’₀, z’₀) is the estimated coordinate of the PD source.

It can be inferred that when the SNR is up to 10 dB, the simulation results of Method 1 and 2 are so precise that the errors of the TDE and location values are zero, and the location error of Method 3 is less than 0.42 m. When the SNR is decreased to −20 dB, the location errors of Method 1 and Method 2 are 0.5 m and 1.06 m, respectively. However, the location coordinate of Method 3 is a false result. When the SNR is below −30 dB, only Method 1 can achieve a relatively accurate location coordinate with a location error of 0.93 m. In Ref. [18], it is claimed that sources within 5 m of the array that have a location error of a few tens of centimeters can satisfy the accuracy requirement, and sources at 12 m can suffer a location error in excess of 2 m. Therefore, the accuracy of Method 1 can satisfy the accuracy requirement when SNR > −30 dB. Method 2 has good performance when SNR > −20 dB. Method 3 has the worst location accuracy, and it is impossible to calculate the true relative location coordinate when SNR < 10 dB.

The comparison results show that the proposed method can work better than the other two approaches when the target signal is mixed with Gaussian noises and narrow-band interference. When the SNR of the signal is low, its location accuracy can be improved by increasing the number of accumulations.

4. Experiments and Verification

The experiment validations are conducted in an open space next to a laboratory building, which contains many pieces of electrical equipment in the laboratory and a box-type transformer substation outside. Hence, the electrometric circumstance surrounding the laboratory building, during working hours, can be treated as a complicated background noise scenario. The experimental arrangement is illustrated in Figure 8. The four UHF omnidirectional antennas are helical antennas, with bandwidths that range from 20 MHz to 2 GHz. The length and the width of the antenna array are both 10 m and their coordinates are #1 (−5, −5, 0), #2 (5, −5, 0), #3 (5, 5, 0), and #4 (−5, 5, 0). A data acquisition and processing system is used to collect and process the received signals using the proposed algorithm in the paper. The sampling frequency is set as 5 GHz, and the sampling length is 2 μs. The coaxial cables connecting the four antennas to the data acquisition systems are the same length.

A spark discharge is generated by a high-voltage discharge generator. The discharge generator is supplied by a DC high-voltage source that can output up to ±300 kV. The discharging brush, with a number of wires as discharge points, is close to the top of a tower. When the voltage applied across the brush increases to breakdown voltage, discharge occurs. Two measurement points, P1 and P2, are set on the roof of the laboratory building; the coordinates of P1 and P2 are (27.3, 23.5, 23.1) and (20, 50, 22), respectively. The arrangement of the discharge source location at measurement point P1 is shown in Figure 9.

The frequency of the background noise is analyzed, as shown in Figure 10. Figure 10a is the background frequency spectrum when the discharge source is turned off. A series of spark discharges are generated by turning the high-voltage source to +80 kV; in this case, the frequency spectrum of the received signal is as in Figure 10b. Comparing the two Figures, we find that the background noise contains Gaussian white noise and narrow-band interference at 20–35 MHz, 80–100 MHz, 200 MHz, 650 MHz, and 850–950 MHz. The narrow-band signals at 80–100 MHz and 200 MHz are radio and television broadcasting signals, and the signals at 650 MHz and 850–950 MHz are wireless communication signals. The signals at 75 kHz–35 MHz are interference of unknown origin, which may be generated by the electrical equipment operating in the laboratory building or the box-type transformer substation. Because the narrow-band signal at 80–100 MHz, 200 MHz, and 850–950 MHz are too strong, we set wave traps before the data acquisition to filter the interference of these noise sources.

The location experiments are conducted at measurement points P1 and P2 with +30 kV high voltage applied at the discharge source. The location results are shown in

Table 2. Location results using the proposed algorithm for measurement points P1 and P2.

Test Condition		Coordinates (m)	Location Errors (m)
P1	N = 100	(27.14, 23.26, 23.2)	0.374
P2	N = 100	(12.4, 31, 12.58)	22.527 (false result)
	N = 5000	(20.68, 49.82, 22.6)	0.934

. For P1, 100 groups of signals are collected for the location algorithm, that is, N = 100. The coordinate of P1 is calculated to be (27.14, 23.26, 23.2). Compared with the real location, the location error is 0.374 m. For P2, when N = 100, the location error is 22.527 m. According to the criteria given in Ref. [18], this is obviously a false result. When N is increased to 5000 times, the coordinate is solved to be (20.68, 49.82, 22.6) with a location error of 0.934 m. This illustrates that, when the distance from the antenna array to the radiation source is too long to locate, the location error can be decreased by increasing the number of accumulations. The location errors calculated in Table 2 may be affected by system synchronization errors, measuring errors, or errors caused by a difference in the coaxial cables. According to Ref. [18], the location results of P1 (N = 100) and P2 (N = 5000) can satisfy accuracy requirements.

5. Conclusions

This paper described a new method for locating pulsed electromagnetic signals, which generally occur in electrical environments. The method is based on an improved fourth-order cumulative time delay estimation (TDE) method combined with energy accumulation. In this method, the UHF waves are received by a four-antenna array. Improved fourth-order cumulants with a smoothed coherence transform (SCOT) window are used in the TDE, by which Gaussian white noises and narrow-band interference can be efficiently suppressed. Moreover, an energy accumulation algorithm is applied to the cross-correlation results, by which the accuracy of the TDE can be enhanced. PD signals simulated by Matlab software mixed with Gaussian white noise and narrow-band interference are processed by the proposed method and two traditional location methods. The results show that the improved fourth-order cumulants TDE parameters accumulation algorithm is superior in accuracy. When the SNR is greater than −30 dB, the localization error is less than 0.93 m. An experimental measurement was conducted in an open space next to a laboratory building. Two PD measurement points located in a complex electromagnetic environment were tested. The results illustrate that the proposed method can effectively suppress Gaussian white and narrow-band noise, and the location results can satisfy accuracy requirements when the measurement points are within 70 m. With this development, location systems can separate radiation sources and locate them remotely and accurately.

The proposed system would be an interesting alternative for spatial orientation and PD fault diagnosis. Furthermore, we expect that this new design will be employed in the real-time detection of UHF signals in high-voltage insulation systems, especially for substations and high-voltage transmission lines.