CN115828552A - Line spectrum purification method based on shore-based passive sonar and optimal path tracking algorithm - Google Patents
Line spectrum purification method based on shore-based passive sonar and optimal path tracking algorithm Download PDFInfo
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Abstract
The invention relates to a line spectrum purification method and an optimal path tracking algorithm based on shore-based passive sonar, wherein the line spectrum purification method adopts an alpha bidirectional filter to filter a Hough transform output frequency spectrum, and comprises the following steps: the signal-to-interference and noise ratio of signals is improved by utilizing the design of an anti-interference steady self-adaptive beam former; line spectrum information is more effectively extracted from an LOFAR spectrogram, and a two-way filter is adopted to filter an output frequency spectrum of Hough transformation; finally, clearer and purer line spectrum information is separated compared with the line spectrum information before post-processing. After the line spectrum purification is completed, the tracking algorithm needs to fully consider the characteristics of the line spectrum in order to realize the detection and tracking of the line spectrum on the LOFAR diagram. According to the line spectrum purification method and the optimal path tracking algorithm, the detection capability is improved by analyzing and extracting the line spectrum radiation characteristics of the target, and a cost function decision model based optimal path searching model is constructed on the basis of an enhanced background equalization processing technology.
Description
Technical Field
The invention relates to the field of design and manufacture of underwater acoustic equipment, in particular to a line spectrum purification method and an optimal path tracking algorithm based on shore-based passive sonar.
Background
An active shore-based fixed sonar generally selects to construct a large-aperture array to improve space gain, in order to improve the self stealth of a system, a passive detection mode is generally adopted, a mode of scanning a pre-formed wave beam in a sonar observable space is adopted, when a target appears in a main lobe interval of a certain wave beam, expected array gain can be obtained, and the detection capability of the underwater weak target is improved.
The broadband energy detection in the passive sonar system is the main detection means that a sonar operator finds and tracks a target most depended on, the sonar operator judges the position of the target by observing the energy of a space beam, the target is tracked in a manual or automatic tracking mode, but the actual background of marine environment noise is complex and variable, a strong interference target often coexists with a weak target, when the two targets are adjacent, the energy history of the weak target is easily submerged by the strong target, and at the moment, the sonar operator is difficult to distinguish the weak target and the position of the weak target, the tracking is lost, and the detection leakage is caused. Therefore, the method of searching and tracking underwater weak targets by means of the broadband energy intensity of the pre-formed beam is far from enough, and more effective means are needed to assist a sonar operator in improving the detection efficiency.
Target signal detection is usually performed at the front end of a typical shore-based passive sonar signal processing model, and is a precondition for subsequent target tracking, positioning and identification. With the rapid development of large-scale integrated circuits, the boosting digital processing capacity is remarkably improved, the passive sonar signal detection means is greatly improved, the current main detection means is widely applied to digital signal processing methods such as LOFAR spectral analysis and DEMON spectral analysis, and good effects are achieved in numerous subdivision directions. In recent years, new shore-based fixed sonar signal passive detection activity is injected into domestic and foreign research, particularly new technologies and new mechanisms such as wavelet analysis and chaotic detection.
Dividing a shore-based passive sonar underwater acoustic target detection technology into two main directions, wherein one type is a passive detection technology based on time domain-frequency domain processing, and extracting target characteristic information for detection by converting a time sequence acquired by a sonar system in a time domain or a frequency domain under a complex background noise condition; the other type is a passive detection technology based on spatial domain processing, aiming at noise and interference with separability in a spatial domain, the passive detection technology processes sound intensity information received in an observation space of a sonar system, firstly, a threshold value is estimated for environmental background noise, and a signal which is determined to be an expected signal is judged to be used for extracting a useful signal when the threshold value is higher than the threshold value.
The detection technology based on airspace processing is widely applied to actual underwater acoustic engineering projects at present, and has the advantages of being tightly combined with the design of a sonar sensor array, solid in theoretical basis and wide in application examples;
however, the hot spot of the current domestic and foreign research focuses on the detection technology of the transform domain processing such as the time domain-frequency domain, and the like, and has more advantages for processing the underwater weak target detection problem under the complex background condition.
Following this thought, we focus on a detection technique based on transform domain processing such as time domain-frequency domain, and in the time domain processing detection technique, since low-frequency inherent line spectrum in ship radiation noise spectrum is often difficult to be eliminated, a technique for detecting by using low-frequency line spectrum components occupies an important position, and can be divided into an instantaneous detection method for power spectrum values observed in real time and an accumulation determination method for observing data history by using time accumulation.
The instantaneous detection method detects a line spectrum by utilizing a real-time power spectrum calculation result, and is often applied to scenes needing quick and visual expression. Cooley and Tukey jointly proposed a Fast Fourier Transform (FFT) as early as 1965, and segmented DFTs performed power spectrum estimation followed by threshold decision. However, in practical application environments, the fluctuation of the marine environmental noise is large, which is not beneficial to obtaining constant detection performance, and a method for adaptively adjusting the amplitude threshold according to the fluctuation of the environmental noise is urgently needed to be researched. In the other research direction, a binary hypothesis test problem is constructed by utilizing the statistical characteristics of single frequency points of the low-frequency line spectrum, and the low-frequency line spectrum is detected through statistical judgment. Kay constructs a generalized likelihood ratio detector on a time domain complex signal, so that the detector can realize constant false alarm, and the test statistical result of the detector consists of power spectrum estimation output of a periodogram method and normalized energy background. In order to solve the problem of environmental noise fluctuation, long-time integration is often selected when line spectrum features with weak signals are detected, and a segmentation processing mode is generally adopted. The segmented DFT processing method is characterized in that a generalized likelihood ratio detector is constructed through power spectrum results of different segments of the same frequency point by utilizing the statistical property of the power spectrum results of a single frequency point, so that a better detection effect compared with an average periodogram algorithm can be obtained, and unfortunately, coherent gains cannot be obtained. In the subsequent research, before a generalized likelihood ratio detector is constructed, phase compensation is firstly carried out, so that coherent accumulation gain among segments is realized, domestic researchers try to gradually improve the precision of phase difference compensation through means such as interpolation, and the performance of the detector is further improved. In 2008, li Qinhu and the like analyze a plurality of signal detection methods suitable for the condition of low signal-to-noise ratio, such as FFT analysis, autocorrelation detection, adaptive line spectrum enhancement and the like, aiming at the problem of detecting single-frequency components in ship radiation noise, and confirm the remarkable advantages of the segmented FFT detection method and have good tolerance to frequency drift. Although the instantaneous detection method can obtain higher detection probability and lower false alarm probability under the condition of high signal-to-noise ratio, the false alarm probability is obviously increased along with the reduction of the signal-to-noise ratio, thereby influencing the engineering practicability. The maschilon provides a method for coherent accumulation through energy leaked to adjacent frequency points by line spectrum signals, constructs a generalized likelihood ratio detector, can effectively obtain coherent gain, and reduces the loss of detection performance.
The accumulation judgment method is to draw a LOFAR spectrogram by using a power spectrum result of continuous accumulation observation, and clear bright lines (spectral lines for short) can be formed at frequency positions corresponding to the line spectrums, so that the detection of signals is equivalent to the detection and extraction of low-frequency line spectrums, and some common image detection and tracking means can be used. The method is also an essential step for LOFAR spectrum background balance so as to realize the promotion of the dynamic range of display, and is more favorable for human eye observation and reduce the duty of work on duty. Classical background equalization methods include alpha filtering, order truncation, median filtering, and the like. Because the accumulation judgment method adopts continuous multi-time observation information, even if part of the spectral lines fused with the historical information have transient observation results with low signal-to-noise ratio, a better detection effect can be obtained, and the processing process is relatively complex.
Because the low-frequency line spectrum component in the underwater target radiation noise has higher energy level and stability than a continuous spectrum, and because the energy is concentrated in a low-frequency band, the loss in the transmission process is less, and meanwhile, a plurality of valuable target parameters and motion information can be extracted from the line spectrum, so that the method based on line spectrum detection is a main means for tracking and identifying the underwater target. However, since the signal received by the underwater sensor is the result of the interaction of the target sound source with the marine environment, the line spectrum characteristics are affected by the fluctuation characteristics of the signal itself, the variations of the marine sound propagation channel, and the relative motion of the platform. The concrete expression is as follows: firstly, ship radiation noise is a time-varying non-stationary process and presents certain transient characteristics and statistical characteristics, researches show that the generation of the transient characteristics is related to the working condition of a certain part of a ship and uncertain human activity factors, and the statistical characteristics of the change of the ship navigation state, particularly the change of the ship speed, are also time-varying, so that the intensity and frequency drift change of a low-frequency line spectrum are caused; secondly, the signal propagation channel is a time-varying and space-varying environment, and inevitably generates a multipath effect, which causes frequency selective fading, and increases the difficulty of low-frequency line spectrum extraction. In addition, the relative movement of the target can also cause line spectrum non-stationarity, which is commonly shown in two aspects, namely, doppler frequency shift caused by relative speed changes the center frequency of the line spectrum in the signals acquired by the receiving array; secondly, the position change caused by the movement also causes the change of the transfer function of the sound propagation channel, and the non-stationarity of the line spectrum is also caused. In summary, these factors that cause the non-stationary characteristic of the low frequency line spectrum significantly limit the conventional means that directly benefit by increasing the integration time.
Disclosure of Invention
In order to solve the technical problem, the line spectrum purification method based on the shore-based passive sonar adopts an alpha bidirectional filter to filter a Hough transform output frequency spectrum, and comprises the following steps:
step S1: the signal-to-interference and noise ratio of signals is improved by utilizing the design of an anti-interference steady self-adaptive beam former;
step S2: line spectrum information is more effectively extracted from an LOFAR spectrogram, and a two-way filter is adopted to filter the Hough transform output spectrum, so that the variation trend of the background noise spectrum is extracted;
and step S3: the noise variation trend is removed from the Hough transform output frequency spectrum, and finally, clear and pure line spectrum information is separated compared with the line spectrum information before post-processing.
In one embodiment of the invention, the LOFAR is integrated over time using the Hough transform in step S2, i.e.
Wherein, T 1 And T 2 For integration time, P (t, f) represents the estimated time-varying spectrum in the LOFAR spectrum.
In one embodiment of the invention, the alpha bilateral filter is a first-order recursive filter, and the Hough transform output spectrum sequence is HF (f) n ) N =1,2 \ 8230n, then the operation steps of the α bidirectional filter are as follows:
for,n＝1,2…N
HF 1 (f 1 )＝HF(f 1 )
HF 1 (f n+1 )＝HF 1 (f n )+[HF(f n+1 )-HF 1 (f n )]/Q
end
for,n＝1,2…N
HF 2 (f N )＝HF(f N )
HF 2 (f n-1 )＝HF 2 (f n )+[HF(f n-1 )-HF 2 (f n )]/Q
end
HF α (f n )＝(HF 1 (f n )+HF 2 (f n ))/2,n＝1,2…N
in the above formula, HF α (f n ) For filtering the output sequence, Q is the recursive coefficient.
The invention also provides another optimal path tracking algorithm based on cost function decision, wherein the tracking algorithm needs to fully consider the characteristics of the spectral lines after completing the line spectrum purification and in order to realize the detection and tracking of the line spectrum on the LOFAR diagram, and the tracking algorithm is on a time-frequency histogram and assumes that the time t is the moment 1 At an arbitrary point P 1 From the start to time t n Arbitrary point P of n Is the minimum path, i.e. the path from point P, is found by using the cost function constructed by the above characteristic components 1 To P n In order to further reduce the computation amount, all frequency points do not need to be traversed, frequency drift or change is considered to be gradual change, and a parameter k is introduced to represent that only frequency points of adjacent windows are considered to calculate a cost function of a current point; the method comprises the following specific steps:
a, step a: at an observation window W of length N N Let the time corresponding to each observation point be t 1 ，...，t N ，(t 1 ＜···＜t N )；
Step b: suppose observation window W N Internal self t 1 The best path from a point in time to point P is
Ternary array giving set point P
Step c: then t 1 Initialization of the ternary array at the mth point in time
Step d: from t 2 Time begins to t N After the moment is finished, searching layer by layer to reach an observation window W N The optimal path of the inner arbitrary point P; to reduce the amount of computation, the current time t is known i Each point
The next time t is the optimal path of i+1 Point m
Need only search for t i K points with time and frequency close to that
The optimal path of (a);
step e: simultaneously for each point P within the observation window i Setting a counter Count (P) i ) When the path optimized by the minimum cost function is found to pass through the point, the counter accumulates 1, and the probability that the optimal path overlaps the point belonging to the line spectrum is inferred to be obviously higher than the probability of passing the point belonging to the noise by considering that the path passed by the line spectrum shows the characteristics of maximum amplitude, minimum curvature and optimal continuity relative to the noise, so that each point P obtained by the method i Number of times Count (P) passed by the best path selection i ) It can be used to determine whether it is a noise point or a line spectrum point;
step f: and continuously traversing all the points by circularly sliding the observation window to realize the processing of the whole time-frequency graph.
In one embodiment of the present invention, the expression formula in the best path of step d is as follows:
where j is some of the k points,
represents from
To
To find a cost function of the path
At a minimum, an optimum path is obtained
At the same time calculate
The ternary array of (2) as the input of the best path at the next time.
In one embodiment of the present invention, the intensity a (ζ) of step b requires the accumulation of the amplitude values on the line spectrum thereof as an identification quantity for discrete signal processing; arbitrary point P in path ζ i Has an amplitude value of a (P) i ) Then the sum of the magnitudes of the sequence of points traversed by the path, a (ζ), may be defined as:
in one embodiment of the invention, the curvature C (ζ) midpoint P of step b i Corresponding frequency value is f (P) i ) Then line segment [ P i ，P i+1 ]The frequency slope of (d) may be defined as:
p(P i ，P i+1 )＝f(P i+1 )-f(P i )
and the curvature of path ζ is:
in one embodiment of the invention, the continuity G (ζ) of step b is accumulated for the number of points traversed by the line spectrum, assuming an arbitrary point P i The continuity of (c) is:
in a real marine environment, the amplitude of marine background noise is not zero, and a threshold value mu needs to be set; point P in the path i Amplitude less than mu, set g (P) i ) Is 1, otherwise g (P) is set i ) Is 0; the continuity of the path ζ is:
the above is to calibrate three feature components according to the characteristics of the line spectrum, and then construct a definition formula of a cost function phi (zeta) for an arbitrary path zeta as follows:
where α and β are weighting coefficients, it can be seen from the above equation that the value of the cost function φ (ζ) of the path ζ is inversely proportional to the magnitude intensity and directly proportional to the curvature and the continuity.
Compared with the prior art, the technical scheme of the invention has the following advantages: the line spectrum purification method and the optimal path tracking algorithm improve the detection capability by analyzing and extracting the line spectrum radiation characteristic of the target, construct a cost function decision model based optimal path searching model on the basis of the enhanced background equalization processing technology, and aim to solve the optimal path with the minimum cost function on an LOFAR (local optimization search) graph, wherein the cost function fully considers the characteristics of the line spectrum, extract line spectrum information by the optimal path local optimal search criterion, lay technical support for improving the low-frequency line spectrum detection capability of non-stationary signals, and have important theoretical significance and application value.
Drawings
In order that the present disclosure may be more readily and clearly understood, reference will now be made in detail to the present disclosure, examples of which are illustrated in the accompanying drawings.
FIG. 1 is a schematic flow chart of a feature extraction processing technology of a line spectrum purification method based on a shore-based sonar passive detection model in the invention;
FIG. 2-1 is a LOFAR plot of the-30 dB DC weighted beam output according to the present invention;
FIG. 2-2 is a Hough transform output spectrum according to the present invention;
FIGS. 2-3 are filtered outputs of the alpha bi-directional filter of the present invention;
FIGS. 2-4 are line spectral information for the purification and local normalization of the present invention;
FIG. 3 is a 2019.8.20-100-300 Hz frequency sweep signal of the present invention;
FIG. 4-a is a time-frequency diagram of the low line spectrum tracking and extracting effect of the strong interference fringes of the present invention;
4-b is a diagram illustrating the result of the optimal path decision line-based spectral tracking and extraction according to the present invention;
FIG. 5-a is a time-frequency diagram illustrating the effect of feature adjustment on line spectrum extraction under strong interference fringes according to the present invention;
FIG. 5-b is a graph of the characteristic quantities "intensity and" greater specific gravity bias data fitness of the present invention;
FIG. 5-c is a graph showing that the characteristic "curvature" of the present invention is more heavily weighted toward sparsity;
FIG. 5-d shows that the feature value "continuity" of the present invention is biased toward sparsity by a large specific gravity.
Detailed Description
The embodiment provides a line spectrum purification method based on a shore-based passive sonar, which adopts an alpha bidirectional filter to filter an output frequency spectrum of Hough transform.
In a real marine environment, detection of underwater weak targets is often accompanied by the condition of a plurality of multi-target interferences around, the detection capability is improved by analyzing and extracting the line spectrum radiation characteristics of the targets, and the resolution and separation of the targets and the interferences need to be solved. One method is to increase the input SINR, usually by using an anti-interference robust adaptive beamforming design to increase the SINR of the signal, and then to extract the line spectrum information more effectively from the LOFAR spectrogram, the invention uses Hough transform to integrate the LOFAR according to time, i.e. the LOFAR is integrated according to time
Wherein, T 1 And T 2 For integration time, P (t, f) represents the estimated time-varying spectrum in the LOFAR spectrum. In image transformation, we usually use Hough transformation to separate out geometric shapes with some kind of same features from the image, and here, the Hough transformation is used to separate out line spectrum information in the LOFAR spectrogram.
True seaThe spectrum of ocean environment noise is non-uniform, so the line spectrum information can be regarded as being superposed on the non-uniform background noise spectrum, thus aiming at weaker line spectrum components, the line spectrum information is inevitably submerged in a higher environment noise spectrum, and the detection and extraction efficiency of the line spectrum is seriously influenced. Where the alpha bilateral filter is a first order recursive filter, the Hough transform output spectrum sequence is assumed to be HF (f) n ),n＝1,2…N，
The operation of the α bilateral filter is as follows:
for，n＝1，2…N
HF 1 (f 1 )＝HF(f 1 )
HF 1 (f n+1 )＝HF 1 (f n )+[HF(f n+1 )-HF 1 (f n )]/Q
end
for，n＝1，2…N
HF 2 (f N )＝HF(f N )
HF 2 (f n-1 )＝HF 2 (f n )+[HF(f n-1 )-HF 2 (f n )]/Q
end
HF α (f n )＝(HF 1 (f n )+HF 2 (f n ))/2，n＝1，2…N
in the above formula, HF α (f n ) The filtering output sequence is Q, the recursive coefficient is selected, the tracking performance is better and the filtering effect is worse when the value of the recursive coefficient is selected to be larger; conversely, when the value of the recursive coefficient is smaller, the filtering effect is better, and the tracking performance is worse.
The line spectrum purification method comprises the following steps:
step S1: the signal-to-interference and noise ratio of signals is improved by utilizing the design of an anti-interference steady self-adaptive beam former;
step S2: line spectrum information is more effectively extracted from an LOFAR spectrogram, and a two-way filter is adopted to filter the Hough transform output spectrum, so that the variation trend of the background noise spectrum is extracted;
and step S3: the noise variation trend is removed from the Hough transform output frequency spectrum, and finally, clear and pure line spectrum information is separated compared with the line spectrum information before post-processing.
In summary, a specific processing flow of the line spectrum feature extraction processing technology based on the shore-based sonar passive detection model is shown in fig. 1.
In the passive sonar signal processing flow, after the anti-interference robust adaptive beam former performs beam scanning, the spectrum information of the preformed beam is extracted, and meanwhile, the multi-beam spectrum characteristics can be fused to generate a spectrum azimuth trajectory diagram. After the first step of line spectrum purification is completed, in order to realize the detection and tracking of the line spectrum on the LOFAR diagram, the characteristics of the spectral line need to be fully considered, the invention provides a method for deciding the optimal path based on the cost function, which aims to solve the optimal path which minimizes the cost function on the LOFAR diagram, and if the optimal path passes through a certain point once, the point corresponds to the numerical standard and is accumulated once. If the cost function fully considers the characteristics of the low-frequency line spectrum, the statistical significance that the probability that the optimal path passes through the line spectrum frequency point is higher than the probability that the optimal path passes through noise is determined, so that the set of the optimal paths reaching all points from the initial time can be calculated, whether the point is the line spectrum frequency point or not is judged by counting the number of the points which the optimal path passes through, and the spectral line is extracted.
In time-frequency histograms, a clearly visible line is usually composed of a sequence of points of great amplitude and connected together. We construct a cost function phi such that the more line spectral features a point on a given path, the smaller its corresponding cost function phi and, conversely, the larger the cost function phi. Assuming an arbitrary path ζ of length N, the sequence of points is ordered in time as { P } 1 ，P 2 ，...，P N }. The cost function phi of the path is then scaled by the following three characteristic components:
a. strength sum A (ζ)
The line spectrum enhanced by the meridian spectrum should have a stronger amplitude and continuity than the surrounding noise, which can be easily observed by the human eye. However, for discrete signal processing, the amplitudes on the line spectrum need to be accumulated as an identification quantity. Assume an arbitrary point P in the path ζ i Has an amplitude value of a (P) i ) Then the sum of the magnitudes of the sequence of points traversed by the path, a (ζ), may be defined as:
b. curvature C (ζ)
For the continuity of the spectral line, two characteristic quantities can be defined to represent the curvature rule of the frequency and the continuity of the path ζ, respectively.
Because the line spectrum is represented as a smooth curve on the time-frequency histogram, the line spectrum can be observed and mastered by human eyes visually. The rate of change of the spectral line curve is therefore chosen to characterize the smoothness of the curve. We can assume point P i Corresponding frequency value is f (P) i ) Then line segment [ P i ，P i+1 ]The frequency slope of (d) may be defined as:
p(P i ，P i+1 )＝f(P i+1 )-f(P i )
the curvature of path ζ is:
c. continuity G (ζ)
Another characteristic of low frequency line spectrum, which is especially important for low snr line spectrum detection and tracking, is that zero amplitude rarely occurs in a sequence of points in the path traveled by the line spectrum, which we refer to as continuity. Under the complex background noise with strong interference, as a component for distinguishing from random background noise, the number of points passed by the line spectrum is accumulated, and an arbitrary point P is assumed i The continuity of (c) is:
in a real marine environment, the amplitude of the marine background noise is not zero, and a threshold value mu needs to be set. Point P in the path i Amplitude less than mu, set g (P) i ) Is 1, otherwise g (P) is set i ) Is 0; the continuity of the path ζ is:
the above is to calibrate three characteristic components according to the characteristics of the line spectrum, and then construct a definition formula of a cost function phi (zeta) for an arbitrary path zeta as follows:
where α and β are weighting coefficients, it can be seen from the above equation that the value of the cost function φ (ζ) for path ζ is inversely proportional to the magnitude strength and directly proportional to the curvature and continuity. Because the path ζ' passed by the line spectrum simultaneously meets the conditions of maximum amplitude, minimum curvature and minimum continuity of the path, the line spectrum tracking problem becomes the optimum problem of obtaining the extremum with the minimum cost function in a tracking path set.
The algorithm implementation steps are as follows: on the time-frequency histogram, let it be assumed that the time t is the following 1 At an arbitrary point P 1 Starting at time t n Arbitrary point P of n Is the minimum path, i.e. the path from point P, is found by using the cost function constructed by the above characteristic components 1 To P n In order to further reduce the computation amount, all frequency points do not need to be traversed, frequency drift or change is considered to be gradual change, and a parameter k is introduced to represent that only adjacent window frequency points are considered to calculate the cost function of the current point.
Step a: at an observation window W of length N N Assuming observation points per lineCorresponding time t 1 ，...，t N ，(t 1 ＜···＜t N )；
Step b: suppose observation window W N Internal self t 1 The best path from a point in time to point P is
Ternary array giving set point P
Step c: then t 1 Initialization of the ternary array at the mth point in time
Step d: from t 2 Time begins to t N After the moment is finished, searching layer by layer to reach an observation window W N The best path for any point P within. To reduce the amount of computation, the current time t is known i Each point
The next time t is the optimal path of i+1 Point m
Need only search for t i K points with time and frequency close to that
The expression formula is as follows:
where j is some of the k points,
represents from
To
To find a cost function of the path
At a minimum, an optimum path is obtained
At the same time calculate
The ternary array of (2) as the input of the best path at the next time.
Step e: simultaneously for each point P within the observation window i Setting a counter Count (P) i ) When the path optimized by the minimum cost function is found to pass through the point, the counter accumulates 1, and the probability that the optimal path overlaps the point belonging to the line spectrum is inferred to be obviously higher than the probability of passing the point belonging to the noise by considering that the path passed by the line spectrum shows the characteristics of maximum amplitude, minimum curvature and optimal continuity relative to the noise, so that each point P obtained by the method i Number of times Count (P) passed by the best path selection i ) It is actually possible to determine whether it is a noise point or a line spectrum point.
Step f: and then continuously traversing all the points by circularly sliding the observation window to realize the processing of the whole time-frequency graph.
The line spectrum purification method and the optimal path tracking algorithm of the embodiment provide line spectrum purification post-processing effects:
firstly, processing a group of measured data of certain shore-based passive sonar at sea in a certain scientific research sea test, analyzing 240-second experimental data of t = 60-64 min, designing a beam former of which the main lobe pointing angle is aligned to the direction of a target, namely 113-114 degrees, wherein the beam forming uses DC weighted beam forming of side lobes such as-30 dB, and the frequency range is 50-300 Hz, wherein the acquired line spectrum of a weak signal is shown in the following graph, the LOFAR graph of display control output is shown in the following graph 2-1.
Fig. 2-1 is a LOFAR plot of beam output using a-30 dB DC weighting. Fig. 2-2 shows the transformed output spectrum after Hough transform, and it can be seen that the low-frequency line spectrum components with stronger energy can be clearly distinguished and located by Hough transform, which are 77.5Hz, 82.2Hz, 85.8Hz, 91.9Hz, 97.7Hz, 104Hz, 110Hz, and 120.2Hz, respectively. Next, the transformation output frequency spectrum of the Hough transformation is processed by an alpha bidirectional filter, the filter parameter Q takes a value of 100, the output result of the alpha bidirectional filter after filtering is shown in fig. 2-3, it can be seen that the change trend of the background noise of the LOFAR diagram is obtained by the alpha bidirectional filter, we can remove the change trend from the Hough transformation output frequency spectrum, and then obtain clearer and cleaner line spectrum information, as shown in fig. 2-4, the line spectrum components which can be clearly distinguished after post-processing are respectively 58.1Hz, 77.4Hz, 82.3Hz, 85.8Hz, 91.9Hz, 97.7Hz, 103.9Hz, 110Hz, 120.2Hz, 130.6Hz, 154.5Hz, 164.6Hz and 253.4Hz.
In addition, after post-processing of line spectrum purification, weak signals can be obviously observed by naked eyes, then, the line spectrum automatic tracking and extracting effects of the weak signals are continuously verified, the processed data come from marine actually-measured weak signals acquired by certain shore-based sonar, and as shown in the following fig. 3, experimental results show that a plurality of weak line spectrums of 164Hz, 184Hz and the like can be observed by naked eyes in a left time-frequency diagram; and the right graph is obtained by trying to solve the problem that the cost function is minimum on the LOFAR graph by adopting a search mode of deciding the optimal path based on the cost function, the characteristics of a line spectrum are fully considered in designing the cost function, and the set of the optimal paths reaching all points from the initial moment is counted, so that the spectral line is extracted. By comparison, the voting result based on the optimal path iterative decision is consistent with the intensity distribution of the line spectrum in the time-frequency diagram of the actually acquired signal, and the voting result can be used as a basis for extracting the line spectrum, namely line spectrum information searched based on the optimal path at each moment can be given.
Meanwhile, the further analysis is carried out by utilizing measured data under the conditions of complex background at sea and multi-target interference, and the fact that the target LOFAR spectrogram often has obvious interference fringes and has strong interference fringe influence on line spectrum tracking and extraction under the weak signal-to-noise ratio is found, as shown in fig. 4-a and 5-a.
And (3) searching an extreme value of a cost function phi (zeta) by adjusting the weighting coefficients alpha and beta to ensure that the path zeta meets the conditions of maximum amplitude intensity, minimum curvature and optimal continuity. As shown in fig. 4-b and 5-b, the intensity and a (ζ) weight are adjusted high, the frequency distribution of the voting extraction reflects a bias towards data fitness, and the spectral line fidelity is high; at the moment, the corresponding sparsity is poor, the voting result is contained in a noisy background, and the spectral line is not easy to distinguish.
As shown in fig. 5-C and fig. 5-d, by continuously adjusting the curvature C (ζ), the weight of the continuity G (ζ) is occupied, the sparsity of the voted result becomes stronger (more zero values), and the spectral line is easy to distinguish; at this time, the corresponding data fitting effect is deteriorated, and the spectral line is easily distorted.
The characteristics and the rules reflected by the method are mastered, and the selection and the utilization can improve the tracking and the extraction capability of the system on the line spectrum with the weak signal-to-noise ratio under the strong interference. When the line spectrum energy is weak and is included in a noisy background and is not easy to distinguish, the curvature C (zeta) is adjusted to be high, and the weight occupied by the continuity G (zeta) is biased to sparsity; when interference fringes with large frequency change appear in the frequency spectrum, the curvature C (zeta) is reduced, and the weight of the continuity G (zeta) is biased to data fitting to avoid spectral line distortion.
As shown in fig. 5, by the above method for deciding the optimal path based on the cost function, the optimal path with the minimum cost function is obtained on the time-frequency diagram, and the intensities of three groups of characteristic quantities, a (ζ), the curvature C (ζ), and the continuity G (ζ) are adjusted, so that a plurality of line spectrums of 163Hz, 212Hz, 226Hz, 324Hz, and the like can be effectively extracted from the time-frequency diagram, and the tracking and extraction of the line spectrum with weak signal-to-noise ratio under strong interference are realized.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.
Claims (8)
1. A line spectrum purification method based on shore-based passive sonar adopts an alpha bidirectional filter to filter a Hough transform output frequency spectrum, and is characterized by comprising the following steps:
step S1: the signal-to-interference and noise ratio of signals is improved by utilizing the design of an anti-interference steady self-adaptive beam former;
step S2: line spectrum information is more effectively extracted from an LOFAR spectrogram, and a two-way filter is adopted to filter the Hough transform output spectrum, so that the variation trend of the background noise spectrum is extracted;
and step S3: the noise variation trend is removed from the Hough transform output frequency spectrum, and finally, clear and pure line spectrum information is separated compared with the line spectrum information before post-processing.
2. The line spectrum purification method of claim 1, wherein: in step S2, the LOFAR is integrated according to time by using Hough transformation, namely
Wherein, T 1 And T 2 For integration time, P (t, f) represents the estimated time-varying spectrum in the LOFAR spectrum.
3. The line spectrum refining method according to claim 1, wherein: the adopted alpha bidirectional filter is a first-order recursive filter, and the output frequency spectrum sequence of Hough transformation is HF (f) n ) N =1,2 \8230, N, then the operation steps of the α bidirectional filter are as follows:
for,n＝1,2…N
HF 1 (f 1 )＝HF(f 1 )
HF 1 (f n+1 )＝HF 1 (f n )+[HF(f n+1 )-HF 1 (f n )]/Q
end
for,n＝1,2…N
HF 2 (f N )＝HF(f N )
HF 2 (f n-1 )＝HF 2 (f n )+[HF(f n-1 )-HF 2 (f n )]/Q
end
HF α (f n )＝(HF 1 (f n )+HF 2 (f n ))/2,n＝1,2…N
in the above formula, HF α (f n ) For filtering the output sequence, Q is the recursive coefficient.
4. An optimal path tracking algorithm based on cost function decision, wherein the tracking algorithm needs to fully consider the characteristics of spectral lines after completing the line spectrum purification and in order to realize the detection and tracking of the line spectrum on a LOFAR graph, and is characterized in that the tracking algorithm is on a time-frequency histogram, and the assumption is made that the time t is the moment 1 At an arbitrary point P 1 From the start to time t n Arbitrary point P of n Is the minimum path, i.e. the path from point P, is found by using the cost function constructed by the above characteristic components 1 To P n In order to further reduce the computation amount, all frequency points do not need to be traversed, frequency drift or change is considered to be gradual change, and a parameter k is introduced to represent that only frequency points of adjacent windows are considered to calculate a cost function of a current point; the method comprises the following specific steps:
step a: at an observation window W of length N N Let t be the time corresponding to each observation point 1 ，...，t N ，(t 1 ＜…＜t N )；
Step b: suppose observation window W N Internal self t 1 The best path from a point in time to point P is
Ternary array giving set point P
Step c: then t 1 Initialization of the ternary array at the mth point in time
Step d: from t 2 Time begins to t N After the moment is finished, searching layer by layer to reach an observation window W N The optimal path of the inner arbitrary point P; to reduce the amount of computation, the current time t is known i Each point
The next time t is the optimal path of i+1 Point m
Need only search for t i K points with time and frequency close to that
The optimal path of (a);
step e: simultaneously for each point P within the observation window i Setting a counter Count (P) i ) When the path optimized by the minimum cost function is found to pass through the point, the counter accumulates 1, and the probability that the optimal path overlaps the point belonging to the line spectrum is inferred to be obviously higher than the probability of passing the point belonging to the noise by considering that the path passed by the line spectrum shows the characteristics of maximum amplitude, minimum curvature and optimal continuity relative to the noise, so that each point P obtained by the method i Number of times Count (P) passed by the best path selection i ) In fact, the method can be used for judging whether the noise point or the line spectrum point;
step f: and continuously traversing all the points by circularly sliding the observation window to realize the processing of the whole time-frequency graph.
5. The optimal path tracking algorithm of claim 4, wherein: the expression formula in the optimal path of the step d is as follows:
where j is some of the k points,
represents from
To
To find a cost function of the path
At a minimum, an optimum path is obtained
At the same time calculate
The ternary array of (2) as the input of the best path at the next time.
6. The optimal path tracking algorithm of claim 4, wherein: the intensity A (zeta) of the step b needs to accumulate the amplitude values on the line spectrum of the discrete signal processing as an identification quantity; arbitrary point P in path ζ i Has an amplitude value of a (P) i ) Then the sum of the magnitudes of the sequence of points traversed by the path, a (ζ), may be defined as:
7. the optimal path tracking algorithm of claim 4, wherein: curvature C (ζ) of step bPoint P i Corresponding frequency value is f (P) i ) Then line segment [ P i ，P i+1 ]The frequency slope of (d) may be defined as:
p(P i ，P i+1 )＝f(P i+1 )-f(P i )
and the curvature of path ζ is:
8. the optimal path tracking algorithm of claim 4, wherein: the continuity G (zeta) of step b is accumulated for the number of points through which the line spectrum passes, assuming any point P i The continuity of (c) is:
in a real marine environment, the amplitude of marine background noise is not zero, and a threshold value mu needs to be set; point P in the path i Amplitude less than mu, set g (P) i ) Is 1, otherwise g (P) is set i ) Is 0; the continuity of the path ζ is:
the above is to calibrate three characteristic components according to the characteristics of the line spectrum, and then construct a definition formula of a cost function phi (zeta) for an arbitrary path zeta as follows:
where α and β are weighting coefficients, it can be seen from the above equation that the value of the cost function φ (ζ) for path ζ is inversely proportional to the magnitude strength and directly proportional to the curvature and continuity.
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