CN119309571B - Rapid pulse period estimation method based on phase difference correction - Google Patents
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Abstract
本发明提出了一种基于相差修正的快速脉冲周期估计方法。所述方法包括：步骤一、确定折叠波形相位差与周期估计误差之间的映射关系；步骤二、分时段对波形进行折叠并计算折叠波形相位差，依据所述映射关系计算周期估计误差；步骤三、设定精度阈值，当折叠波形相位差满足精度阈值时，依据周期估计误差计算脉冲周期估计值。相较于传统的历元折叠的周期估计方法，本发明大幅提高了计算速度，同时在精度上与现有技术相当，对观测时长不敏感，对于在轨实时脉冲接收周期估计具有重要意义。
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
The invention belongs to the technical field of aerospace navigation, and particularly relates to a phase difference correction-based rapid pulse period estimation method.
Background
With the continuous development of deep space exploration technology, it is imperative to improve the autonomous navigation ability of the deep space exploration. The X-ray pulsar navigation is one of a plurality of astronomical navigation modes, and becomes a deep space autonomous navigation technology with great potential by the unique characteristics and advantages, so that the X-ray pulsar navigation is a research hot spot in recent years.
The key to realizing high-precision pulsar navigation is to acquire high-precision pulse time delay information. The acquisition of pulse delay information needs to process the data of photon arrival Time (TOA), so a pulse delay estimation method based on photon TOA data processing is a key for determining the navigation performance of the pulsar. The pulse delay estimation includes pulse receiving period estimation and pulse initial phase estimation, and the pulse receiving period estimation can be divided into a frequency domain estimation method and a time domain estimation method.
The fast fourier transform (Fast Fourier Transform, FFT) method is a common method for analyzing a discrete time series spectrum, and has higher accuracy and calculation efficiency, but the FFT requires that the processed data is uniformly distributed on a time axis, and the time of arrival of each photon at a detector is recorded by pulsar photon TOA data, the time interval between data points is not uniform, if the TOA data is to be processed by using the FFT method, the interpolation processing must be performed on the data first, the inaccuracy of the interpolation process directly affects the subsequent result, so the FFT method estimation period cannot obtain a high-precision result but only can be roughly analyzed.
In order to solve the problem of unavoidable non-uniform time intervals in the photon TOA signal processing process, a learner researches a frequency domain Lomb algorithm to process pulsar data. The Lomb algorithm is advantageous in that it can directly perform spectrum analysis on time-domain non-equally spaced signals, but is disadvantageous in that it requires a large amount of computation and a large amount of data to suppress noise. Later, a learner researches a time delay estimation method based on bispectrum analysis, which reduces the computational complexity to a great extent, but is only applicable to signals with high signal-to-noise ratio. In summary, the frequency domain estimation method can be used for estimating the period of the pulsar signal, but has the problem of complex calculation or limited precision, and other methods or a combination of the frequency domain method and other methods need to be considered.
The pulse time delay estimation method based on Epoch Folding (EF) is one of the main stream methods for analyzing and processing pulsar data in the field of time domain estimation methods, and has the limitation that the problem of time consumption in calculation exists. The overall accuracy of the EF-based time domain estimation method is better than that of the frequency domain method. The final result obtained by each specific method is quite accurate, so that the important development direction of the method is to reduce the calculation complexity as much as possible so as to achieve faster calculation speed, and in addition, the noise resistance of the algorithm is an important measurement standard, particularly under the condition of low signal to noise ratio.
In combination with the current research situation, the current pulse period estimation method has large calculated amount and insufficient algorithm rapidity, and is not easy to meet the requirement of navigation real-time under the actual navigation condition. Therefore, a rapid pulse period estimation method capable of ensuring high precision is urgently needed, a large number of repeated operation operations on a period test value are avoided, and algorithm calculation speed is improved on the premise of not losing precision.
Disclosure of Invention
In order to solve the problems, the invention provides a rapid pulse period estimation method based on phase difference correction, which has higher calculation speed and lower dependency on observation time compared with the traditional method, and is definitely a period estimation method more suitable for the development of the future pulsar navigation technology.
In order to achieve the above purpose, the invention adopts the following technical scheme:
A phase difference correction-based rapid pulse period estimation method comprises the following steps:
Step one, determining a mapping relation between a folding waveform phase difference and a period estimation error;
Folding the waveform in a time-sharing way, calculating the phase difference of the folded waveform, and calculating a period estimation error according to the mapping relation;
Setting an accuracy threshold, and calculating a pulse period estimated value according to the period estimated error when the folding waveform phase difference meets the accuracy threshold.
The invention has the beneficial effects that:
(1) The invention uses the iterative algorithm to continuously correct the pulse estimation period until the phase difference meets the preset precision requirement, and can greatly improve the calculation speed on the premise of maintaining or even improving the period estimation precision;
(2) The method has lower dependency on the observation time and has important significance on the on-orbit real-time pulse receiving period estimation.
Drawings
Fig. 1 is a flowchart of a fast pulse period estimation method based on phase difference correction according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
As shown in fig. 1, the present invention provides a rapid pulse period estimation method based on phase difference correction, which uses an iterative algorithm to continuously correct the pulse period until the phase difference meets a predetermined accuracy requirement. The method can greatly improve the calculation speed on the premise of keeping or even improving the period estimation precision.
The technical principle of the invention is that a time-interval folding mode is selected to calculate folding waveform phase difference information under the condition of unknown real initial phase, and the linear mapping relation between the deduced folding waveform phase difference and the cycle estimation error is utilized to correct the cycle estimation value, thereby avoiding repeated epoch folding operation in the traditional method. The implementation process is specifically described below:
1. Phase difference of folding waveform Error of period estimationStudy of mapping relation between:
The pulse shape is effectively a rate function of the non-homogeneous poisson process according to the definition of the non-homogeneous poisson process When the velocity component of the spacecraft in the direction of the pulsar sight is a certain valueAt the time, the rate functionIs a periodic function with a fourier series expansion into the form:
(1)
In the formula, The direct current is used as the direct current quantity,Is the firstAmplitude, angular frequency of order harmonicWhereinFor a real pulse period of time,As a function of the time variable,Is the firstThe phase angle of the order harmonic. Set total observation time periodFor the test periodInteger multiples of (i.e.)(Typically due toSo even ifNot be ofAnd the influence on the analysis results is small). The whole observation time lengthIs equally divided into lengths ofA kind of electronic deviceThe wave phase difference between two adjacent intervals isWherein the period estimates the errorLet it be from the test periodAnd the real periodAmount of phase change due to difference betweenThen (1)The phase shift of the adjacent waveforms of the order harmonic isAfter folding the (th)Order harmonic waveCan be expressed as:
(2)
In the formula, Represent the firstA plurality of observation intervals;
According to Euler's formula Formula (2) is rewritten as:
(3)
In the formula, The representation takes the real part of the operation,Is an imaginary unit of number and is,Representing an exponential function;
using a complex summation geometry, formula (3) is rewritten as follows:
(4)
In the middle of To fold the summed waveform amplitude, equation (4) is converted back to cosine form:
(5)
In fact, after folding It is explained that the folded waveform has not only phase difference but also distortion, but the waveform is ignoredThe higher order and above harmonics can be approximated as:
(6)
In the formula, Representing the total observation periodIs provided with a number of divided segments of (a),Is a constant value, which is set to be a constant value,Representing a transpose;
the folded normalized waveform (unit time folded waveform) is thus approximated as:
(7)
When the original pulse waveform (real waveform) is ignored When the order is higher order harmonic, the original waveform has the following form:
(8)
A time shift exists between the folded pulse waveform and the original pulse waveform The time shift corresponds to the folding waveform phase differenceThe method comprises the following steps:
(9)
Based on real pulse period Unknown andFormula (9) is replaced by the following approximation:
(10)
equation (10) shows the folding waveform phase difference Error of period estimationIs matched with a linear mapping relation whenWithin a proper range, the expression has high accuracy, and thus periodic correction can be performed using the expression (10).
2. Folding waveform phase differenceAnd cycle estimation errorIs calculated by (1):
folding waveform phase difference on the left of the equal sign of (10) Has the following form:
(11)
In the formula, Representing the total observation timeThe received photon TOA is folded to obtain the waveform initial phase,Representing the initial phase of the real pulse waveform;
general formula (10) and formula (11):
(12)
Since in the actual pulsar navigation, Is an unknown quantity, so that in equation (12) there are two unknowns, namelyAnd (3) withObviously, it can not be directly obtained by an equation. However, if two equations are constructed simultaneously using equation (12), the two equations have the same true initial phaseCan be directly eliminated by adopting a primordial elimination method. Specifically, the photon TOA received in the first 50% of the observation time period is folded once, and the initial phase of the waveform obtained by folding isThen, according to equation (12), the following equation set holds:
(13)
The difference between the two formulas (13) is obtained to obtain the folding waveform phase difference :
(14)
Thus cycle estimation errorThe method comprises the following steps:
(15)
In summary, the phase difference and the period estimation error are calculated under the condition that the real initial phase is unknown by selecting a time-division folding mode.
3. The fast pulse period estimation method based on phase difference correction is briefly described in the flow chart:
In actual navigation, a pulsar signal model is utilized to perform preliminary estimation on a pulse receiving period to obtain an initial test period Is a value of (2). FIG. 1 is a flow chart of a phase difference correction based fast pulse period estimation method, as shown, after an initial test period is obtainedThen, the observed TOA data are respectively folded in full-time period and in the first 50% time period, and the phase difference of the two folded waveforms is calculated by a cross-correlation algorithmCalculating a cycle estimation error according to equation (15). Presetting an accuracy thresholdTo reflect the level of accuracy that the final period estimate needs to achieve if the waveform phase difference is foldedThe absolute value of (2) is equal to or greater than the precision thresholdWill thenAs a new test periodRepeating waveform folding and waveform phase difference folding calculation until the precision threshold is metIf the waveform phase difference is foldedIs less than the accuracy thresholdWill thenAs a final pulse period estimateAnd outputting.
What is not described in detail in the present specification belongs to the prior art known to those skilled in the art. It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
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| CN103776454A (en) * | 2014-01-21 | 2014-05-07 | 西安电子科技大学 | Maximum likelihood phase estimation method based on X-ray pulsar |
| CN107328409A (en) * | 2017-07-28 | 2017-11-07 | 北京控制工程研究所 | A kind of X-ray pulsar navigation method based on dynamic pulse accumulation window |
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| CN103776454A (en) * | 2014-01-21 | 2014-05-07 | 西安电子科技大学 | Maximum likelihood phase estimation method based on X-ray pulsar |
| CN107328409A (en) * | 2017-07-28 | 2017-11-07 | 北京控制工程研究所 | A kind of X-ray pulsar navigation method based on dynamic pulse accumulation window |
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