A method for estimating pulsar period

Abstract

The present invention provides a method for estimating the period of a pulsar. First, the weighted epoch folding of the pulsar profile is performed in combination with the photon energy information; second, the folded pulsar profile signal is encoded by an inverse space filling curve, and the one-dimensional pulsar profile sequence is converted into a two-dimensional image signal without damaging the profile information; finally, a dual convolutional neural network model under different period search steps is designed and trained to perform feature recognition on the pulsar image information and estimate the optimal period. The present invention provides a method for estimating the period of a pulsar that combines the inverse space filling curve encoding of the folding of photon energy information with the recognition of a dual convolutional neural network, which has the advantages of high precision and fast calculation speed, and can significantly improve the navigation performance of X-ray pulsars.

Description

Technical Field

[0001] The present invention relates to the technical field of pulsar navigation, and in particular to a method for estimating a pulsar period. Background Art

[0002] In recent years, with the continuous development of deep space exploration technology, the research on autonomous celestial navigation of deep space probes has become more and more in-depth. As a navigation method that is more suitable for deep space exploration missions, celestial navigation technology has been widely used in the field of deep space exploration. According to the different measurements, celestial navigation can be divided into angle measurement navigation, velocity measurement navigation and distance measurement navigation. Traditional astronomical angle measurement navigation methods (such as starlight angular distance navigation) are greatly affected by the distance between the spacecraft and the near celestial body, and their navigation accuracy is often not guaranteed. However, as an emerging astronomical distance measurement navigation method, X-ray pulsar navigation has a highly stable time standard and ultra-high positioning measurement accuracy, and is an ideal deep space probe navigation method.

[0003] A pulsar is a high-speed spinning neutron star with a stable spin period, which continuously radiates stable periodic signals into the universe. X-ray pulsar navigation measures the time delay between the pulse signal reaching the spacecraft and the center of mass of the solar system, and then converts it into the distance between the spacecraft and the center of mass of the solar system for positioning. However, since the photon signal emitted by a pulsar in the X-ray band is very weak, the detector cannot directly receive the complete pulsar period wave, but receives the time when a series of photon signals arrive at the detector. In order to use the pulse signal to calculate the time delay between the spacecraft and the center of mass of the solar system, it is necessary to use the photon arrival time (PTOA) to estimate the pulsar period in order to restore the complete pulse signal.

[0004] At present, frequency domain estimation and time domain estimation are two common period estimation methods. In 1987, Leahy et al. first proposed to use fast Fourier transform in the frequency domain to process PTOA signals and estimate pulsar periods. However, since fast Fourier transform requires the processed signal to be uniformly distributed, PTOA data needs to be interpolated, which leads to low accuracy of period estimation. On this basis, Zhou Qingyong et al. proposed to use frequency domain Lomb algorithm to process PTOA non-uniform data, and Shen et al. proposed a period estimation method based on frequency subdivision combined with continuous Lomb algorithm, but these methods have the problem of excessive algorithm calculation and are not suitable for real-time navigation solution.

[0005] In the time domain estimation of pulsar period, Leahy et al. proposed a classic period estimation method based on epoch folding and used χ 2 The test function determines the period. Subsequently, Buccheri, R. et al. proposed using Z 2To test and process pulsar data to estimate the period, De Jager proposed using the H test to estimate the period. However, these methods all use the statistical parameters of the folded profile as the test function, which is greatly affected by noise interference. Liu Jin et al. also proposed a fast period estimation method based on compressed sensing matrix. Compared with the traditional estimation method, their calculation speed has been improved, but there is still room for improvement in calculation accuracy. Zheng Wei et al. proposed a pulsar period estimation method based on variable encapsulation segments with equal photon distribution. By selecting the optimal bin number, the period estimation accuracy was greatly improved, but the amount of calculation also increased. T.Cassanelli et al. proposed a waterfall chart principal component analysis method, which divides the one-dimensional time series into M parts, performs epoch folding respectively, and combines the M folded profiles into a two-dimensional signal. The optimal period is determined by observing the consistency of the folded profile, but in actual navigation tasks, if the observation time is short and the amount of observation data is small, the period estimation effect of this method is not good. The above methods cannot solve the problem of mutual constraints between period estimation accuracy and calculation speed. At the same time, these methods only use photon number information for epoch folding, and do not consider the influence of photon energy information on profile folding. Summary of the invention

[0006] The technical problem to be solved by the present invention is: in view of the problem that when using pulsar TOA data for X-ray pulsar navigation, the X-ray pulsar navigation performance is degraded due to insufficient pulsar period estimation accuracy. A pulsar period estimation method is provided to improve the pulsar period estimation accuracy and thus enhance the X-ray pulsar navigation performance.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A pulsar period estimation method uses photon energy information to perform epoch folding, converts one-dimensional profile information into a two-dimensional image signal through an inverse space filling curve, and identifies the profile image features through a convolutional neural network model to determine the optimal period, specifically comprising the following steps:

[0009] Step 1: Count the arrival time of pulsar photons received by the detector, and prepare for folding the pulsar profile epoch based on the photon number information;

[0010] Step 2: weighted epoch folding of pulsar profiles is performed in combination with photon energy information;

[0011] Step 3: Encode the folded pulsar profile signal using an inverse space filling curve, and convert the one-dimensional pulsar profile signal into a two-dimensional image signal without damaging the pulsar profile signal;

[0012] Step 4: Preprocess the pulsar two-dimensional image signal: generate training sets and test sets, and perform random phase shifts on the sample sets to enhance the generalization ability of network training. Finally, mark the sample labels.

[0013] Step 5: Within a larger cycle search range, a larger cycle search step size is set to design and train the convolutional neural network 1, and the cycle search range is initially and quickly narrowed;

[0014] Step 6: Combine the preliminary search results of step 5, narrow the cycle search range, set a smaller cycle search step, design and train the convolutional neural network 2, and perform a detailed search to determine the optimal cycle.

[0015] Furthermore, the implementation method of step 1 is that in the pulsar period estimation experiment, the total observation time is T ob The experimental period is P, and the entire observation period is divided into N p At the same time, for each equally divided segment, follow T b Divide into N b Each observation time period after division is called bin, and the specific relationship between them is as follows:

[0016] T ob =N p ·P (1)

[0017] P=T b ·N b (2)

[0018] The specific operations for preparing the pulsar profile epoch folding by combining the photon number information are as follows: First, in the total observation time T ob In each time period of length P, the total number of photons arriving at the i-th bin is superimposed on the first time period T b Secondly, count the total number of photons in each bin.

[0019] Furthermore, in step 2, when performing epoch folding of the pulsar period profile, weighted folding is performed in combination with photon energy information:

[0020] The steps of weighted folding of the profile in combination with the photon energy information are as follows: first, according to the arrival time of the pulsar photons, the photons arriving at the i-th bin in a time period of length P are placed in the corresponding bin of the first time period; second, the total number of photons in each bin in the first time period is counted and accumulated according to the energy value carried by the photons; finally, the photon energy value in each bin is normalized to obtain the pulsar profile signal n E (t i );

[0021]

[0022] In the formula, e j (t i ) represents the energy carried by the photon in the i-th bin in the j-th time period.

[0023] Furthermore, in step 3, the one-dimensional contour signal of the pulsar is converted into two-dimensional image information through an inverse space filling curve, and the optimal estimation of the pulsar period is achieved through two-dimensional image feature extraction.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] (1) The present invention combines the number of photons and the photon energy information to perform weighted epoch folding on the pulsar period. Traditional epoch folding algorithms usually directly add the number of photons in each bin when calculating the pulse profile. This operation is equivalent to treating each photon with equal weights. In fact, although the energy carried by the photons reaching the detector is distributed within a fixed range, the energy of each photon is different. If the pulse profile is folded only according to the number of photons arriving, it is likely that there will be a large gap between the restored profile and the true profile of the pulsar, resulting in profile distortion. Therefore, the present invention performs weighted processing on the number of photons according to the photon energy information, and performs epoch folding according to the weight of each photon, which effectively suppresses the distortion problem of the folded profile and improves the accuracy of period estimation.

[0026] (2) The present invention uses a space filling curve to losslessly convert the one-dimensional profile information of the pulsar into a two-dimensional image signal. The space filling curve is a "bridge" connecting one-dimensional signals and multi-dimensional signals, and is often used for image storage and search. It can realize the conversion of multi-dimensional data to one-dimensional data while ensuring that local features remain unchanged. The present invention uses an inverse space filling curve to convert the one-dimensional signal processing problem into a two-dimensional image space for period estimation.

[0027] (3) The present invention uses a convolutional neural network model to perform feature learning on the pulsar contour image to estimate the optimal period. Traditional period estimation methods mainly use statistical parameters of the folded contour to evaluate the quality of period estimation, which is greatly affected by noise. Only by evaluating from the perspective of the structural characteristics of the folded contour can the impact of noise on period estimation be minimized. Therefore, using a convolutional neural network model to learn and identify the structural characteristics of the folded contour can reduce the impact of noise and significantly improve the estimation accuracy of the pulsar period. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1It is a flow chart of a pulsar period estimation method combining reverse space filling curve coding with photon energy information folding and dual convolutional neural network recognition according to the present invention;

[0029] Figure 2 It is a schematic diagram of weighted epoch folding of pulsar profile combined with photon energy information;

[0030] Figure 3 It is the design diagram of convolutional neural network 1;

[0031] Figure 4 It is the design diagram of convolutional neural network 2;

[0032] Figure 5 It is a comparison diagram of the effects of folding contours of the traditional period estimation method and the new method of the present invention. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the exemplary embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings of the specification. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0034] like Figure 1 As shown, the pulsar period estimation method combining reverse space filling curve coding with photon energy information folding and dual convolutional neural network recognition of the present invention adopts the following technical solution: The Crab pulsar is taken as an example to illustrate the specific implementation steps of the present invention:

[0035] Step 1: Prepare the pulsar profile epoch folding based on the photon number information:

[0036] Since the detector receives the pulsar photon arrival time (PTOA) sequence, it is necessary to use PTOA to restore the profile of the pulsar signal. The epoch folding method is the most commonly used method to restore the profile. Assume that in the pulsar period estimation experiment, the total observation time is T ob s, the experimental period is P, and the entire observation period is divided into N p At the same time, for each equally divided segment, follow T b s is divided into N b Each observation period after division is called bin. The specific relationship between them is as follows:

[0037] T ob =N p ·P (1)

[0038] P=T b ·N b (2)

[0039] The specific operations for preparing for folding the pulsar profile epochs by combining the photon number information are: first, within the total observation time, add the total number of photons arriving at the i-th bin in each time period of length P to the first time period; second, count the total number of photons in each bin.

[0040] Step 2: Combine the photon energy information to perform weighted epoch folding of the pulsar profile:

[0041] The present invention mainly performs epoch folding based on photon energy information. The epoch folding process is as follows: Figure 2 As shown in Figure 1, first, according to the total number of photons in each bin in the first time period counted in step 1, the photon energy value is accumulated according to the energy value carried by the photon; secondly, the photon energy value in each bin is normalized to obtain the pulsar profile signal n E (t i ).

[0042]

[0043] In the formula, e j (t i ) represents the energy carried by the photon in the i-th bin in the j-th time period.

[0044] Step 3: Encode the folded pulsar profile signal using the inverse space filling curve, and convert the one-dimensional pulsar profile signal into a two-dimensional image signal without damaging the pulsar profile signal:

[0045] The space filling curve is a "bridge" connecting one-dimensional signals and multi-dimensional signals, and is often used for image storage and search. It can realize the conversion of multi-dimensional data to one-dimensional data while ensuring that local features remain unchanged. There are many filling methods such as Hilbert and Peano. The present invention mainly uses the Hilbert curve to reversely encode the pulsar profile sequence.

[0046] (x0,y0)=H -1 (t0) (4)

[0047] In the formula, H -1 (·) represents the reverse Hilbert coding, and x0 and y0 represent the two-dimensional coordinate values ​​of the pulsar profile signal at time t0 obtained by reverse Hibert curve coding.

[0048] Adjacent signals in one-dimensional space remain adjacent in the two-dimensional image, which minimizes the damage to the original data structure caused by dimensional conversion, so that the characteristics of the pulsar profile signal can be preserved. Without destroying the time domain characteristics of the pulsar profile signal, in order to reduce the amount of calculation and improve the calculation efficiency, the present invention divides the pulsar period into 256 parts, so the fourth-order inverse Hilbert curve can be used to convert the one-dimensional pulsar profile signal (1×256) into a two-dimensional image signal (16×16).

[0049] Step 4: Preprocess the pulsar two-dimensional image signal:

[0050] First, it is necessary to generate a training set and a test set, and randomly divide the training set and the test set according to the ratio of 8:2. Secondly, in order to enhance the generalization ability of the network, data enhancement processing is required. The contour phase generated by simulation is consistent. In order to improve the generalization ability of the network, the sample set is randomly phase-shifted while ensuring that the contour signal characteristics remain unchanged; at the same time, the processed sample set is encoded into a two-dimensional image signal through the reverse Hilbrt curve; finally, the sample label is generated. The convolutional neural network models of the present invention are all two-class output networks. The first class is a two-dimensional image with a standard period, and the output label result is: 1; the second class is a two-dimensional image with a non-standard period, and the output label result is: 0.

[0051] Step 5: Design and train convolutional neural network 1:

[0052] Convolutional neural network 1 mainly extracts features and outputs classification for two-dimensional images with a large cycle search step size, and achieves the effect of quickly narrowing the range within the initially set large cycle search range, providing a feasible range for convolutional neural network 2 to perform cycle refinement search. Since the feature information of the two-dimensional image is more obvious when the cycle search step size is large, in order to improve the computational efficiency, the network structure of convolutional neural network 1 can be specifically as follows: Figure 3 The design is shown in the figure. The convolutional neural network 1 network is mainly designed as three blocks, each of which is composed of "convolution-normalization-activation-pooling", which can enhance the network's deep learning ability for image features. The convolution kernel size of the convolutional neural network 1 is set to 3×3, and the number of channels is set to 8, 16, and 32 respectively; in order to enhance the convergence speed and stability of the model and improve the generalization ability of the model, normalization operation is performed after convolution; the activation layer selects the ReLU function; the pooling layer selects the maximum pooling function to reduce the amount of calculation and maintain spatial invariance; the fully connected layer sets 2 output nodes to ensure the output of the image in two categories.

[0053] Step 6: Design and train convolutional neural network 2:

[0054] Convolutional neural network 2 mainly learns the features of two-dimensional images with a small period search range and outputs them in a classified manner. The effect achieved is to finely distinguish two-dimensional images within a small period range, thereby determining the optimal period. Since the image features distinguished by convolutional neural network 2 are similar, a more complex deep network structure should be adopted. At the same time, in order to prevent the network structure from being too deep and causing data overfitting, the network needs to be processed to prevent overfitting. The specific network structure design of convolutional neural network 2 is as follows: Figure 4 As shown. Convolutional neural network 2 is designed as 5 blocks, all of which are composed of "convolution-normalization-activation-convolution-normalization-activation-pooling-Dropout". Each block performs 2 convolution operations to obtain more abstract and deeper image features. In order to prevent overfitting in network training, a Dropout layer is added after each block to enhance the generalization ability of the network by "randomly discarding some neurons during training to forcibly enhance the flexible learning ability of the network".

[0055] The experimental simulation of the present invention is as follows:

[0056] The simulation experiment parameters were set at a duration of 1000 seconds, a pulse period of 33.7 ms, and an effective photon flux of 1.54 ph / cm 2 / s, background photon flux 0.005ph / cm 2 / s, the true value of θ0 is 0, and the effective area of ​​the detector is 42cm 2 , the number of bins is 256. The Monte Carlo method can be used to obtain the period estimation results obtained by the traditional period estimation method and the method of the present invention, as shown in Table 1 below.

[0057] Table 1 Mean and root mean square error of the estimation errors of the two methods

[0058] method Mean estimation error (ns) Estimation root mean square error (ns) Traditional period estimation method 1.5600 1.2147 Period estimation method of the present invention 0.5350 0.3786

[0059] Compared with the traditional period estimation method, the period estimation method proposed in the present invention has higher period estimation accuracy. Figure 5 The comparison diagram of the pulsar profile signal obtained by folding the period estimated by the estimation method of the present invention and the traditional period method in the simulation experiment is shown. It can be found from the figure that the pulsar profile folded by the method of the present invention has more prominent profile features than the traditional method, which is more conducive to improving the TOA calculation accuracy in the later stage.

[0060] The above embodiments are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the present invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the present invention should all be included within the scope of the present invention.

Claims

1. A pulsar period estimation method, characterized in that: The photon energy information is used to perform epoch folding, and the one-dimensional contour information is converted into a two-dimensional image signal through the inverse space filling curve. The contour image features are identified through the convolutional neural network model to determine the optimal period, which specifically includes the following steps: Step 1: Count the arrival time of pulsar photons received by the detector, and prepare for folding the pulsar profile epoch based on the photon number information; Step 2: weighted epoch folding of pulsar profiles is performed in combination with photon energy information; Step 3: Encode the folded pulsar profile signal using an inverse space filling curve, and convert the one-dimensional pulsar profile signal into a two-dimensional image signal without damaging the pulsar profile signal; Step 4: Preprocess the pulsar two-dimensional image signal: generate training sets and test sets, and perform random phase shifts on the sample sets to enhance the generalization ability of network training. Finally, mark the sample labels. Step 5: Within a larger cycle search range, a larger cycle search step size is set to design and train the convolutional neural network 1, and the cycle search range is initially and quickly narrowed; Step 6: Combine the preliminary search results of step 5, narrow the cycle search range, set a smaller cycle search step, design and train the convolutional neural network 2, and perform a detailed search to determine the optimal cycle; The implementation method of step 1 is that in the pulsar period estimation experiment, the total observation time is The experimental period is , and the entire observation period is divided into At the same time, for each equally divided segment, Divided into Each observation time period after division is called bin, and the specific relationship between them is as follows: (1) (2) The specific operations for preparing the pulsar profile epoch folding by combining the photon number information are: first, in the total observation time In each Arrive at the The total number of photons in each bin is added to the first time period Secondly, count the total number of photons in each bin; In step 2, when performing epoch folding of the pulsar period profile, weighted folding is performed in combination with photon energy information: The steps of weighted folding of profiles combined with photon energy information are as follows: First, the length of Arrive at the The photons in each bin are placed into the corresponding bin of the first time period; secondly, the total number of photons in each bin in the first time period is counted and accumulated according to the energy value carried by the photons; finally, the photon energy value in each bin is normalized to obtain the pulsar profile signal ; ， In the formula, Indicates The time period The energy carried by the photons in a bin.

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