A spectrum redshift measurement method and device based on density point cross correlation

Abstract

The present invention discloses a spectral redshift measurement method and device based on density point cross-correlation, which obtains a spectral line spectrum after preprocessing of a spectrum to be measured and extracts first characteristic spectral line information therefrom; generates a first redshift candidate set of the spectrum to be measured based on the second characteristic spectral line information and the first characteristic spectral line information of the stationary spectrum; classifies the redshift values ​​in the first redshift candidate set to obtain several redshift candidate subsets; generates a second redshift candidate set based on the several redshift candidate subsets; and determines the spectral redshift value of the spectrum to be measured based on the redshift values ​​in the second redshift candidate set. The spectral redshift measurement method based on density point cross-correlation of the present invention fully draws on the respective advantages of a cross-correlation method and a density estimation method, greatly improves the calculation efficiency of the cross-correlation method while achieving a measurement accuracy close to that of the cross-correlation method, and realizes fast and high-precision measurement of the spectral redshift value.

Description

Technical Field

[0001] The present invention belongs to the technical field of spectral redshift navigation, and in particular relates to a spectral redshift measurement method and device based on density point cross correlation. Background Art

[0002] Spectral redshift navigation is an emerging autonomous navigation method for astronomical velocity measurement. It offers advantages such as high velocity measurement accuracy and wide applicability, and holds broad application prospects in deep space exploration. This method uses the redshift values ​​of the spectra of stars or solar system objects as a navigation information source. Based on the principle of spectral redshift, it calculates the radial velocity of the probe relative to the navigation object. Furthermore, it uses an orbital dynamics model to filter and estimate navigation parameters such as the probe's position and velocity. Because the performance of spectral redshift navigation relies heavily on the measurement of spectral redshift values, the design of the redshift measurement algorithm is crucial to the implementation of this navigation system.

[0003] Current research on spectral redshift measurement methods can be divided into two categories: full-spectrum matching and line matching. The most successful full-spectrum matching method is the cross-correlation method. Its core is to cross-correlate the spectral line spectrum of the measured spectrum with a redshifted template spectrum. The template spectrum and redshift with the highest correlation are used as the measurement result. This method can provide accurate measurement results when the measured and template spectra are similar. However, because the cross-correlation method using full-spectrum matching is an exhaustive search matching algorithm, it is computationally very complex and therefore unsuitable for spectral redshift navigation systems that require rapid redshift measurement. Line matching searches for strong emission or absorption lines in the measured spectrum. The extracted lines of the measured spectrum are then compared with the stationary lines provided by the spectral line table to calculate the spectral redshift value. The most typical line matching method is the density estimation method. This method identifies a set of redshift candidates based on spectral line authentication. By performing density estimation on this set of candidates, the redshift determination problem is transformed into the problem of finding the point of maximum density. It is computationally fast and has good stability. However, the performance of density estimation methods for redshift measurements depends on the extraction of characteristic spectral lines, which can easily affect measurement accuracy. Currently, the key to achieving high-precision, real-time navigation using spectral redshift navigation systems is the rapid and highly accurate measurement of redshift values ​​from noisy spectral information. Summary of the Invention

[0004] The purpose of the present invention is to provide a spectral redshift measurement method and device based on density point cross-correlation. On the basis of fully absorbing the respective advantages of the cross-correlation method and the density estimation method, the basic framework of the cross-correlation method is used to perform cross-correlation processing on the redshift candidate set obtained by the density estimation method, which can provide technical support for the high-precision real-time application of the spectral redshift navigation system.

[0005] The present invention adopts the following technical solution: a spectral redshift measurement method based on density point cross correlation, comprising the following steps:

[0006] Obtaining a spectrum line spectrum after preprocessing of the spectrum to be measured, and extracting the first characteristic spectrum line information therefrom;

[0007] generating a first redshift candidate set of the spectrum to be measured based on the second characteristic spectral line information and the first characteristic spectral line information of the stationary spectrum;

[0008] Classifying the redshift values ​​in the first redshift candidate set to obtain several redshift candidate subsets;

[0009] generating a second redshift candidate set according to the plurality of redshift candidate subsets;

[0010] The spectrum redshift value of the spectrum to be measured is determined based on the redshift values ​​in the second redshift candidate set.

[0011] Furthermore, generating a first redshift candidate set of the spectrum to be measured based on the second characteristic spectral line information and the first characteristic spectral line information of the stationary spectrum includes:

[0012] The density estimation method is used to obtain the first redshift candidate set. The calculation method for each redshift value in the first redshift candidate set is:

[0013]

[0014] Among them, z k is the kth redshift value in the first redshift candidate set, (λ i f ,t i f ) is the first characteristic spectrum line information of the i-th, λ i f is the characteristic wavelength of the first characteristic spectral line information of the i-th type, t i f is the spectral line type of the i-th first characteristic spectral line information, i=1,2,…,U f , U f is the number of the first characteristic spectral line information, (λ j s ,t j s ) is the jth second characteristic line information of the stationary spectrum, λ j s is the characteristic wavelength of the jth second characteristic spectral line information, t j s is the spectral line type of the jth second characteristic spectral line information, j = 1, 2, ..., U s , U s is the number of the second characteristic spectral line information, U f ·Us is the number of redshift values ​​in the first redshift candidate set.

[0015] Furthermore, classifying the elements in the first redshift candidate set includes:

[0016] Deleting abnormal redshift values ​​in the first redshift candidate set to obtain a third redshift candidate set;

[0017] The redshift values ​​in the third redshift candidate set are classified.

[0018] Furthermore, classifying the redshift values ​​in the third redshift candidate set includes:

[0019] The Parzen window method is used to classify the redshift values ​​in the third redshift candidate set. The window function is:

[0020]

[0021] Among them, the window function φ k (z′ i ) represents the i-th redshift value z′ to be classified in the third redshift candidate set i According to the jth redshift value z′ j Classified into the kth category, i≠j, U r is the number of redshift candidate subsets, and ε is the error bound.

[0022] Furthermore, generating a second redshift candidate set according to the plurality of redshift candidate subsets includes:

[0023] Calculate the mean of each redshift candidate subset;

[0024] Several means are combined to obtain the second redshift candidate set.

[0025] Furthermore, determining the spectrum redshift value of the spectrum to be measured based on the redshift values ​​in the second redshift candidate set includes:

[0026] Determine a template spectrum set according to the second redshift candidate set, and perform cross-correlation processing on the template spectrum set and the spectral line spectrum to obtain a number of intensity correlation coefficients;

[0027] The redshift value in the second redshift candidate set corresponding to the maximum value in the correlation coefficient is selected as the spectral redshift value.

[0028] Furthermore, determining the template spectrum set according to the second redshift candidate set includes:

[0029] constructing a first spectral template;

[0030] The redshift values ​​in the second redshift candidate set are added to the first spectrum template one by one to obtain a template spectrum set.

[0031] Furthermore, performing cross-correlation processing on each element and line spectrum in the template spectrum set includes:

[0032] Calculating the intensity covariance between each second spectrum template and the spectral line spectrum in the template spectrum set;

[0033] The intensity correlation coefficient between each second spectrum template and the spectral line spectrum in the template spectrum set is calculated based on the intensity covariance.

[0034] Furthermore, the intensity correlation coefficient is calculated as follows:

[0035]

[0036] Among them, ρ j is the jth intensity correlation coefficient, Cov j is the intensity covariance between the jth second spectrum template and the spectrum line spectrum, σ j s is the jth element in the standard deviation sequence of the intensity of the spectrum line, σ j z is the intensity standard deviation of the j-th second spectrum template.

[0037] Another technical solution of the present invention: a spectral redshift measurement device based on density point cross-correlation, including a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, it implements the above-mentioned spectral redshift measurement method based on density point cross-correlation.

[0038] The beneficial effects of the present invention are as follows: by classifying the first redshift candidate set and generating several redshift candidate subsets, and then regenerating the second redshift candidate set based on the redshift candidate subsets, the present invention can reduce the cardinality of the redshift candidate set, greatly reduce the amount of calculation, and improve the real-time performance of the redshift value calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a spectrum diagram of Class A stars used in the verification example of the present invention;

[0040] Figure 2 This is a comparison chart of the redshift measurement errors of the method of the present invention, the density estimation method, and the cross-correlation method in the verification embodiment of the present invention;

[0041] Figure 3 This is a comparison chart of the measurement accuracy of the method according to the embodiment of the present invention, the density estimation method, and the cross-correlation method;

[0042] Figure 4 This is a comparison chart of the computational time of the method according to the embodiment of the present invention, the density estimation method, and the cross-correlation method. DETAILED DESCRIPTION

[0043] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] The spectral line matching algorithm searches for strong emission or absorption lines in the spectrum to be measured, then compares the extracted spectral lines to the stationary lines provided by the spectral line table to calculate the redshift value of the spectrum. The most typical spectral line matching method is the density estimation method. This method confirms the redshift candidate set based on spectral line authentication and transforms the redshift determination problem into the problem of solving the maximum density point by performing density estimation on the candidate set. It has fast calculation speed and good stability. However, the performance of the density estimation method for redshift measurement depends on the extraction of characteristic spectral lines, and thus the measurement accuracy is easily affected. Currently, how to quickly and accurately measure redshift values ​​from noisy spectral information has become the key to the realization of high-precision real-time navigation of spectral redshift navigation systems.

[0045] In the present invention, the spectrum to be measured is first preprocessed. Cosmic ray noise, skylight noise, and photon noise contained in the spectrum to be measured are denoised using median filtering and wavelet soft thresholding. Continuous spectrum fitting is then used to remove the continuous spectrum from the spectrum to obtain a more accurate line spectrum of the spectrum to be measured. Next, the first characteristic line information is extracted. The first characteristic line information is extracted from the obtained line spectrum through threshold processing, line boundary confirmation, and line center confirmation, thereby removing the influence of pseudo-lines in the line spectrum on the redshift measurement results. Next, the redshift candidate set is calculated and classified. A density estimation method is used to obtain a redshift candidate set containing the redshift value of the spectrum to be measured. The resulting redshift candidate set is classified using the window function of the Parzen window method. Based on this, the redshift values ​​classified into the same category are averaged to reduce the cardinality of the candidate set. Next, cross-correlation processing is performed. The line spectrum of the spectrum to be measured is cross-correlated with a template spectrum containing the redshift candidate set, and the correlation coefficient between the two is calculated. Finally, the redshift value is determined. Find the maximum value in the correlation coefficient sequence obtained in step 4. The redshift value corresponding to the maximum value is the final spectral redshift measurement value.

[0046] Specifically, an embodiment of the present invention discloses a spectral redshift measurement method based on density point cross-correlation, including the following steps: obtaining a spectral line spectrum after preprocessing of the spectrum to be measured, and extracting first characteristic spectral line information therefrom; generating a first redshift candidate set of the spectrum to be measured based on the second characteristic spectral line information and the first characteristic spectral line information of the stationary spectrum; classifying the redshift values ​​in the first redshift candidate set to obtain several redshift candidate subsets; generating a second redshift candidate set based on the several redshift candidate subsets; and determining the spectral redshift value of the spectrum to be measured based on the redshift values ​​in the second redshift candidate set.

[0047] The present invention classifies the first redshift candidate set and generates several redshift candidate subsets, and then regenerates the second redshift candidate set based on the redshift candidate subsets. This can reduce the cardinality of the redshift candidate set, greatly reduce the amount of calculation, and improve the real-time performance of the redshift value calculation.

[0048] More specifically, the preprocessing process includes the following steps:

[0049] (1) First, median filtering is used to remove pulse noise such as skylight noise and cosmic ray noise in the measured spectrum. The specific formula is as follows:

[0050]

[0051] Among them, S i is the element of the intensity sequence S of the spectrum to be measured at wavelength i; i∈[λ b ,λ e ],λ b ,λ e are the wavelengths of the spectrum to be measured at the start and end positions respectively; Med{·} is the function of taking the median; W is the window width of the median filter; u∈N * ,N * is a positive integer, 2u+1 and 2u represent odd and even numbers respectively; S′ i is the element of the spectral intensity sequence S′ at wavelength i after median filtering.

[0052] (2) Secondly, the wavelet soft threshold method is used to denoise the Gaussian white noise such as photon noise contained in the measured spectrum. This method includes three main steps, namely wavelet decomposition, threshold processing and signal reconstruction.

[0053] ①Wavelet decomposition.

[0054] The Mallat algorithm is used to implement the wavelet decomposition process. The coefficient matrix of the low-pass filter in the wavelet decomposition is denoted as h, and the coefficient matrix of the high-pass filter is denoted as g. Their sizes are determined by the selected wavelet basis function and scaling function. At the same time, the low-frequency coefficients and high-frequency coefficients obtained by the j+1 (j=0,1,...,N-1) level wavelet decomposition are denoted as a. (j+1) and d (j+1) The spectral intensity sequence S′ after median filtering is used as the input signal a of the N-level wavelet decomposition. (0) , a (j+1) and d (j+1) It can be calculated according to the following formula:

[0055]

[0056] Among them, a i (j+1) and d i(j+1) are respectively a (j+1) and d (j+1) The i-th element of (j) is the length of the j-th level low-frequency coefficient and high-frequency coefficient; and are the nth order of h and g respectively (j) -2i elements.

[0057] By analogy, all low-frequency coefficients and high-frequency coefficients of the spectrum after N-level wavelet decomposition can be obtained.

[0058] ②Threshold processing.

[0059] The threshold of wavelet transform is determined according to the Birge-Massart strategy. The absolute values ​​of all wavelet coefficients are arranged in descending order to generate the wavelet coefficient sequence w, and the standard deviation σ of the first level wavelet coefficient is g As the noise standard deviation of the spectrum to be measured, the global threshold T is calculated as follows g :

[0060]

[0061] Among them, a (1) and d (1) are the low-frequency coefficients and high-frequency coefficients of the first-level wavelet decomposition respectively; Med{·} is the median function; H(g) min Indicates taking the minimum value of the function H(g), is the solution that minimizes the function H(g); is the tuning term in the penalty rule (must be greater than 1), generally set α = 2; w i is the i-th element of the wavelet coefficient sequence w; M is the length of w; is the first elements.

[0062] Since Gaussian white noise mainly corresponds to the high-frequency coefficients of wavelet decomposition, the wavelet soft threshold is used to process the high-frequency coefficients (the low-frequency coefficients remain unchanged). The process is as follows:

[0063]

[0064] That is, when the absolute value of the high-frequency coefficient is greater than the selected threshold T g When , the absolute value of the high-frequency coefficient is subtracted from the threshold; otherwise, the high-frequency coefficient is considered to be noise and set to 0. In formula (4), sgn(·) is a step function; T g is the global threshold; is the value of the j-th level high frequency coefficient at wavelength i after being processed by the soft threshold method.

[0065] ③Wavelet reconstruction.

[0066] Wavelet reconstruction is the inverse process of wavelet decomposition. Wavelet reconstruction is performed using the high-frequency coefficients processed by formula (4) and the original low-frequency coefficients, as shown in the following formula:

[0067]

[0068] Where, j = N, N-1, ..., 1, and a (N) are the Nth level low-frequency coefficients after wavelet reconstruction and the Nth level low-frequency coefficients after wavelet decomposition, respectively; is the j-1th level low-frequency coefficient after wavelet reconstruction The i-th element of ; and The i-2nth of h and g respectively (j) elements; n (j) is the length of the j-th level low-frequency coefficient and high-frequency coefficient.

[0069] Similarly, by performing wavelet reconstruction step by step, we can get the 0th level low-frequency coefficient It is used as the spectrum intensity sequence S″ to be measured from which the Gaussian white noise has been removed.

[0070] (3) Finally, the wavelet transform method is used to fit the continuous spectrum and remove the continuous spectrum in the spectrum to be measured, thereby obtaining a more accurate line spectrum.

[0071] Perform N on the intensity sequence S of the undenoised spectrum to be measured S Level wavelet decomposition and reconstruction. Since the noise mainly exists in the high-frequency coefficients, the high-frequency coefficients of the wavelet decomposition are set to 0 to eliminate the interference of the noise, and only the low-frequency coefficients are retained, and then reconstruction is performed. The reconstruction expression is as follows:

[0072]

[0073] Among them, a i,s (j-1) is the j-1th level low-frequency coefficient a after wavelet reconstruction s (j-1) The i-th element of ; is the i-2nth low-pass filter coefficient matrix h (j) elements; n (j) is the length of the j-th level low-frequency coefficient.

[0074] N s The low-frequency coefficient a obtained after wavelet reconstruction s (0) (i.e., the 0th-order low-frequency coefficient after reconstruction of formula (6)) as the intensity sequence S of the continuous spectrum cThe maximum normalization factor is used to remove the continuous spectrum of the spectrum to be measured and perform intensity normalization to obtain the spectral line spectrum sequence S″′ of the spectrum to be measured. The calculation formula is as follows:

[0075]

[0076] Where S″ is the intensity sequence of the spectrum to be measured after removing Gaussian white noise; max{·} is the function of taking the maximum value.

[0077] The spectrum after this preprocessing is called a line spectrum. Due to the heavy noise contamination of astronomical spectral signals and the inherent errors in the continuous spectrum fitting process, the resulting line spectrum still contains a large number of spurious lines. To address this, the present invention sets a local threshold on the line spectrum to relatively accurately extract the first characteristic line information.

[0078] First, a calculation window is set near the wavelength i of the spectrum line, the root mean square of the spectrum intensity in the window is calculated, and then multiplied by the amplification parameter to obtain the local threshold at wavelength i; and so on, traversing all wavelengths, so as to calculate the local threshold sequence T of the entire spectrum. l The calculation formula is as follows:

[0079] T i l =RMS i ·P (8)

[0080] Among them, T i l is the local threshold sequence T l The element at wavelength i; i∈[λ b ,λ e ],λ b and λ e are the wavelengths of the measured spectrum at the start and end positions respectively; RMS i is the root mean square of the spectral intensity in the window where wavelength i is located; P is the amplification parameter, which is usually set to 2.

[0081] Secondly, according to the local threshold sequence T l , calculate the intensity sequence of the spectrum line after local threshold processing The formula is as follows:

[0082]

[0083] in, and S i ″′ are the intensity sequences of the spectral lines and S″′ at wavelength i. It should be noted that U in f The non-zero items are the characteristic spectral line sequences of the spectrum to be measured.

[0084] Finally, the boundaries of each characteristic line of the spectrum to be measured are detected, the wavelengths at the starting and ending points of the spectrum are recorded, and the distribution intervals of different characteristic lines are determined. At the same time, the maximum value of the spectral intensity in each distribution interval is calculated, and the wavelength corresponding to the maximum value is used as the characteristic wavelength of each characteristic line to complete the line center confirmation. Therefore, the information of the first characteristic line of the spectrum to be measured can be recorded as {(λ i f ,t i f )i=1,2,…,U f}, where λ i f and t i f are the characteristic wavelength and spectral line type of the first characteristic spectral line information of the spectrum to be measured (the emission line and absorption line are 1 and -1 respectively), U f is the number of the first characteristic spectral line information of the spectrum to be measured.

[0085] The second characteristic line information of the known stationary spectrum is {(λ j s ,t j s )j=1,2,…,U s}, where λ j s and t j s They represent the characteristic wavelength and line type of the jth characteristic line of the stationary spectrum, U s is the number of characteristic spectral lines of the stationary spectrum. Considering the spectral line type makes the present invention applicable to various types of celestial spectra. Based on the first characteristic spectral line information of the spectrum to be measured and the second characteristic spectral line information of the stationary spectrum, the density estimation method is used to obtain the initial redshift candidate set z of the spectrum to be measured:

[0086] That is, generating a first redshift candidate set of the spectrum to be measured based on the second characteristic spectral line information and the first characteristic spectral line information of the stationary spectrum includes: obtaining the first redshift candidate set using a density estimation method; wherein the calculation method of each redshift value in the first redshift candidate set is:

[0087]

[0088] Among them, z k is the kth redshift value in the first redshift candidate set, (λ i f ,t i f ) is the first characteristic spectrum line information of the i-th, λ i f is the characteristic wavelength of the first characteristic spectral line information of the i-th type, ti f is the spectral line type of the i-th first characteristic spectral line information, i=1,2,…,U f , U f is the number of the first characteristic spectral line information, (λ j s ,t j s ) is the jth second characteristic line information of the stationary spectrum, λ j s is the characteristic wavelength of the jth second characteristic spectral line information, t j s is the spectral line type of the jth second characteristic spectral line information, j = 1, 2, ..., U s , U s is the number of the second characteristic spectral line information, U f ·U s is the number of redshift values ​​in the first redshift candidate set.

[0089] Next, the elements in the first redshift candidate set need to be classified. In this case, the abnormal redshift values ​​in the first redshift candidate set are first deleted to obtain the third redshift candidate set; then the redshift values ​​in the third redshift candidate set are classified.

[0090] When deleting abnormal redshift values ​​in the first redshift candidate set, it is necessary to exclude z in the first redshift candidate set due to mismatch of spectral line wavelength or type. k +1 is a negative outlier. Then, the remaining data set is the third redshift candidate set {z′ i ,i=1,2,…,U z}, where U z is the number of elements in the redshift candidate set.

[0091] In the embodiment of the present invention, classifying the redshift values ​​in the third redshift candidate set includes classifying the redshift values ​​in the third redshift candidate set using a Parzen window method, where the window function is:

[0092]

[0093] Among them, the window function φ k (z′ i ) represents the i-th redshift value z′ to be classified in the third redshift candidate set i According to the jth redshift value z′ j Classified into the kth category, i≠j, U r is the number of redshift candidate subsets, and ε is the error bound.

[0094] Compared with the solution in this embodiment, the traditional spectral line matching method only selects the point with the largest density in the redshift candidate set and takes the average of its neighborhood as the redshift measurement result. When two or more points with the largest density appear, it cannot solve the problem of redshift determination. In addition, its redshift measurement results are greatly affected by the aforementioned spectral preprocessing and spectral line extraction. Moreover, when constructing the redshift candidate set, the situation of mismatch in wavelength or type of characteristic spectral lines is not considered.

[0095] In the embodiment of the present invention, according to formula (11), the redshift candidate set z′ can be classified into U r Redshift candidate subset z″ k (k=1,2,…,U r ). Calculate the above U respectively r The mean of the redshift candidate values ​​in the subsets, i.e. the density point:

[0096]

[0097] Among them, V k is z″ k The number of elements; z″ k,i is z″ k The i-th element of ; is z″ k The mean of the medium redshift candidates.

[0098] On this basis, in order to improve the computational efficiency of the redshift measurement algorithm, U r The mean of the redshift candidate subsets Form a new set, that is, the redshift candidate set with reduced cardinality

[0099] That is, generating the second redshift candidate set according to the plurality of redshift candidate subsets includes: calculating the mean of each redshift candidate subset; and combining the plurality of means to obtain the second redshift candidate set.

[0100] Specifically, determining the spectral redshift value of the spectrum to be measured based on the redshift value in the second redshift candidate set includes: determining a template spectrum set according to the second redshift candidate set, and performing cross-correlation processing on the template spectrum set and the spectral line spectrum to obtain several intensity correlation coefficients; selecting the redshift value in the second redshift candidate set corresponding to the maximum value in the correlation coefficient as the spectral redshift value.

[0101] More specifically, determining the template spectrum set according to the second redshift candidate set includes: constructing a first spectrum template; in this embodiment, using a maximum normalization factor to remove the continuous spectrum of the observed celestial body's static spectrum and performing intensity normalization, using it as the first spectrum template, and adding the redshift values ​​in the second redshift candidate set to the first spectrum template one by one Get the template spectrum set.

[0102] Next, performing cross-correlation processing on each element in the template spectrum set and the spectral line spectrum includes: calculating the intensity covariance between each second spectrum template in the template spectrum set and the spectral line spectrum; and calculating the intensity correlation coefficient between each second spectrum template in the template spectrum set and the spectral line spectrum based on the intensity covariance.

[0103] In one embodiment, the wavelength range of the template spectrum (i.e., the second spectrum template) with the redshift candidate value added is compared with the wavelength range of the spectrum of the spectral line to be measured to determine the starting wavelength and the ending wavelength of the overlapping range. r Repeat this process by adding the template spectrum of the redshift candidate value to obtain a r Starting wavelength sequence λ b r and the end wavelength sequence λ e r .

[0104] Then, the intensity covariance Cov between the spectrum of the spectral line to be measured and the template spectrum with the redshift candidate value added (i.e., the second spectrum template) is calculated one by one. The calculation method is:

[0105]

[0106] Among them, Cov j is the jth element in the covariance sequence Cov (i.e., the intensity covariance between the jth second spectrum template and the spectrum line spectrum); μ s is the intensity mean sequence of the spectral line, μ j s μ s The jth element of z is the intensity mean sequence of the template spectrum with the redshift candidate value added, μ j z μ z The jth element of i is the flux intensity of the spectrum line at wavelength i; S i,j z is the flux intensity of the jth template spectrum with the redshift candidate set at wavelength i; b,j r and λ e,j r are λ b r and λ e r The jth element of U, j = 1, 2, ..., U r .

[0107] The intensity variance sequence of the line spectrum is Var s , plus the intensity variance sequence of the template spectrum of the redshift candidate set is Varz , then from formula (13) we can know:

[0108]

[0109] Among them, Var j s and Var j z Var s and Var z The jth element of U, j = 1, 2, ..., U r .

[0110] Finally, according to the idea of ​​cross-correlation method, the intensity correlation coefficient ρ between the line spectrum and the template spectrum with the redshift candidate set is obtained using the following formula:

[0111]

[0112] Among them, ρ j is the jth element of ρ (i.e., the jth intensity correlation coefficient); σ s is the intensity standard deviation sequence of the spectral line; σ z is the intensity standard deviation sequence of the template spectrum with the redshift candidate set added; σ j s and σ j z σ s and σ z The jth element of j s is the jth element in the standard deviation sequence of the intensity of the spectrum line, σ j z is the intensity standard deviation of the jth second spectrum template, j=1,2,…,U r .

[0113] Finally, find the maximum value in the obtained correlation coefficient sequence ρ:

[0114] ρ′=max{ρ j ,j=1,2,…,U r} (16)

[0115] Among them, max{·} is the function of taking the maximum value; ρ j is the jth element in the correlation coefficient sequence ρ.

[0116] Then in the second redshift value candidate set Find the redshift value corresponding to the maximum correlation coefficient ρ′ This is the final determined spectral redshift measurement value.

[0117] In order to verify the effectiveness of the method of the present invention, the following verification test was also carried out.

[0118] The performance of the proposed spectral redshift measurement method is evaluated with the help of existing astronomical spectral data. The experimental steps are as follows: First, four stellar spectra with spectral type A and signal-to-noise ratio (SNR) > 400 (very high signal-to-noise ratio, which means the spectrum is noise-free) are selected from the stellar spectrum library, namely Figure 1 4 graphs in the figure; after removing the red shift and cutting the wavelength range As a template spectrum. Secondly, considering the possible redshift range in spectral redshift navigation, redshift values ​​were randomly generated within the interval of redshift value |z| ≤ 0.1 and added to the template spectrum, generating 200 redshifted spectra. Furthermore, these 200 spectra were superimposed with Gaussian white noise of varying intensities to generate a spectrum to be measured with a signal-to-noise ratio (SNR) in the range of [2, 20]. Finally, the redshift values ​​of the spectra to be measured were measured using the classical density estimation method, the cross-correlation method, and the spectral redshift measurement method proposed in this paper, respectively. The measurement errors, accuracy rates, and computational time were statistically analyzed.

[0119] In the process of spectral preprocessing, the median filter window width is selected The wavelet basis function is selected as Haar wavelet; the wavelet decomposition level of soft threshold denoising is 4; the wavelet decomposition level of continuous spectrum fitting is 6. In the process of characteristic spectrum line extraction, the calculation window width of the local threshold is selected as At the same time, the absorption line of the spectrum is selected as the measurement object of the spectrum red shift. The computer CPU used for experimental verification is Intel(R) Core(TM) i5-8250U, with 12G memory, and the calculation tool is Matlab software.

[0120] Figure 2 The redshift measurement errors of the method according to the present invention, the density estimation method, and the cross-correlation method are shown. As can be seen from the figure, as the signal-to-noise ratio increases, the redshift measurement accuracy of the three methods gradually improves due to reduced interference caused by noise and pseudo-spectral lines in the measured spectrum. Under the same signal-to-noise ratio, the cross-correlation method has the highest measurement accuracy, while the density estimation method has the worst. Although the measurement accuracy of the method according to the present invention is slightly lower than that of the cross-correlation method, it is significantly higher than that of the density estimation method.

[0121] Figure 3 The comparison results of the measurement accuracy of the method of the embodiment of the present invention, the density estimation method and the cross-correlation method are given. The measurement accuracy is defined as follows: if the absolute error of the redshift measurement is less than 0.005, the measurement is considered accurate, otherwise the measurement is inaccurate. Figure 2The results presented are consistent, with the cross-correlation method achieving slightly higher accuracy than the spectral redshift measurement method proposed in the present invention, while the density estimation method is significantly less accurate than the first two methods. It should be noted that when the signal-to-noise ratio is greater than 6, the proposed method can achieve a measurement accuracy exceeding 85%, which is close to that of the cross-correlation method.

[0122] The reason for the above experimental results is that compared with the density estimation method, the method of the embodiment of the present invention and the cross-correlation method both determine the redshift value through a cross-correlation strategy, which requires less preprocessing of the spectrum to be measured, and the measurement accuracy does not completely depend on the extraction effect of the characteristic spectral lines. Therefore, it has better adaptability to unknown noise and pseudo-spectral line interference.

[0123] Figure 4 The computational time for a single redshift measurement using the method of the embodiment of the present invention, the density estimation method, and the cross-correlation method is given. It can be seen that the density estimation method has the shortest computational time, which is only 0.341s; the cross-correlation method has the longest computational time, which is 14.244s, 41.8 times that of the density estimation method; the computational time of the method of the embodiment of the present invention is 4.982s, which is only 35% of the cross-correlation method. The reason is that: when determining the redshift measurement value, the density estimation method only needs to search for the maximum density point in the redshift candidate set, and the computational complexity is small; the cross-correlation method is a resource-exhausting search algorithm, which requires cross-correlation processing for each data in the redshift candidate set, and the computational complexity is extremely high; and the proposed method, because the redshift candidate set is classified, reduces the cardinality of the candidate set, thereby significantly reducing the amount of data required for cross-correlation calculation and improving computational efficiency. It should be pointed out that as the number of spectra to be measured increases, the computational time of the cross-correlation method will continue to increase sharply, while the corresponding increase in computational complexity of the density estimation method and the method proposed in the present invention is relatively small.

[0124] In summary, the spectral redshift measurement method based on density point cross-correlation proposed in this paper leverages the respective advantages of cross-correlation and density estimation methods. While achieving measurement accuracy close to that of cross-correlation, it significantly improves the computational efficiency of the latter method, enabling rapid and high-precision measurement of spectral redshift values. This method has important implications for theoretical research on spectral redshift measurement and the high-precision, real-time application of spectral redshift navigation systems.

[0125] Based on the full absorption of the respective advantages of the cross-correlation method and the density estimation method, the present invention utilizes the basic framework of the cross-correlation method to perform cross-correlation processing on the redshift candidate set obtained by the density estimation method, and proposes a spectral redshift measurement method that is both fast and highly accurate, which can provide technical support for the high-precision real-time application of the spectral redshift navigation system.

[0126] The present invention also discloses a spectral redshift measurement device based on density point cross-correlation, comprising a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the above-mentioned spectral redshift measurement method based on density point cross-correlation is implemented.

[0127] The processor may include one or more processors such as a central processing unit, an application processor (AP), and a baseband processor. The processor may generate an operation control signal based on the instruction opcode and timing signal to complete the control of instruction fetching and execution. The memory may be used to store computer executable program code, and the executable program code includes instructions. The processor executes various functional applications and data processing of the network device by running the instructions stored in the memory. The memory may include a program storage area and a data storage area. For example, the memory may be a double data rate synchronous dynamic random access memory (DDR) or a flash memory. The computer program includes computer program code, and the computer program code may be in source code form, object code form, executable file, or some intermediate form.

Claims

1. A spectrum redshift measurement method based on density point cross correlation, characterized in that: The following steps are involved: Obtaining a spectrum line spectrum after preprocessing of the spectrum to be measured, and extracting the first characteristic spectrum line information therefrom; generating a first redshift candidate set of the spectrum to be measured based on the second characteristic spectral line information of the stationary spectrum and the first characteristic spectral line information; classifying the redshift values ​​in the first redshift candidate set to obtain a plurality of redshift candidate subsets; generating a second redshift candidate set according to the plurality of redshift candidate subsets; determining a spectral redshift value of the spectrum to be measured based on the redshift values ​​in the second redshift candidate set; Categorizing the elements in the first redshift candidate set includes: Deleting abnormal redshift values ​​in the first redshift candidate set to obtain a third redshift candidate set; classifying the redshift values ​​in the third redshift candidate set using a Parzen window method; Determining the spectral redshift value of the spectrum to be measured based on the redshift values ​​in the second redshift candidate set includes: determining a template spectrum set according to the second redshift candidate set, and performing cross-correlation processing on the template spectrum set and the spectral line spectrum to obtain a plurality of intensity correlation coefficients; The redshift value in the second redshift candidate set corresponding to the maximum value in the correlation coefficient is selected as the spectral redshift value.

2. The method for measuring spectral redshift based on density point cross correlation according to claim 1, wherein: Generating a first redshift candidate set of the spectrum to be measured based on the second characteristic spectral line information of the stationary spectrum and the first characteristic spectral line information includes: The first redshift candidate set is obtained by using a density estimation method; wherein the calculation method for each redshift value in the first redshift candidate set is: ， in, is the kth redshift value in the first redshift candidate set, is the i-th characteristic spectrum line information, is the characteristic wavelength of the i-th characteristic spectral line information, is the spectral line type of the i-th characteristic spectral line information, , is the number of the first characteristic spectral line information, is the jth second characteristic line information of the stationary spectrum, is the characteristic wavelength of the jth second characteristic spectral line information, is the spectral line type of the j-th second characteristic spectral line information, , is the number of the second characteristic spectral line information, is the number of redshift values ​​in the first redshift candidate set.

3. The method for measuring spectral redshift based on density point cross correlation according to claim 2, wherein: The window function of the Parzen window method is: ， Among them, the window function Indicates that the i-th redshift value to be classified in the third redshift candidate set According to the jth redshift value Classified into the kth category, i≠j, is the number of redshift candidate subsets, is the error limit.

4. A method for measuring spectral redshift based on density point cross correlation according to any one of claims 2-3, characterized in that: Generating a second redshift candidate set according to the plurality of redshift candidate subsets includes: Calculating a mean of each of the redshift candidate subsets; Several of the means are combined to obtain the second redshift candidate set.

5. The method for measuring spectral redshift based on density point cross correlation according to claim 4, wherein: Determining a template spectrum set according to the second redshift candidate set includes: constructing a first spectral template; The redshift values ​​in the second redshift candidate set are added to the first spectrum template one by one to obtain the template spectrum set.

6. The method for measuring spectral redshift based on density point cross correlation according to claim 5, characterized in that: Performing cross-correlation processing on each element in the template spectrum set and the spectral line spectrum includes: Calculating the intensity covariance between each second spectrum template in the template spectrum set and the spectrum line spectrum; An intensity correlation coefficient between each second spectrum template in the template spectrum set and the spectral line spectrum is calculated based on the intensity covariance.

7. The method for measuring spectral redshift based on density point cross correlation according to claim 6, wherein: The calculation method of the intensity correlation coefficient is: ， in, is the jth intensity correlation coefficient, is the intensity covariance between the jth second spectrum template and the spectrum line, is the jth element in the intensity standard deviation sequence of the spectral line, is the intensity standard deviation of the j-th second spectrum template.

8. A spectral redshift measurement device based on density point cross correlation, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method for measuring spectral redshift based on density point cross correlation according to any one of claims 1 to 7 is implemented.

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