Inter-satellite link system on-orbit reference frequency stability estimation method

Abstract

The application discloses an in-orbit reference frequency stability estimation method of an inter-satellite link system, which comprises the following steps: calculating a combined phase measurement value Θ p (t) according to a two-way phase measurement value Θ(t) without time scale correction; calculating a relative frequency error δf i ‑δf j ; calculating a relative frequency error sampling value, repeating the sampling according to a nominal sampling frequency, and calculating a relative Allan variance. The application is improved based on the calculation formula of the Allan variance, can accurately estimate the relative frequency stability between two stars of the inter-satellite link, and further estimate the frequency stability of a single star.

Description

Technical Field

[0001] This invention belongs to the field of satellite inter-satellite link technology, specifically involving the post-processing of output data from ranging and time-frequency transmission systems to calculate the stability of onboard reference frequency sources. Background Technology

[0002] In applications such as the micrometer-level precision ranging system (KBR) for gravity measurement satellites, the inter-satellite link system for stereo reconnaissance satellites, the inter-satellite link system of the BeiDou constellation, and other scientific measurement fields, crystal oscillators (or atomic clocks) are key components of inter-satellite link payload systems. They serve as the time and frequency reference for signal processing equipment and even the entire payload, with all measurements referenced to the reference frequency output by the frequency source. During on-orbit operation, the frequency source is affected by various factors such as temperature, radiation, and device aging, causing changes in the stability of the output frequency, which in turn affects inter-satellite time and frequency synchronization and the accuracy of measurement data.

[0003] Based on the engineering development of my country's low-low tracking gravity measurement satellite, the KBR system under our research utilizes an ultra-stable crystal oscillator (USO), which serves as the time and frequency reference for both the KBR and GNSS receivers. The frequency stability directly determines the accuracy of inter-satellite ranging and velocity measurement. Regarding this application background, there are currently no directly related patents available. Existing patents only cover methods for direct ground testing and indirect ground data analysis, with typical methods including the following:

[0004] (1) The invention patent "A Real-Time Frequency Stability Analysis Method" from the National Time Service Center of the Chinese Academy of Sciences provides a real-time frequency stability analysis method for use in a ground testing environment. This method sequentially identifies gross errors and records their states, performs data fitting and interpolation, adaptively determines the sampling interval, and iterates the data to ultimately obtain the frequency stability characterized by Allen's variance. This invention enables real-time frequency stability analysis and also provides real-time output and display of the analysis results, simplifying the user's work. Furthermore, based on the characteristics of frequency stability analysis, this invention designs a data preprocessing method to enhance the system's fault tolerance, providing a low-cost solution for achieving real-time frequency standard stability analysis using common equipment such as frequency counters and phase meters.

[0005] (2) The invention patent "Method and Device for Measuring Signal Frequency Stability" from Jianghan University discloses a method and device for measuring signal frequency stability, belonging to the field of atomic frequency standards. The method includes: using a first frequency measuring instrument to simultaneously measure the output frequencies of the frequency source under test and the compensation detection source; determining whether the output frequency values ​​of the frequency source under test and the compensation detection source simultaneously exhibit abnormal fluctuations; if abnormal fluctuations occur simultaneously, deleting the abnormal fluctuations in the frequency measurement results of the frequency source under test; and calculating the frequency stability of the frequency source under test. This invention, by determining whether the output frequency values ​​in the frequency measurement results of the frequency source under test and the compensation detection source simultaneously exhibit abnormal fluctuations, and deleting the abnormal fluctuations in the frequency measurement results of the frequency source under test when they occur simultaneously, not only reduces the workload but also improves the measurement accuracy of frequency stability.

[0006] (3) The invention patent "A Frequency Stability Measurement Device" from the Beijing Radio Metrology and Testing Institute relates to a frequency stability measurement device that can measure the accurate frequency characteristics, long-term frequency stability characteristics, and additional frequency instability of two-port components such as amplifiers and frequency multipliers in atomic frequency standards, built-in crystal oscillators in electronic instruments and equipment, and frequency synthesizers. The measurement resolution of this device can reach 1E-14. Based on the device described in this invention, it can be further expanded to N channels (N≥2) to realize the synchronous testing of (N+1) sources under test.

[0007] Analysis of existing methods reveals the following shortcomings:

[0008] (1) No research has been conducted on relevant methods specifically for the application environment of satellite payloads in orbit.

[0009] (2) All data are obtained directly from instrument measurements, rather than from joint analysis of other relevant data, and are not suitable for on-orbit working conditions. Summary of the Invention

[0010] The technical problem solved by this invention is as follows: Starting from the principle of bidirectional measurement and high-precision time difference correction of on-orbit satellite inter-satellite links, this invention conducts in-depth research on the indirect calculation method of frequency source frequency stability. Based on the basic definition of Allan variance, a formula for calculating the relative frequency error from inter-satellite measurements is given, and a mathematical model of relative Allan variance is further established.

[0011] The technical solution of this invention is:

[0012] A method for estimating the stability of an on-orbit reference frequency in an inter-satellite link system includes the following steps:

[0013] 1) Obtain the bidirectional phase measurement value Θ(t) without time-scale correction;

[0014] 2) Obtain the bidirectional phase measurement value Θ(t) uniform to the i-th star time. i );

[0015] 3) Calculate the combined phase measurement Θ(t) based on the untime-corrected bidirectional phase measurement Θ(t). p (t);

[0016] 4) Based on the bidirectional phase measurement value Θ(t) obtained in step 2) and unified to the i-star time, i The combined phase measurement value Θ obtained in step 1) and step 2) p (t), calculate the relative frequency error δf i -δf j ;

[0017] 5) The relative frequency error δf obtained in step 4) i -δf j Calculate the relative frequency error sample value

[0018] 6) Repeat steps 1) to 5) at the nominal sampling frequency to obtain the relative frequency error sampling value corresponding to each frequency point. The relative frequency error sample value corresponding to each frequency point obtained Perform sampling at equal sampling intervals and calculate the relative Allan variance σ. y (τ).

[0019] Preferably, the method for obtaining the bidirectional phase measurement value Θ(t) without time-scale correction is as follows:

[0020]

[0021] in,

[0022] f i f is the output frequency of star i; j The output frequency of star J;

[0023] The propagation time of the signal from satellite i to satellite j;

[0024] The propagation time of the signal from satellite j to satellite i;

[0025] δf i This represents the deviation of the i-star's output frequency from its nominal frequency; the nominal frequency is the theoretical frequency at which the onboard system transmits and receives signals.

[0026] δf j The deviation of the output frequency of star j from its nominal frequency;

[0027] Δt iThe time difference between the measured time and the nominal time of satellite i;

[0028] Δt j The time difference between the measured time and the nominal time for satellite j.

[0029] Preferably, the bidirectional phase measurement value Θ(t) is obtained uniformly to the i-th star time. i The method is as follows:

[0030]

[0031] Preferably, the combined phase measurement value Θ is calculated. p The method for (t) is as follows:

[0032] Θ p (t)=Θ(t)+(f i -f j )(Δt i -Δt j ).

[0033] Preferably, the relative frequency error δf is calculated. i -δf j The method is as follows:

[0034]

[0035] Preferably, the relative frequency error sample value is calculated. The method is as follows:

[0036]

[0037] Preferably, the relative Allan variance σ is calculated. y The method of (τ) is as follows:

[0038]

[0039] Where k represents the sampling number, η represents the sampling interval, and N is a positive integer not less than 100.

[0040] Preferably, the nominal sampling frequency is 1Hz.

[0041] Preferably, the sampling interval η = 10 R Where R is a positive integer and R∈[0,4].

[0042] The advantages of this invention compared to the prior art are:

[0043] 1) This invention is based on an improved formula for calculating Allan variance. The mathematical model is simple and the computational complexity is low, making it suitable for on-orbit embedded systems.

[0044] 2) This invention can accurately estimate the relative frequency stability between two satellites in an inter-satellite link to a certain extent, and further estimate the frequency stability of a single satellite, thus enabling real-time on-orbit monitoring.

[0045] 3) This invention can be used to estimate the onboard frequency source in any inter-satellite link system with a measurement link between two satellites and capable of outputting distance measurement values, and has wide applicability. Attached Figure Description

[0046] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0047] To assist in ground data processing, load performance evaluation, and anomaly analysis, a requirement for real-time monitoring of the frequency stability of on-orbit frequency sources was proposed, and a specific estimation algorithm was studied.

[0048] This invention relates to a method for estimating the stability of an on-orbit reference frequency in an inter-satellite link system, such as... Figure 1 As shown, the steps are as follows:

[0049] 1. Direct measurement of inter-satellite link

[0050] Typically, inter-satellite link systems are designed to transmit signals at distinct frequencies. The two satellites participating in the network are numbered i and j, and their transmission frequencies are denoted by f. i and f j It means that f i ≠f j The two satellites receive radio frequency signals and independently measure the carrier phase of the radio frequency signals. The bidirectional phase measurement value Θ(t) is based on the combination of the two independent measurements. Without adjusting the time scale of the two satellites, Θ(t) can be expressed as:

[0051]

[0052] in,

[0053] f i : i star's output frequency; f j The output frequency of star j; the frequency in this embodiment of the invention is: f i =32.703GHz, f j =32.702GHz;

[0054] The carrier phase is transmitted from satellite j to satellite i and measured by satellite i.

[0055] Δt i : The time difference between the measurement time and the nominal time of i-satellite;

[0056] The carrier phase is transmitted from satellite i to satellite j and measured by satellite j.

[0057] Δt j The time difference between the measurement time and the nominal time of satellite J;

[0058] The propagation time of the signal from satellite i to satellite j;

[0059] The propagation time of the signal from satellite j to satellite i;

[0060] δf i The deviation of iStar's output frequency from its nominal frequency;

[0061] δf j The deviation of the output frequency of star J from its nominal frequency;

[0062] E: The total system measurement error, which can be set to zero.

[0063] Therefore, at the nominal time t, the distance measurement R(t) between the two stars can be obtained as follows:

[0064] R(t)=λΘ(t), λ=c / (f i +f j (2)

[0065] in:

[0066] λ: Bidirectional combined equivalent wavelength;

[0067] c is the speed of light in a vacuum: its nominal value under vacuum conditions is 299,792,458 (m / s).

[0068] 2 Measurements based on binary star timescale correction

[0069] Based on the time difference information generated by inter-satellite measurements, i.e., Δt in formula (1) i -Δt j (Inter-satellite link internal time difference measurement value), the local measurement data time scale of satellite j is precisely adjusted so that the time scales of the two satellites are unified with the measurement time of satellite i. Then, the measurement values ​​of i and j are recombined to obtain the bidirectional phase measurement value Θ(t) unified to the time of satellite i. i (i.e., the bidirectional phase measurement value corrected by the instantaneous scale):

[0070]

[0071] 3. Calculation of relative frequency error

[0072] Subtracting equation (1) from equation (3) and ignoring smaller quantities, we get:

[0073] Θ(t i)-Θ(t)=(f i -f j )(Δt i -Δt j )+(δf i -δf j )(Δt i -Δt j (4)

[0074] Define the combined phase measurement value Θ p (t), calculate directly:

[0075] Θ p (t)=Θ(t)+(f i -f j )(Δt i -Δt j (5)

[0076] Subtracting equation (5) from equation (4), we get

[0077] Θ(t i )-Θ p (t)=(δf i -δf j )(Δt i -Δt j (6)

[0078] Therefore, the relative frequency error can be obtained as follows:

[0079]

[0080] 4. Calculation of relative Allen variance

[0081] The Allen variance standard used to estimate signal frequency stability is defined as follows:

[0082]

[0083] in:

[0084] N: The number of frequency sampling points used to estimate the Allen variance; N is a positive integer not less than 100.

[0085] η: The time interval between two adjacent frequency difference sampling points; η = 10 R R is a positive integer and R∈[0,4]; the data is generally one of five typical values: 1 second, 10 seconds, 100 seconds, 1000 seconds and 10000 seconds.

[0086] y k+1 : No. k +1 frequency difference sample value;

[0087] y iy is the i-th frequency difference sampled value. That is, y is calculated from the sequence data of inter-satellite phase measurements at the nominal sampling frequency. i Sequence data.

[0088] In this embodiment of the invention, the nominal sampling frequency of Θ(t) is 1Hz.

[0089] Sampled values ​​are generated based on the relative frequency deviation of the two-star reference frequency sources.

[0090]

[0091] Substituting formula (9) into formula (8), we can obtain the formula (mathematical model) for the relative Allan variance of the binary reference frequency source.

[0092]

[0093] Since the reference frequency sources of the two satellites operate independently, the stability level of a single frequency source can be estimated as the combined stability level of both frequency sources. Right now:

[0094]

[0095] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make possible variations and modifications to the technical solutions of the present invention using the disclosed methods and techniques without departing from the spirit and scope of the invention. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention, without departing from the content of the technical solutions of the present invention, shall fall within the protection scope of the present invention. Where there is no conflict, the embodiments of this application and the technical features thereof can be combined with each other.

[0096] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for estimating the stability of an on-orbit reference frequency in an inter-satellite link system, characterized in that, The steps include the following: 1) Obtain the bidirectional phase measurement value Θ(t) without time-scale correction; 2) Obtain the bidirectional phase measurement value Θ(t) uniform to the i-th star time. i ); 3) Calculate the combined phase measurement Θ(t) based on the untime-corrected bidirectional phase measurement Θ(t). p (t); 4) Based on the bidirectional phase measurement value Θ(t) obtained in step 2) and unified to the i-star time, i The combined phase measurement value Θ obtained in step 1) and step 2) p (t), calculate the relative frequency error δf i -δf j ; 5) The relative frequency error δf obtained in step 4) i -δf j Calculate the relative frequency error sample value y; 6) Repeat steps 1) to 5) at the nominal sampling frequency to obtain the relative frequency error sample value y corresponding to each frequency point; for the obtained relative frequency error sample value y corresponding to each frequency point, perform sampling at equal sampling intervals and calculate the relative Allan variance σ. y (τ).

2. The method for estimating the on-orbit reference frequency stability of an inter-satellite link system according to claim 1, characterized in that, The method for obtaining the bidirectional phase measurement value Θ(t) without time-scale correction is as follows: in, f i f is the output frequency of star i; j The output frequency of star J; The propagation time of the signal from satellite i to satellite j; The propagation time of the signal from satellite j to satellite i; δf i This represents the deviation of the i-star's output frequency from its nominal frequency; the nominal frequency is the theoretical frequency at which the onboard system transmits and receives signals. δf j The deviation of the output frequency of star j from its nominal frequency; Δt i The time difference between the measured time and the nominal time of satellite i; Δt j The time difference between the measured time and the nominal time for satellite j.

3. The method for estimating the on-orbit reference frequency stability of an inter-satellite link system according to claim 2, characterized in that, Obtain the bidirectional phase measurement Θ(t) unified to the i-star time. i The method is as follows:

4. The method for estimating the on-orbit reference frequency stability of an inter-satellite link system according to claim 2, characterized in that, Calculate the combined phase measurement value Θ p The method for (t) is as follows: Θ p (t)=Θ(t)+(f i -f j )(Δt i -Δt j )。 5. The method for estimating the on-orbit reference frequency stability of an inter-satellite link system according to claim 2, characterized in that, Calculate the relative frequency error δf i -δf j The method is as follows:

6. The method for estimating the on-orbit reference frequency stability of an inter-satellite link system according to claim 2, characterized in that, Calculate the relative frequency error sample value The method is as follows:

7. A method for estimating the on-orbit reference frequency stability of an inter-satellite link system according to any one of claims 2 to 6, characterized in that, Calculate the relative Allen variance The method is as follows: Where k represents the sampling number, η represents the sampling interval, and N is a positive integer not less than 100.

8. The method for estimating the on-orbit reference frequency stability of an inter-satellite link system according to claim 7, characterized in that, The nominal sampling frequency is 1Hz.

9. The method for estimating the on-orbit reference frequency stability of an inter-satellite link system according to claim 8, characterized in that, The sampling interval η = 10 R Where R is a positive integer and R∈[0,4].

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