Mathematical modeling of underwater signal anomaly perception based on multi-sensor data fusion

Abstract

There is a lot of interference in underwater environment, which can affect underwater signal transmission. For this reason, an abnormal perception model of underwater signals based on multi-sensor data fusion is proposed. The underwater frequency hopping communication method is used to select the channel and construct the mathematical model of underwater communication signal. A signal modulation and recognition system for multi-sensor reception is established, and the multi-sensor data fusion model is obtained by calculating the support margin. The energy spectrum distribution is obtained by decomposition of abnormal features with wavelet detector in time domain. The deep learning algorithm is used to reorganize the signal with the minimum detection error, and the mathematical model of underwater signal anomaly perception is obtained. The experimental results show that the average accuracy of the method for locating abnormal underwater communication signals is 95.5%, the misrecognition rate of abnormal underwater signals is less than 2%, and the time-consuming for sensing abnormal signals of 420 MB underwater communication is less than 3 s.

Keywords

Multi-sensor sensor data fusion underwater signal anomaly perception time domain analysis

1. Introduction

Different from the radio channel, the acoustic absorption and scattering effects of the underwater acoustic channel make the channel have strict band-limited characteristics. The inhomogeneity of the medium in the underwater acoustic channel and the unevenness of the sea surface and the sea bottom will produce strong acoustic reflection and scattering of the sound wave, which has an obvious multi-path effect. In addition, the noise of the underwater acoustic channel also has a linear spectrum in the background of the continuum spectrum. Due to the above characteristics of the underwater acoustic channel, digital communications are commonly used in underwater communications to achieve the purpose of resisting multi-path and reducing accumulated errors. The underwater wireless sensor network collects data from the underwater environment and transmits these data to the surface base station, and the data collected by the base station is then sent to the monitoring center for processing, using optical camera communication systems such as underwater applications [1]. Underwater is a three-dimensional dynamic environment. The influence of currents, waves, vortices and other factors will cause difficulties in underwater data transmission. Nowadays, the most recognized underwater transmission method is the underwater acoustic transmission method. Therefore, the underwater acoustic transmission device is an underwater group, which is necessary equipment for the network. The acoustic channel has the following characteristics: the bandwidth is very low, the transmission distance is short, when the terminal node is far away from the acquisition node, the data cannot be received, the bit error rate is high, and the signal is often not received [2, 3]. Some moving targets such as ships, etc. It may block the communication between the two parts of the network; the propagation delay is longer than that of the wireless channel on the surface; underwater noise will also affect the throughput of the communication channel. Due to the complex water environment, there is a lot of noise in the water, which will interfere with the propagation of underwater signals. For this reason, scholars in related fields have made research on the abnormal perception of underwater signals.

According to the properties and requirements of the measurement matrix in compressed sensing, on the basis of the rotation deterministic measurement matrix, by adjusting the coefficients of each column element of the measurement matrix to enhance the correlation between columns, the generalized rotation measurement matrix is obtained in, and applied it to the compressed sensing observation of underwater echo signals [4]. Through the variation of the matching degree and relative error of different measurement matrices with the compression ratio under no noise, and the three signal-input-to-noise ratios of 4, 0, and $-$ 3 dB. The output signal-to-noise ratio and matching degree of different measurement matrices change with the compression ratio, and the underwater echo signals are processed respectively. Li et al. [5] proposed the detection of magnetic anomaly signals of underwater targets based on the decomposition of standard orthonormal basis functions, and through the transformation of its basis functions, a method of variable scale orthonormal basis function (VSOBF) decomposition was proposed. This method can estimate the distance R0 in the detection process, and uses the gradient ascent method to improve the calculation speed and accuracy. The above methods all play a certain role in the perception of abnormal underwater signals, but the application effect of the methods in the perception of abnormal underwater signals and the effect still needs to be improved. The above methods mainly have the problems of low average accuracy of positioning and time-consuming detection of abnormal signals. Li et al. [6] proposed a stochastic resonance detection method based on singular value decomposition for underwater magnetic anomaly signals. Aiming at the poor detection ability of underwater target magnetic anomaly signals with low signal-to-noise ratio, they proposed the singular value decomposition stochastic resonance (SVD-RS) method. The method simulates the underwater target’s magnetic dipole signal based on the magnetic dipole signal and selects the optimal sub-signal through the singular value decomposition, and then passes the sub-signal through the stochastic resonance system, and constructs the test statistic to detect the underwater target’s magnetic anomaly signal. This method can effectively detect underwater abnormal signals, but its detection time is long, and the practical application effect is not as expected. Huang and Zadeh [7] studied a kind of underwater acoustic signal detection and down-conversion based on opto-mechanical resonance oscillation, and studied the performance of opto-mechanical resonators and oscillators as high-sensitivity acoustic and optical receivers and signal processors. In the presence of OPTO-mechanical oscillations, it is shown that OPTO-mechanical oscillators can be used as both an acoustooptic transducer and a frequency downconverter to extract IF or baseband underwater signals from the ultrasonic carrier without the need for RF local oscillators and mixers. This method is effective in detecting underwater acoustic signals, but its detection effect on abnormal signals is poor, and the detection time is long.

Aiming at the problems existing in the above methods, this paper proposes a mathematical modeling method for underwater signal abnormality perception based on multi-sensor data fusion. This method mainly uses the multi-sensor data fusion method, on this basis, combined with other algorithms to optimize the underwater signal anomaly sensing method, so as to solve the problems of poor underwater signal anomaly sensing effect and long detection time. The overall research route is as follows:

(1)
Signal tracking method in underwater communication: Accurately select the channel in underwater communication, and construct the mathematical model of underwater communication signal.
(2)
Mathematical model of underwater signal anomaly perception based on multi-sensor data fusion: Multi-sensor data fusion is introduced, the fusion model is constructed, the abnormal features of underwater signals are extracted, the mathematical model of underwater signal anomaly perception is constructed, and the underwater signal anomaly perception is realized by multi-sensor data fusion.
(3)
Experimental analysis: The experimental environment and data are introduced, and the performance of different methods is analyzed by three performance indexes, such as positioning accuracy, abnormal signal perception misrecognition rate and underwater communication abnormal signal perception time, to illustrate the experimental results.
(4)
Conclusion: The research background is explained, the design method is highly summarized, and the research results are expounded.

2. Signal tracking method in underwater communication

2.1 Accurate selection of tracking channel for underwater communication

Compared with the traditional communication mode, FH communication has the following advantages:

(1)
Good anti-interference performance: The frequency hopping signal can avoid various interference factors in a certain frequency domain by its own continuous hopping. The extension of the frequency hopping bandwidth, the increase of the number of frequencies and the increase of the speed can improve the anti-interference performance of the system.
(2)
The probability of interception is low: The carrier frequency of the signal is constantly hopping, so it is difficult for the outside world to intercept the communication information during the communication process. Under the pseudo randomness of frequency hopping sequence, frequency hopping also has pseudo randomness.
(3)
Multi-access networking capability. Multi-address communication can be realized through underwater frequency hopping technology: Any user has a unique address code in the network, and can only accept the communication information consistent with his address code, and information sent to other users will be subject to block, but the information it transmits will not be leaked.
(4)
Strong anti-fading ability. Frequency hopping communication has diversity reception capability, which can effectively improve the fading defect of signal transmission: The frequency diversity of the channel is generated by the frequency hopping of the frequency-hopping carrier. In the fading channel, the bandwidth value is lower than the hopping frequency value, and the hopping interval is very short, which can also ensure the strong transmission capability of the signal in the fading channel.
(5)
Compatible with narrowband communication systems: On the surface, the frequency hopping system belongs to the wideband system, but the function is closer to the instantaneous narrowband system. Compatibility means that the system can communicate with the general narrowband communication system in terms of frequency and so on. A frequency hopping module can also be added to the narrowband communication system to make it a frequency hopping communication system.

By selecting the actual channel, the impact of the time-varying signals on the channel can be mitigated, thereby providing a good solution for the accurate tracking of signals in subsequent channels. environment. In the marine underwater acoustic environment, the block selection method can be used to correct the channel impact of a certain continuous time, and the whole data block can be divided into several small sub-blocks. The basic idea of this block channel selection method is: the impact of the current sub-block equalization is the estimated value of the channel impact of the previous sub-block. After the sub-block equalizes and recovers the signal, the equalized signal is used to re-estimate the impact of the current channel. All subsequent sub-blocks are processed in this way.

The block-based channel selection needs to divide the data of length N into several small sub-blocks. Assuming that the data length of the sub-block is $N_{s}$ , in order to preserve the inter-symbol interference of the current sub-block to the next sub-block, the data with a length of $N_{t}$ is attached to the tail. In order to retain complete inter-symbol interference, $N_{s}>N_{t}>L$ needs to be satisfied, and $L$ represents the maximum identifiable path of the channel. Figure 1 shows the segmentation structure of the data frame based on the channel selection of the segmentation.

Figure 1.
Segmentation structure of data frame based on block-based channel selection.

When channel selection is performed for the signal of underwater communication, the inter-symbol interference of the previous sub-block to the current sub-block is first eliminated, and then the estimated impact of the previous sub-block is equalized and controlled to restore the first N data of the current sub-block. The recovered data is used as a training sequence to re-estimate the impact of the current channel, and the trailing interference of the current sub-block is calculated to facilitate the processing of the next sub-block data.

Perform spectral decomposition operation on underwater communication signals:

$\displaystyle X(t)=\int_{-\infty}^{+\infty}{\frac{x(t)}{({1-T_{s}})h(t)}}dt$ (1)

where $X(t)$ represents the stationary random sequence distribution of the underwater communication signal transmission, $x(t)$ represents the joint parameter estimation value of the time and frequency of the underwater communication signal, $x(n)$ represents the discrete signal of the underwater communication signal, and $h(t)$ represents the abnormal detection of the underwater communication signal. Window function, $T=1/T_{s}$ represents the spectral width of the underwater communication signal. Calculate the DOA parameters of the jth signal, decompose the underwater communication signal, use iterative phase compensation technology combined with high-order statistical feature detection method, statistical analysis method, carry out channel equalization configuration, and examine the position difference vector of the array, which can be expressed as for:

$\displaystyle d_{T}=\sqrt{\frac{({1-j})x(n)}{2\pi}}\int_{-\infty}^{+\infty}{X(% t)dt}$ (2)

Perform feature detection and ambiguity matching on the abnormal features of underwater communication signals, and obtain the estimated values of the far-field narrowband signal parameters of underwater communication:

$\displaystyle{X}^{\prime}(t)=\frac{({d_{T}-d_{s}})\times t_{s}}{X(t)}$ (3)

where $d_{s}$ represents the scale parameter of the abnormal signal and $t_{s}$ represents the delay parameter of the abnormal signal. Through the analysis process, the real-time and accurate tracking of the channel in underwater communication is realized.
2.2 Establishment of mathematical model for underwater communication signal tracking

Usually, an instantaneous linear mixed mathematical model is constructed for multiple underwater communication frequency hopping signals $x(t)$ :

$\displaystyle x(t)=a_{1}s_{1}(t)+\ldots a_{k}s_{k}(t)+a_{k}s_{k}(t)+w(t)$ (4)

where $s_{k}(t),k=1,2,\ldots,K$ represents the unprocessed independent underwater communication frequency hopping signal, $a_{k}$ represents the mixing coefficient of the $k$ th signal transmission point, and $w(t)$ represents the zero-mean Gaussian white noise with undetermined covariance. Assuming that the data sequence is $\bar{\alpha}$ , the expression for $s_{k}(t)$ is as follows:

$\displaystyle s_{k}(t)=E_{b}\sum\limits_{l=-\infty}^{\infty}p({t-lN_{b}T})\cos% ({2\pi f_{l}+\theta_{l}})g(t)$ (5)

where $E_{b}$ represents the symbol energy value, $T$ represents the time width, $N_{b}$ describes the number of bits transmitted during the frequency hopping process of underwater communication, $p({t-lN_{b}T})$ represents a rectangular time window with a width of $N_{b}T$ , $f_{l}$ represents the carrier frequency, and $\theta_{l}$ represents the carrier. The raw phase information, which is a random variable with uncertainty, is distributed in interval $[{0,2\pi}]$ .

$g(t)$ represents the impulse response of the Gaussian filter to be modulated, and its expression is:

$\displaystyle g(t)=\left\{{Q\left[{B_{b}\left({t-\frac{T_{b}}{2}}\right)}% \right]-Q\left[{B_{b}\left({t+\frac{T_{b}}{2}}\right)}\right]}\right\}$ (6)

In:

$\displaystyle Q(t)=\frac{1}{\sqrt{2\pi}}\int_{t}^{\infty}{e^{-\frac{t^{2}}{2}}% }dt$ (7)

where $B_{b}$ represents the normalized bandwidth of the filter, $T_{b}$ represents the standard spectrum width of underwater communication signals. Therefore, it can be clearly seen that the characteristics of the underwater communication frequency hopping burst signal have strong time-varying and non-stationary characteristics.

However, if the underwater communication frequency hopping signal is divided into several segments according to the time axis, especially when it happens to be equal to each underwater communication frequency hopping pulse, according to the communication principle, $s_{k}(t),t\in[{({l-1})N_{b}T,lN_{b}T}]$ is generally considered to meet the stability requirements. Therefore, from a statistical point of view, the received underwater communication frequency hopping sequence is a segmented stable sequence, so this belongs to the short-term stability of the underwater communication frequency hopping signal [8].

Combined with the formula, for $t\in[{({l-1})N_{b}T,lN_{b}T}]$ , but when many underwater communication frequency hopping signals coincide in the same pulse, the stability of the coincidence region is expressed as:

$\displaystyle E\{{x^{2}(t)}\}-E\{{x^{2}({t^{\prime}})}\}=E\{{({a_{1}s_{1}(t)+% \ldots a_{k}s_{k}({t^{\prime}})+w({t^{\prime}})})^{2}}\}{}-E({a_{k}^{2}s_{k}^{% 2}({t^{\prime}})})+E({w^{2}(t)})-E({w^{2}({t^{\prime}})})+E({a_{1}s_{1}({t^{% \prime}})a_{k}s_{k}}){}+E({a_{k}s_{k}(t)w(t)})-E({a_{k}s_{k}({t^{\prime}})w({t% ^{\prime}})})$ (8)

where, because there is an independent and temporarily stable relationship among $s_{k}(t)$ , $s_{1}(t)$ and Gaussian white noise $w(t)$ , the following formula is obtained:

$\displaystyle\left\{{\begin{array}[]{l}E\{{s_{i}^{2}(t)}\}-E\{{s_{i}^{2}({t^{% \prime}})}\}=0,t\neq t^{\prime}\\ E\{{s_{i}(t)s_{k}(t)}\}=E\{{x^{2}(t)}\}-E\{{s_{k}(t)}\}=0\\ \end{array}}\right.$ (9)

From the formula analysis, it can be obtained:

$\displaystyle E\{{x^{2}(t)}\}E\{{x^{2}({t^{\prime}})}\}=0,t\neq t^{\prime}$ (10)

According to Eq. (10), the overlapping part also has the characteristics of stability, so the underwater communication frequency hopping signal can be regarded as a piecewise stable random time series.

3. Anomaly sensing mathematical model for multi-sensor data fusion

In the underwater communication process, due to the multipath effect, the receiving point receives a vector superposition of signals from multiple paths, and the quality of the signals received by different receiving points is different. Single-sensor reception cannot take advantage of the signal differences of different locations, while multi-sensor reception can use different locations to obtain signals with different reception qualities, and improve the quality of received signals by means of data fusion. Therefore, multi-sensor reception can improve the signal-to-noise ratio and reduce the influence of multi-path fading compared to single-sensor reception.

3.1 Multi-sensor underwater signal data fusion model

The modulation recognition system received by multi-sensor is shown in Fig. 2. The whole system consists of three parts, namely unknown signal source, K sensor sub-nodes and sensor main node (fusion center). The signal sequence sent by the unknown signal source passes through the Gaussian white noise channel and the noise is received by K sensor sub-nodes distributed in different receiving environments, throughout the process, a node can be part of a cluster or act as a separate entity [9]. The sensor sub-node sends the local SNR estimate and the extracted identification feature vector to the sensor main node, and the sensor main node makes a joint decision based on the received information.

Figure 2.

Signal modulation and identification system received by multiple sensors.

In actual sensor network, due to the difference of sensor distribution position, signal transmission path and the interference of environmental noise [10, 11, 12], the signal-to-noise ratios of the signals received by each node are different. In multi-sensor reception, each node as a participant of the whole system has a positive contribution to the final modulation recognition result. During the fusion process of multi-sensor information in underwater communication, if the data information monitored by the sensors is relatively close, it indicates that there is a mutual support relationship between the two sensors. The data support degree of the two sensors is the support margin of the sensor.

Based on the analysis, the relationship function between sensor data information is established, and the process is shown in the following formula:

$\displaystyle z_{ij}=\left\{{{\begin{array}[]{l}{1,|{x_{i}-x_{j}}|\leqslant M}% \\ {0,|{x_{i}-x_{j}}|>M}\\ \end{array}}}\right.$ (11)

where the established relation function is marked as $z_{ij}$ , the data information monitored by the $i$ th sensor is $x_{i}$ , the data information monitored by the $j$ th sensor is $x_{j}$ , and the sensor threshold is $M$ .

Due to the different data gaps, the support margins between sensors are also different. In order to avoid the absoluteization of the calculation results, the exponential form is used to establish the support margin function of the sensor monitoring data. The process is shown in the following formula:

$\displaystyle z_{ij}=D^{-|{x_{i}-x_{j}}|}$ (12)

where the established support margin function is $z_{ij}$ , and the constant is marked in the form of $D$ . Through the calculation of the function, it can be seen that when the difference between the monitoring information $x_{i}$ of sensor $i$ and the monitoring information $x_{j}$ of sensor $j$ is not obvious, the support margin value is close to 1, and when the difference between the two is large, the support margin value is 0. It can be seen that when the gap between $x_{i}$ and $x_{j}$ gradually increases, the support margin value gradually decreases.

Set a fixed threshold of $M$ , calculate the support margin function, and obtain the high-dimensional matrix of the data. The process is as follows:

$\displaystyle D=\left[{{\begin{array}[]{*{20}c}{d_{11}}&\cdots&{d_{1n}}\\ \vdots&\vdots&\vdots\\ {d_{n1}}&\cdots&{d_{nn}}\\ \end{array}}}\right]$ (13)

where the number of data is $n$ and the dimension is $D$ . The support margin between the monitoring information of the two sensors is $z_{ij}$ [13]. In the support margin matrix, the data information is compared with itself in each row of the matrix, so this information is redundant information, it is used as part of the support margin when assigning weights to improve the fusion accuracy of sensor information. When multi-sensors perform data fusion [14], redundant and complementary information of sensors is used to coordinate and complement each other between data to avoid the limitations of data fusion and improve the efficiency of sensors.

Based on the analysis results, combined with information fusion [15], the support margin matrix is updated, and the result is as follows:

$\displaystyle{Z}^{\prime}=\left[{{\begin{array}[]{*{20}c}{z_{\sigma_{1}}}&% \cdots&{z_{1n}}\\ \vdots&\vdots&\vdots\\ {z_{n1}}&\cdots&{z_{\sigma_{n}}}\\ \end{array}}}\right]$ (14)

where the updated support margin matrix is ${Z}^{\prime}$ , and the support margin value between the two sensor data is $z_{\sigma_{n}}$ .

The process of underwater communication multi-sensor monitoring data fusion is as follows:

(1)

The monitoring of underwater communication multi-sensor monitoring information is collected as the original data, and the support margin value is obtained by calculating the data through the support margin value.

(2)

Through the calculation of multi-sensor data information, the data support margin matrix is established.

(3)

Calculate the corresponding support margin factor $\sigma_{i}$ of the sensor. First, set the sensor to monitor $m$ data in a fixed period $T$ , which is expressed in $X=\{{x_{1},x_{2},\cdots,x_{m}}\}$ forms, and obtain the mean value and error of the sensor monitoring data through calculation. The process is shown in the following formula:

$\displaystyle\sigma_{i}=\sqrt{\frac{1}{m-1}\sum\limits_{i=1}^{m}{({\Delta x_{i% }-\Delta\bar{x}})^{2}}}$ (15)

where $\sigma_{i}$ denotes the corresponding support margin factor of the sensor, $m$ represents the total number of data, the error label is $\Delta x_{i}$ , the error mean is $\Delta\bar{x}$ . Put the calculated data standard deviation into $z_{\sigma_{i}}=A^{-\sigma_{i}}$ , and calculate the $z_{\sigma_{i}}$ value corresponding to each sensor, which is more like a support margin matrix through calculation.

(4)

Set the comprehensive factor of the sensor to $h_{i}$ and $H=ZK$ . Among them, the comprehensive factor set is $H$ , the non-zero vector is $K$ , and the support margin matrix is $Z$ . Fix $h_{i}$ to $h_{i}=k_{1}z_{i1}+k_{2}z_{i2}+\cdots+k_{n}z_{in}$ form.

(5)

Obtain the maximum eigenvalue $\lambda$ of the matrix through calculation.

(6)

Give weight to the calculation result and normalize it, and the result is as follows:

$\displaystyle a_{i}=\frac{k_{i}}{k_{1}+k_{2}+\cdots+k_{n}}$ (16)

where the normalization result is $a_{i}$ , and the data vector is $k_{i}$ .

Through the calculation process, the fusion of underwater communication multi-sensor data information is completed.

3.2 Abnormal feature extraction of underwater signals based on multi-sensor data fusion

The multi-sensor data fusion is introduced. Firstly, the characteristic sampling points of the detection length of the underwater communication signal are obtained through the multi-resolution reconstruction of the signal. Secondly, the abnormal characteristics of the underwater communication signal are decomposed in time domain by the wavelet detector to obtain the matrix distribution of the abnormal characteristics of the underwater communication information. Thirdly, the effective feature quantity of the underwater communication signal is obtained based on the approximate norm function analysis method. Finally, extract the high-resolution spectrum results of the abnormal features of underwater communication signals to obtain the abnormal features of underwater communication information. Through the multi-resolution reconstruction of the signal, the detection length of the underwater communication signal is obtained:

$\displaystyle l=\frac{a_{i}\cdot n_{b}^{\left({\sin\frac{\alpha}{2}-1}\right)}% }{\mu(n)}$ (17)

where $n_{b}$ represents the characteristic sampling point, $\alpha$ represents the phase angle of the eigenvalue, $\beta$ represents an underwater communication signal, $a_{i}$ represents the feature decomposition coefficient. The wavelet detector is used to decompose the abnormal features of the underwater communication signal in the time domain, and the matrix distribution of the abnormal features of the underwater communication signal is obtained as:

$\displaystyle s_{m}=\frac{l}{\sqrt{\cos\{{2k_{1}[{d+\bar{E})}]}\}}}$ (18)

where $\bar{E}$ represents the energy of the underwater communication signal, $\max E$ denotes the maximum value of the abnormal characteristic distribution of the underwater communication signal, and $k_{1}$ denotes a correlation coefficient of signal enhancement. Based on the method of approximate norm function analysis, the effective feature quantity of the underwater communication signal is obtained, which represents the maximum difference between the peak and the trough of the underwater communication signal:

$\displaystyle z_{\max}=s_{m}(E_{\max}-\bar{E})$ (19)

where $E_{\max}$ is the maximum peak value of abnormal distribution of underwater communication signals. According to the effective feature quantities of underwater communication signals, the eigenvalues of the signals are decomposed, and the high-resolution spectrum results of abnormal features are extracted to obtain the abnormal features of underwater communication signals:

$\displaystyle u_{m}=\cos({2\theta-\alpha})z_{\max}$ (20)

The beam spacing equalization control method is used to extract abnormal features of underwater communication signals.

3.3 Mathematical modeling of abnormal perception of underwater signals

The deep learning algorithm is adopted to recombine the signal with the minimum detection error to obtain the abnormal spectral distribution of the underwater communication signal, which is described as:

$\displaystyle R=\int_{-\infty}^{+\infty}{({c_{i}-u_{m}})dn}$ (21)

where $c_{i}$ represents the high-order spectral component of the underwater communication signal. Using the fourth-order cumulant joint parameter fusion, the state space function of the underwater communication signal is obtained as $\{{x_{1},x_{2},\cdots x_{n}}\}$ , and the abnormal characteristic quantity of the signal is linearly reconstructed, and the linear subspace of the abnormal characteristic distribution of the underwater communication signal is obtained as:

$\displaystyle Z_{t}=R-\sum\limits_{i=1}^{n}{u_{m}}$ (22)

The signal model of the underwater communication signal is constructed, and pattern recognition of the signal output source is performed. The value range of any $m\times n$ dimensional matrix $A$ is defined as:

$\displaystyle J=\left|{\frac{1}{\rho}-\frac{\sum\limits_{i=1}^{n}{x_{i}}}{n}}\right|$ (23)

where $\rho$ represents the abnormal energy spectral density of the underwater communication signal. Let $A\in C^{n\times n}(n\times n)$ be the covariance matrix of the abnormal feature distribution of the underwater communication signal, combined with the three-dimensional feature distribution of the underwater communication signal, the output quantitative feature of the information reconstruction is obtained as $\frac{\partial J}{\partial x_{i}}=0$ , and the joint probability density parameter of the abnormal spectrum distribution of the underwater communication signal is obtained:

$\displaystyle\rho_{I}=k_{1}\sum\limits_{i=1}^{I}{\upsilon_{i}}E_{\max}S_{i}$ (24)

where $S_{i}$ represents the spectrum anomaly distribution of underwater communication signals, and $\{{\upsilon_{1},\cdots,\upsilon_{I}}\}$ represents the fuzzy autocorrelation feature matching function. In summary, the abnormal perception of underwater communication signals is realized.

4. Experimental analysis

4.1 Experimental environment and experimental data

In order to verify the validity of the mathematical model of underwater signal anomaly perception based on multi-sensor data fusion proposed in this paper, a simulation comparison experiment is designed.

First, it is necessary to simulate communication signals and underwater noise. In medium- and long-distance underwater acoustic communication, the communication signal frequency does not exceed 100 kHz, and the symbol rate is in the order of thousands of baud. For the underwater digital communication signals MFSK and MPSK simulated in all experiments in this paper, the carrier frequency is selected from 0 to 100 kHz with moderate probability. Model underwater noise as a symmetric steady-state distribution, where a $=$ 1.8. For the underwater acoustic communication channel, the Rayleigh channel is used for simulation, and three typical multipaths are taken. The delay of the latter two is 10 and 20 times the sampling interval of the first, respectively, and the average amplitude attenuation is 0 dB, $-$ 3 dB, $-$ 4 dB respectively. The incoming signal is obtained at the receiving end, and the discrete time sequence is obtained by sampling. According to the sampling theorem, the sampling rate is 2 times the maximum signal frequency, that is, 200 kHz.

The detection frequency of the set signal is set to 26 KHz, the length of the signal acquisition is 1024, and the statistical characteristics of the signal distribution are shown in Table 1.

Table 1
Statistical features of signal distribution

Wireless sensor node	Sensor node component/KHz	FM component/HZ
1	0.854	23.65
2	0.856	25.47
3	0.912	26.35
4	0.868	26.81
5	0.904	25.72

According to the parameter settings, the time domain distribution of abnormal underwater communication signals is obtained as shown in Fig. 3.

Figure 3.

Time domain distribution of abnormal signals in underwater communication.

Points A, B and C in Fig. 3 are abnormal signal points of underwater communication.

4.2 Experimental results

According to the time domain distribution of abnormal underwater communication signals in Fig. 3, the location results of abnormal underwater communication feature points are obtained as shown in Fig. 4.

Figure 4.

The location results of abnormal feature points of underwater communication.

Figure 4 shows that the method in this paper can effectively locate the abnormal feature points of underwater communication. The methods of reference [6] and reference [7] are used as experimental comparison methods to test the positioning accuracy, and the comparison results are shown in Fig. 5.

Figure 5.

Positioning accuracy comparison test.

Figure 5 shows that the average accuracy of underwater signal anomaly sensing method designed by multi-sensor data fusion for locating abnormal underwater communication signals is 95.5%, and the average accuracy of the literature method is 70.3% and 76.4%, respectively. The abnormal signal sensing method designed in this paper is 25.2% and 19.1% higher than the literature method, respectively, which shows that the method in this paper has a higher accuracy for the location of abnormal underwater communication feature points.

On the basis of the experiments, the comparison results of the misrecognition rate of abnormal signal perception are tested, as shown in Fig. 6.

Figure 6.

Comparison of the misrecognition rate of abnormal signal perception.

From Fig. 6, it can be seen that compared with the other two methods, the false recognition rate of the abnormal underwater communication signal of the method in this paper is always lower than 2%, there is no obvious fluctuation, and it is basically not affected by the number of samples. The perceived misidentification rate of the reference [6] method fluctuates greatly, the highest is about 11.1%, and the reference [7] method has the most obvious fluctuation of the misrecognition rate, the highest is about 19.5%. Comparing these data, the proposed method reduced by 9.1% and 17.5%, it can be seen that the method in this paper has the best abnormal signal recognition effect, and has high reliability and stability of underwater communication abnormal signal recognition.

The experiment analyzes the time-consuming abnormal signal perception of the three methods under different number of samples, and the results are described in Fig. 7.

Figure 7.

Time-consuming comparison of abnormal signal perception in underwater communication.

From Fig. 7, it can be seen that with the increase of the number of samples, the time-consuming of the three methods for sensing abnormal signals of underwater communication shows an upward trend, but the time-consuming increase of the method in this paper is extremely slow. The time-consuming is not more than 3 s, when the number of samples is less than 180, the time consumption of reference [6] method and reference [7] method is close to that of the proposed method. When the number of samples is more than 180, the time consumption of reference [6] method increases rapidly and then gradually becomes stable, while that of reference [7] method continues to rise rapidly. When the number increases to 420, the literature method can sense the abnormal signal of underwater communication for the longest time, up to 15 seconds, while the sensing time of the abnormal signal sensing method designed in this paper is only 2.6 seconds. Comparing these data, it can be seen that the method in this paper takes the shortest time to perceive abnormal signals of underwater communication, and has the optimal speed of perception of abnormal signals of underwater communication.

5. Conclusion

In order to solve the problem of poor positioning and high misjudgment rate of abnormal signals in underwater communication, an underwater signal anomaly sensing model based on multi-sensor data fusion was proposed. In this method, the multi-sensor data fusion algorithm is introduced, and the frequency hopping communication method is used to establish the data fusion model of the signal modulation and recognition system for multi-sensor reception, and combined with the deep learning algorithm, the underwater signal anomaly perception is realized. According to the experimental analysis, the average positioning accuracy of the proposed method for underwater communication abnormal signals is increased by 25.2% and 19.1%, the misjudgment rate of underwater communication abnormal signals is reduced by 9% and 17%, and the perception time of 420 MB underwater communication abnormal signals is less than 3 seconds. The experimental results show that the method has good underwater signal anomaly sensing performance, and can be applied to underwater signal acquisition and transmission process to improve the performance of data communication. In the subsequent work, the CPU ratio during the operation of the method will be deeply studied to further improve the practical application value of the underwater signal anomaly sensing model based on multi-sensor data fusion, so that it can work efficiently without affecting the operation of other software.

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Mathematical modeling of underwater signal anomaly perception based on multi-sensor data fusion

Abstract

Keywords

1. Introduction

2.1 Accurate selection of tracking channel for underwater communication

3.1 Multi-sensor underwater signal data fusion model

4.1 Experimental environment and experimental data

Table 1 Statistical features of signal distribution

References

Table 1
Statistical features of signal distribution