CN110207689B - Pulsar signal denoising and identifying method based on wavelet entropy - Google Patents
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Abstract
The invention belongs to the technical field of pulsar signal processing, and discloses a method for denoising and identifying pulsar signals based on wavelet entropy. Firstly, decomposing pulsar signals by using wavelet transformation, and calculating the wavelet entropy of each subinterval after wavelet decomposition. And combining the wavelet entropy and the wavelet threshold value to determine the threshold value of the high-frequency wavelet coefficient of each layer. And processing the pulsar signal with noise by using a threshold. And calculating the wavelet entropy values of all pulsar signals in each interval in the sample according to the characteristic that the energy values of different pulsar signals in each interval show differentiation. And recording the wavelet entropy value result of each pulsar signal, constructing characteristic parameters by combining corresponding names, loading the characteristic parameters into a database, comparing the characteristic parameters with unknown pulsar signal characteristics, and finishing the identification of the pulsar signals. The invention only uses wavelet entropy algorithm, and can extract the wavelet entropy value of the signal as the characteristic quantity to complete the task of identification while denoising the signal.
Description
Technical Field
The invention belongs to the technical field of pulse signal processing, and particularly relates to a pulsar signal denoising and identifying method based on wavelet entropy.
Background
Currently, the closest prior art: the ultrahigh stability of the pulsar signal cycle provides a new research direction for spacecraft navigation, but the received pulsar signal contains strong noise due to the long propagation distance, the high interference of interstellar space materials and the performance of receiving equipment. In general, the noise removal process is performed to remove noise from the effective signal that is to be used. In the process of pulsar identification, denoising processing is also required to be performed first. The existing algorithm mostly divides the de-noising and the identification of the pulsar signal into two parts for research, and different algorithms are provided for the two parts. These algorithms are all used to solve a single problem, and two algorithms are used to solve two compatible signal processing problems of de-noising and recognition of the pulsar navigation system, which reduces the efficiency of the system.
In summary, the problems of the prior art are as follows: the existing pulse signal processing algorithm is used for solving a single problem, two algorithms are used for solving two compatible signal processing problems of denoising and identification of the pulsar navigation system, and the efficiency of the system is reduced.
The difficulty of solving the technical problems is as follows:
the method is used for solving the two problems of denoising and identification at the same time, and the purposes of filtering noise and extracting noise are achieved. The prior art aims to suppress and eliminate noise signals and extract signal characteristics by other means. The prior art does not provide the possibility of extracting these two features, while the wavelet entropy method effectively extracts the noise signal features and the pulsar signal features after signal decomposition.
The significance of solving the technical problems is as follows:
the X-ray pulsar signal processing is a key part of the navigation technology and restricts the navigation precision. Therefore, the research on the denoising and the identification of the X-ray pulsar signals has important significance for improving the precision and the efficiency of the X-ray pulsar navigation system.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a pulsar signal denoising and identifying method based on wavelet entropy.
The invention is realized in such a way, and the pulsar signal denoising and identifying method based on the wavelet entropy comprises the following steps:
decomposing pulsar signals by using wavelet transformation, and calculating wavelet entropy of each subinterval after wavelet decomposition; combining the wavelet entropy and the wavelet threshold to determine the threshold of each layer of high-frequency wavelet coefficient; processing a pulsar signal with noise by using a threshold;
secondly, presenting differentiation characteristics according to the energy values of different pulsar signals in each interval; calculating the wavelet entropy values of all pulsar signals in each interval in the sample;
and thirdly, combining the wavelet entropy value result of each pulsar with corresponding names, constructing characteristic parameters, loading the characteristic parameters into a database, comparing the characteristic parameters with unknown pulsar signals, and finishing the identification of the pulsar signals.
Further, the first step specifically includes:
(1) firstly, carrying out wavelet transformation of m scales on noisy pulsar signals x (n) to obtain discrete wavelet coefficients of each scale, wherein the coefficient of high-frequency components at the k moment under the j-th decomposition scale is represented as d j，k The coefficient of the low frequency component is denoted as a j，k The sampling frequency of the signal is denoted as f s Wherein j is 1, 2 …, 5; k is 1, 2 …, 10; preferably, db6 is used as a wavelet basis function, and 5-scale discrete wavelet transform is carried out on the pulsar sequence;
(2) respectively calculating the wavelet energy E of the high-frequency coefficient of each interval according to the discrete wavelet coefficients of each layer j，k (ii) a Layer j coefficient d of the signal j，k Equally dividing into n intervals, the energy of each interval of the layer is:
wherein m is the number of sampling points;
(3) the wavelet energy distribution probability is the energy E of the wavelet coefficient of the kth sub-interval j，k Total energy E of wavelet coefficient of the layer j The ratio of (A) to (B);
P j，k ＝E j，k /E j ；
wavelet entropy W of K interval k Is as follows;
W k ＝-∑ j P j，k ln(P j，k )；
finding an interval with the maximum wavelet entropy value, and calculating the noise estimation variance sigma of the interval:
wherein
The wavelet entropy value in the wavelet coefficient interval reaches the wavelet coefficient median value of the maximum interval. The specific calculation method of the coefficient median is as follows:
wherein, γ 1 Adjustment factor of threshold
Beta; the threshold is adaptively determined by adjusting the values of the coefficients and the factors according to the characteristics of the signal. Lambda [ alpha ] j If the high frequency coefficient threshold is obtained, the high frequency coefficient threshold is;
wherein, gamma is 2 Adjusting the threshold of each layer of coefficient according to the actual condition, wherein N is the length of the sample signal;
carrying out threshold processing on the high-frequency coefficient to obtain a denoised pulsar signal for reconstruction; calculating a mean square error to obtain a performance index of a denoising effect;
where x' (n) is the denoised signal.
Further, the second step specifically includes:
(1) establishing a pulsar signal database, sequentially calculating wavelet entropies of all intervals as characteristic parameters, and storing the characteristic parameters and pulsar signal names in the database;
(2) calculating a wavelet entropy value of an unknown pulsar signal, and comparing the wavelet entropy value with data in a database; comparing the variances between the two groups of signal characteristic parameters to determine whether the characteristics have uniqueness; the variance formula of the characteristic parameters is as follows;
wherein, s1 j (n)，s2 j (n) wavelet entropy values of j-th layers of the two signals;
(3) it was concluded whether the pulsar PSR 0531+21 signal is present in the existing database. If present, the variance is 0; otherwise, the pulsar is deemed not in the known database.
The invention also aims to provide a spacecraft applying the wavelet entropy based pulsar signal denoising and identifying method.
Another objective of the present invention is to provide a pulsar signal processing system applying the wavelet entropy based pulsar signal denoising and identifying method.
In summary, the advantages and positive effects of the invention are: in view of the defects of the existing algorithm, the invention provides a pulsar signal denoising and identifying method based on wavelet entropy; only the wavelet entropy algorithm is used, and the wavelet entropy value of the signal can be extracted as the characteristic quantity to complete the identification task while the signal is denoised.
Drawings
Fig. 1 is a flowchart of a method for denoising and identifying a pulsar signal based on wavelet entropy according to an embodiment of the present invention.
Fig. 2 is a waveform diagram of an original signal without noise according to an embodiment of the present invention.
Fig. 3 is a waveform diagram of a noisy signal with a signal-to-noise ratio of 20db according to an embodiment of the present invention.
Fig. 4 is a waveform diagram of discrete wavelet coefficients at various scales according to an embodiment of the present invention.
Fig. 5 is a diagram illustrating wavelet entropy values of coefficients of respective layers according to an embodiment of the present invention.
Fig. 6 is a waveform diagram of a denoised signal according to an embodiment of the present invention.
Fig. 7 is a comparison graph of an original signal, a noisy signal, and a denoised signal according to an embodiment of the present invention.
Fig. 8 is a line graph of wavelet entropy of different layers of pulsar signals according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention combines the high-frequency coefficient of wavelet transform to determine a proper threshold value, thereby achieving the purpose of denoising. And the calculated wavelet entropy is used as a characteristic parameter of the identification signal, so that the purpose of identifying the pulsar signal is achieved.
The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.
As shown in fig. 1, the method for denoising and identifying a pulsar signal based on wavelet entropy according to the embodiment of the present invention includes the following steps:
s101: decomposing pulsar signals by using wavelet transformation, and calculating wavelet entropy of each subinterval after wavelet decomposition; combining the wavelet entropy and the wavelet threshold to determine the threshold of each layer of high-frequency wavelet coefficient; processing a pulsar signal with noise by using a threshold;
s102: presenting a differentiated characteristic according to the energy values of different pulsar signals in each interval; calculating the wavelet entropy values of all pulsar signals in each interval in the sample;
s103: and (3) combining the wavelet entropy value result of each pulsar with corresponding names, constructing characteristic parameters, loading the characteristic parameters into a database, comparing the characteristic parameters with unknown pulsar signals, and finishing the identification of the pulsar signals.
The pulsar signal denoising and identifying method based on the wavelet entropy provided by the embodiment of the invention specifically comprises the following steps:
denoising;
(1) firstly, carrying out wavelet transformation of m scales on noisy pulsar signals x (n) to obtain discrete wavelet coefficients of each scale, wherein the coefficient of high-frequency components at the k moment under the j-th decomposition scale is represented as d j，k The coefficient of the low frequency component is denoted as a j，k The sampling frequency of the signal is denoted as f s Wherein j is 1, 2 …, 5; k is 1, 2 …, 10; preferably, db6 is used as a wavelet basis function, and discrete wavelet transform of 5 scales is carried out on the pulsar sequence;
(2) respectively calculating the wavelet energy E of the high-frequency coefficient of each interval according to the discrete wavelet coefficients of each layer j，k . Layer j coefficient d of the signal j，k Equally dividing into n intervals, the energy of each interval of the layer is:
where m is the number of sampling points.
(3) The wavelet energy distribution probability is the energy E of the wavelet coefficient of the kth sub-interval j，k Total energy E of wavelet coefficient of the layer j The ratio of (A) to (B);
P j，k ＝E j，k /E j (3)
wavelet entropy W of K interval k Is as follows;
W k ＝-∑ j P j，k ln(P j，k ) (4)
finding an interval with the maximum wavelet entropy value, and calculating the noise estimation variance sigma of the interval:
wherein
The wavelet entropy value in the wavelet coefficient interval reaches the wavelet coefficient median value of the maximum interval. The specific calculation method of the coefficient median is as follows:
wherein, γ 1 Adjustment factor of threshold
Beta is then added. The values of the coefficients and factors are adjusted based on the characteristics of the signal to adaptively determine the threshold. Lambda [ alpha ] j If the high frequency coefficient threshold is obtained, the high frequency coefficient threshold is;
wherein, γ 2 And adjusting the threshold of each layer of coefficient according to the actual condition, wherein N is the length of the sample signal.
And (4) carrying out threshold processing on the high-frequency coefficient through the formula (6) to obtain a denoised pulsar signal for reconstruction. And (8) the expression of the mean square error is obtained, and the performance index of the denoising effect is obtained by calculating the mean square error.
Where x' (n) is a denoised signal.
Step two: classification of
(1) And (3) establishing a pulsar signal database, sequentially calculating the wavelet entropy of each interval according to the formula (7), and storing the wavelet entropy as a characteristic parameter in the database together with the pulsar signal name.
(2) And calculating the wavelet entropy value of the unknown pulsar signal, and comparing the wavelet entropy value with data in a database. And comparing the variances between the two groups of signal characteristic parameters to determine whether the characteristics have uniqueness. The variance formula of the characteristic parameters is as follows;
VAR j ＝[∑ n (s1 j (n)-s2 j (n)) 2 ] 1/2 (9)
wherein, s1 j (n)，s2 j (n) wavelet entropy values for the j-th layer of both signals.
(3) It was concluded whether the pulsar PSR 0531+21 signal is present in the existing database. If present, the variance is 0; otherwise, the pulsar is deemed not in the known database.
The application of the principles of the present invention will now be described in further detail with reference to specific embodiments.
The following describes a specific embodiment of the present invention with reference to the drawings by taking PSR 0531+21 signals as an example for denoising and establishing a database identification.
In order to more efficiently process the problems of de-noising and identification of the pulsar signals, the invention uses wavelet entropy to simultaneously process the two problems. After the signal is subjected to wavelet transformation, the entropy reflects the position of noise intensity and the characteristics of energy distribution. By combining the two points, the invention solves the two problems through threshold denoising and characteristic comparison. Meanwhile, the invention establishes 29 groups of pulsar signal characteristic databases as examples in simulation examples, and compares residual values among 21 groups of pulsar signals, so that the comparison process can be quickly completed. For unknown pulsar signals that are not in the database, the pulsar name can be determined and then included in the database. The feature information continuously updated in the feature database can also be used as a reference for other research contents. The specific implementation process comprises the following steps:
step S1: the Pulsar observation Data is obtained from a European Pulsar database (EPNDA), and is processed to obtain a Pulsar PSR 0531+21 signal sequence. A wavelet threshold denoising program is written in MATLAB. The pulsar signal sequence is read from the document and the profile curve of the pulsar is plotted as shown in fig. 2. Taking wavelet threshold denoising for noisy signals with the signal-to-noise ratio of 20db as an example.
In this embodiment, the PSR 0531+21 signal is used, and the wavelet threshold denoising step is as follows:
s1-1: as shown in fig. 3, the PSR 0531+21 signal profile with gaussian white noise is plotted. And respectively carrying out wavelet transformation on the noisy pulsar signals to obtain discrete wavelet coefficients of all scales. Different values are set, and optimization is performed to find a suitable number of decomposition layers. Finally, db6 is used as a wavelet basis function to perform 5-scale discrete wavelet transform on the pulsar sequence. The pulsar signal transformation result is shown in fig. 4.
S1-2: each layer is divided equally into 10 intervals. As shown in table 1, the wavelet energy values of the high frequency coefficients of the respective intervals are calculated according to equation (2). As shown in fig. 5, wavelet entropy values of the respective intervals are calculated according to equation (4).
Table 110 interval wavelet energy value of high frequency coefficient
The interval in which the wavelet entropy value is the largest is the sixth interval, and the noise estimation variance σ of this interval is calculated according to equation (5) to be 0.0142. The values of the coefficients and factors are adjusted based on the characteristics of the signal to adaptively determine the threshold. Adjustment coefficient gamma of threshold value threshold 1 ＝1.5，γ 2 0.8, adjustment factor
β ═ 1. As shown in table 2, the threshold value of the high frequency coefficient was obtained from equation (7).
TABLE 2 threshold values for high frequency coefficients of the layers
| Number of |
1 | 2 | 3 | 4 | 5 |
| Threshold value | 0.0796 | 0.0632 | 0.0300 | 0.0070 | 0.0066 |
And (4) carrying out threshold processing on the high-frequency coefficient through the formula (6) to obtain a denoised pulsar signal for reconstruction. As shown in fig. 4, a denoised pulsar signal waveform diagram is obtained. And (5) calculating the mean square error by using the formula (8) to obtain the performance index of the denoising effect. As shown in table 3, the denoising effect becomes better and better as the signal-to-noise ratio becomes higher. The processor of the computer used for the simulation experiment was Intel (R) core (TM) i5-3470CPU @3.20Ghz, the system type was a 64-bit operating system, X64 based processor. The program runs on a matlabR2017 platform, and the simulation time is 0.349 s. The calculation method of the embodiment is simple, does not involve complex operation, and has high running speed.
TABLE 3 PSR 0531+21 Signal-to-noise ratio and mean variance
| SNR/ |
5 | 10 | 20 | 25 | 30 | 35 |
| RMSE | 0.5098 | 0.2961 | 0.1048 | 0.0585 | 0.0348 | 0.0231 |
Step S2: and (4) taking a signal sequence of 25 pulsar as a sample, and verifying whether the wavelet entropy can become a characteristic parameter.
S2-1: according to the matching degree of the characteristic signals, the step of determining whether the wavelet entropy can be used as the characteristic parameters is as follows:
s2-1-1: the observational Data of Pulsar were obtained from European Pulsar Network Data Archive (EPNDA) to obtain a signal sequence of 25 pulsars.
S2-1-2: a wavelet entropy recognition program was written in MATLAB. Reading the pulsar signal sequence from the file, and establishing a database pulsar. And (4) sequentially calculating the wavelet entropy of each interval according to the formula (7), and storing the wavelet entropy as a characteristic parameter and the pulsar signal name into a database pul _ feature.
S2-1-3: and drawing wavelet entropy folding lines of different pulsar signals on each layer in the same coordinate system according to the information of the database. As shown in fig. 7, where the first 25 pulsar signals are wavelet entropy values of the original pulsar without noise. From the figure, we can obtain that the wavelet entropy values of the layers of different pulsar signals stored in the database do not completely overlap. For the same pulsar at different observation frequencies, the overlapping phenomenon occurs at partial levels, which just indicates that the same pulsar has a similar profile. Under different observation frequencies, the contour has different performance characteristics. Different white Gaussian noises are added to the same pulsar signal, the difference of wavelet entropies of different levels is less, and line segments in the graph tend to be gentle. The wavelet entropy values of different levels float in a certain area. The occurrence of straight lines is less. The amplitude of the polygonal line fluctuation can be obtained from the experimental result of the sample, different pulsar signals have different wavelet entropy values, and the wavelet entropy can be used as a parameter for pulsar signal characteristic identification.
S2-2: variance is carried out on 25 groups of pulsar data in the database and the wavelet entropy data of one group of PSR 0531+21 signals and other 24 groups of signals, so that the variance of the wavelet entropy of different levels can be obtained.
S2-2-1: in this example, the PSR 0531+21 signal is used, and the wavelet entropy identification is performed as follows:
s2-2-1: calculating the wavelet entropy value of the PSR 0531+21 signal, and obtaining the comparison result by using a variance formula (9). As shown in table 4.
TABLE 4 variance of pulse star signal in database and wavelet entropy values of each layer of PSR 0531+21 signal
S2-3: it was concluded that the PSR 0531+21 signal had a residual of 0 only from the same PSR 0531+21 signal present in the database, and that the residual of the remaining signals were all greater than 0.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. A pulsar signal denoising and identifying method based on wavelet entropy is characterized by comprising the following steps:
decomposing pulsar signals by using wavelet transformation, and calculating wavelet entropy of each subinterval after wavelet decomposition; combining the wavelet entropy and the wavelet threshold to determine the threshold of each layer of high-frequency wavelet coefficient; processing a pulsar signal with noise by using a threshold;
secondly, presenting differentiation characteristics according to the energy values of different pulsar signals in each interval; calculating the wavelet entropy values of all pulsar signals in each interval in the sample;
and thirdly, combining the wavelet entropy value result of each pulsar with corresponding names, constructing characteristic parameters, loading the characteristic parameters into a database, comparing the characteristic parameters with unknown pulsar signals, and finishing the identification of the pulsar signals.
2. The wavelet entropy-based pulsar signal denoising and identifying method as recited in claim 1, wherein the first step specifically comprises:
(1) firstly, wavelet transformation of m scales is carried out on noisy pulsar signals x (n) with the length of n to obtain discrete wavelet coefficients of each scale, and the coefficient of high-frequency components at the k moment under the j-th decomposition scale is represented as d j，k The coefficient of the low frequency component is denoted as a j，k The sampling frequency of the signal is denoted as f s Wherein j is 1, 2 …, 5; k is 1, 2 …, 10; db6 is used as a wavelet basis function to perform discrete wavelet transform of 5 scales on the pulsar signal;
(2) according toRespectively calculating wavelet energy E of high-frequency coefficient of each interval by using discrete wavelet coefficients of each layer j，k (ii) a Layer j coefficient d of the signal j，k Equally dividing into n intervals, the energy of each interval of the layer is:
wherein m is the number of sampling points;
(3) the wavelet energy distribution probability is the energy E of the wavelet coefficient of the kth sub-interval j，k Total energy E of wavelet coefficient of the layer j The ratio of (a) to (b);
P j，k ＝E j，k /E j ；
wavelet entropy W of K interval k Comprises the following steps:
W k ＝-∑ j P j，k ln(P j，k )；
finding an interval with the maximum wavelet entropy value, and calculating the noise estimation variance sigma of the interval:
wherein
The specific calculation method of the coefficient median is as follows for the wavelet coefficient median of the wavelet entropy value in the wavelet coefficient interval reaching the maximum interval:
wherein, gamma is 1 Adjustment factor of threshold
Beta; according to the characteristics of the signal, adjusting the values of the coefficient and the factor, and adaptively determining the threshold; lambda [ alpha ] j The threshold of the high frequency coefficient is:
wherein, gamma is 2 Adjusting the threshold of each layer of coefficient according to the actual condition, wherein N is the length of the sample signal;
carrying out threshold processing on the high-frequency coefficient to obtain a denoised pulsar signal for reconstruction; calculating a mean square error to obtain a performance index of a denoising effect;
where x' (n) is the denoised signal.
3. The wavelet entropy-based pulsar signal denoising and identifying method as recited in claim 2, wherein the second step specifically comprises:
(1) establishing a pulsar signal database, sequentially calculating wavelet entropies of all intervals as characteristic parameters, and storing the characteristic parameters and pulsar signal names in the database;
(2) calculating a wavelet entropy value of an unknown pulsar signal, and comparing the wavelet entropy value with data in a database; comparing the variances between the two groups of signal characteristic parameters to determine whether the characteristics have uniqueness; the variance formula of the characteristic parameters is as follows;
VAR j ＝[∑ n (s1 j (n)-s2 j (n)) 2 ] 1/2 ；
wherein n is the length of the noisy pulsar signal s1 j (n)，s2 j (n) are two sets of signalsWavelet entropy value of j-th layer;
(3) to conclude, from the variance VAR j Judging whether the pulsar signal exists in the existing database or not; if present, the variance is 0; otherwise, the pulsar is deemed not in the known database.
4. A spacecraft applying the wavelet entropy based pulsar signal denoising and identifying method as claimed in any one of claims 1-3.
5. A pulsar signal processing system applying the wavelet entropy based pulsar signal denoising and identifying method according to any one of claims 1-3.
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