A method for processing pulsar data based on non-uniform epoch folding for variable-speed models

Abstract

The present invention discloses a method for processing pulsar data of a variable speed model based on non-uniform epoch folding, the method comprising: obtaining external observation data of a spacecraft; converting the external data into an equivalent phase difference; non-uniformly dividing the time axis according to the equivalent phase difference; performing epoch folding operations based on the divided time axis; estimating the signal receiving frequency at the initial moment; and calculating the pulse delay. The present invention proposes a method for processing data of a variable speed model equivalent to a fixed speed model, which solves the contradiction between the short-time frequency invariance assumption and the solution accuracy caused by data segmentation, improves the pulse delay estimation accuracy of the variable speed model, and provides a feasible technical approach for processing pulsar data of a variable speed model.

Description

Technical Field

[0001] The present invention relates to the technical field of pulsar navigation, and in particular to a pulsar TOA data processing method. Background Art

[0002] Pulsar navigation technology is an ideal autonomous navigation method for spacecraft, especially deep space probes, and has great development prospects. The advantages of pulsar navigation technology include: it can provide complete positioning, attitude determination, and timing services, covering all navigation needs of deep space probes; X-ray pulsars have obvious characteristics in the X-band, which can effectively avoid interference from other signals; X-ray pulsar navigation can be used in all stages of deep space exploration (Earth orbiting stage, transfer stage, approach / capture stage), and has a wide range of applications.

[0003] The pulse delay estimation algorithm is the core technology of pulsar navigation. The pulse delay estimation method used in pulsar navigation is essentially a parameter estimation method based on the pulsar signal model. Specifically, the pulsar signal model can be divided into a constant speed model and a variable speed model according to whether the spacecraft speed change is considered, and the parameter estimation is mainly divided into pulse reception frequency estimation and pulse initial phase estimation. For the constant speed model, the pulse frequency estimation method can be divided into frequency domain estimation method and time domain estimation method at this stage, and the pulse initial phase estimation method mainly includes the estimation algorithm based on epoch folding and the maximum likelihood estimation method. For the variable speed model, a reasonable pulse delay estimation scheme is the focus of current research.

[0004] The advantage of using a constant-speed model to analyze pulsar delays is that when the relative speed between the spacecraft and the pulsar changes slowly over time, the constant-speed model analysis and calculation complexity is low and the required accuracy can be achieved. However, when the spacecraft speed changes dramatically over time, or when the navigation accuracy is very high, data processing using the theoretical method of the constant-speed model will produce large errors. Therefore, it is necessary to develop a pulsar data processing solution under a variable-speed model to cope with application scenarios where the speed changes dramatically.

[0005] When the variable speed model is used to process pulsar data, a long observation period is divided into several shorter observation periods. In each short period after the division, the receiving frequency is regarded as a certain value, that is, the data is processed according to the fixed speed model after the division. In this way, the variable speed model data processing problem that is difficult to solve by relying solely on TOA data is converted into several fixed speed model data processing problems. This is the best way to deal with such problems in engineering applications.

[0006] However, existing theories all have an irreconcilable contradiction between the need to segment the data and the inability to achieve sufficient accuracy when using the segmented data for calculations. The characteristics of pulsar TOA data fundamentally limit the accuracy of the above methods. The pulsar photon signals suitable for navigation are very weak and the background noise is large. Therefore, long-term observations are required to obtain sufficient data to suppress the influence of noise. In actual situations, the variance of the estimate will only show obvious signs of convergence when the amount of data exceeds a certain threshold. Therefore, the accuracy of the results obtained by using data from a short period of time for data processing is unreliable. Summary of the invention

[0007] The technical problem to be solved by the present invention is: in view of the problem of insufficient pulse delay estimation accuracy in pulsar data processing based on a variable speed model in a high dynamic environment, i.e., an application environment where the spacecraft speed changes more drastically, a variable speed model pulsar data processing method based on non-uniform epoch folding is provided to improve the estimation accuracy of the pulse delay.

[0008] Technical solution of the present invention:

[0009] In a first aspect, the present invention provides a method for processing pulsar data of a variable-speed model based on non-uniform epoch folding, comprising the following contents:

[0010] S1. Use the onboard accelerometer to obtain the spacecraft acceleration information, or use the Doppler velocity measurement scheme of the onboard spectrometer to obtain the spacecraft real-time velocity information, as well as the arrival time data of the pulsar photons received by the detector as external observation information;

[0011] S2, processing the spacecraft acceleration and the spacecraft real-time speed in the external observation information in S1 into the phase of the spacecraft receiving signal, and establishing a variable speed model based on the spacecraft acceleration and the spacecraft real-time speed and their changes, and based on the variable speed model, non-uniformly dividing the observation time period according to the principle of equal phase difference, and converting it into several constant speed models;

[0012] The equal phase difference principle is that each observation time period corresponds to the same phase interval, and each observation time period after division is called a bin. The position and size information of each bin after division is obtained, which is the bin division result. Each bin corresponds to a constant speed model. According to the bin division result, the arrival time data of pulsar photons in the external observation information is converted into a photon density sequence of non-uniform epoch folding.

[0013] S3, folding and normalizing the non-uniform epoch folded photon density sequence of S2 to obtain the final folded waveform; performing a cyclic cross-correlation operation on the final folded waveform and the standard waveform sequence with an initial phase of 0 to obtain the estimated initial phase of the received signal, which is the final result of data processing.

[0014] Furthermore, in S2: obtaining the photon density sequence of non-uniform epoch folding is specifically implemented as follows:

[0015] A. The standard for non-uniform division of the observation time period according to the principle of equal phase difference is that each bin corresponds to the same phase interval That is, the phase interval between the n+1th bin and the nth bin is

[0016]

[0017] Where Φ(·) is the phase of the spacecraft received signal after the spacecraft acceleration and the spacecraft real-time velocity in the external observation information are processed, N b is the number of bins in the observation period, which is set according to actual needs; t0 is the initial time of the observation period, T' b (k) is the duration of the kth bin, i.e., the bin division result;

[0018] B. According to the bin division results, the arrival time data of pulsar photons in the external observation information is converted into a non-uniform epoch-folded photon density sequence x'(k):

[0019] x'(k)=d(t' b (k),t' b (k)+T' b (k))

[0020] Among them, t b '(k) is the start time of the kth bin, and d(·) is defined as the time interval [t′ b (k),t′ b (k)+T′ b (k)) is the photon density, that is:

[0021]

[0022] Among them, c(t′ b (k),t′ b (k)+T′ b (k)) is the observation period [t′ b (k),t′ b (k)+T′ b (k)) The total number of photons received in the external observation information.

[0023] In a second aspect, the present invention provides an electronic device (computer, server, smart phone, etc.), including a processor and a memory;

[0024] Memory, used to store computer programs;

[0025] The processor is used to execute the computer program stored in the memory, and implements a variable speed model pulsar data processing method based on non-uniform epoch folding during execution.

[0026] In a third aspect, the present invention provides a computer-readable storage medium (such as ROM / RAM, disk, CD) having a computer program stored thereon, which, when executed by a processor, implements a variable-speed model pulsar data processing method based on non-uniform epoch folding.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1) The present invention overcomes the problem of insufficient pulse delay estimation accuracy in pulsar data processing based on a variable speed model in a high dynamic environment, and provides a variable speed model pulsar data processing method based on non-uniform epoch folding, which converts the variable speed model problem into a constant speed model problem, overcomes the fundamental problem of the existing solution that the signal-to-noise ratio is reduced due to data segmentation, processes the spacecraft acceleration and the spacecraft real-time speed into the phase of the spacecraft receiving signal, and utilizes the non-uniform epoch folding operation to avoid data segmentation in the traditional method, thereby solving the contradiction between the short-time frequency invariance assumption and the solution accuracy caused by data segmentation, and improving the data processing accuracy.

[0029] (2) The present invention uses acceleration or velocity information as external observation information, and defines the phase difference generated by the accumulation of the signal reception frequency difference over time as the equivalent phase difference. The present invention divides the time axis according to the size of the equivalent phase difference. Such a non-uniform epoch folding method is equivalent to considering the phase change speed, that is, the time axis is non-uniformly divided after considering the phase change, thereby improving the estimation accuracy of the pulse delay.

[0030] (3) By comparing the waveform obtained by the method of the present invention with the waveform obtained by the traditional epoch folding method and comparing it with the standard waveform, it is found that the waveform obtained by the non-uniform epoch folding method is in good agreement with the standard waveform, and the waveform obtained by the traditional epoch folding method produces large distortion and phase shift, which will have a negative impact on the estimation of the initial phase. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a flow chart of a variable speed model pulsar data processing method based on non-uniform epoch folding of the present invention;

[0032] Figure 2 It is a schematic diagram of the non-uniform epoch folding;

[0033] Figure 3 It is a schematic diagram of non-uniformly dividing the time axis in the non-uniform epoch folding method;

[0034] Figure 4 It is a comparison chart of the traditional epoch folding and non-uniform epoch folding waveforms. DETAILED DESCRIPTION

[0035] The present invention is further described in detail below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to clearly and completely describe the present invention and are not used to limit the present invention.

[0036] like Figure 1 As shown, the present invention adopts the following technical solution: The following takes the Crab pulsar as an example to illustrate the specific implementation steps of the present invention:

[0037] S1. Use the onboard accelerometer to obtain the spacecraft acceleration information, or use the Doppler velocity measurement scheme of the onboard spectrometer to obtain the spacecraft real-time velocity information, as well as the arrival time data of the pulsar photons received by the detector as external observation information;

[0038] S2. Processing the spacecraft acceleration and the real-time speed of the spacecraft in the external observation information in S1 into the phase of the spacecraft receiving signal. Since the spacecraft acceleration and the real-time speed are taken into consideration, the present invention considers the change of the spacecraft speed to establish a variable speed model, and based on the variable speed model, the observation time period is non-uniformly divided according to the principle of equal phase difference, and converted into several constant speed models; the principle of equal phase difference is that each observation time period corresponds to the same phase interval, and each observation time period after division is called a bin, and the position and size information of each bin after division is obtained, which is the bin division result, and each bin is a constant speed model; according to the bin division result, the time data of the pulsar photon arrival in the external observation information is converted into a photon density sequence folded by non-uniform epoch;

[0039] 1. As described in S2, establish a pulsar signal speed change model based on the spacecraft acceleration or real-time speed

[0040] A. The number of photons received by the detector at any time obeys a non-homogeneous Poisson process, and the photon arrival rate function λ(t) has the following relationship with the initial phase:

[0041]

[0042] Where α and β are the average arrival rate of useful signal photons and the average arrival rate of background signal photons, respectively, which are two constants; θ0 is the initial phase at time t0; h(·) is the waveform function, which is usually specified to have a period of 1; (t0, t) is the observation time interval; f(t) is the signal receiving frequency;

[0043] B. For the variable speed model, the signal receiving frequency f(t) is in the form of:

[0044]

[0045] In the formula, f s is the natural frequency of the pulsar, c is the speed of light, and v(t) is the speed of the spacecraft in the direction of the pulsar's line of sight.

[0046] C. At any time t, the pulse signal receiving phase Φ(t) and the signal receiving frequency f(t) have the following relationship:

[0047]

[0048] Wherein, θ0 is the initial phase, (t0, t) is the observation time interval, τ is the integral variable, and the present invention does not consider the second-order and higher Doppler effects.

[0049] 2. As described in S2, in the established variable speed model, the probability distribution of the total number of detected photons is a non-homogeneous Poisson distribution;

[0050] In the time period (s, t), the total number of photons detected is k with probability:

[0051]

[0052] Among them, for the observation time interval (t0,t), represents the total number of photons detected during this period, and s represents the initial moment of the detection time period. It is a non-homogeneous Poisson process, and the photon arrival rate function λ(t) represents the frequency of events occurring in a very short time interval.

[0053] 3. As described in S2, in the established speed-changing model, the rate function λ(t) in the non-homogeneous Poisson process is:

[0054] A. When the number of photons received by the detector is selected as the counting object, the relationship between the rate function λ(t) and Φ(t) in the non-homogeneous Poisson process is:

[0055] λ(t)=β+αh(Φ(t))

[0056] B. The specific expression of the rate function λ(t) is:

[0057]

[0058] 4. As described in S2, before the observation time period is non-uniformly divided, the photon arrival time data needs to be converted into a time series

[0059] A. Bins in epoch folding operations

[0060] In the traditional epoch folding operation, bin represents the smallest photon counting unit. The traditional epoch folding scheme assumes that the signal frequency f(t) remains at a constant value f throughout the observation interval. This frequency is usually uniformly selected within the possible range according to a specific step size. When the test frequency f' is determined, the corresponding test period P' can be determined. If T obs is not an integer multiple of P', then T obs The truncated part should be smaller than P'. Then the whole observation interval will be evenly divided into N p segments, each of length P. For each interval obtained, it will be further divided into N b Segments, each segment is called a bin, which covers T b time range.

[0061] B. Photon density sequence x(k) represents.

[0062] The process of converting photon arrival time data into a photon density sequence x(k) is equivalent to one-dimensional density estimation. a ,t b ), the photon density is defined as:

[0063]

[0064] Among them, c(t a ,t b ) is in [t a ,t b ) is the total number of photons received by the detector in the k-th bin. For the k-th bin, the time series x(k) is expressed as:

[0065] x(k)=d(t b (k),t b (k)+T b )

[0066] Among them, t b (k) is the start time of the nth bin.

[0067] 5. As described in S2, before the observation time period is divided non-uniformly, the expected value of the photon density sequence is required

[0068] The number of photons arriving at the detector in the same time interval is a non-homogeneous Poisson process. In the kth bin, the mathematical expectation of the time series is:

[0069]

[0070] Where E(·) is the mathematical expectation.

[0071] When T bWhen it approaches 0, according to L'Hôpital's rule, it has the following form:

[0072]

[0073] Due to t b (k) = (k-1)T b +t0, we get:

[0074] E[x(k)]=λ(kT b +t0)

[0075] in, is an arithmetic progression.

[0076] 6. As described in S2, the observation time period is divided unevenly, such as Figure 2 The variable speed model pulsar data processing method based on non-uniform epoch folding and the Figure 3 The time axis is evenly divided and non-uniform epoch folding is performed.

[0077] like Figure 2 As shown, the present invention first obtains the acceleration a(t) through an accelerometer or obtains the velocity v(t) through a spectral velocity measurement system, and then or The measurement information is equivalent to the phase conversion. Where ΔΦ(t) is the phase difference, f s is the frequency of the detector, [t0, t) is the integration interval of the observation time period, and s and τ are both integration variables. As input data, the time axis is non-uniformly divided. Then, for each time period t i (i=1,2,...,N p ) and the input TOA data t k (k=1,2,...,K) perform epoch folding calculation to obtain the final estimated waveform.

[0078] like Figure 3 As shown, the present invention performs non-uniform segmentation on the time axis. Wherein, t0 represents the time starting point of the time axis, and P represents the length of each time period before segmentation. It can be seen that the lengths of each time period before segmentation are equal. b (i) (i = 1, 2, ..., n) represents the length of each time period after the time axis is non-uniformly divided, t' b (i) (i = 1, 2, ..., n) represents the initial time of the i-th time period after the non-uniform segmentation. x'(n) = d(t' b (n),t' b (n)+T' b(n)) is the photon density during the time period of the non-uniform epoch folding.

[0079] A. The non-uniform epoch folding described in the present invention abandons the assumption that the real-time signal receiving frequency f(t) of the spacecraft remains unchanged. x'(k) is taken as the photon density in the kth bin, but the length of the kth bin should be determined according to the frequency change received by the spacecraft. When the value of f(t) is large, a shorter bin should be used, and when the value of f(t) is small, a longer bin should be used.

[0080] Each bin corresponds to the same phase interval That is, the phase interval between the n+1th bin and the nth bin is

[0081]

[0082] Where Φ(·) is the phase of the signal received by the spacecraft, N b is the number of bins in the observation period, which can be set according to actual needs. t0 is the initial time of the observation period, T' b (k) is the duration of the kth bin, let t b '(k) is the starting time of the kth bin in the proposed method, then:

[0083] x'(k)=d(t' b (k),t' b (k)+T' b (k))

[0084] Among them, x'(k) represents the new photon density sequence after non-uniform epoch folding.

[0085] B. In traditional epoch folding, E[x(k)] = λ(kT b +t0); the expected value of the photon density x'(k) for the non-uniform epoch folding is:

[0086]

[0087] In the traditional epoch folding signal model, λ(t)=β+αh(Φ(t)), the rate function with phase as the independent variable is defined as:

[0088]

[0089] The expected value of the photon density x'(k) for the non-uniform epoch fold is:

[0090]

[0091] λ φ(·) is a periodic function with period 1.

[0092] exist in,sequence Is a common difference Therefore, E[x'(k+N b )] is:

[0093]

[0094] Where E[x'(k)] is N b is a periodic sequence of periods. That is, the non-uniform epoch folding of the present invention retains the periodicity of E[x'(k)], and its periodicity does not change with the observation time T obs increased and destroyed.

[0095] S3, folding and normalizing the photon density sequence of the non-uniform epoch folding of S2 to obtain the final folding waveform; performing a cyclic cross-correlation operation on the final folding waveform and the standard waveform sequence with an initial phase of 0 to obtain the initial phase of the estimated received signal, which is the final result of data processing, as follows:

[0096] By folding the obtained sequence x'(k), the folded waveform sequence is obtained The specific folding expression is:

[0097]

[0098] Suppose there is another standard waveform sequence with an initial phase of 0 The folded waveform sequence Standard waveform sequence with initial phase 0 To perform a circular cross-correlation operation, first The sequence is extended periodically, and the new sequence period is N b * , the circular cross-correlation operation is defined as follows:

[0099]

[0100] For the newly obtained sequence There is the following relationship between the sequence number corresponding to its maximum value and the initial phase θ0 of the received signal:

[0101]

[0102] 7. Simulation Experiment Results

[0103] The simulation experiment parameters were set at a duration of 1000 seconds and an acceleration of 10 m / s. 2, pulse period is 33ms, effective photon flux is 1.54ph / cm 2 / s, background photon flux 0.005ph / cm 2 / s, the true value of θ0 is 0, the velocity output frequency is 1Hz, and the effective area of ​​the detector is 45cm 2 The pulse waveforms obtained by the non-uniform epoch folding and epoch folding methods are compared with the standard pulse waveform.

[0104] like Figure 4 As shown, curve A represents the waveform obtained by the traditional epoch folding method, curve B represents the waveform obtained by the non-uniform epoch folding method of the present invention, and curve C is the standard waveform of the simulation experiment. It can be seen that the waveform obtained by the non-uniform epoch folding method of the present invention is consistent with the standard waveform very well, while the waveform obtained by the traditional epoch folding method produces large distortion and phase shift, which will have a negative impact on the estimation of the initial phase.

[0105] Based on the same inventive concept, another embodiment of the present invention provides an electronic device (computer, server, smart phone, etc.), which includes a memory and a processor, the memory stores a computer program, the computer program is configured to be executed by the processor, and the computer program includes instructions for executing each step in the method of the present invention.

[0106] Based on the same inventive concept, another embodiment of the present invention provides a computer-readable storage medium (such as ROM / RAM, disk, CD), which stores a computer program. When the computer program is executed by a computer, it implements the various steps of the method of the present invention.

[0107] 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 method for processing pulsar data of a variable-speed model based on non-uniform epoch folding, characterized in that: S1. Use the onboard accelerometer to obtain the spacecraft acceleration information, or use the Doppler velocity measurement scheme of the onboard spectrometer to obtain the spacecraft real-time velocity information, as well as the arrival time data of the pulsar photons received by the detector as external observation information; S2, processing the spacecraft acceleration and the spacecraft real-time speed in the external observation information in S1 into the phase of the spacecraft receiving signal, and establishing a variable speed model based on the spacecraft acceleration and the spacecraft real-time speed and their changes, and based on the variable speed model, non-uniformly dividing the observation time period according to the principle of equal phase difference, and converting it into several constant speed models; The equal phase difference principle is that each observation time period corresponds to the same phase interval, and each observation time period after division is called a bin. The position and size information of each bin after division is obtained, which is the bin division result. Each bin corresponds to a constant speed model. According to the bin division result, the arrival time data of pulsar photons in the external observation information is converted into a photon density sequence of non-uniform epoch folding. S3, folding and normalizing the non-uniform epoch folded photon density sequence of S2 to obtain the final folded waveform; performing a cyclic cross-correlation operation on the final folded waveform and the standard waveform sequence with an initial phase of 0 to obtain the estimated initial phase of the received signal, which is the final result of data processing.

2. The variable speed model pulsar data processing method based on non-uniform epoch folding according to claim 1 is characterized in that: In S2, obtaining the photon density sequence of non-uniform epoch folding is specifically implemented as follows: A. The standard for non-uniform division of the observation time period according to the principle of equal phase difference is that each bin corresponds to the same phase interval , that is, the phase interval between the n+1th bin and the nth bin is : ， In the formula, It is the phase of the spacecraft receiving signal after the spacecraft acceleration in the external observation information is processed with the spacecraft real-time velocity; It is the number of bins in the observation period, which is set according to actual needs; is the initial time of the observation period, is the duration of the kth bin; B. According to the bin division results, the arrival time data of pulsar photons in the external observation information is converted into a non-uniform epoch-folded photon density sequence : ， in, is the start time of the kth bin, Defined as the observation period The photon density inside is: ， in, During the observation period The total number of photons received by the detector in external observation information.

3. An electronic device, characterized in that: including a processor and a memory; Memory, used to store computer programs; A processor is used to execute a computer program stored in a memory, and implement the method described in claim 1 or 2 when executed.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to claim 1 or 2 is implemented.

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