UT1 fusion method based on EAM data set

Abstract

The invention provides a UT1 fusion method based on an EAM data set, and the method employs a Kalman fusion algorithm to fuse angular momentum data EAM based on the field of geophysics and VLBI and GNSS data based on the field of space geodetic survey, and obtains high-precision, high-continuity and high-stability UT1 data. Compared with the prior art, the method has the advantages that angular momentum data EAM based on the field of geophysics is fused, the angular momentum data EAM is corrected to correct the deviation with a GNSS LOD data set, and finally, the angular momentum data EAM is fused with the GNSS LOD data set and a VLBI UT1 data set by using a Kalman fusion algorithm. Compared with the prior art, the fusion precision is improved, and the robustness of the fusion method is higher.

Description

Technical Field

[0001] The invention belongs to the field of time-space science and technology, and specifically relates to a UT1 fusion method based on an EAM data set. Background Art

[0002] Universal Time (UT1) is a time defined based on the rotation of the Earth. It is an important component of national standard time, a parameter that describes the rotation state of the Earth in space, an important component of the Earth Orientation Parameter (EOP), and the core parameter for realizing the coordinate transformation between the celestial reference frame and the terrestrial reference frame. It is an indispensable parameter for satellite navigation, inertial navigation and deep space exploration.

[0003] At present, the authoritative UT1 data in the world are mainly provided by the International Earth Rotation and Reference System Service (IERS), including rapid / forecast products (Bulletin A, finals.daily), monthly reports (Bulletin B) and long-term results (C04, C01), etc. Among them, the rapid product is obtained by the fusion of very long baseline interferometry (VLBI) and global satellite navigation (GNSS), and the accuracy is relatively low; the forecast product uses the atmospheric angular momentum (AAM) data set; the monthly report and long-term results are obtained by VLBI, GNSS, satellite laser ranging (SLR), laser lunar ranging (LLR), satellite Doppler orbit determination and positioning system (DORIS) and other technologies. Among the above products, the C04 product has the highest accuracy, but the real-time performance is poor, and it lags behind by one month. It is usually only used for data set evaluation and as a historical data set for EOP forecast.

[0004] A large number of studies have shown that there is a high correlation between interannual and short-term LOD and effective angular momentum (EAM), and EAM plays an important role in UT1 forecasting. EAM consists of AAM, ocean angular momentum (OAM), hydrosphere angular momentum (HAM), sea level angular momentum (SLAM), etc. At present, the accuracy of the atmospheric and ocean angular momentum model based on global meteorological and oceanographic monitoring data has reached an accuracy level comparable to that of the earth's rotation. Therefore, with the improvement of EAM's measurement accuracy and its important role in UT1 forecasting, studying the improvement of UT1 fusion accuracy by EAM data will become a new hot topic.

[0005] The internationally used Vondrak combination method uses VLBI and GNSS data sets to fuse, which can only obtain specific fusion values, but cannot calculate formal errors. Although the Vondrak combination method can combine the measurement accuracy of VLBI with the measurement continuity of GNSS to obtain a continuous and stable UT1 sequence, this method is limited to VLBI data and GNSS data, and the fusion accuracy needs to be improved. In addition, this fusion method cannot calculate formal errors, and can only evaluate the accuracy of its fusion results by subtracting with other standard files. Therefore, this fusion method lacks robustness. Summary of the invention

[0006] In order to solve the above problems existing in the prior art, the present invention provides a UT1 fusion method based on EAM data set. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0007] A UT1 fusion method based on the EAM dataset includes:

[0008] S100, sampling to obtain EAM dataset, VLBI UT1 dataset and GNSS LOD dataset;

[0009] S200, performing Fourier transform on the GNSS LOD data set to obtain periodic terms and system deviations;

[0010] S300, deducting the tidal data in the VLBI UT1 dataset and the GNSS LOD dataset to obtain VLBI UT1R data and GNSS LODR data;

[0011] S400, using the GNSS LODR data, correcting the EAM data set to obtain EAMLODR ​​data;

[0012] S500, based on the periodic term and the system deviation, fusing the VLBI UT1R data, the GNSS LODR data and the EAM LODR data through a Kalman fusion algorithm to obtain a fused UT1R data set;

[0013] S600, performing tidal compensation on the fused UT1R dataset to obtain a UT1 dataset.

[0014] Beneficial effects:

[0015] The present invention proposes a UT1 fusion method based on an EAM data set. The method uses a Kalman fusion algorithm to fuse angular momentum data EAM based on the geophysical field with VLBI and GNSS data based on the space geodetic field to obtain high-precision, high-continuity, and high-stability UT1 data. Compared with the prior art, the present invention fuses the angular momentum data EAM based on the geophysical field, and corrects it to correct the deviation from the GNSS LOD data set, and finally fuses it with the GNSS LOD data set and the VLBI UT1 data set using the Kalman fusion algorithm. Compared with the prior art, the present invention improves the fusion accuracy and the fusion method is more robust.

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of a flow chart of a UT1 fusion method based on an EAM data set provided by the present invention;

[0018] Figure 2 It is a flow chart of a UT1 fusion example based on an EAM data set provided by the present invention;

[0019] Figure 3 is a flow chart of EAM data set correction provided by the present invention;

[0020] Figure 4 It is a WHU LOD spectrum analysis effect diagram provided by the present invention;

[0021] Figure 5 This is an effect diagram of the EAM data set correction provided by the present invention;

[0022] Figure 6 is a difference map between the fused UT1 data set provided by the present invention and C04 UT1;

[0023] Figure 7 The present invention provides Figure 5 Box plot of . DETAILED DESCRIPTION

[0024] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0025] The idea of ​​the present invention is to fuse three different data sets, namely, an EAM data set, a VLBI UT1 data set, and a GNSS LOD data set. In the fusion process, firstly, the EAM data set is constructed, and the AAM, OAM, HAM, and SLAM are converted into the EAM data set; then, the GNSS LOD data set is Fourier transformed, and the periodic term and the system deviation of the LOD data set are analyzed; next, the GNSS LOD and VLBI UT1 data are tidal deducted to obtain the GNSS LODR data set and the VLBI UT1R data set, and the EAM data set is corrected by using the GNSS LODR data set to obtain the system difference EAM LODR data set; finally, the EAMLODR ​​data set, the GNSS LODR data set, and the VLBI UT1R data set are fused by using the Kalman fusion algorithm to obtain the fused UT1R data set; and the fused UT1R data set is tidal compensated to obtain the UT1 data set.

[0026] Combination Figure 1 and Figure 2 The present invention provides a UT1 fusion method based on the EAM data set, including:

[0027] S100, sampling to obtain EAM dataset, VLBI UT1 dataset and GNSS LOD dataset;

[0028] This step includes S110, sampling atmospheric angular momentum (AAM), ocean angular momentum (OAM), terrestrial hydrosphere angular momentum (HAM) and sea level angular momentum (SLAM), and summing them up to obtain EAM, and forming an EAM data set; the sampling interval of EAM is 1 day. The EAM data set includes EAM, and the EAM represents effective angular momentum; S120, downloading the GNSS LOD data set and the VLBI UT1 data set from the website.

[0029] It should be noted that the sampling interval of AAM data and OAM data is 3 hours, while the sampling interval of HAM data and SLAM data is 24 hours. Therefore, it is necessary to convert the data with a 3-hour interval into the EAM data with a 1-day interval by weighting.

[0030] S200, performing Fourier transform on the GNSS LOD data set to obtain periodic terms and system deviations;

[0031] In order to better model the Kalman fusion method, it is necessary to perform Fourier transform on the GNSS LOD data set to determine the periodicity and systematic deviation of the data set. When performing spectrum analysis on data segments of different lengths, the periodic term components and sizes obtained will be slightly different. Therefore, when performing analysis, long-span data segments should be selected as much as possible for spectrum analysis to obtain reliable systematic deviations and periodic components.

[0032] S300, deducting the tidal data in the VLBI UT1 dataset and the GNSS LOD dataset to obtain VLBI UT1R data and GNSS LODR data;

[0033] In this step, the VLBI UT1 dataset and the GNSSLOD dataset can be tidally corrected according to the empirical model given by the IERS protocol to obtain the VLBI UT1R data and the GNSSLODR data after deducting the solid tidal terms.

[0034] S400, using the GNSS LODR data, correcting the EAM data set to obtain EAMLODR ​​data;

[0035] Although the EAM dataset and the GNSS LOD dataset have a very high correlation, there is still a large deviation between the EAM dataset and the GNSS LOD dataset, so they need to be corrected.

[0036] In an optional embodiment of the present invention, reference Figure 3 , S400 includes:

[0037] S410, converting the GNSS LODR data into GAM using Liouville equation; the Liouville equation is expressed as:

[0038]

[0039] In the formula, Ψ 1 is GAM, Ω is the average Earth rotation angular velocity, LODR represents the GNSS LODR sequence, UT1R is the sequence formed by VLBIUT1R data, Ψ 2 It is EAM, used to realize the conversion between EAM and LODR sequence.

[0040] S420, subtracting the GAM from the EAM to obtain GAM-EAM;

[0041] In order to fit the GAM-EAM data more accurately, the least squares method of annual segmentation is adopted. The least squares fitting is expressed by the formula:

[0042]

[0043] In the formula, f GAM-EAM (t) represents the least squares fitting function of the difference between GAM and EAM, t represents the time variable in days, a 0 , a 1 , a 2 , a 3 , a 4 , a 5 , a 6 , a 7 are the linear terms of the least squares fit, c i and d i Represent the periodic parameters, T i Represents the cycle length, n represents the number of cycles, and i represents the independent variable.

[0044] S430, fitting the long-term trend term of the GAM-EAM using least squares, and adding the fitted long-term trend term to the angular momentum of the EAM data set to obtain EAM LODR data.

[0045] S500, based on the periodic term and the system deviation, fusing the VLBI UT1R data, the GNSS LODR data and the EAMLODR ​​data through a Kalman fusion algorithm to obtain a fused UT1R data set;

[0046] In an optional implementation manner of the present invention, S500 includes:

[0047] S510, establishing observation equations using VLBI UT1R data, GNSS LODR data, and EAM LODR data respectively; the observation equations are expressed as follows:

[0048] Z(k)=HX(k)+V(k);

[0049] Among them, the observation equations of VLBI UT1R data, GNSS LODR data and EAM LODR data are expressed as follows:

[0050] Z v (k) = H v X v (k)+V v (k)

[0051] Z g (k) = H g X g (k)+V g (k)

[0052] Z e (k) = H e Xe (k)+V e (k)

[0053] In the formula, H is the observation matrix, and the observation matrices corresponding to the three types of data are H v , H g , H e , respectively expressed as:

[0054] H v =[1,0,0,1,0,0,0,0,0,0,0]

[0055] H g =[0,1,0,0,1,0,0,0,0,0,0]

[0056] H e =[0,0,1,0,1,0,0,0,0,0,0]

[0057] V(k) is the observation noise at time k. The observation noises corresponding to the three types of data are V v (k), V g (k), V e (k), the state equations of the three types of data are expressed as: v (k), X g (k), X e (k), X(k) is the general expression of the state equation, expressed as:

[0058] X(k)=FX(k-1)+W(k-1);

[0059] In the formula,

[0060]

[0061] W(k-1) is the uncorrelated white noise with zero mean and variance Q at time k-1; M u represents the system deviation pre-evaluated using the VLBIUT1 dataset, M l Represents the system deviation obtained by analyzing and processing the GNSS LOD data set, A, B, C, D, E, F f represent the estimated coefficients of the periodic component, a and 1-a are the weights of GNSS LODR data and EAM-LODRE in the Kalman combination, the prior value of a is the error of EAM LODR data / (the error of GNSS LODR data + the error of EAM LODR data), β 1 ,β 2 ,β 3 ,β 4 ,β 5 ,β6 It is a periodic function obtained by analyzing and processing the GNSS LOD data set. The error of GNSSLODR data is a statistical value, which is the standard deviation of the difference between the least squares fitting residuals of GNSS LODR and the least squares fitting residuals of C04LODR during the period from 2019 to 2023; the error of EAM LODR data is the standard deviation of the difference between the least squares fitting residuals of EAM LODR data and the least squares fitting residuals of C04 LODR during the period from 2019 to 2023. It should be explained that since EAM data has no formal error, the standard deviation of the difference between the least squares fitting residuals of C04 LODR is used to determine the prior value of the weight. After the initial value is given, the covariance matrix is ​​used to iteratively adjust a.

[0062] S520, using the observation equation to establish a Kalman prediction equation; the Kalman prediction equation formula is expressed as:

[0063] X(k / k)=X(k / k-1)+K(k)Z(k)-HX(k / k-1);

[0064] X(k / k-1)=FX(k-1 / k-1);

[0065] In the formula, X(k / k) represents the final state estimate of Kalman at time k; X(k / k-1) represents the state prediction value of Kalman at time k, and K(k) is the Kalman gain, which is expressed as:

[0066]

[0067] Where R is the covariance matrix of observation noise, Q is the covariance matrix of state noise, H is the observation matrix, and P(k / k-1) represents the covariance matrix of X(k / k-1), which is expressed as:

[0068] P(k / k-1)=FP(k-1 / k-1)F T +Q;

[0069] P(k / k)=(1-K(k)H)P(k / k-1)

[0070] In the formula, P(k / k) represents the covariance matrix of X(k / k), and Q is the covariance matrix of the state noise. P(k / k) is a symmetric matrix whose diagonal elements are the variance of each state estimate, representing the expectation of the square of the error between the true value and the filtered value, and its square root is the uncertainty of the Kalman filter estimate. The covariance matrix is ​​used to derive the Kalman gain, calculate the Kalman error, and calculate the weight a.

[0071] S530, using the Kalman prediction equation and the Kalman correction equation to fuse the VLBI UT1R data, the GNSSLODR data and the EAM LODR data to obtain a fused UT1R data set.

[0072] In this step, the VLBI UT1R data, GNSS LODR data and EAM LODR data are input into the Kalman prediction equation to obtain the final state estimation value of the Kalman at time k, and the final state estimation value is used as the fused UT1R data set.

[0073] It is worth noting that the present invention uses Kalman to perform fusion. In the fusion process, the same parameters in the same Kalman combination are used to constrain the processing of the three data mutually, and finally output the final state estimation value of the three data, that is, X v (k / k),X g (k / k) and X e (k / k).

[0074] S600, performing tidal compensation on the fused UT1R dataset to obtain a UT1 dataset.

[0075] After S600, the present invention further includes evaluating the UT1 data set obtained in S600.

[0076] The technical effects of the present invention are described below with actual experimental data.

[0077] 1. Dataset Preparation

[0078] The UT1 measured data set observed and solved by the National Time Service Center (NTSC) of the Chinese Academy of Sciences based on the VLBI system was selected; the LOD data set solved by Wuhan University (WHU) based on the GNSS system was selected; the AAM, OAM, HAM, and SLAM data sets released by the German Geoscience Center (GFZ) were selected and combined into an EAM data set with a daily interval.

[0079] 2. Spectrum Analysis

[0080] The spectral analysis of the WHU_LOD data from 2019 to 2023 was performed using Fourier transform to obtain its periodic terms and systematic deviations, as follows Figure 4 shown.

[0081] Figure 4 The horizontal axis is frequency, indicating the number of occurrences in a year, and the vertical axis is amplitude, in microseconds. The left figure is the FFT transform of WHU LOD from 2019 to 2023, and the right figure is the periodic amplitude of the difference between the LOD of C04 and WHU. Figure 4From the left figure, we can see that LOD has obvious periodic components, such as short-period 9.13, 13.66, 27.55, etc. Figure 4 The right figure clearly shows that WHU has an obvious DC component at zero frequency, that is, a system deviation of 20.17μs.

[0082] 3. EAM correction

[0083] The WHU LOD series after deducting the tidal term from 2019 to 2023 is converted into GAM using the axial Liouville equation, and subtracted from EAM to obtain GAM-EAM; then, the long-term trend term of GAM-EAM is fitted using the least squares method; finally, the fitted long-term trend term is added to EAM to obtain the corrected EAM (C_EAM), as shown in Figure 5 shown. Figure 5 The blue, orange, and green colors in the middle left image are the EAM dataset, the WHU LODR-converted GAM dataset, and the EAM LODR dataset, respectively; Figure 4 The blue and green colors in the middle right figure are the difference between the WHU LODR-converted GAM dataset and the EAM, and the difference between the WHU LODR-converted GAM dataset and the corrected EAM.

[0084] 4. Kalman Fusion

[0085] The corrected EAM data set is converted into EAM LODR data through the Liouville equation, and the VLBI UT1 and WHU LOD are deducted by tidal terms to obtain VLBI UT1R and WHU LODR data after tidal terms are deducted. The three types of data are input into the constructed Kalman fusion model, and Kalman fusion is performed to obtain the fused UT1R data set. Finally, the UT1R data set is tidally compensated to obtain the UT1 data set.

[0086] 5. Evaluation

[0087] The UT1 data after Kalma fusion were evaluated with the IERS C04 dataset. Figure 6 and Figure 7 shown. Figure 6 The middle red NTSC-WE represents the difference between UT1 and C04 UT1 after Kalman fusion and tidal compensation using NTSC's VLBI UT1R and WHU's LODR and the corrected EAM LODR; the green NTSC-W represents the difference between UT1 and C04 UT1 after Kalman fusion and tidal compensation using NTSC's VLBI UT1R and WHU's LODR; the light blue NTSC represents the difference between NTSC UT1 and C04 UT1; Figure 7 Box plot of the difference.

[0088] Table 1 UT1 fusion data statistics

[0089]

[0090] In Table 1, the standard deviation of NTSC UT1 is 102.65μs, the standard deviation of UT1 after the three data fusion is 43.21μs, and the standard deviation after the fusion without using the EAM data set is 53.48μs. The median and maximum values ​​after fusion are smaller than the original sequence. After the fusion algorithm, a more continuous and stable UT1 sequence can be obtained, and the formal error is consistent with the standard deviation, indicating that the fusion algorithm has high robustness and reliability. Among them, the accuracy of the EAM data set is improved by 57.90% after fusion, and the accuracy of the EAM data set is improved by 47.90% without using the EAM data set. The fusion result is more stable after using the EAM data set. The above analysis shows that the UT1 fusion method based on the EAM data set is a feasible and effective method, which can significantly improve the accuracy and robustness of UT1.

[0091] It is worth noting that the terms "first" and "second" in the present invention are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0092] Although the present application is described herein in conjunction with various embodiments, in the process of implementing the claimed application, those skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality of components or steps.

[0093] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A UT1 fusion method based on EAM dataset, characterized in that: include: S100, sampling to obtain EAM dataset, VLBI UT1 dataset and GNSS LOD dataset; S200, performing Fourier transform on the GNSS LOD data set to obtain periodic terms and system deviations; S300, deducting the tidal data in the VLBI UT1 dataset and the GNSS LOD dataset to obtain VLBI UT1R data and GNSS LODR data; S400, using the GNSS LODR data, correcting the EAM data set to obtain EAM LODR data; S500, based on the periodic term and the system deviation, fusing the VLBI UT1R data, the GNSS LODR data and the EAMLODR ​​data through a Kalman fusion algorithm to obtain a fused UT1R data set; S600, performing tidal compensation on the fused UT1R dataset to obtain a UT1 dataset.

2. The UT1 fusion method based on the EAM data set according to claim 1 is characterized in that: S100 includes: S110, sampling atmospheric angular momentum, ocean angular momentum, terrestrial hydrosphere angular momentum and sea level angular momentum, and summing them to obtain EAM, and forming an EAM data set; the sampling interval of EAM is 1 day, the EAM data set includes EAM, and the EAM represents effective angular momentum; S120, download the GNSS LOD dataset and VLBI UT1 dataset from the website.

3. The UT1 fusion method based on EAM data set according to claim 1 is characterized in that: S400 includes: S410, converting GNSS LODR data to GAM using Liouville equation; S420, subtracting the GAM from the EAM to obtain GAM-EAM; S430, fitting the long-term trend term of the GAM-EAM using least squares, and adding the fitted long-term trend term to the angular momentum of the EAM data set to obtain EAM LODR data.

4. The UT1 fusion method based on EAM data set according to claim 3 is characterized in that: The Liouville equation is expressed in the formula: Where Ψ1 is GAM, Ω is the average Earth rotation angular velocity, LODR represents the GNSS LODR sequence, UT1R is the sequence formed by VLBI UT1R data, and Ψ2 is EAM, which is used to realize the conversion between EAM and LODR sequences.

5. The UT1 fusion method based on EAM data set according to claim 3 is characterized in that: The least squares fit is expressed by the formula: In the formula, f GAM-EAM (t) represents the least squares fitting function of the difference between GAM and EAM, t represents time, a0, a1, a2, a3, a4, a5, a6, a7 are the linear terms of the least squares fitting, c i and d i Represent the periodic parameters, T i Represents the cycle length, n represents the number of cycles, and i represents the independent variable.

6. The UT1 fusion method based on EAM data set according to claim 1, characterized in that: S500 includes: S510, establishing observation equations using VLBI UT1R data, GNSS LODR data, and EAM LODR data respectively; S520, establishing a Kalman prediction equation using the observation equation; S530: Using the Kalman prediction equation, the VLBI UT1R data, the GNSS LODR data and the EAM LODR data are fused to obtain a fused UT1R data set.

7. The UT1 fusion method based on EAM data set according to claim 6 is characterized in that: S530 includes: The VLBI UT1R data, GNSS LODR data and EAM LODR data are input into the Kalman prediction equation to obtain the final state estimation value of the Kalman at time k, and the final state estimation value is used as the fused UT1R data set.

8. The UT1 fusion method based on EAM data set according to claim 6 is characterized in that: The observation equation is expressed as: Z(k)=HX(k)+V(k); Where H is the observation matrix, V(k) is the observation noise at time k, and X(k) is the state equation, expressed as: X(k)=FX(k-1)+W(k-1); In the formula, W(k-1) is the uncorrelated white noise with zero mean and variance Q at time k-1; M u represents the systematic bias pre-evaluated using the VLBI UT1 dataset, M l Represents the system deviation obtained by analyzing and processing the GNSS LOD data set, A, B, C, D, E, F f represent the estimated coefficients of the periodic component respectively, a and 1-a are the weights of GNSS LODR data and EAM-LODRE in the Kalman combination respectively, the prior value of a is the error of EAM LODR data / (error of GNSS LODR data + error of EAM LODR data), β1, β2, β3, β4, β5, β6 are the periodic term functions obtained by analyzing and processing the GNSS LOD data set.

9. The UT1 fusion method based on EAM data set according to claim 8, characterized in that: The Kalman prediction equation is expressed as: X(k / k)=X(k / k-1)+K(k)Z(k)-HX(k / k-1); X(k / k-1)=FX(k-1 / k-1); Where X(k / k-1) represents the Kalman state prediction value at time k, X(k / k) represents the final state estimate of Kalman at time k; K(k) is the Kalman gain, expressed as: Where R is the covariance matrix of observation noise, Q is the covariance matrix of state noise, H is the observation matrix, and P(k / k-1) represents the covariance matrix of X(k / k-1), which is expressed as: P(k / k-1)=FP(k-1 / k-1)F T +Q; P(k / k)=(1-K(k)H)P(k / k-1); In the formula, P(k / k) represents the covariance matrix of X(k / k), and Q is the covariance matrix of state noise. P(k / k) is a symmetric matrix, and its diagonal elements are the variance of each state estimate, representing the expectation of the square of the error between the true value and the filtered value, and its square root is the uncertainty of the Kalman filter estimate.

10. The UT1 fusion method based on EAM data set according to claim 1, characterized in that: After S600, the UT1 fusion method based on the EAM data set further includes: The UT1 data set obtained in S600 is evaluated.

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