CN117411583A - Inter-satellite bidirectional time delay comparison non-stationary clock difference Kalman filtering method - Google Patents
Inter-satellite bidirectional time delay comparison non-stationary clock difference Kalman filtering method Download PDFInfo
- Publication number
- CN117411583A CN117411583A CN202311204889.0A CN202311204889A CN117411583A CN 117411583 A CN117411583 A CN 117411583A CN 202311204889 A CN202311204889 A CN 202311204889A CN 117411583 A CN117411583 A CN 117411583A
- Authority
- CN
- China
- Prior art keywords
- clock
- difference
- inter
- stationary
- satellite
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000001914 filtration Methods 0.000 title claims abstract description 98
- 238000000034 method Methods 0.000 title claims abstract description 75
- 230000002457 bidirectional effect Effects 0.000 title claims abstract description 40
- 238000005259 measurement Methods 0.000 claims abstract description 49
- 230000008859 change Effects 0.000 claims abstract description 20
- 238000001514 detection method Methods 0.000 claims abstract description 11
- 239000011159 matrix material Substances 0.000 claims description 22
- 238000012360 testing method Methods 0.000 claims description 4
- 238000005070 sampling Methods 0.000 claims description 3
- 230000008569 process Effects 0.000 abstract description 35
- 238000004364 calculation method Methods 0.000 description 5
- 238000005516 engineering process Methods 0.000 description 5
- 230000007547 defect Effects 0.000 description 4
- 230000005540 biological transmission Effects 0.000 description 3
- 230000006870 function Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 230000007704 transition Effects 0.000 description 3
- 238000013461 design Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 230000001360 synchronised effect Effects 0.000 description 2
- 230000002159 abnormal effect Effects 0.000 description 1
- 230000002411 adverse Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000012512 characterization method Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 125000004122 cyclic group Chemical group 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000010187 selection method Methods 0.000 description 1
- 230000001629 suppression Effects 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
- 230000036962 time dependent Effects 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
- 230000017105 transposition Effects 0.000 description 1
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04J—MULTIPLEX COMMUNICATION
- H04J3/00—Time-division multiplex systems
- H04J3/02—Details
- H04J3/06—Synchronising arrangements
- H04J3/0635—Clock or time synchronisation in a network
- H04J3/0638—Clock or time synchronisation among nodes; Internode synchronisation
- H04J3/0658—Clock or time synchronisation among packet nodes
-
- 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
- G01S19/13—Receivers
- G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
-
- 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
- G01S19/13—Receivers
- G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
- G01S19/25—Acquisition or tracking or demodulation of signals transmitted by the system involving aiding data received from a cooperating element, e.g. assisted GPS
-
- 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
- G01S19/13—Receivers
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
- G01S19/37—Hardware or software details of the signal processing chain
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04J—MULTIPLEX COMMUNICATION
- H04J3/00—Time-division multiplex systems
- H04J3/02—Details
- H04J3/06—Synchronising arrangements
- H04J3/0635—Clock or time synchronisation in a network
- H04J3/0682—Clock or time synchronisation in a network by delay compensation, e.g. by compensation of propagation delay or variations thereof, by ranging
Abstract
A method for comparing non-stationary clock differences by bidirectional time delay between satellites adopts a form of combining clock difference non-stationary characteristic detection with Kalman filtering to obtain a fast and accurate tracking process of the non-stationary clock differences after reestablishing a chain after the inter-satellite chain establishment is interrupted and a stable and accurate estimating process of the clock speed in the stable chain establishment process. The inter-satellite bidirectional delay comparison non-stationary clock difference Kalman filtering is to detect the non-stationary change of the clock difference by adopting the primary difference of inter-satellite bidirectional delay comparison measurement quantity, the clock difference prediction residual error and the primary difference of the clock difference prediction residual error, and to estimate the clock speed of the non-stationary change by adopting non-linear estimation, thereby realizing the rapid tracking of the non-stationary clock difference and the accurate estimation of the stable link establishment clock speed.
Description
Technical Field
The invention relates to a Kalman filtering method for inter-satellite bidirectional delay comparison non-stationary clock difference, and belongs to the technical field of satellite time synchronization.
Background
The inter-satellite bidirectional time delay comparison time synchronization technology is a basis for ensuring inter-satellite coordination work and completing inter-satellite high-precision time distribution and timing, and is one of important support technologies for low-orbit satellite-ground time synchronization and low-orbit inter-satellite time synchronization. However, due to the unique non-stationary characteristics of the inter-satellite bidirectional delay comparison process in practice, such as chain establishment interruption and electromagnetic environment change caused by on-off of other on-satellite single machines, great challenges are brought to inter-satellite bidirectional delay comparison clock difference and clock speed estimation Kalman filtering design. The traditional Kalman filtering is proposed for the inter-satellite clock difference obeying the linear change rule, so that only the clock difference signal with linear change dynamics can be accurately tracked theoretically. For the clock-difference step dynamic signal introduced by chain-building interruption, the traditional Kalman filtering needs a long-time re-convergence process, which cannot realize the rapid tracking of the clock difference between step-type stars.
Disclosure of Invention
The invention aims to solve the technical problems that: the method overcomes the defects of the prior art, and solves the problem that the fast tracking of the step-type inter-satellite clock difference cannot be realized by non-stationary clock difference Kalman filtering.
The invention aims at realizing the following technical scheme:
the satellite carrying atomic clock with inter-satellite bidirectional clock difference filtering is used as an on-satellite frequency source, and time synchronization between two satellites is realized through inter-satellite bidirectional time comparison. In general, the inter-satellite bi-directional clock difference measurement can be described by a deterministic variation component and a random variation component, as shown in the following formula
y＝a 0 +a 1 t+ε x (t) (1)
The first two terms are components of the satellite clock difference certainty variation, a 0 Is the initial clock difference, a, between two satellite clocks 1 Is the initial frequency deviation between two satellite clocks, t is a linearly increasing time variable, y is an inter-satellite bi-directional clock that varies with the time variable tDifference measurement, ε x And (t) is the clock-difference random noise component between the two satellite clocks. Typically, the deterministic variation model parameters a in (1) after two satellites are stabilized and linked 0 And a 1 The Kalman filtering, which is a constant that does not change with time, is called stationary clock-difference Kalman filtering in this case. In practice, the bidirectional clock error has multiple chain building caused by chain building interruption, thereby leading to a parameter a in the formula (1) 0 A is time-varying 0 (t) thereby causing non-stationary inter-satellite clock-difference processes. Parameter a in the same manner as in (1) 1 Time variation a 1 (t) also results in non-stationary inter-satellite clock-difference processes. A typical sequence of clock differences for a non-stationary inter-satellite bi-directional delay alignment solution is shown in fig. 1.
As can be seen from fig. 1, there is a non-stationary characteristic of the time-dependent variation of the clock-difference model parameters in the measured clock-difference sequence. The clock-difference sequence transitions exhibit high dynamic characteristics. The adoption of Kalman filtering under the steady assumption of inter-satellite clock errors can cause larger clock error estimation errors. The non-stationary inter-satellite clock difference sequence is defined as the inter-satellite clock difference not operating according to an atomic clock model, parameter a in the model 0 And a 1 Is a time-varying parameter, which is respectively defined by a 0 (t) and a 1 (t) characterization.
The invention provides an inter-satellite bidirectional time delay comparison non-stationary clock difference Kalman filtering method, which essentially adopts a clock difference non-stationary characteristic detection combined Kalman filtering mode to obtain a fast and accurate tracking process of a non-stationary clock difference after a newly built chain is reestablished after an inter-satellite chain is interrupted, and a stable and accurate estimation process of a clock speed in a stable chain building process, wherein the working flow of the fast and accurate tracking process is shown in a figure 2.
The inter-satellite bidirectional delay comparison non-stationary clock difference Kalman filtering is a technology for detecting the non-stationary change of the clock difference by adopting the primary difference of inter-satellite bidirectional delay comparison measurement quantity, the clock difference prediction residual error and the primary difference of the clock difference prediction residual error and adopting nonlinear estimation on the clock speed of the non-stationary change, thereby realizing rapid tracking on the non-stationary clock difference and accurately estimating the stable link establishment clock speed. The technology is characterized in that the clock difference and the clock speed in the non-stable change process of the clock difference are tracked rapidly, and the clock speed in the non-stable and stable process of the link establishment can be estimated stably.
In fig. 2, the pseudo-range measurement value of the a-star is TA, the pseudo-range measurement value of the B-star is TB, and the a-star and the B-star have a characteristic of multiple chain establishment from a long time view by the characteristic of the inherent orbit visibility between the a-star and the B-star. Ranging values for the a-and B-satellites are converted to inter-satellite bi-directional delay contrast clock differences in fig. 2.
Aiming at the clock difference data with stable chain construction, the traditional method directly adopts Kalman filtering estimation to obtain the clock difference output and clock speed estimation after filtering noise reduction. The Kalman filtering initial value of the method is generally set as a zero vector. The convergence speed of the traditional clock-difference Kalman filtering process tends to be too slow because the filtering initial value is far from the true clock-difference and clock speed. The clock difference estimation value and the clock speed estimation value in the filter convergence process are theoretically in an unavailable state.
In the method, a zero vector is not used as an initial value of a Kalman filter in the stable chain building process, five groups of inter-satellite bidirectional time delay comparison clock difference measurement values are accumulated, and then linear least square fitting is performed to calculate a number which is closer to a distance clock difference value and a clock speed true value as the initial value, so that the fast convergence of the Kalman filter is realized. For the non-stable chain building process caused by chain building interruption and resumption, the method mainly comprises a clock difference measurement primary difference module, a clock difference prediction residual calculation module, a clock difference prediction residual primary difference module, a clock difference non-stable change detection module and a non-stable clock speed non-linear estimation module.
As shown in fig. 3, the main flow of the method of the invention is as follows: the A star measures the pseudo-range measurement value TA, the B star sends the measured pseudo-range measurement value TB to the A star, the A star calculates the inter-star bidirectional time delay to compare the clock difference measurement value y, meanwhile, calculates the primary difference yTest of the clock difference measurement value, calculates the prediction residual error e between the measured clock difference y and the Kalman prediction clock difference, further carries out primary difference on the clock difference prediction residual error to obtain the primary difference d of the clock difference prediction residual error, comprehensively utilizes yTest, e, d three test statistics to detect the non-stationary change of the clock difference, if the non-stationary characteristic of the clock difference is detected, the least square fit clock speed estimation is needed, the Kalman filtering is adopted to carry out clock speed estimation, the non-linear clock speed estimation under the principle of the minimum clock speed absolute value is adopted to carry out re-estimation updating on the clock speed, and the current measured clock difference is utilized as the filtering clock difference. If no non-stationary characteristic of the clock difference is detected, the clock difference and the clock speed are output by Kalman filtering.
Compared with the prior art, the invention has the following beneficial effects:
(1) Aiming at the application scene of bidirectional time delay comparison between satellites and time synchronization clock difference Kalman filtering, the invention overcomes the defect of slow tracking convergence of non-stationary clock difference Kalman filtering, and adopts three test statistics of primary difference of inter-satellite bidirectional clock difference measurement, primary difference of clock difference prediction residual error and primary difference of clock difference prediction residual error to detect the non-stationary change characteristic of the clock difference. If no clock skew non-stationary characteristics occur, clock skew filtering and clock speed estimation are performed according to normal Kalman filtering. If the characteristic of clock difference non-stationary exists, the clock speed is estimated according to the least square fitting of the clock speed, and the measured clock difference is adopted as the filtered clock difference output.
(2) Compared with the traditional clock difference Kalman filtering method, the inter-satellite bidirectional time delay comparison non-stationary clock difference Kalman filtering method has the following three main advantages: the clock difference step dynamic change signal can be stably and rapidly tracked, the non-stationary clock difference Kalman filtering clock difference residual error sequence is a Gaussian white noise sequence with approximate zero mean value, and the clock speed is a value close to a fixed constant in the stable chain building process, so that the continuous correct estimation of the clock speed in the non-stationary clock difference process can be ensured.
(3) The invention provides an inter-satellite bidirectional delay comparison non-stationary clock difference Kalman filtering method, which combines good clock difference high dynamic tracking characteristic and clock speed quick stability estimation characteristic with quick first convergence characteristic, can simultaneously work under two working conditions of stationary clock difference and non-stationary clock difference to finish filter estimation of the inter-satellite clock difference and the inter-satellite clock speed, can realize quick tracking of the clock difference and the clock speed in the switching process of the stationary clock difference and the non-stationary clock difference, has no re-convergence process of the traditional Kalman filtering, has the same hardware structure and requirement as the traditional clock difference Kalman filtering, does not increase hardware additional expenditure and design complexity, and has wider application market space in the application fields of inter-satellite precise clock difference measurement, inter-satellite high-precision time frequency synchronization, inter-satellite high-precision time conservation and the like.
(4) The non-stationary clock difference Kalman filtering post-clock difference residual sequence is a Gaussian white noise sequence with approximate zero mean value, which shows that the invention achieves the theoretical filtering effect and overcomes the defect that the clock difference sequence of the traditional Kalman filtering method is introduced with colored noise due to the high dynamic change of the clock difference.
(5) The clock speed of the non-stationary clock difference Kalman filtering method is a value close to a fixed constant in the stable chain building process, so that the continuous correct estimation of the clock speed in the non-stationary clock difference process can be ensured, and the defect of inaccurate estimation of the clock speed in the initial chain building stage of the traditional Kalman filtering method is overcome.
Drawings
FIG. 1 is a graph showing the filtering result of a conventional Kalman filtering on a non-stationary clock difference;
FIG. 2 is a schematic block diagram of a Kalman filtering scheme for inter-satellite bi-directional delay comparison with non-stationary clock differences;
FIG. 3 is a flowchart of a Kalman filtering process for inter-satellite bi-directional delay comparison with non-stationary clock differences;
FIG. 4 is a schematic diagram of an inter-satellite bi-directional delay comparison process;
FIG. 5 is a graph showing tracking characteristics of conventional Kalman filtering versus inter-satellite clock differences;
FIG. 6 is a sequence of clock-difference residuals for inter-satellite clock-difference conventional Kalman filtering;
FIG. 7 is a graph showing the tracking characteristics of Kalman filtering versus inter-satellite clock differences according to the present invention;
FIG. 8 is a sequence of clock error residuals for the inter-satellite clock error Kalman filtering of the present invention;
FIG. 9 is a conventional Kalman filter of non-stationary inter-satellite clock differences;
FIG. 10 is a conventional Kalman filtering residual of non-stationary inter-satellite clock differences;
FIG. 11 is a graph showing the tracking characteristics of Kalman filtering versus non-stationary inter-satellite clock differences of the present invention;
FIG. 12 is a graph of the residual clock of Kalman filtering versus non-stationary inter-satellite clock filtering according to the present invention;
FIG. 13 is a graph showing the result of Kalman filtering versus the estimated corresponding clock speed for non-stationary inter-satellite clock differences according to the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.
An inter-satellite bidirectional delay comparison non-stationary clock difference Kalman filtering method comprises the following steps:
1) Acquiring forward pseudo-range and reverse pseudo-range corresponding to inter-satellite bidirectional propagation delay
As shown in FIG. 4, the A star and the B star move on the respective orbits, the time synchronization of atomic clocks between the A star and the B star is determined by adopting an inter-satellite bidirectional time delay comparison method, wherein Deltat is the clock difference between the A star and the B star, the time transfer aims at estimating the clock difference by high-precision filtering, and the time correction processing is carried out so that the time of the A star and the time of the B star are kept synchronous.
A star sends to B star with own sending time scale T a1 Recording local signal receiving time T when receiving signal by star B b1 The free space propagation delay experienced by the signal from A-star to B-star is τ AB . Similarly, the B star will also have its own transmission time T b2 The clock synchronous signal of (a) is sent to A star, and A star records the receiving time T a2 . The signal propagation delay experienced by B star to a star is tba. t is t at Is the hardware time delay of the A star transmitter, t bt Is the hardware time delay of the B star transmitter, t ar For the hardware time delay of the A star receiver, t br Is the hardware delay of the B star receiver.
Axing T a1 Transmitting, B star T b1 The receiving time is
T b1 ＝T a1 +t at +τ AB +t br -Δt (2)
B Star T b2 Time of day transmission, AXING T a2 Time of day reception may be expressed as
T a2 ＝T b2 +Δt+t bt +τ BA +t ar (3)
T-shaped memory B ＝T b1 -T a1 The propagation delay of signals obtained for B-star measurement, also known as reverse pseudo-range. T-shaped memory A ＝T a2 -T b2 The signal propagation delay measured for the a-star is also known as forward pseudorange.
Hereinafter, the inter-satellite bidirectional clock difference is simply referred to as clock difference, and the inter-satellite bidirectional clock speed is simply referred to as clock speed.
2) Calculating inter-satellite bidirectional clock difference measurement quantity
The measurement of the inter-satellite bi-directional clock difference can be expressed as
Wherein the hardware time delay of the transmission and the reception of the A star and the B star can be determined by ground zero value measurement and upper-filling a priori. (τ) BA -τ AB ) And/2 is a systematic error of inter-satellite clock difference determination caused by link asymmetry, and the error can be corrected by satellite position and speed at signal receiving and transmitting time.
3) Primary difference for calculating inter-satellite bidirectional clock difference measurement quantity
And calculating a primary difference yTest of the clock difference measurement quantity according to the current n-moment inter-satellite bidirectional clock difference measurement quantity y (n) and the previous n-1-moment inter-satellite bidirectional clock difference measurement quantity y (n-1).
yTest＝y(n)-y(n-1) (5)
Where yprev=y (n-1).
4) Setting a process covariance matrix and a measurement covariance matrix
Setting a process covariance matrix and a measurement covariance matrix as according to prior information
R＝1e6 (7)
5) Calculating initial state variable estimation value and covariance initial value
The nth clock difference and clock speed are calculated as initial values by 5-point least squares linear fitting in the following manner. The least squares linear fit matrix a can be expressed as
Where T is the sampling interval. Inter-satellite bidirectional clock difference measuring vector y composed of current inter-satellite bidirectional clock difference measuring quantity y (n) and previous 4 inter-satellite bidirectional clock difference measuring quantities 0 Is that
y(0)＝[y(n),y(n-1),y(n-2),y(n-3),y(n-4)] T (9)
Wherein [] T Representing a matrix transposition operation.
The joint estimated initial value intermediate value ζ of the clock difference and the clock speed can be calculated as
ζ＝(A T A) -1 A T y(0) (10)
The joint estimated initial value x (0) of the clock difference and the clock speed can be expressed as
x(0)＝[ζ 2 ,ζ 1 ] T (11)
Wherein ζ 1 And zeta 2 A first element and a second element respectively representing ζ, and a state variable covariance initial matrix P (0) corresponding to a joint estimation initial value x (0) of clock difference and clock speed is set as
6) Calculating a state prior estimated value of the current moment according to a state variable of the previous moment
Wherein the method comprises the steps ofIs the state prior estimated value at the current moment, and the state variable is +.>dt r Representing the filtered estimated clock difference, dt r Is an estimate of Δt, +.>Representing the filtered estimated clock speed.
7) Covariance matrix for calculating state prior estimated value at current moment
The noise covariance matrix of the state prior estimated value at the current moment is calculated according to the following formula
P - (n)＝ΦP(n-1)Φ T +Q (15)
P - (n) is the noise covariance matrix of the state prior estimate at the current time, n, and P (n-1) is the covariance matrix of the state posterior estimate at the previous time, n-1.
8) Calculating Kalman gain matrix at current moment
The Kalman gain matrix K (n) and the measurement matrix H at the current time can be calculated as follows
K(n)＝P - (n)H T [HP - (n)H T +R] -1 (16)
H＝[1 0] (17)
9) Calculating the clock difference residual error of the current time
10 Primary difference for calculating the clock difference residual of the current time
The test statistic of the non-steady change of the clock speed is mainly obtained by one differential calculation of the clock speed parameter at the current moment, namely
d(n)＝e(n)-e(n-1) (19)
11 Determining whether the absolute value of the primary difference of the clock difference measurement quantity exceeds the detection threshold
The primary difference yTest of the clock difference measurement is taken as an absolute value, and the detection threshold is set as alpha, and the typical threshold value is alpha=20ns. If the |yTest| is not less than 20ns, the state posterior estimated value at the current moment is calculated according to the following formula
If |yTest| < 20ns, then a determination is continued as to whether the clock difference residual exceeds its threshold.
12 Judging whether the absolute value of the current clock speed residual exceeds a detection threshold
The absolute value of the current clock difference residual e (n) is taken, and the detection threshold is set as beta, and a typical threshold value beta=3ns. If |e (n) | is not less than 3ns, the state posterior estimation value at the current moment is calculated according to the following formula
If |e (n) | < 3ns, a posterior estimate of the current time state is calculated using Kalman filtering.
13 Calculating state variable Kalman posterior estimation value at current moment
14 Calculating the covariance posterior estimation value of the state variable at the current moment
P(n)＝[I-K(n)H]P - (n) (23)
15 Judging whether the absolute value of the first difference of the clock difference residual exceeds the detection threshold
In this step, the detection threshold of the absolute value |e (n) | of the residual error amount of the clock is set to γ, and a typical value of γ is γ=0.5 ns. The detection threshold of the primary differential absolute value |d (n) | of the clock difference residual is δ, and a typical value of δ is δ=0.1 ns.
If |e| > gamma&&If d > delta is true, the Kalman filtered posterior estimation value is normally outputOtherwise according to the last 5 clock differencesThe sliding window data of the quantity is subjected to first-order least square linear fitting to calculate a group of estimated clock speed values.
The nth clock difference and the clock speed are calculated as estimated values by 5-point least squares linear fitting in the following manner. The least squares linear fit matrix a can be expressed as
Where T is the sampling interval. The current clock difference y (n) and the clock difference measurement buffer buf5 filled by cyclic shift
buf5＝[y(n),buf5(1:end-1)] T (25)
The joint estimated initial value intermediate value p of the clock difference and the clock speed can be calculated as
p＝(A T A) -1 A T (buf5) (26)
The alternative clock speed vector clkDrift may be represented as
Wherein the method comprises the steps ofRepresenting a Kalman filtered clock speed estimate, which is +.>Is a second element of (2); p is p 1 Is the first element of p.
16 Non-linear clock speed estimation)
The element in the alternative clock speed vector clkDrift is firstly taken absolute value, and then the element subscript with smaller clock speed absolute value is compared and found out
[～,idx]＝min(abs(clkDrift)) (28)
Pressing calculation of current moment state posterior estimation value
Wherein clkDrift idx Is the idx-th element of clkDrift.
To further verify the scientificity, correctness and effectiveness of the method of the invention, a specific example of the method of the invention is given below.
Embodiment one: the initial fast convergence filtering function of the method is verified. The whole experiment mainly comprises the following steps:
first, inter-satellite two-way pseudo-range measurement data during stable link establishment is selected, and an inter-satellite measurement clock difference is calculated from an A-satellite measurement pseudo-range and a B-satellite measurement pseudo-range according to FIG. 4.
Secondly, setting an initial value of Kalman filtering, wherein the initial value of the clock difference is obtained by measuring the clock difference and the initial value of the clock speed is obtained by two-point difference calculation of the clock difference.
And thirdly, selecting a section of clock difference data with clock differences conforming to the operation characteristics of the atomic clock, performing Kalman filtering, analyzing the tracking characteristics of the Kalman filtering on the measured clock differences, and observing the distribution characteristics of the clock difference residual errors.
According to the traditional Kalman filtering initial value selection method, the tracking characteristic of Kalman filtering on the inter-satellite clock difference is obtained as shown in figure 5. Inter-satellite clock-difference the sequence of clock-difference residuals for conventional Kalman filtering is shown in fig. 6.
As can be seen from fig. 5, there is a significant convergence process in the tracking process of the inter-satellite clock difference in the conventional Kalman filtering, and the convergence process has a long duration, which means that the clock difference filtered in the filter convergence process cannot correctly reflect the real inter-satellite clock difference variation characteristic. As can be seen from fig. 6, the inter-satellite clock-difference conventional Kalman-filtered clock-difference residual sequence needs to become zero-mean white noise after the filter converges, so as to correctly reflect the random noise component filtered by Kalman. The clock difference residual when the filter is not converging contains both non-randomly varying components and randomly varying components. Non-randomly varying clock-difference residuals may adversely affect the correct estimation of the clock-difference.
Finally, according to the calculation method of the state variable initial value, a group of initial values which are relatively close to the true value of the distance clock difference and the true value of the clock speed are calculated through a 5-point least square linear fitting mode, the initial values are substituted into a Kalman filter to filter the clock difference during stable chain establishment, the tracking result of the Kalman filter on the inter-satellite clock difference is shown in fig. 7, and the corresponding clock difference residual sequence is shown in fig. 8.
As can be seen from fig. 7, in the steady stage of inter-satellite double-star link establishment, the convergence process of the Kalman filter of the invention is fast, the change of the inter-satellite clock difference is quickly and accurately tracked almost at the beginning, and the tracking efficiency of the Kalman filter on the inter-satellite clock difference is greatly improved. As can be seen from fig. 8, the clock difference residual sequence body of the inter-satellite clock difference Kalman filtering according to the invention is composed of random noise with zero mean value and contains interference burr components, which indicates that the inter-satellite clock difference Kalman filtering according to the invention can effectively filter the random noise components in the measured clock differences, and meanwhile eliminates abnormal interference burrs in the clock differences and improves the accuracy of clock difference estimation.
Embodiment two: the method of the invention is verified to have a non-stationary clock difference filtering function. The whole experiment mainly comprises the following steps:
first, the inter-satellite two-way pseudo-range measurement data of a plurality of time links are selected, and the inter-satellite measurement clock difference is calculated from the A-satellite measurement pseudo-range and the B-satellite measurement pseudo-range according to FIG. 4.
Secondly, setting initial values of Kalman filtering, and calculating a group of initial values which are closer to a true value of a distance clock difference and a true value of a clock speed in a 5-point least square linear fitting mode.
And thirdly, performing Kalman filtering on the clock error data containing the non-stationary change of the clock error, analyzing the tracking characteristic of the Kalman filtering on the measured clock error, and observing the distribution characteristic of the clock error residual error.
The tracking characteristics of Kalman filtering on non-stationary inter-satellite clock differences are shown in fig. 9. The conventional Kalman filter clock-difference residual for non-stationary inter-satellite clock-differences is shown in fig. 10.
It can be seen from fig. 9 that the measured non-stationary clock difference comprises three independent chain building processes, and the clock difference of the first time of chain building can be correctly estimated by adopting the conventional Kalman filtering, and for the clock difference during the chain building transition period and the clock differences in the second and third chain building processes, the measurement quantity of the inter-satellite clock difference is difficult to quickly track by adopting the conventional Kalman filtering. As can be seen from fig. 10, the conventional Kalman filtering clock error residual is a random number close to zero only in the first time of chain building, and the clock error residual is a non-random value with large amplitude variation in the chain building transition period and the second and third time of chain building. This illustrates that conventional Kalman filtering is not applicable to application scenarios where inter-satellite clock differences are not smoothly varying, and the filtered clock difference residual is not a random quantity with zero mean.
Finally, the Kalman filtering is utilized to filter inter-satellite clock difference data of multiple links, the tracking condition of the Kalman filtering on the non-stationary clock difference is analyzed, the random distribution characteristic of a clock difference residual sequence is observed, and the change characteristic of a clock speed estimation sequence is analyzed.
The tracking characteristics of the Kalman filtering of the invention for non-stationary inter-satellite clock differences are shown in FIG. 11. As can be seen from FIG. 11, the Kalman filtering of the present invention can rapidly and accurately track the variation of the non-stationary inter-satellite clock differences in the non-stationary clock difference process caused by the measurement of the inter-satellite clock differences with a plurality of time of chain establishment.
The residual sequence after Kalman filtering of the non-stationary inter-satellite clock difference filtering is shown in FIG. 12.
As can be seen from fig. 12, the residual error after the filtering by the Kalman filtering method of the present invention is zero-mean gaussian white noise, and most of the error is distributed within 0.5ns. Some components with larger variances in the filtered clock error residual sequence have an absolute value of about 2.0ns, which indicates that the Kalman filtering has an ideal suppression effect on random noise. The result of the Kalman filtering of the invention for estimating the corresponding clock speed of the non-stationary inter-satellite clock difference is shown in FIG. 13.
From the results of fig. 13, it can be seen that the method of the present invention has good estimation characteristics for a non-stationary change in clock speed. Meanwhile, the method has piecewise linear estimation function on the clock speed during the stable chain establishment, and the clock speed during the stable chain establishment is a constant with an absolute value close to zero, which is consistent with the physical characteristic that the clock speed estimation of an original clock in a normal chain establishment scene is basically a constant with an absolute value close to zero.
What is not described in detail in the present specification is a well known technology to those skilled in the art.
Although the present invention has been described in terms of the preferred embodiments, it is not intended to be limited to the embodiments, and any person skilled in the art can make any possible variations and modifications to the technical solution of the present invention by using the methods and technical matters disclosed above without departing from the spirit and scope of the present invention, so any simple modifications, equivalent variations and modifications to the embodiments described above according to the technical matters of the present invention are within the scope of the technical matters of the present invention.
Claims (10)
1. The inter-satellite bidirectional delay comparison non-stationary clock difference Kalman filtering method is characterized by comprising the following steps of:
for both satellites A and B, the A satellite measures a pseudorange measurement T A Pseudo range measurement T to be measured by the B star B Sending the result to an A star;
the A star calculates inter-star bidirectional time delay to compare the clock difference measurement quantity y, determines primary difference yTest of the clock difference measurement quantity, determines a prediction residual error e between y and Kalman prediction clock difference, and further performs primary difference on the prediction residual error e to obtain primary difference d of the clock difference prediction residual error; the detection of the non-stationary change in clock skew was performed using yTest, e, d three test statistics:
if the non-stationary characteristic of the clock difference is detected, the least square fitting clock speed estimation is utilized, the Kalman filtering is adopted to estimate the clock speed, then the clock speed is estimated and updated again, and the current measuring clock difference is utilized as the filtering clock difference;
if no non-stationary characteristic of the clock difference is detected, the clock difference and the clock speed are output by Kalman filtering.
2. The inter-satellite bidirectional delay comparison non-stationary clock difference Kalman filtering method according to claim 1, wherein the method for determining the clock difference measurement y is as follows:
wherein the free space propagation delay of the signal from the A star to the B star is tau AB The signal propagation delay from star B to star A is τBA, t at Is the hardware time delay of the A star transmitter, t bt Is the hardware time delay of the B star transmitter, t ar For the hardware time delay of the A star receiver, t br Is the hardware delay of the B star receiver.
3. The inter-satellite bidirectional delay comparison non-stationary clock difference Kalman filtering method according to claim 1, wherein a primary difference yTest of the clock difference measurement is calculated according to the current time inter-satellite bidirectional clock difference measurement y (n) and the previous time inter-satellite bidirectional clock difference measurement y (n-1):
yTest＝y(n)-y(n-1)
where n is the sampling index at the current time.
4. The method of inter-satellite bi-directional delay comparison non-stationary clock skew Kalman filtering according to claim 1, wherein when the absolute values of yTest, e and d respectively do not exceed the corresponding set thresholds, no non-stationary clock skew characteristic is detected.
5. The inter-satellite bi-directional delay comparison non-stationary clock difference Kalman filtering method according to claim 1, wherein the nth clock difference and clock speed calculate the initial value by least squares linear fitting as follows:
based on the least square linear fitting matrix A, determining a joint estimated initial value intermediate value zeta of the clock difference and the clock speed;
and calculating a state prior estimated value at the current moment according to the state variable at the previous moment.
6. The method for comparing non-stationary clock differences with Kalman filtering according to claim 5, wherein a covariance matrix of the state prior estimate of the current moment is calculated according to the state prior estimate of the current moment, and is used for determining a Kalman gain matrix of the current moment.
7. The method of inter-satellite bi-directional delay comparison non-stationary clock difference Kalman filtering according to claim 6, wherein the Kalman gain matrix K (n) and the measurement matrix H at the current moment are:
K(n)＝P - (n)H T [HP - (n)H T +R] -1
H＝[1 0]
P - and (n) is a noise covariance matrix of the state prior estimated value of the current moment n, and R is a measurement covariance matrix.
8. The inter-satellite bi-directional delay comparison non-stationary clock difference Kalman filtering method of claim 7, wherein the current clock difference residual is:
y (n) is the current time inter-satellite bidirectional clock difference measurement quantity,is a priori estimate of the state at the current time.
9. The inter-satellite bi-directional delay comparison non-stationary clock difference Kalman filtering method according to claim 1, wherein the primary difference of the current clock difference residuals is:
d(n)＝e(n)-e(n-1)
n and n-1 are time series.
10. The inter-satellite bi-directional delay comparison non-stationary clock difference Kalman filtering method according to any one of claims 1 to 9, wherein the least square is used to fit the clock speed estimation and the Kalman filtering is used to perform the clock speed estimation, and based on the two estimation results, the non-linear clock speed estimation is determined by using the minimum principle of the absolute value of the clock speed.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311204889.0A CN117411583A (en) | 2023-09-18 | 2023-09-18 | Inter-satellite bidirectional time delay comparison non-stationary clock difference Kalman filtering method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311204889.0A CN117411583A (en) | 2023-09-18 | 2023-09-18 | Inter-satellite bidirectional time delay comparison non-stationary clock difference Kalman filtering method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN117411583A true CN117411583A (en) | 2024-01-16 |
Family
ID=89497011
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202311204889.0A Pending CN117411583A (en) | 2023-09-18 | 2023-09-18 | Inter-satellite bidirectional time delay comparison non-stationary clock difference Kalman filtering method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117411583A (en) |
-
2023
- 2023-09-18 CN CN202311204889.0A patent/CN117411583A/en active Pending
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US5585954A (en) | Apparatus for measuring optical transmission characteristic | |
| US7358895B2 (en) | System and method for acquiring weak signals in a global positioning satellite system | |
| US7640463B2 (en) | On-chip receiver eye finder circuit for high-speed serial link | |
| CN110995241B (en) | LVDS delay circuit with self-adaptive phase adjustment | |
| EP0833476A2 (en) | Fast resynchronization system for high-speed data transmission | |
| CN108196267B (en) | GNSS CP technology-based uninterrupted time transfer method | |
| CN108873029B (en) | Method for realizing clock error modeling of navigation receiver | |
| US7684478B2 (en) | Generating an eye diagram of integrated circuit transmitted signals | |
| KR100246030B1 (en) | Synchronization equipment | |
| CN111239775A (en) | Clock error compensation-based hardware delay calibration method and system for time service receiver | |
| CN101604990B (en) | Frequency deviation compensation method and frequency deviation compensation device | |
| CN105182373A (en) | GPS weak signal tracking method in high dynamic environment | |
| JP2008530633A (en) | Apparatus and method for determining maximum correlation point | |
| CN113534205B (en) | Satellite navigation signal abnormality determination method, satellite navigation method, and receiver | |
| EP0894366B1 (en) | Adaptive compensation of doppler shift in a mobile communication system | |
| WO2023014476A3 (en) | Satellite signal environment determination and/or position estimate selection | |
| CN117411583A (en) | Inter-satellite bidirectional time delay comparison non-stationary clock difference Kalman filtering method | |
| US7627063B2 (en) | Device and method for determining a time of arrival of a receive sequence | |
| US7977989B2 (en) | Method and apparatus for detecting and adjusting characteristics of a signal | |
| US7302365B2 (en) | Apparatus and method for performing eye scan | |
| CN110149197B (en) | High-precision synchronization method and system for clock synchronization system | |
| KR100216019B1 (en) | Method of characteristic search in digital mobile radio system | |
| US9219600B1 (en) | Synchronization through waveform correlation | |
| CN113179234B (en) | High dynamic long signal accumulation method based on block Doppler compensation | |
| CN112946568B (en) | Method for directly estimating track vector of radiation source |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |