Performance evaluation method and system of KF applied to GNSS satellite clock observation clock error preprocessing

Abstract

The invention provides a performance evaluation method and system for KF applied to GNSS satellite clock observation clock error preprocessing and a medium. The method comprises the following steps: acquiring an observation clock error of a GNSS satellite clock-ground time reference based on different modes; preprocessing the observation clock difference according to a classical two-state KF to obtain a time estimation value and a frequency estimation value containing different periodic fluctuation items; determining a theoretical conclusion of a time estimator and a frequency estimator obtained by the steady-state KF estimation; and comparing a test result with a theoretical conclusion, and performing performance evaluation on a preprocessing result. The technical scheme of the invention is applied to the atomic clock state estimation field and all the fields using the KF to carry out state estimation, especially when the observation equation and the state equation of the KF are inconsistent with the actual observation characteristics, the GNSS satellite clock data can be preprocessed by the KF through the technical scheme of the invention, and the performance of the preprocessing result can be evaluated.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and in particular to a performance evaluation method and system for applying a two-state variable Kalman filter (Kalman filter, KF) to preprocessing of satellite clock observation clock errors of a global navigation satellite system (global navigation satellite system, GNSS). Background Art

[0002] KF plays an important role in the fields of satellite navigation, time and frequency. For example, for a satellite-ground joint distributed timekeeping system that uses a combination of optical clock groups and atomic clock groups, KF is needed to pre-process the observed clock difference between two optical clocks (or atomic clocks) obtained through star-to-star, satellite-to-ground, and ground-to-ground comparison links, filter out link noise, and more accurately obtain the relative time deviation and relative frequency deviation estimates between the two optical clocks (or atomic clocks). The subsequent establishment of a time benchmark, clock error prediction, and the use of an optical clock group to drive an atomic clock group all need to be based on these estimates. Therefore, the estimation accuracy of KF directly affects the timekeeping performance.

[0003] For the estimation of observation clock error using KF, the traditional theory regards the KF algorithm as the optimal estimation algorithm in the time domain, and believes that when the observation equation and state equation of KF, as well as the selected process noise covariance (Q) and observation noise variance (R) matrices are completely consistent with the characteristics of the actual observation clock error, KF gives the optimal estimation result in the time domain in the sense of the least mean square. Therefore, in order to ensure that the use of KF to pre-process the observation clock error can achieve the ideal effect, it is first necessary to perform a priori analysis of the observation clock error, select a suitable KF model (that is, the KF model is as consistent as possible with the actual observation of the atomic clock), and determine the Q and R values ​​in advance.

[0004] However, in practical applications, the observation equation and state equation of KF, as well as the selected Q and R values, are inconsistent with the characteristics of the actual observed clock error in most cases. For example, for GNSS satellite clocks, due to the influence of various perturbations and relativistic effects, the observed clock error between the satellite clock and the ground time reference shows obvious periodic fluctuations, and this periodic fluctuation term cannot be accurately modeled by KF.

[0005] Reference [1]: Yiwei Wu, Determination of theoretical performances of Kalman filter used for atomic clock estimation. IEEE Transactions on Aerospace and Electronic Systems, 2023, 59(6): 7908-7921. In view of the above situation, a method is proposed to determine the theoretical performance of KF for atomic clock (or time scale) state estimation when the selected KF model and the observed clock error are not completely consistent. This method innovatively equates the classical two-state KF entering the steady state to multiple linear time-invariant (LTI) systems, and proves that the structure of these LTI systems is determined by the KF model, and the coefficients are determined by the selected Q and R values, which are independent of the actual observed clock error. For any form of actual observed clock error, the homogeneity and superposition of the equivalent LTI system can be used to accurately determine the theoretical performance of each item in the estimate given by KF. In fact, the Q and R values ​​of KF are selected according to the noise diffusion coefficient of the observed clock error. However, it is not easy to obtain the noise diffusion coefficient when the observation noise is too large or the amplitude of periodic fluctuations is too large, making it impossible to accurately estimate parameter values ​​such as the noise diffusion coefficient.

[0006] Reference [2]: Wu Yiwei, et al. Atomic clock model and frequency stability analysis method [J]. Journal of Wuhan University (Information Science Edition), 2019, 44(8): 1226–1232. A method for iteratively estimating the noise diffusion coefficient based on historical data, KF estimation results and Allan deviation diagram is proposed. The experimental results show that this method can effectively obtain the estimated value of the noise diffusion coefficient; then, the Q and R values ​​of KF are set according to these estimated values.

[0007] However, there has been no complete experimental analysis on how to comprehensively apply the methods of references [1] and [2] to preprocess the observed clock errors of GNSS satellite clocks. On this basis, the existing technology has not yet addressed whether the theoretical and experimental performance of the estimated observed clock errors for satellite clocks with different noise characteristics can meet the requirements of various subsequent prediction, steering, weighting and other algorithms. Summary of the invention

[0008] In order to solve the above technical problems, the present invention proposes a performance evaluation method, system and medium for applying KF to clock error preprocessing of GNSS satellite clock observations.

[0009] In a first aspect, the present invention proposes a performance evaluation method for applying KF to preprocessing of GNSS satellite clock observation clock errors, the method comprising the following steps:

[0010] Obtain the observed clock difference between GNSS satellite clock and ground time reference based on different modes;

[0011] After preprocessing the observed clock error according to the classical two-state KF, a time estimate and a frequency estimate containing different periodic fluctuation terms are obtained, and a theoretical conclusion of the time estimate and the frequency estimate obtained by the steady-state KF estimation is determined;

[0012] The test results are compared and analyzed with the theoretical conclusions to obtain the performance evaluation results.

[0013] As a further improvement of the present invention, the steps of obtaining the observed clock difference between the GNSS satellite clock and the ground time reference based on different modes include:

[0014] Generate observational clock errors based on simulations, or download measured observational clock errors from the IGS or IGMAS websites.

[0015] As a further improvement of the present invention, the steps of preprocessing the observed clock error according to the classical two-state KF to obtain a time estimate and a frequency estimate containing different periodic fluctuation terms include:

[0016] According to the estimation results of the time state component and frequency state component of the classical two-state KF and the Allan deviation diagram, the estimated values ​​of the atomic clock noise and observation noise intensity are obtained, and the period and amplitude of the periodic fluctuation are estimated. After determining the process noise covariance Q value and the observation noise variance R value of the two-state KF, the two-state KF is run to obtain the time estimation value and frequency estimation value containing different periodic fluctuation terms.

[0017] As a further improvement of the present invention, the step of determining the theoretical conclusion of the time estimate and the frequency estimate obtained by the steady-state KF estimation includes:

[0018] The two-state KF entering the steady state is equivalent to three linear time-invariant systems, and the corresponding transfer functions are generated. According to the transfer functions, the theoretical conclusion based on the time estimation value and the frequency estimation value is obtained.

[0019] As a further improvement of the present invention, the steps of comparing and analyzing the test results with the theoretical conclusions and obtaining the performance evaluation results include:

[0020] The experimental results, including the original observed clock error curve, time estimation curve; the observed clock error curve, time estimation curve and frequency estimation curve after deducting frequency drift; the estimation error curve; and the Allan deviation curve of the observed clock error curve, time estimation curve and frequency estimation curve, are compared and analyzed with the theoretical conclusions to obtain the performance evaluation results of the GNSS satellite clock observation clock error preprocessing.

[0021] In a second aspect, the present invention further proposes a performance evaluation system for applying KF to GNSS satellite clock observation clock error preprocessing, the system comprising:

[0022] An observation clock error acquisition module is used to obtain the observation clock error of the GNSS satellite clock and the ground time reference based on different modes;

[0023] A preprocessing module is used to preprocess the observed clock difference according to the classical two-state KF to obtain a time estimate and a frequency estimate containing different periodic fluctuation terms; and to determine a theoretical conclusion of the time estimate and the frequency estimate obtained by the steady-state KF estimation;

[0024] The performance evaluation module compares and analyzes the test results with the theoretical conclusions to obtain the performance evaluation results.

[0025] As a further improvement of the present invention, the observation clock error acquisition module includes:

[0026] A first parameter acquisition module, used to acquire parameters selected by a user when the observed clock error is generated through simulation;

[0027] The second parameter acquisition module is used to obtain parameter estimates based on the atomic clock model and frequency stability analysis when the observed clock error is obtained through actual measurement, so as to determine the process noise covariance Q value and the observation noise variance R value.

[0028] As a further improvement of the present invention, the performance evaluation module includes:

[0029] A theoretical conclusion generation submodule is used to determine the transfer function of the equivalent LTI system after the KF enters the steady state, and obtain the theoretical conclusion based on the time estimation value and the frequency estimation value according to the transfer function;

[0030] The test result generation submodule is used to generate test results, wherein the test results include the original observed clock error curve, time estimation curve; the observed clock error curve, time estimation curve and frequency estimation curve after deducting frequency drift; the estimation error curve; and the Allan deviation curve of the observed clock error curve, time estimation curve and frequency estimation curve.

[0031] The evaluation submodule is used to compare and analyze the test results with the theoretical conclusions to obtain performance evaluation results.

[0032] In a third aspect, the present invention further provides an electronic device, comprising:

[0033] A memory on which application programs and an operating system are stored;

[0034] A processor is used to implement the steps of the performance evaluation method of applying KF to GNSS satellite clock observation clock error preprocessing as described in the first aspect when executing the program or instruction.

[0035] In a fourth aspect, the present invention proposes a readable storage medium having an application and an operating system stored thereon, wherein the program or instructions, when executed by a processor, implements the steps of the performance evaluation method for applying KF to GNSS satellite clock observation clock error preprocessing as described in the first aspect. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of the method for evaluating the performance of preprocessing of clock errors of GNSS satellite clock observations using the KF proposed in the present invention.

[0037] Figure 2 is z in the embodiment of the present invention k and curve.

[0038] Figure 3 is z after deducting the frequency drift in the embodiment of the present invention k and curve.

[0039] Figure 4 In the embodiment of the present invention curve.

[0040] Figure 5 In the embodiment of the present invention curve.

[0041] Figure 6 In the embodiment of the present invention curve.

[0042] Figure 7 : is an amplitude-frequency response diagram of an equivalent LTI system in an embodiment of the present invention.

[0043] Figure 8 : is a phase-frequency response diagram of an equivalent LTI system in an embodiment of the present invention.

[0044] Fig. 9 is zk in the embodiment of the present invention, and Allan deviation curve.

[0045] Fig.10 This is a framework diagram of the performance evaluation system proposed in the present invention based on KF applied to GNSS satellite clock observation clock error preprocessing. DETAILED DESCRIPTION

[0046] For ease of understanding, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] The technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems are described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present application will be described below in conjunction with the accompanying drawings.

[0048] like Figure 1 As shown, the present invention proposes a performance evaluation method for applying KF to GNSS satellite clock observation clock error preprocessing, which includes the following contents:

[0049] S101. Obtain the observed clock difference between the GNSS satellite clock and the ground time reference based on different modes.

[0050] In this embodiment, the observed clock error of "GNSS satellite clock-ground time reference" can be obtained by various methods, such as simulating and generating the observed clock error, or downloading the measured observed clock error from websites such as IGS and IGMAS.

[0051] For a typical "GNSS satellite clock-ground time reference" observation clock error, it can be expressed as:

[0052]

[0053] Among them, t k represents the moment, z(t k ) represents t k The first three items represent the quadratic polynomial part of the observed clock error, x0 and y0 represent the initial values ​​of the time state and frequency state, and d represents the frequency drift; the fourth item represents N periodic fluctuation items, A i is the amplitude of the ith periodic fluctuation term, f i is the frequency of the ith periodic fluctuation term, is the initial phase of the ith periodic fluctuation term; the 5th to 7th terms represent white frequency modulation noise (WFM), walk random modulation noise (RWFM), and white phase modulation noise (WPM), respectively, where WFM and RWFM are atomic clock noises, WPM is observation noise, and W1(t k ), W2(s) and W0(t) represent three independent Wiener processes, and σ1, σ2 and σ0 represent diffusion coefficients.

[0054] S102. After preprocessing the observed clock difference according to the classical two-state KF, the time estimation value and the frequency estimation value based on different periodic fluctuation terms are obtained, and the theoretical conclusion of the time estimation value and the frequency estimation value obtained by the steady-state KF estimation is determined.

[0055] In this embodiment, the clock model adapted to the classic two-state KF is expressed as:

[0056]

[0057] Among them, t represents the time, x(t) and y(t) represent the time state and frequency state of the atomic clock at time t.

[0058] The discrete form of formula (2) is the state equation of KF, which is expressed as:

[0059]

[0060] Where T is the time interval, T = t k+1 -t k .

[0061] The observation equation of KF is expressed as:

[0062]

[0063] Among them, z(t k ) represents the observed clock error, that is, x(t k ) observation, which is equivalent to x(t k ) is superimposed with observation noise.

[0064] Equations (3) and (4) correspond to the state equation and observation equation of the classical two-state KF, respectively. Comparing equations (4) and (1), it can be clearly seen that the model of the classical two-state KF is inconsistent with the actual observed clock error, mainly because there are fewer N periodic fluctuation terms in equation (4).

[0065] Before running the KF, you must first determine the Q and R values ​​of the KF.

[0066] The process noise covariance (denoted as Q) of formula (3) is expressed as:

[0067]

[0068] The observation noise variance (denoted as R) of formula (4) is expressed as:

[0069]

[0070] From equations (5) and (6), we can see that the values ​​of Q and R are determined by the values ​​of the diffusion coefficients (σ1, σ2, σ0). Therefore, to determine the values ​​of Q and R, we first need to obtain the estimated values ​​of (σ1, σ2, σ0).

[0071] In practical applications, the estimated value of (σ1, σ2, σ0) can be obtained by fitting the Allan variance curve. For the observed clock error shown in formula (1), the mathematical expectation of its Allan variance is expressed as:

[0072]

[0073] in, represents the Allan variance, σ y (τ) denotes the Allan deviation (i.e., the square root of the Allan variance), τ denotes the smoothing time, and E[·] denotes the mathematical expectation.

[0074] In this embodiment, it can be known from formula (7) that the slopes of the observation noise (WPM), WFM, RWFM and linear frequency drift in the logarithmic Allan variance diagram are -2, -1, 1 and 2 respectively, and the slopes in the logarithmic Allan deviation diagram are -1, -1 / 2, 1 / 2 and 1 respectively. Secondly, if there is a large periodic fluctuation in the time difference, then the Allan variance also has obvious periodic fluctuations, that is, the Allan variance will be convex in a certain smooth time period in the middle.

[0075] In this embodiment, the research results of reference [2] are directly adopted to obtain the estimated values ​​of atomic clock noise and observation noise intensity (i.e. and The estimated value of the method); secondly, three different methods are used to estimate the linear frequency drift amplitude d, and they are mutually verified; finally, in order to solve the problem that the periodic fluctuation is not obvious in the time difference, the atomic clock model is combined to comprehensively estimate the periodic fluctuation period f by combining the KF state estimation results and the logarithmic Allan deviation diagram. i and amplitude A i In addition, f can be estimated from the frequency domain by Fourier transforming the observed clock error. i and A i .

[0076] Substituting the estimated values ​​of (σ1, σ2, σ0) into equations (5) and (6), the Q and R values ​​of the KF are determined.

[0077] In this embodiment, after the Q value and R value of KF are determined, KF is run to pre-process the observed clock error. KF can obtain the observed clock error z(t k ) to obtain the estimated time value and frequency value, which are recorded as and On the other hand, for It also filters out z(t k ) in the observation noise. The specific process is as follows:

[0078]

[0079] P k,k-1 =φP k-1,k-1 φ T +Q (9)

[0080] K k =P k,k-1 H T (HP k,k-1 H T +R) -1 (10)

[0081]

[0082] P k,k =(IK k H)P k,k-1 (12)

[0083] in, represents the process equation transfer matrix; H =

[10] represents the observation equation transfer matrix; I represents the 2×2 unit matrix; Represents in t k-1 Moment of k-1 An estimated value of Represents in t k Moment of k-1 One-step prediction value of K k represents KF gain; P k,k and P k,k-1 represent the estimated covariance and predicted covariance, respectively.

[0084] S103. Compare and analyze the time estimation and frequency estimation results obtained by steady-state KF estimation with the theoretical conclusions to obtain performance evaluation results.

[0085] In this embodiment, the performance evaluation includes three aspects: the analytical expression of the deterministic term, the theoretical PSD of the random (noise) term, and the estimated mean-squared error (MSE) (i.e. Theoretical values ​​and the theoretical values ​​of each item in it.

[0086] From the above analysis, we can see that the model (4) of the classical two-state KF is inconsistent with the actual observed clock error (1), mainly because there are N periodic fluctuation terms missing in equation (4). Therefore, the traditional method can no longer determine the theoretical performance of KF, and the method proposed in reference [1] is needed. Reference [1] equates the two-state KF entering the steady state to three linear time-invariant (LTI) systems. Their transfer functions are denoted as Hx(z), Hy(z) and Hy int (z), expressed as:

[0087]

[0088] Where Ks1 and Ks2 represent the 2×1 K in the steady state in equation (10). k The values ​​of the first and second rows of the matrix (denoted as Ks); Hx(z) represents the KF input z k and The transfer function between the outputs, Hy(z) represents the KF input z k and The transfer function between the outputs, Hy int (z) represents KF input z k and The transfer function between the outputs, yes The integral of performance.

[0089] Put z k , and The Z transforms are denoted as Z(z), X(z), Y(z) and Y INT (z). In the Z domain, their relationship is:

[0090]

[0091] In this way, the theoretical performance of the steady-state KF can be determined from the perspective of the LTI system. For given Q and R values, the simultaneous equations (9), (10) and (12) give the values ​​of Ks1 and Ks2. Substituting the values ​​of Ks1 and Ks2 into equations (13)-(15) yields the transfer function of the equivalent LTI system. Reference [1] proves that the KF model (4) completely determines the structure of the equivalent LTI system, and the values ​​of Q and R completely determine the values ​​of the coefficients (Ks1 and Ks2) of the equivalent LTI system, i.e., the transfer functions of these LTI systems are completely determined by the KF model and the values ​​of Q and R, and have nothing to do with actual observations.

[0092] According to the literature [1], when the selected Q and R values ​​are completely consistent with the actual noise characteristics, for the observed clock error (4), the steady-state KF gives or It is expressed as:

[0093]

[0094] in, and Respectively represent and The amplitude of the i-th periodic fluctuation term in ; and Respectively represent and The phase of the i-th periodic fluctuation term in ; these values ​​can be calculated by the amplitude-frequency response and phase-frequency response of the equivalent LTI system; and The noise terms in can be expressed as and , where the “hat” symbol represents the estimated amount.

[0095] In this embodiment, according to the literature [1], based on formula (17), the following conclusions are given:

[0096] 1) Formula (17) gives and Analytical expressions for the deterministic terms in ; first, and The steady-state tracking errors introduced when Hx(z) and Hy(z) track the frequency drift terms are mainly due to the fact that both Hx(z) and Hy(z) are second-order systems. When the second-order system tracks the quadratic terms in the polynomial, there will be steady-state tracking errors. Secondly, after the periodic fluctuation terms in the form of sinusoidal waves pass through the LTI system, their phase and amplitude will change differently, and the degree of change of the phase and amplitude in the periodic fluctuation terms of different frequencies are also different.

[0097] 2) When the selected Q and R values ​​are completely consistent with the actual noise characteristics, equation (17) shows that The randomness term in contains only WFM and RWFM with the same noise intensity (σ1, σ2), The randomness term in the RWFM only contains the same noise intensity σ2; however, the noise term and It is not a random process of arbitrary orbits, and its constraints are:

[0098]

[0099] Where Ps is the P in steady state in equations (8)-(12) k,k , Ps(1,1) and Ps(2,2) are the 1st row, 1st column and the 2nd row, 2nd column of Ps. As mentioned above, the value of Ps is completely determined by the values ​​of Q and R. Substituting the values ​​of Q and R into the simultaneous equations (9), (10) and (12), we can solve the values ​​of Ps(1,1) and Ps(2,2).

[0100] 3) Put z k , and The deterministic terms in are denoted as D z k , and The randomness terms are denoted as S z k , and At this time there is

[0101]

[0102] According to formula (19), the theoretical value of KF estimated MSE and the theoretical values ​​of each item therein can be obtained; among them, the deterministic part of the estimated MSE can be obtained by substituting formulas (17) and (1) into the corresponding parts of formula (19), and the random part of the estimated MSE is Ps(1,1) and Ps(2,2).

[0103] In summary, equations (17) to (19) are the complete conclusions of the KF theoretical performance when the selected Q and R values ​​are completely consistent with the actual noise characteristics.

[0104] When the selected Q and R values ​​do not match the actual noise characteristics, the randomness expression in equation (17) and equation (18) are no longer applicable, but and The power spectral density (PSD) of the randomness term in can be calculated theoretically, and equation (19) still holds.

[0105] The following describes the invention in conjunction with embodiments.

[0106] In this embodiment, the simulation generates the observed clock difference z of “GNSS satellite clock-ground time reference” k The data length is 10,000 data points, and the time interval between data points is 60 seconds.

[0107] The selected parameters are: The following is an explanation of each parameter. The selection of x0 and y0 values ​​has no effect on the display and evaluation of the KF estimation effect, so simply select x0 = y0 = 0. The selected d value is d = 1 × 10 –18 s –1 The selected (A1, f1, A2, f2, A3, f3) values ​​are basically consistent with the measured performance of a typical satellite-borne rubidium clock, that is, the amplitudes of the periodic fluctuation terms with three periods of 6 hours, 12 hours, and 24 hours are 0.75ns, 2.5ns, and 1.5ns respectively. The value has no effect on the display and evaluation of the KF estimation effect, so simply select Selected The value is consistent with the noise characteristics of a satellite-borne rubidium clock. The value is consistent with the noise characteristics of satellite-to-earth observations, which is equivalent to a noise standard deviation of 0.5ns. In order to verify the theoretical performance of the estimated MSE, the simulation generates x k , that is, z without observation noise k . (As shown in formula (4)). It should be noted that: for the measured observation clock error, x k It is not available.

[0108] Will Substituting the values ​​into equations (5) and (6), we get the values ​​of Q and R. Run KF and calculate the observed clock error z k After preprocessing, we get and Figure 2 Draw z k and The black curve is z k , the green curve is Figure 3 Draw the following diagram according to d = 1 × 10 –18 s –1 z after deducting frequency drift k and The black curve is z k , the green curve is Figure 4 Draw out curve. Figure 5The estimated error is plotted as curve. Figure 6 The estimated error is plotted as curve.

[0109] According to the literature [1], and First, the system of equations (9), (10) and (12) is solved by substituting the values ​​of Q and R into them to obtain Ks1 = 2.41 × 10 –2 and Ks2=9.68×10 –7 Substituting the values ​​of Ks1 and Ks2 into equations (13), (14) and (15), the transfer function of the equivalent LTI system of KF after entering the steady state is expressed as:

[0110]

[0111] Figure 7 and Figure 8 The amplitude-frequency response and phase-frequency response curves of the equivalent LTI system shown in equations (20)–(22) are plotted respectively.

[0112] according to Figure 7 and Figure 8 , it is calculated that for f1, f2 and f3, the corresponding amplitude changes and phase changes are shown in the following table:

[0113] Table 1 Amplitude change and phase change

[0114]

[0115] According to formula (17), we can get and The analytical expression of the deterministic term in is:

[0116]

[0117] To evaluate the randomness term, we make z k , and The Allan deviation curve is as follows: Fig. 9 shown.

[0118] Substituting the expressions of the deterministic terms in equation (23) and equation (1) into equation (19), we can obtain the deterministic part of the estimated MSE: and Theoretical value. For the values ​​of (A1, f1, A2, f2, A3, f3) in this embodiment, the theoretical value is: and

[0119] In the given embodiment, the simultaneous equations (9), (10) and (12) are substituted into the equations with the values ​​of Q and R to obtain Ps(1,1)=6.04×10 –21 s 2 and Ps(2,2)=9.97×10 –29 s 2 , thus we get the theoretical value of the random component in the estimated MSE, that is, and

[0120] Finally, according to formula (19), the theoretical value of estimated MSE is and according to Figure 6 The curve is calculated: The test value is 5.03×10 –19 s 2 In summary, it can be considered that The experimental values ​​are basically consistent with the theoretical values.

[0121] Combine the following Figure 2 to Figure 9 The experimental results and theoretical analysis conclusions of the KF preprocessing results are evaluated, and the conclusions are as follows:

[0122] from Figure 2 , Figure 3 , Figure 5 See: z k and The curves basically overlap. The maximum deviation is less than 4ns, indicating that KF can effectively k It is estimated that And the estimation error is small. Combining the conclusions of theoretical analysis (Equation (23) and Equation (1)), due to z k and The corresponding periodic fluctuation term in the curve has amplitude and phase changes, so the estimation error There are also certain periodic fluctuations in caused by.

[0123] Combination Figure 8 And (7), the steady-state KF from z k The estimated and in z is completely filtered out k The WPM in z k WFM and RWFM in z is completely filtered out kThe WPM and WFM in the KF are changed, while the RWFM is retained. and The noise terms in can be expressed as and expressed in the form of .

[0124] for according to Figure 6 The estimated MSE experimental value calculated by the curve is basically consistent with the estimated MSE experimental value calculated according to formula (19). Furthermore, in the estimated MSE theoretical value calculated according to formula (19), the deterministic component is The value is significantly larger than the random component, that is, illustrate The steady-state tracking error of the equivalent LTI system for frequency drift, as well as the amplitude and phase changes of the periodic fluctuation term caused by the amplitude-frequency response and phase-frequency response of the equivalent LTI system have an impact on the estimated MSE.

[0125] According to the purpose of the present invention, the embodiment of the present application also proposes a performance evaluation system for applying KF to GNSS satellite clock observation clock error preprocessing, such as Fig.10 As shown, the system 10 includes:

[0126] An observation clock error acquisition module 11 is used to acquire the observation clock error of the GNSS satellite clock and the ground time reference based on different modes;

[0127] A preprocessing module 12 is used to preprocess the observed clock difference according to the classical two-state KF to obtain a time estimate and a frequency estimate containing different periodic fluctuation terms; and to determine a theoretical conclusion of the time estimate and the frequency estimate obtained by the steady-state KF estimation;

[0128] The performance evaluation module 13 is used to compare and analyze the test results with the theoretical conclusions to obtain performance evaluation results.

[0129] As a further improvement of the present invention, the observation clock error acquisition module 11 includes:

[0130] A first parameter acquisition module 111 is used to acquire parameters selected by a user when the observed clock error is generated through simulation;

[0131] The second parameter acquisition module 112 is used to obtain parameter estimates based on the atomic clock model and frequency stability analysis when the observed clock error is obtained through actual measurement, so as to determine the process noise covariance Q value and the observation noise variance R value.

[0132] As a further improvement of the present invention, the performance evaluation module 13 includes:

[0133] Theoretical conclusion generation submodule 131 is used to determine the transfer function of the equivalent LTI system after the KF enters a steady state, and obtain a theoretical conclusion based on the time estimation value and the frequency estimation value according to the transfer function;

[0134] The test result generating submodule 132 is used to generate the test results based on the KF curve, wherein the test results include the original observed clock error curve, the time estimation curve; the observed clock error curve, the time estimation curve and the frequency estimation curve after deducting the frequency drift; the estimation error curve; and the Allan deviation curve of the observed clock error curve, the time estimation curve and the frequency estimation curve.

[0135] The evaluation submodule 133 is used to compare and analyze the test results with the theoretical conclusions to obtain performance evaluation results.

[0136] The embodiment of the present application also provides an electronic device, and the electronic device described in the embodiment is a general data processing device, including a general computer hardware structure, which at least includes a processor and a memory. The processor and the memory are connected via a bus. The memory is suitable for storing instructions or programs executable by the processor. The processor can be an independent microprocessor or a collection of one or more microprocessors. Thus, the processor executes the instructions stored in the memory, thereby executing the method flow of the embodiment of the present invention as described above to realize the processing of data and the control of other devices. The bus connects the above-mentioned multiple components together, and at the same time connects the above-mentioned components to a display controller, a display device, and an input / output (I / O) device. The input / output (I / O) device can be a mouse, a keyboard, a modem, a network interface, a touch input device, a somatosensory input device, a printer, and other devices known in the art. Typically, the input / output device is connected to the system via an input / output (I / O) controller.

[0137] The memory may store software components such as an operating system, a communication module, an interaction module, and an application program. Each of the modules and applications described above corresponds to a set of executable program instructions that implement one or more functions and methods described in the embodiments of the invention.

[0138] An embodiment of the present application also provides a readable storage medium, on which a program or instruction is stored. When the program or instruction is executed by a processor, each process of the above-mentioned performance evaluation method embodiment is implemented, and the same technical effect can be achieved. To avoid repetition, it will not be repeated here.

[0139] The processor is the processor in the electronic device in the above embodiment. The readable storage medium includes a computer readable storage medium, such as a computer read-only memory ROM, a random access memory RAM, a magnetic disk or an optical disk.

[0140] The embodiment of the present application further provides a chip, the chip includes a processor and a communication interface, the communication interface is coupled to the processor, the processor is used to run programs or instructions, implement the various processes of the above-mentioned performance evaluation method embodiment, and can achieve the same technical effect, to avoid repetition, it is not repeated here. It should be understood that the chip mentioned in the embodiment of the present application can also be called a system-level chip, a system chip, a chip system or a system-on-chip chip, etc.

[0141] It should be noted that, in this article, the terms "comprise", "include" or any other variant thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise one..." do not exclude the presence of other identical elements in the process, method, article or device including the element. In addition, it should be pointed out that the scope of the methods and devices in the embodiments of the present application is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in reverse order according to the functions involved, for example, the described method may be performed in an order different from that described, and various steps may also be added, omitted, or combined. In addition, the features described with reference to certain examples may be combined in other examples.

[0142] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a computer software product, which is stored in a storage medium (such as ROM / RAM, a disk, or an optical disk), and includes a number of instructions for a terminal (which can be a mobile phone, a computer, a server, or a network device, etc.) to execute the methods of each embodiment of the present application.

[0143] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present application, ordinary technicians in this field can also make many forms without departing from the purpose of the present application and the scope of protection of the claims, all of which are within the protection of the present application.

Claims

1. The performance evaluation method of KF applied to the preprocessing of GNSS satellite clock observation clock errors is characterized by: The method comprises the following steps: Obtain the observed clock difference between GNSS satellite clock and ground time reference based on different modes; After preprocessing the observed clock error according to the classical two-state KF, a time estimate and a frequency estimate containing different periodic fluctuation terms are obtained, and a theoretical conclusion of the time estimate and the frequency estimate obtained by the steady-state KF estimation is determined; The test results are compared and analyzed with the theoretical conclusions to obtain the performance evaluation results.

2. The performance evaluation method of KF applied to GNSS satellite clock observation clock error preprocessing according to claim 1 is characterized in that: The steps of obtaining the observed clock difference between the GNSS satellite clock and the ground time reference based on different modes include: Generate observational clock errors based on simulations, or download measured observational clock errors from the IGS or IGMAS websites.

3. The performance evaluation method of KF applied to GNSS satellite clock observation clock error preprocessing according to claim 2 is characterized in that: The steps of preprocessing the observed clock error according to the classical two-state KF to obtain a time estimate and a frequency estimate containing different periodic fluctuation terms include: According to the estimation results of the time state component and frequency state component of the classical two-state KF and the Allan deviation diagram, the estimated values ​​of the atomic clock noise and observation noise intensity are obtained, and the period and amplitude of the periodic fluctuation are estimated. After determining the process noise covariance Q value and the observation noise variance R value of the two-state KF, the two-state KF is run to obtain the time estimation value and frequency estimation value containing different periodic fluctuation terms.

4. The performance evaluation method of KF applied to GNSS satellite clock observation clock error preprocessing according to claim 3 is characterized in that: The steps of determining a steady-state KF estimate to obtain a theoretical conclusion based on the time estimator and the frequency estimator include: The two-state KF entering the steady state is equivalent to three linear time-invariant systems, and the corresponding transfer functions are generated. According to the transfer functions, the theoretical conclusion based on the time estimation value and the frequency estimation value is obtained.

5. The performance evaluation method of KF applied to GNSS satellite clock observation clock error preprocessing according to claim 4 is characterized in that: The steps of comparing and analyzing the test results with the theoretical conclusions and obtaining the performance evaluation results include: The experimental results, including the original observed clock error curve, time estimation curve; the observed clock error curve, time estimation curve and frequency estimation curve after deducting frequency drift; the estimation error curve; and the Allan deviation curve of the observed clock error curve, time estimation curve and frequency estimation curve, are compared and analyzed with the theoretical conclusions to obtain the performance evaluation results of the GNSS satellite clock observation clock error preprocessing.

6. KF is applied to the performance evaluation system of GNSS satellite clock observation clock error preprocessing, characterized by: The system comprises: An observation clock error acquisition module is used to obtain the observation clock error of the GNSS satellite clock and the ground time reference based on different modes; A preprocessing module is used to preprocess the observed clock difference according to the classical two-state KF to obtain a time estimate and a frequency estimate containing different periodic fluctuation terms; and to determine a theoretical conclusion of the time estimate and the frequency estimate obtained by the steady-state KF estimation; The performance evaluation module is used to compare and analyze the test results with the theoretical conclusions to obtain the performance evaluation results.

7. The KF performance evaluation system for GNSS satellite clock observation clock error preprocessing according to claim 6 is characterized in that: The observation clock error acquisition module comprises: A first parameter acquisition module, used to acquire parameters selected by a user when the observed clock error is generated through simulation; The second parameter acquisition module is used to obtain parameter estimates based on the atomic clock model and frequency stability analysis when the observed clock error is obtained through actual measurement, so as to determine the process noise covariance Q value and the observation noise variance R value.

8. The KF performance evaluation system for GNSS satellite clock observation clock error preprocessing according to claim 7 is characterized in that: The performance evaluation module includes: A theoretical conclusion generation submodule, used for determining a transfer function of an equivalent LTI system after the KF enters a steady state, and obtaining a theoretical conclusion based on the time estimate and the frequency estimate according to the transfer function; The test result generation submodule is used to generate the test results, wherein the test results include the original observed clock error curve, the time estimation curve; the observed clock error curve, the time estimation curve and the frequency estimation curve after deducting the frequency drift; the estimation error curve; and the Allan deviation curve of the observed clock error curve, the time estimation curve and the frequency estimation curve; The evaluation submodule is used to compare and analyze the test results with the theoretical conclusions to obtain performance evaluation results.

9. An electronic device, characterized in that: include: A memory on which application programs and an operating system are stored; A processor, used for implementing the steps of applying the KF as described in any one of claims 1 to 5 to preprocess the clock errors of GNSS satellite clock observations when executing the program or instruction.

10. A readable storage medium having an application program and an operating system stored thereon, characterized in that: When the program or instruction is executed by the processor, the steps of applying the KF as described in any one of claims 1 to 5 to preprocess the clock errors of GNSS satellite clock observations are implemented.

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