CN110687555A - Navigation satellite atomic clock weak frequency hopping on-orbit autonomous rapid detection method - Google Patents

Navigation satellite atomic clock weak frequency hopping on-orbit autonomous rapid detection method Download PDF

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CN110687555A
CN110687555A CN201910896602.2A CN201910896602A CN110687555A CN 110687555 A CN110687555 A CN 110687555A CN 201910896602 A CN201910896602 A CN 201910896602A CN 110687555 A CN110687555 A CN 110687555A
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蒙艳松
杜二旺
秦晓伟
孙云峰
王国永
何冬
孟彦春
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Xian Institute of Space Radio Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
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    • G01S19/20—Integrity monitoring, fault detection or fault isolation of space segment
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    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
    • G01R23/14—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage by heterodyning; by beat-frequency comparison

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Abstract

A navigation satellite atomic clock weak frequency hopping in-orbit autonomous rapid detection method comprises the following steps: sampling to obtain phase differences between the atomic clocks of the N sampling points and the reference signal, and determining the relative frequency deviation between the atomic clock of each sampling point and the reference signal; estimating the R value and the Q value of parameters in a kalman filter frequency difference model; determining a frequency difference estimation value corresponding to the relative frequency deviation of each sampling point; determining a differential value after sliding filtering corresponding to each sampling point; determining a working threshold; giving alarm information when the difference value after the sliding filtering is larger than a working threshold value; and giving a normal working state when the differential value after the sliding filtering is smaller than a working threshold value. The method not only can rapidly and accurately filter the burrs in the frequency difference, but also can accurately detect the smaller frequency jump in the atomic clock frequency difference in real time.

Description

Navigation satellite atomic clock weak frequency hopping on-orbit autonomous rapid detection method
Technical Field
The invention relates to an on-orbit autonomous and rapid detection method for weak frequency jump of a navigation satellite atomic clock, and belongs to the technical field of atomic clock frequency integrity monitoring.
Background
In a satellite navigation system, the continuity and stability of a satellite-borne atomic clock signal directly influence the precision of navigation, positioning and time service. Due to the influences of factors such as the change of the working environment of the satellite-borne atomic clock, space irradiation, aging and internal instability, abnormal disturbance may occur in the frequency of the output signal of the atomic clock.
Abnormal disturbance phenomena existing in the frequency of the satellite-borne atomic clock, such as frequency fast change, frequency slow change, burr and the like, directly affect the performance of the satellite navigation system and the use of a user, so that the frequency change rule of the satellite-borne atomic clock in the satellite navigation system is detected in real time, and the abnormal change of the frequency is corrected and compensated in time, so that the normal use of the user is ensured.
Fig. 1 shows a model of atomic clock frequency jump detection. The method widely used in the atomic clock frequency jump detection is based on the noise model of the atomic clock, and a prediction model is established according to the priori knowledge of the frequency change rule. The prediction model predicts the frequency change trend according to the known measurement frequency signal y1(k), and the measurement module obtains the frequency change situation at the current moment. The variation between the prediction signal and the measurement signal is obtained by comparing the prediction signal and the measurement signal, namely an error signal, and then the detection module is used for judging the error signal to determine whether abnormal frequency jump exists in the atomic clock frequency.
Currently, the main methods for detecting frequency jump of an atomic clock include: the method comprises the following steps of block averaging, sequence averaging, dynamic Allen's variance, least square fitting and a frequency jump detection method based on a Kalman filter. Both block averaging and sequence averaging are commonly used methods, but their detection time is relatively long, and the sequence averaging method cannot distinguish the phenomena of frequency drift and frequency hopping. The dynamic allon variance method can detect any type of frequency hopping, but cannot distinguish the type of frequency hopping, and requires a very large amount of computation.
The frequency jump detection of the satellite-borne atomic clock of the navigation satellite needs to consider the real-time performance and accuracy of fault detection. At present, the most used algorithms for atomic clock frequency hopping mainly include a kalman filter-based frequency hopping detection method and a least square fitting-based frequency hopping detection method.
The frequency jump detection method based on the kalman filter mainly comprises the following steps: a method, detector using difference v [ n ] between current state measured value and previous state predicted value]Sum threshold k · σv[n]And comparing to determine whether frequency jump exists in the measurement. The criterion of frequency jump detection is | v [ n]|≥k·σv[n]. The method has high false alarm rate and low detection capability due to the fact that the detector uses a single measurement result as a criterion of frequency jump and the Kalman filter has long time response time. The method is based on the method a, when the frequency of an atomic clock has abnormal jump, the Kalman filter gains are increased, so that the Kalman filter obtains shorter response time, the detection capability is improved, and the false alarm rate is reduced. However, increasing the gain of the kalman filter results in an increase in the prediction value noise. And c, realizing the frequency variation trend based on a kalman filter, calculating the difference value between the predicted value and the measured value, namely an error signal z (i), and analyzing whether abnormal frequency jump exists in the error signal through a detection module. The frequency jump detection criterion is
Figure BDA0002210423870000021
γ is the detection threshold and N is the length of the sliding window. The larger N is, the smaller the detection signal is, the smaller the false alarm rate is, but the detection time is obviously increased. When the frequency hopping phenomenon exists, the detection time is at least N seconds.
The frequency hopping detection method based on least square fitting mainly comprises the following steps: the method a comprises the steps of firstly carrying out least square fitting by using a frequency difference measurement value in a sliding window with the length of N1 to obtain a plurality of frequency difference measurement valuesThe polynomial model is used for obtaining a predicted value mu in a sliding window with the length of N2p(k) According to the measured value y (k) and the predicted value mu of the frequency difference at the current time tp(k) To obtain an error signal y0(k) In that respect Establishing a sliding window of length N3 within a sliding window of length N2, wherein N3≤N2. Solving for the error signal y within a sliding window N30(k) Average value of (2)
Figure BDA0002210423870000022
Finally, according to the frequency jump detection criterion
Figure BDA0002210423870000023
It is determined whether there is a frequency jump, where γ is a threshold. And b, obtaining a predicted value of the relative frequency deviation according to the least square model, then calculating the error between the predicted value and the measured value, and determining whether frequency jump exists by comparing the magnitude between an error signal and a threshold value.
It can be seen that the detection time based on the kalman filter atomic clock frequency jump detection method depends on the length N of the window in the criterion device, so that the detection time is at least N measurement periods; the atomic clock frequency hopping detection method based on least square fitting has certain dependence on the binomial model obtained by fitting. When the relative frequency deviation sample of the calculated binomial model is small, the error of the binomial model obtained through fitting is large, and the error of the predicted signal is increased.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method can quickly and accurately smooth single frequency jump in frequency difference data and also can quickly and accurately detect larger continuous frequency jump in the frequency difference of the atomic clock; meanwhile, the method can quickly detect the weak frequency jump of the atomic clock, and has high detection capability and low false alarm rate.
The technical scheme of the invention is as follows:
a navigation satellite atomic clock weak frequency hopping in-orbit autonomous rapid detection method comprises the following steps:
1) sampling to obtain phase differences between the atomic clocks of the N sampling points and the reference signal, and determining the relative frequency deviation between the atomic clock of each sampling point and the reference signal; wherein N is a positive integer; the method for determining the relative frequency deviation Y1(n) between the atomic clock of the nth sampling point and the reference signal comprises the following specific steps:
Figure BDA0002210423870000031
wherein, tau0For a sampling interval, N ∈ [1, N ∈ ]]。
2) Establishing a kalman filter frequency difference model, and estimating a parameter R value and a parameter Q value in the kalman filter frequency difference model according to the relative frequency deviation of each sampling point in the step 1);
3) determining a frequency difference estimation value corresponding to the relative frequency deviation of each sampling point according to the relative frequency deviation of each sampling point in the step 1) and the R value and the Q value of the parameters in the step 2);
4) respectively carrying out forward difference processing on the frequency difference estimated value corresponding to the relative frequency deviation of each sampling point in the step 3) to obtain a primary difference value corresponding to each sampling point; the method for determining the first differential value Y3(n) corresponding to the nth sampling point specifically includes:
Y3(n)＝Y2(n-1)-Y2(n)；
wherein Y2(n-1) is the frequency difference estimation value corresponding to the relative frequency deviation of the nth-1 sampling point, and Y2(n) is the frequency difference estimation value corresponding to the relative frequency deviation of the nth sampling point.
5) Performing sliding filtering processing according to the primary differential value corresponding to each sampling point in the step 4) to obtain a differential value after sliding filtering corresponding to each sampling point; the method for determining the sliding-filtered differential value Y4(n) corresponding to the nth sampling point includes:
Figure BDA0002210423870000041
wherein m belongs to [1, N ], N belongs to [1, N ], and m is less than N.
6) Determining a working threshold gamma according to the differential value after the sliding filtering in the step 5); the method for determining the working threshold gamma specifically comprises the following steps:
Figure BDA0002210423870000042
wherein M is a positive integer and is less than N, and M is based on the false alarm rate PfaThe design value of (2) is determined, specifically:
Figure BDA0002210423870000043
7) comparing the difference value after the sliding filtering in the step 5) with the working threshold value gamma in the step 6), and giving alarm information when the difference value after the sliding filtering is larger than the working threshold value gamma; and giving a normal working state when the differential value after the sliding filtering is less than or equal to a working threshold gamma.
Compared with the prior art, the invention has the beneficial effects that:
1) the invention has strong detection capability for weak frequency jump of the atomic clock. In the invention, the relative frequency deviation data output by the Kalman filter is processed by combining the forward difference and the sliding filter, so that the estimation value of the relative frequency deviation data becomes a stable sequence, and the weak frequency hopping signal is separated from the frequency noise, thereby improving the detection capability of the weak frequency signal.
2) The invention has quick detection time for detecting the frequency jump of the atomic clock. Because the weak frequency hopping signal and the frequency noise signal are obviously separated in the algorithm, the sliding window with the length of N processes front-end relative frequency deviation data in real time, and each measurement period can give out a determined detection result.
3) The invention establishes a Kalman filter model of the relative frequency deviation of the atomic clock based on an atomic clock difference model, and carries out forward difference and sliding filtering processing aiming at the relative frequency deviation estimated value output by the Kalman filter, so that the method has quick detection time and strong detection capability for weak frequency jump.
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FIG. 1 is a model of atomic clock frequency jump detection;
FIG. 2 is a block diagram of atomic clock frequency jump detection;
FIG. 3 is a Kalman estimate of the present invention
FIG. 4 is a Kalman estimate difference processing result Y1 of the present invention;
fig. 5 is the relative frequency difference data Y2 after passing through the sliding filter;
FIG. 6 is a flow chart of covariance matrix parameter setting according to the present invention.
Detailed Description
A navigation satellite atomic clock weak frequency hopping in-orbit autonomous rapid detection method comprises the following steps:
1) sampling to obtain phase differences between the atomic clocks of the N sampling points and the reference signal, and determining the relative frequency deviation between the atomic clock of each sampling point and the reference signal by using an average frequency difference calculation formula; wherein N is a positive integer; the method for determining the relative frequency deviation Y1(n) between the atomic clock of the nth sampling point and the reference signal comprises the following specific steps:
Figure BDA0002210423870000052
wherein, tau0For a sampling interval, N ∈ [1, N ∈ ]]。
2) Establishing a kalman filter frequency difference model, and estimating a parameter R value and a parameter Q value in the kalman filter frequency difference model according to the relative frequency deviation of each sampling point in the step 1);
3) determining a frequency difference estimation value corresponding to the relative frequency deviation of each sampling point by using a kalman filter according to the relative frequency deviation of each sampling point in the step 1) and the R value and the Q value of the parameter in the step 2);
4) respectively carrying out forward difference processing on the frequency difference estimated value corresponding to the relative frequency deviation of each sampling point in the step 3) to obtain a primary difference value corresponding to each sampling point; the method for determining the first differential value Y3(n) corresponding to the nth sampling point specifically includes:
Y3(n)＝Y2(n-1)-Y2(n)；
wherein Y2(n-1) is the frequency difference estimation value corresponding to the relative frequency deviation of the nth-1 sampling point, and Y2(n) is the frequency difference estimation value corresponding to the relative frequency deviation of the nth sampling point.
5) Performing sliding filtering processing by using a sliding filter according to the primary differential value corresponding to each sampling point in the step 4) to obtain a differential value after sliding filtering corresponding to each sampling point; the method for determining the sliding-filtered differential value Y4(n) corresponding to the nth sampling point includes:
Figure BDA0002210423870000061
wherein m belongs to [1, N ], N belongs to [1, N ], and m is less than N.
6) Determining a working threshold gamma according to the differential value after the sliding filtering in the step 5); the method for determining the working threshold gamma specifically comprises the following steps:
Figure BDA0002210423870000062
wherein M is a positive integer and is less than N, and M is based on the false alarm rate PfaThe design value of (2) is determined, specifically:
Figure BDA0002210423870000063
7) comparing the difference value after the sliding filtering in the step 5) with the working threshold value gamma in the step 6), and giving alarm information when the difference value after the sliding filtering is larger than the working threshold value gamma; and giving a normal working state when the differential value after the sliding filtering is less than or equal to a working threshold gamma.
The invention is described in further detail below with reference to the figures and the detailed description.
The invention verifies the effectiveness and feasibility of the detection method through mathematical modeling and simulation analysis, and FIG. 2 shows a block diagram of the frequency jump detection of an atomic clock, which mainly comprises the following steps: phase-frequency conversion, kalman filter, frequency estimation difference, sliding filter, etc.
The time deviation x (t) of the satellite-borne atomic clock can be described by a deterministic variation component and a stochastic variation component, as shown in equation (1).
Figure BDA0002210423870000071
Wherein x is0Is the initial phase deviation, y, of the atomic clock0Is the initial frequency deviation of the atomic clock, D is the linear frequency drift of the atomic clock, and belongs tox(t) is the random variation of the atomic clock time deviation. According to classical phase noise theory, is epsilonx(t) there are five independent noise components: phase white noise, phase flicker noise, frequency white noise, frequency flicker noise, and frequency random walk noise.
The instantaneous relative frequency deviation y (t) of the atomic clock can be deduced according to the formula (1), and is shown in the formula (2).
y(t)＝y0+Dt+∈y(t) (2)
The first two terms on the right side of the equal sign in the formula (2) are deterministic components of the instantaneous relative frequency deviation of the atomic clock, and are epsilony(t) is a randomly varying component thereof.
And (4) calculating the relative frequency deviation of the atomic clock according to the measured atomic clock phase difference data by using a formula (3).
Figure BDA0002210423870000072
In the formula (3), x (t) is phase difference data at time t, y (t) is relative frequency difference data at time t, and tau0Is the sampling time interval.
Suppose that the atomic clock relative frequency deviation y (t) is made up of frequency white noise yWFN(t) frequency random walk noise yRWFN(t) and a frequency drift rate d (t), as shown in equation (4).
y(t)＝yWFN(t)+yRWFN(t)+d(t) (4)
Wherein the frequency white noise yWFN(t) obedience mean zero, variance σ2White gaussian noise. Frequency random walk noise yRWFN(t) can be viewed as a Vigrella process, as shown in equation (5).
Figure BDA0002210423870000073
In the discrete domain, formula (4) can be expressed as formula (6), formula (7), formula (8):
y(k)＝yWFN(k)+yt(k) (6)
yt(k)＝yRWFN(k)+d(k) (7)
yRWFN(k)＝yRWFN(k-1)+ΔyRWFN(k-1) (8)
wherein, yWFN(k) Representing frequency white noise, yRWFN(k) Frequency random walk noise, and d (k) frequency drift rate.
The abnormal jump in the relative frequency deviation of the atomic clock can be expressed as equation (9).
y′(k)＝yWFN(k)+yt(k)+u(k-n)Δf (9)
In equation (9), n represents the time when frequency hopping occurs, and Δ f represents the frequency hopping size.
Equations (6), (8) are modeled using a kalman filter, as shown in equations (10) and (11).
X(k+1)＝A·X(k)+B·U(k) (10)
Y(k+1)＝HT·X(k)+w(k) (11)
Wherein, A is a state matrix, H is an observation matrix, U (k) process noise comprises two parts of frequency random walk noise and frequency drift rate, and frequency white noise is regarded as observation noise w (k).
Taking the relative frequency deviation in the formula (3) as the input of a kalman filter, and obtaining the estimation value of the relative frequency deviation through the kalman filter
Figure BDA0002210423870000081
As shown in fig. 3.
When the relative frequency hopping magnitude is small, the frequency hopping is almost similar to the frequency noise. By estimating the relative frequency deviation
Figure BDA0002210423870000082
First order differentiation of
Figure BDA0002210423870000083
Non-stationary relative frequency difference sequences can be smoothed. Fig. 4 shows forward difference data for the kalman estimate.
Selecting a sequence of sliding filter pairs of window length N
Figure BDA0002210423870000084
Filtering to obtain a sequence
Figure BDA0002210423870000085
Then by comparison
Figure BDA0002210423870000086
And the threshold value y determines whether there is frequency hopping. Wherein the threshold value
Figure BDA0002210423870000087
When in use
Figure BDA0002210423870000088
The detector alarms when the alarm is over; when in use
Figure BDA0002210423870000089
When the detector is in operation, the detector is in operation. Fig. 5 shows the relative frequency difference data after the sliding filter.
The method comprises the following specific implementation steps:
(1) and (5) establishing a relative frequency deviation model of the atomic clock. Constructing a relative frequency deviation model according to the noise composition characteristics of the instantaneous relative frequency deviation of the atomic clock, as shown in formula (4), respectively constructing frequency white noise yWFN(t) and frequency random walk noise yRWFN(t) noise model, settingVariance of frequency white noise
Figure BDA00022104238700000810
Variance of frequency random walk noise
Figure BDA0002210423870000091
And a frequency drift rate d (k). And (4) establishing atomic clock frequency hopping with different magnitudes according to a formula (9), and setting the frequency hopping size delta f value.
(2) And establishing a Kalman filter model. Constructing a Kalman filter clock error model according to the noise characteristics of the atomic clock, and respectively setting measurement noise R and process noise Q; and the initial values of the state quantity X and the error covariance matrix P. Since the error covariance matrix may diverge over multiple iterations, resulting in divergence of the kalman filter output, simplification of the error covariance is considered. In the invention, a constraint condition is set for the error covariance matrix, and after the Kalman filter calculates N times, the error covariance matrix is re-assigned, thereby ensuring that the error covariance matrix P is in a convergence state. As shown in fig. 6.
(3) The estimated values are differentiated. And in each measurement period, carrying out forward difference on the estimated value of the relative frequency deviation obtained by the kalman filter to obtain a stable frequency difference sequence.
(4) Sliding filtering of the sequence. Processing the data in step (3) by using a moving average filter, firstly, selecting a proper window length N, and then, in each measurement period, according to the method
Figure BDA0002210423870000092
And calculating smoothed data.
(5) A detector is applied to decide frequency hopping. Firstly, setting window length N1 of threshold value according to threshold value calculation formula
Figure BDA0002210423870000093
A threshold value gamma is obtained. And judging whether frequency jump exists according to the relation between the data after the sliding filter and the threshold value. When in use
Figure BDA0002210423870000094
The detector alarms when the alarm is over; when in use
Figure BDA0002210423870000095
When the detector is in operation, the detector is in operation.
Those skilled in the art will appreciate that the details of the invention not described in detail in the specification are within the skill of those skilled in the art.

Claims (5)

1. A navigation satellite atomic clock weak frequency hopping in-orbit autonomous rapid detection method is characterized by comprising the following steps:
1) sampling to obtain phase differences between the atomic clocks of the N sampling points and the reference signal, and determining the relative frequency deviation between the atomic clock of each sampling point and the reference signal; wherein N is a positive integer;
2) establishing a kalman filter frequency difference model, and estimating a parameter R value and a parameter Q value in the kalman filter frequency difference model according to the relative frequency deviation of each sampling point in the step 1);
3) determining a frequency difference estimation value corresponding to the relative frequency deviation of each sampling point according to the relative frequency deviation of each sampling point in the step 1) and the R value and the Q value of the parameters in the step 2);
4) respectively carrying out forward difference processing on the frequency difference estimated value corresponding to the relative frequency deviation of each sampling point in the step 3) to obtain a primary difference value corresponding to each sampling point;
5) performing sliding filtering processing according to the primary differential value corresponding to each sampling point in the step 4) to obtain a differential value after sliding filtering corresponding to each sampling point;
6) determining a working threshold gamma according to the differential value after the sliding filtering in the step 5);
7) comparing the difference value after the sliding filtering in the step 5) with the working threshold value Y in the step 6), and giving alarm information when the difference value after the sliding filtering is larger than the working threshold value gamma; and giving a normal working state when the differential value after the sliding filtering is less than or equal to a working threshold gamma.
2. The method for autonomously and rapidly detecting weak frequency jump of an atomic clock of a navigation satellite in orbit according to claim 1, wherein the method for determining the relative frequency deviation Y1(n) between the atomic clock of the nth sampling point and the reference signal in step 1) specifically comprises:
Figure FDA0002210423860000011
wherein, tau0For a sampling interval, N ∈ [1, N ∈ ]]。
3. The method according to claim 1, wherein the method for determining the first differential value Y3(n) corresponding to the nth sampling point in step 4) comprises:
Y3(n)＝Y2(n-1)-Y2(n)；
wherein Y2(n-1) is the frequency difference estimation value corresponding to the relative frequency deviation of the nth-1 sampling point, and Y2(n) is the frequency difference estimation value corresponding to the relative frequency deviation of the nth sampling point.
4. The method according to claim 3, wherein the step 5) of determining the sliding-filtered differential value Y4(n) corresponding to the nth sampling point comprises:
Figure FDA0002210423860000021
wherein m belongs to [1, N ], N belongs to [1, N ], and m is less than N.
5. The method for autonomously and rapidly detecting weak frequency hopping of a navigation satellite atomic clock in orbit according to any one of claims 1 to 4, wherein the method for determining the operation threshold γ in step 6) specifically comprises:
Figure FDA0002210423860000022
wherein M is a positive integer and is less than N, and M is based on the false alarm rate PfaThe design value of (2) is determined, specifically:
Figure FDA0002210423860000023
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