A fast pulse period estimation method based on phase difference correction

Abstract

The present invention proposes a fast pulse period estimation method based on phase difference correction. The method comprises: step one, determining the mapping relationship between the folded waveform phase difference and the period estimation error; step two, folding the waveform in time periods and calculating the folded waveform phase difference, and calculating the period estimation error according to the mapping relationship; step three, setting an accuracy threshold, and when the folded waveform phase difference meets the accuracy threshold, calculating the pulse period estimation value according to the period estimation error. Compared with the traditional epoch folding period estimation method, the present invention greatly improves the calculation speed, and at the same time is comparable to the prior art in accuracy, is insensitive to the observation duration, and is of great significance for on-orbit real-time pulse reception period estimation.

Description

Technical Field

[0001] The invention belongs to the technical field of aerospace navigation, and in particular relates to a fast pulse period estimation method based on phase difference correction. Background Art

[0002] With the continuous development of deep space exploration technology, it is imperative to improve the autonomous navigation capability of deep space probes. X-ray pulsar navigation is one of the many astronomical navigation methods. With its unique characteristics and advantages, it has become a potential deep space autonomous navigation technology and a research hotspot in recent years.

[0003] The key to achieving high-precision pulsar navigation is to obtain high-precision pulse delay information. The acquisition of pulse delay information requires processing the photon arrival time (TOA) data, so the pulse delay estimation method based on photon TOA data processing is the key to determining the performance of pulsar navigation. Pulse delay estimation includes pulse reception period estimation and pulse initial phase estimation, and pulse reception period estimation can be divided into frequency domain estimation method and time domain estimation method.

[0004] Fast Fourier Transform (FFT) is a commonly used method for analyzing the spectrum of discrete time series. It has high accuracy and computational efficiency. However, FFT requires that the processed data be evenly distributed on the time axis. The pulsar photon TOA data records the time when each photon arrives at the detector, and the time intervals between data points are not uniform. If the FFT method is to be used to process TOA data, the data must first be interpolated. The inaccuracy of the interpolation process will directly affect the subsequent results. Therefore, the FFT method cannot obtain high-precision results for estimating the period and can only be used for rough analysis.

[0005] In order to solve the problem of non-uniform time intervals that cannot be avoided in the process of photon TOA signal processing, scholars have studied the frequency domain Lomb algorithm to process pulsar data. The advantage of the Lomb algorithm is that it can directly perform spectral analysis on time domain non-uniformly spaced signals, but the disadvantage is that the algorithm requires a lot of calculations and a lot of data to suppress noise. Later, some scholars studied a time delay estimation method based on dual spectrum analysis, which greatly reduced the computational complexity, but is only applicable to high signal-to-noise ratio signals. In summary, the frequency domain estimation method can be used to estimate the period of pulsar signals, but there are problems with complex calculations or limited accuracy, and it is necessary to consider using other methods or combining the frequency domain method with other methods.

[0006] The pulse delay estimation method based on epoch folding (EF) is one of the mainstream methods for analyzing and processing pulsar data in the field of time domain estimation. Its limitation is that it is time-consuming to calculate. To solve this problem, a fast epoch folding method is introduced to speed up the calculation of epoch folding, but it only reduces part of the calculation burden. The overall accuracy of the time domain estimation method based on EF is better than that of the frequency domain method. Since the final results obtained by each specific method are of comparable accuracy, the current focus of this type of method is to reduce the computational complexity as much as possible in order to achieve faster calculation speed; in addition, the algorithm's anti-noise ability, especially its performance under low signal-to-noise ratio conditions, is also an important criterion.

[0007] Combined with the current research status, the current pulse period estimation method has a large amount of calculation and the algorithm is not fast enough, which is not easy to meet the real-time requirements of navigation in actual navigation situations. Therefore, there is an urgent need for a fast and high-precision pulse period estimation method to avoid a large number of repeated operations on the period test values ​​and improve the algorithm calculation speed without losing accuracy. Summary of the invention

[0008] In order to solve the above problems, the present invention proposes a fast pulse period estimation method based on phase difference correction. Compared with the traditional method, the phase difference correction period estimation method has a faster calculation speed and a lower dependence on the observation time. From this perspective, the phase difference correction period estimation method is undoubtedly a period estimation method that is more suitable for the development of future pulsar navigation technology.

[0009] In order to achieve the above object, the present invention adopts the following technical scheme:

[0010] A fast pulse period estimation method based on phase difference correction, comprising:

[0011] Step 1: determine the mapping relationship between the folded waveform phase difference and the period estimation error;

[0012] Step 2: fold the waveform in time periods and calculate the phase difference of the folded waveform, and calculate the period estimation error according to the mapping relationship;

[0013] Step 3: Set the accuracy threshold. When the phase difference of the folded waveform meets the accuracy threshold, calculate the pulse period estimation value based on the period estimation error.

[0014] The beneficial effects of the present invention are:

[0015] (1) The present invention uses an iterative algorithm to continuously correct the pulse estimation period until the phase difference meets the predetermined accuracy requirement, which can greatly improve the calculation speed while maintaining or even improving the period estimation accuracy;

[0016] (2) The proposed method has a lower dependence on observation time and is of great significance for the estimation of on-orbit real-time pulse reception period. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 The present invention is a flow chart of a fast pulse period estimation method based on phase difference correction. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. 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.

[0019] like Figure 1 As shown, the present invention provides a fast pulse period estimation method based on phase difference correction, which uses an iterative algorithm to continuously correct the pulse estimation period until the phase difference meets the predetermined accuracy requirement. The method can significantly improve the calculation speed while maintaining or even improving the period estimation accuracy.

[0020] The technical principle of the present invention is to select the time-segment folding method to calculate the folded waveform phase difference information when the true initial phase is unknown, and use the derived linear mapping relationship between the folded waveform phase difference and the period estimation error to correct the period estimation value, thereby avoiding the repeated epoch folding operation in the traditional method. The implementation process is described in detail below:

[0021] 1. About the phase difference of folded waveform and period estimation error Study on the mapping relationship between:

[0022] According to the definition of non-homogeneous Poisson process, the pulse waveform is actually the rate function of non-homogeneous Poisson process. , when the velocity component of the spacecraft in the line of sight of the pulsar is a certain value When is a periodic function, which has the following Fourier series expansion:

[0023] (1)

[0024] In the formula, is the DC flow, For the Amplitude and angular frequency of the harmonic ,in is the real pulse period, is the time variable, For the The initial phase angle of the first harmonic. Assume that the total observation time For the test cycle An integer multiple of (usually due to , so even if Not for The whole observation time is an integer multiple of , which has little impact on the analysis results. Divide into equal parts of length of The phase difference between two adjacent intervals is , where the period estimation error is , assuming that the test cycle With the real cycle The phase change caused by the difference between , then The phase shift of adjacent waveforms of the order harmonics is , after folding Harmonics It can be expressed as:

[0025] (2)

[0026] In the formula, Indicates observation interval;

[0027] According to Euler's formula , rewrite formula (2) as:

[0028] (3)

[0029] In the formula, represents the real part operation, is an imaginary unit, represents the exponential function;

[0030] Using the geometric method of complex number summation, equation (3) can be rewritten as follows:

[0031] (4)

[0032] In the formula To obtain the amplitude of the waveform after folding and summing, convert equation (4) back to cosine form:

[0033] (5)

[0034] In fact, after folding , indicating that the folded waveform not only has phase difference but also distortion. However, if we ignore The higher-order harmonics can be approximately considered as:

[0035] (6)

[0036] In the formula, Indicates the total observation time The number of separation segments, is a constant, represents transpose;

[0037] Therefore, the normalized waveform after folding (the folded waveform per unit time) is approximately:

[0038] (7)

[0039] When ignoring the original pulse waveform (real waveform) When there are higher-order harmonics of level 1 and above, the original waveform has the following form:

[0040] (8)

[0041] There is a time shift between the folded pulse waveform and the original pulse waveform , the folded waveform phase difference corresponding to this time shift is for:

[0042] (9)

[0043] Based on the real pulse period Unknown and , formula (9) is replaced by the following approximate form:

[0044] (10)

[0045] Equation (10) shows that the folded waveform phase difference and period estimation error There is a linear mapping relationship between them. In a suitable range, this expression has high accuracy, so the period correction can be performed using equation (10).

[0046] 2. Folded waveform phase difference and period estimation error Calculation:

[0047] The folded waveform phase difference on the left side of the equation (10) is Has the following form:

[0048] (11)

[0049] In the formula, Indicates the total observation time The initial phase of the waveform is obtained by folding the TOA of the photons received. Indicates the initial phase of the real pulse waveform;

[0050] Combining formula (10) and formula (11):

[0051] (12)

[0052] Because in actual pulsar navigation, is an unknown quantity, so there are actually two unknown quantities in equation (12), namely and Obviously, it is impossible to directly obtain However, if we use equation (12) to construct two equations at the same time, so that the two equations have the same real initial phase , we can use the elimination method to directly eliminate Specifically, the TOA of the photons received during the first 50% of the entire observation period is folded once, and the initial phase of the folded waveform is , then according to formula (12), the following equations are established:

[0053] (13)

[0054] The difference between the two equations (13) is the phase difference of the folded waveform: :

[0055] (14)

[0056] Therefore, the period estimation error for:

[0057] (15)

[0058] In summary, the time period folding method is selected to calculate the phase difference and period estimation error when the true initial phase is unknown.

[0059] 3. A brief description of the process of fast pulse period estimation method based on phase difference correction:

[0060] In actual navigation, the pulsar signal model is used to make a preliminary estimate of the pulse reception period and obtain the initial test period The value of . Figure 1 This is a flow chart of the fast pulse period estimation method based on phase difference correction. As shown in the figure, after obtaining the initial test period Afterwards, the observed TOA data were subjected to full-time waveform folding and first 50% time period waveform folding, and the phase difference between the two folded waveforms was calculated using the cross-correlation algorithm. , calculate the period estimation error according to formula (15) . Preset an accuracy threshold It is used to reflect the accuracy level that the final period estimation needs to achieve. If the folded waveform phase difference The absolute value of is greater than or equal to the accuracy threshold , then As a new test cycle Repeat the waveform folding and calculation of the folded waveform phase difference until the accuracy threshold is met ; If the folded waveform phase difference The absolute value of is less than the precision threshold , then As the final pulse period estimate Output.

[0061] The contents not described in detail in the specification of the present invention belong to the prior art known to the professional and technical personnel in the field. It is easy for the technical personnel in the field to understand that the above description is only the preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A fast pulse period estimation method based on phase difference correction, characterized in that: The method comprises: Step 1: determine the mapping relationship between the folded waveform phase difference and the period estimation error; Step 2: fold the waveform in time periods and calculate the phase difference of the folded waveform, and calculate the period estimation error according to the mapping relationship; Step 3: Set the accuracy threshold. When the phase difference of the folded waveform meets the accuracy threshold, calculate the pulse period estimation value according to the period estimation error. Determining the folded waveform phase difference and period estimation error The mapping relationships include: Based on the pulse waveform conforming to the rate function of the non-homogeneous Poisson process ,Will According to the Fourier series expansion, it becomes the following form: (1) In the formula, is the DC flow, For the Amplitude and angular frequency of the harmonic ,in is the actual pulse period, is the time variable, For the The initial phase angle of the harmonic order is , and the total observation time is For the test cycle An integer multiple of Number of segments , the waveform phase difference between two adjacent intervals is , where the period estimation error is , assuming that the test cycle The actual pulse period The phase change caused by the difference between , then The phase shift of adjacent waveforms of the order harmonics is , after folding Harmonics It is expressed as: (2) In the formula, Indicates observation interval; According to Euler's formula , x represents the angle radian variable in Euler's formula, and formula (2) is rewritten as: (3) In the formula, represents the real part operation, represents the imaginary unit, represents the exponential function; Using the geometric method of complex number summation, equation (3) can be rewritten as follows: (4) In the formula, To obtain the amplitude of the waveform after folding and summing, convert equation (4) back to cosine form: (5) Set Ignore And higher order harmonics: (6) In the formula, For the The amplitude of the harmonics, After folding and summing The waveform amplitude of the order harmonic, is a constant, represents transpose; Therefore, the folded normalized waveform is: (7) When the original pulse waveform is ignored, that is, the real waveform For higher-order harmonics of the order and above, the original pulse waveform has the following form: (8) There is a time shift between the folded pulse waveform and the original pulse waveform , the folded waveform phase difference corresponding to this time shift is for: (9) Based on the real pulse period Unknown and , formula (9) is transformed into: (10) The calculated folded waveform phase difference and period estimation error include: The folded waveform phase difference on the left side of the equation (10) is Has the following form: (11) In the formula, Indicates the total observation time The initial phase of the waveform is obtained by folding the TOA of the photons received. Indicates the initial phase of the real pulse waveform; Combining formula (10) and formula (11): (12) Total observation time The TOA of the photons received during the first 50% of the observation time is folded once, and the initial phase of the folded waveform is ,have: (13) The difference between the two equations (13) is the phase difference of the folded waveform: : (14) Therefore, the period estimation error for: (15) The step three comprises: The pulsar signal model is used to estimate the pulse reception period in actual navigation and obtain the initial test period. ; The observed TOA data are folded for the entire period and the first 50% period, and the phase difference of the folded waveforms is calculated. , calculate the period estimation error according to formula (15) , if the folded waveform phase difference The absolute value of is greater than or equal to the accuracy threshold ,Will As a new test cycle Repeat the waveform folding and calculation of the folded waveform phase difference until the accuracy threshold is met ; If the folded waveform phase difference The absolute value of is less than the precision threshold , then As the final pulse period estimate Output.

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