Method and system for eliminating interference effect of electrostatic accelerometer

Abstract

The present invention provides a method and system for eliminating the interference effect of an electrostatic accelerometer, belonging to the measurement technical field of electrostatic accelerometers. The specific method is as follows: comparing the satellite angular acceleration signal measured by the rotational degree of freedom of the electrostatic accelerometer with the satellite angular acceleration obtained by observing data through a star sensor or an inertial measurement unit; if there is a large angular acceleration difference between the two, and there is a strong correlation between the angular acceleration differences of different degrees of freedom, extracting the common-mode signal between the angular acceleration signal differences, and then obtaining the basic mode; on this basis, further calculating the correlation coefficient between the linear acceleration signal and the basic mode, and giving the proportion of the basic mode in the linear acceleration signal; finally, eliminating the basic mode corresponding to the proportional coefficient in the linear acceleration signal measured by the electrostatic accelerometer. This method is beneficial to improving the elimination of the common interference effect of the electrostatic accelerometer and improving the effectiveness, accuracy and measurement precision of the linear acceleration observation.

Description

Technical Field

[0001] The present invention belongs to the technical field of measurement of electrostatic accelerometers, and more specifically, relates to a method and system for eliminating interference effects of electrostatic accelerometers. Background Art

[0002] Electrostatic accelerometers are one of the key payloads for satellite gravity measurement, and their measurement data is of great significance for research such as gravity field inversion, atmospheric density model determination, and precise satellite orbit determination.

[0003] Electrostatic accelerometers can simultaneously measure accelerations in six degrees of freedom (three translational degrees of freedom and three rotational degrees of freedom). In satellite gravity measurement, electrostatic accelerometers are used to measure non-conservative forces acting on the satellite. Therefore, the measurement of the three translational degrees of freedom is more concerned, and their measurement errors directly affect the accuracy of the recovery of the Earth's gravity field.

[0004] Due to the interference of satellite platform environments such as vibration, temperature, and magnetic field, there are certain errors in the measurement of non-conservative forces by electrostatic accelerometers, which affect the accuracy of gravity field inversion. For gravity field inversion, high-precision measurement information of electrostatic accelerometers is crucial. Therefore, it is necessary to adopt appropriate methods to suppress interference effects. Summary of the Invention

[0005] Aiming at the defects of the prior art, the purpose of the present invention is to provide a method and system for eliminating interference effects of electrostatic accelerometers, aiming to solve the problem that the existing electrostatic accelerometers have poor accuracy in recovering the Earth's gravity field due to measurement errors in the three translational degrees of freedom during satellite gravity measurement.

[0006] To achieve the above purpose, the present invention provides a method for eliminating interference effects of electrostatic accelerometers, including the following steps:

[0007] Compare the satellite angular acceleration signal measured by the rotational degrees of freedom of the electrostatic accelerometer with the satellite angular acceleration obtained by observing data through a star sensor or an inertial measurement unit. If there is an angular acceleration difference exceeding a preset range between the two, obtain the corresponding difference of the angular acceleration signal;

[0008] Calculate the correlation coefficients between the pairwise corresponding angular acceleration signal differences of the three rotational degrees of freedom. If there is a linear relationship exceeding a first preset correlation coefficient between the angular acceleration signal differences corresponding to at least two rotational degrees of freedom, extract the common-mode signal between the angular acceleration signal differences corresponding to the rotational degrees of freedom, and perform normalization processing on the common-mode signal to obtain the basic mode of the interference effect;

[0009] Calculate the correlation coefficients between the linear acceleration signals measured in three translational degrees of freedom and the fundamental mode respectively. If the correlation coefficients between the linear acceleration signals and the fundamental mode present a linear relationship exceeding the second preset correlation coefficient, calculate the proportion of the fundamental mode in the linear acceleration signals;

[0010] Eliminate the corresponding proportion of the fundamental mode in the linear acceleration signals measured by the electrostatic accelerometer to achieve the elimination of the interference effect.

[0011] Further preferably, the calculation formula for the correlation coefficient between the differences of the angular acceleration signals corresponding to two rotational degrees of freedom is:

[0012]

[0013] Where, β x , β y respectively represent the differences of the angular acceleration signals corresponding to two rotational degrees of freedom; r(β x , β y ) is the correlation coefficient between β x and β y ; cov(β x , β y ) is the covariance between β x and β y ; var(β x ), var(β y ) are the variances of β x , β y respectively.

[0014] Further preferably, the extraction method of the fundamental mode is:

[0015] For the differences of k angular acceleration signals, calculate the common mode signal β CM ;

[0016] Normalize the common mode signal β CM to obtain the fundamental mode e0;

[0017] Where, the common mode signal β CM is:

[0018]

[0019] Where, represents the pseudo-inverse matrix of any angular acceleration signal difference β1 among the differences of k angular acceleration signals; β j represents the jth angular acceleration signal.

[0020] Further preferably, the calculation method for the correlation coefficient between the linear acceleration signals measured in three translational degrees of freedom and the fundamental mode is:

[0021]

[0022] Among them, a i represents the linear acceleration signal of the translational degree of freedom, and r(a i , e0) is the correlation coefficient between a i and e0, and cov(a i , e0) is the covariance between a i and e0, and var(a i ) and var(e0) are the variances of a i and e0 respectively.

[0023] Further preferably, the calculation method of the proportion of the basic mode in the linear acceleration signal is:

[0024]

[0025] Among them, a i,sim represents the linear acceleration obtained by simulating the non-conservative force model for the i-th degree of freedom. The non-conservative force model includes the solar radiation pressure, atmospheric drag, and earth radiation pressure received by the spacecraft; a i,out is the satellite linear acceleration signal measured by the electrostatic accelerometer.

[0026] On the other hand, the present invention provides a system for eliminating the interference effect of an electrostatic accelerometer, including:

[0027] A first subtractor, configured to compare the satellite angular acceleration signal measured by the rotational degree of freedom of the electrostatic accelerometer with the satellite angular acceleration obtained from the observation data of the star sensor or the inertial measurement unit. If there is an angular acceleration difference exceeding a preset range between the two, the corresponding difference of the angular acceleration signal is obtained;

[0028] A first correlation coefficient calculation unit, configured to calculate the correlation coefficient between the differences of the angular acceleration signals corresponding to each pair of the three rotational degrees of freedom;

[0029] A first discriminator, configured to determine whether there is a linear relationship between the differences of the angular acceleration signals corresponding to at least two rotational degrees of freedom that exceeds a first preset correlation coefficient;

[0030] A common-mode signal extractor, configured to extract the common-mode signal between the differences of the angular acceleration signals corresponding to the rotational degrees of freedom;

[0031] A normalization processor, configured to perform normalization processing on the common-mode signal to obtain the basic mode of the interference effect;

[0032] A second correlation coefficient calculation unit, configured to calculate the correlation coefficient between the linear acceleration signals measured by the three translational degrees of freedom and the basic mode respectively;

[0033] The second discriminator is used to determine whether the correlation coefficient between the linear acceleration signal and the basic mode exceeds a second preset correlation coefficient;

[0034] The proportional coefficient calculation unit is used to calculate the proportion of the basic mode in the linear acceleration signal;

[0035] The second subtractor is used to eliminate the corresponding proportion of the basic mode in the linear acceleration signal measured by the electrostatic accelerometer, so as to eliminate the interference effect.

[0036] Further preferably, the calculation formula for the correlation coefficient between the angular acceleration signal differences corresponding to two rotational degrees of freedom is:

[0037]

[0038] where β x , β y respectively represent the angular acceleration signal differences corresponding to two rotational degrees of freedom; r(β x , β y ) is the correlation coefficient between β x and β y ; cov(β x , β y ) is the covariance between β x and β y ; var(β x ), var(β y ) are the variances of β x , β y respectively.

[0039] Further preferably, the method for extracting the basic mode is:

[0040] For k angular acceleration signal differences, calculate the common mode signal β CM ;

[0041] Normalize the common mode signal β CM to obtain the basic mode e0;

[0042] where the common mode signal β CM is:

[0043]

[0044] where represents the pseudo-inverse matrix of any angular acceleration signal difference β1 among the k angular acceleration signal differences; β j represents the jth angular acceleration signal.

[0045] Further preferably, the calculation method for the correlation coefficient between the linear acceleration signals measured by three translational degrees of freedom and the basic mode is:

[0046]

[0047] Among them, a i represents the linear acceleration signal of the translational degree of freedom, and r(a i , e0) is the correlation coefficient between a i and e0, and cov(a i , e0) is the covariance between a i and e0, and var(a i ) and var(e0) are the variances of a i and e0 respectively.

[0048] Further preferably, the calculation method of the proportionality coefficient of the basic mode in the linear acceleration signal is as follows:

[0049]

[0050] Among them, a i,sim represents the linear acceleration obtained by simulating the non-conservative force model for the i-th degree of freedom. The non-conservative force model includes the solar radiation pressure, atmospheric drag, and earth radiation pressure received by the spacecraft; a i,out is the satellite linear acceleration signal measured by the electrostatic accelerometer.

[0051] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the following beneficial effects are obtained:

[0052] The present invention provides a method and system for eliminating the interference effect of an electrostatic accelerometer. By comparing the angular acceleration signal measured by the accelerometer itself with the angular motion observed by a star sensor or an inertial measurement unit of the spacecraft platform, etc., the basic mode of the interference effect is identified and extracted. On this basis, the interference effect in the linear acceleration signal is eliminated, and data processing basically does not need to consider the influence of time correction, etc., which is beneficial to improving the elimination accuracy of the common interference effect of the electrostatic accelerometer and improving the effectiveness, accuracy, and measurement accuracy of linear acceleration observation. This method is applicable to improving the signals of high-precision multi-degree-of-freedom synchronous observation accelerometers. Description of the Drawings

[0053] Figure 1 is the flowchart for extracting the interference effect mode of the electrostatic accelerometer provided by the embodiment of the present invention;

[0054] Figure 2 is the flowchart for eliminating the interference effect of the electrostatic accelerometer provided by the embodiment of the present invention. Detailed Embodiment

[0055] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0056] The satellite acceleration signal a measured by the electrostatic accelerometer i,out can be regarded as being composed of the basic signal a i,b , the interference effect a i,e and the instrument noise a i,n ; among them, the basic signal a i,b is a non-conservative force signal or a satellite angular acceleration signal; in the translational degree of freedom, the basic signal is a non-conservative force signal; in the rotational degree of freedom, the basic signal is a satellite angular acceleration signal; a i,out = a i,b + a i,e + a i,n ; where i represents each degree of freedom; if there are interference effects such as those from spacecraft platform vibration, temperature, and electromagnetic field changes, the six-degree-of-freedom outputs of the accelerometer will in principle have the same response, with simultaneity and a basically consistent response mode, which is called the basic mode in the present invention; for the interference effect, the accelerometer interference effect can be expressed as a i,e = C i ·e0, different degrees of freedom have the same basic mode e0, but the coefficient C i is different; the common interference effect can be extracted from the angular acceleration observation signal, thereby improving the observation accuracy of the linear acceleration.

[0057] Embodiment

[0058] On the one hand, as Figure 1 shown, the present invention provides a method for eliminating the interference effect of an electrostatic accelerometer, including the following steps:

[0059] S1: Compare the satellite angular acceleration signal measured by the rotational degree of freedom of the electrostatic accelerometer (ACC) with the satellite angular acceleration obtained from the observation data (angle, angular velocity) of the star sensor (SCA) or inertial measurement unit (IMU) carried by the spacecraft platform. If there is a large angular acceleration difference between the two, obtain the angular acceleration signal difference of the three rotational degrees of freedom;

[0060] S2: Calculate the correlation coefficient between the angular acceleration signals of any two of the three rotational degrees of freedom. If there is a high linear relationship between two of the angular acceleration signals, it is considered that there is interference from the same source, and then extract the common mode signal between the angular acceleration signal differences of the three rotational degrees of freedom, that is, the basic mode e0 in the interference effect;

[0061] The calculation formula for the correlation coefficient between the differences in angular acceleration signals corresponding to the two-by-two rotational degrees of freedom is as follows:

[0062]

[0063] Among them, β x and β y respectively represent the differences in angular acceleration signals corresponding to two rotational degrees of freedom; r(β x , β y ) is the correlation coefficient between β x and β y ; cov(β x , β y ) is the covariance between β x and β y ; var(β x ), var(β y ) are the variances of β x and β y respectively.

[0064] The method for extracting the basic mode is as follows:

[0065] For the differences in k angular acceleration signals, calculate the common-mode signal β CM ;

[0066] Normalize the common-mode signal β CM to obtain the basic mode e0;

[0067] Among them, the common-mode signal β CM is:

[0068]

[0069] Among them, represents the pseudo-inverse matrix of any one of the differences in k angular acceleration signals, β1; β j represents the jth angular acceleration signal.

[0070] As Figure 2 shown, the method for eliminating the interference effect of the electrostatic accelerometer is as follows:

[0071] S3: Calculate the correlation coefficients between the linear acceleration signals measured by the three translational degrees of freedom of the electrostatic accelerometer and the basic mode e0 of the interference effect respectively. If there is a highly linear relationship between the linear acceleration signal and the basic mode e0, it is considered that there is interference from the same source as the basic mode e0 in the translational degree of freedom, and then calculate the proportionality coefficient C i of the basic mode e0 in the linear acceleration signal;

[0072] More specifically, the calculation method for the correlation coefficients between the linear acceleration signals measured by the three translational degrees of freedom and the basic mode is as follows:

[0073]

[0074] Among them, a i represents the linear acceleration signal of the translational degree of freedom, and r(a i , e0) is the correlation coefficient between a i and e0, and cov(a i , e0) is the covariance between a i and e0. var(a i ) and var(e0) are the variances of a i and e0 respectively.

[0075] The calculation method of the proportion of the basic mode in the linear acceleration signal is as follows:

[0076]

[0077] Among them, a i,sim represents the linear acceleration obtained by simulating the non-conservative force model for the i-th degree of freedom. The non-conservative force model includes the solar radiation pressure, atmospheric drag, and earth radiation pressure acting on the spacecraft; a i,out is the satellite linear acceleration signal measured by the electrostatic accelerometer.

[0078] For the elimination of the interference effect, the corresponding proportion C i of the basic mode e0 in the linear acceleration signal measured by the electrostatic acceleration is eliminated to achieve the elimination of the interference effect.

[0079] On the other hand, the present invention provides a system for eliminating the interference effect of an electrostatic accelerometer, including:

[0080] A first subtractor, configured to compare the satellite angular acceleration signal measured by the rotational degree of freedom of the electrostatic accelerometer with the satellite angular acceleration obtained by observing data through a star sensor or an inertial measurement unit. If there is a large angular acceleration difference between the two, the corresponding difference of the angular acceleration signal is obtained;

[0081] A first correlation coefficient calculation unit, configured to calculate the correlation coefficient between the differences of the angular acceleration signals corresponding to each pair of the three rotational degrees of freedom;

[0082] A first discriminator, configured to determine whether there is a linear relationship between the differences of the angular acceleration signals corresponding to at least two rotational degrees of freedom that exceeds the first preset correlation coefficient;

[0083] A common-mode signal extractor, configured to extract the common-mode signal between the differences of the angular acceleration signals corresponding to the rotational degrees of freedom;

[0084] A normalization processor, configured to perform normalization processing on the common-mode signal to obtain the basic mode of the interference effect;

[0085] The second correlation coefficient calculation unit is configured to calculate the correlation coefficients between the linear acceleration signals measured in three translational degrees of freedom and the basic mode respectively;

[0086] The second discriminator is configured to determine whether the correlation coefficient between the linear acceleration signal and the basic mode exceeds a second preset correlation coefficient;

[0087] The proportional coefficient calculation unit is configured to calculate the proportion of the basic mode in the linear acceleration signal;

[0088] The second subtractor is configured to eliminate the basic mode corresponding to the proportional coefficient in the linear acceleration signal measured by the electrostatic accelerometer, so as to eliminate the interference effect.

[0089] Further preferably, the calculation formula for the correlation coefficient between the differences of the angular acceleration signals corresponding to two rotational degrees of freedom is:

[0090]

[0091] where β x , β y respectively represent the differences of the angular acceleration signals corresponding to two rotational degrees of freedom; r(β x , β y ) is the correlation coefficient between β x and β y ; cov(β x , β y ) is the covariance between β x and β y ; var(β x ), var(β y ) are the variances of β x , β y respectively.

[0092] Further preferably, the extraction method of the basic mode is:

[0093] For k differences of angular acceleration signals, calculate the common mode signal β CM ;

[0094] Normalize the common mode signal β CM to obtain the basic mode e0;

[0095] where the common mode signal β CM is:

[0096]

[0097] where, represents the pseudo-inverse matrix of any angular acceleration signal difference β1 among the k angular acceleration signal differences; β j represents the jth angular acceleration signal.

[0098] Further preferably, the calculation method of the correlation coefficient between the linear acceleration signals measured by the three translational degrees of freedom and the fundamental mode is as follows:

[0099]

[0100] where a i represents the linear acceleration signal of the translational degree of freedom, and r(a i , e0) is the correlation coefficient between a i and e0, cov(a i , e0) is the covariance between a i and e0, and var(a i ) and var(e0) are the variances of a i and e0 respectively.

[0101] Further preferably, the calculation method of the proportion of the fundamental mode in the linear acceleration signal is as follows:

[0102]

[0103] where a i,sim represents the linear acceleration obtained by simulating the non-conservative force model for the i-th degree of freedom. The non-conservative force model includes the solar radiation pressure, atmospheric drag, and earth radiation pressure acting on the spacecraft; a i,out is the satellite linear acceleration signal measured by the electrostatic accelerometer.

[0104] Compared with the prior art, the present invention identifies and extracts the fundamental mode of the interference effect by comparing the angular acceleration signals measured by the electrostatic accelerometer with the angular acceleration signals observed by star sensors or inertial measurement units carried on the spacecraft platform, etc. Then, on this basis, the interference effect in the linear acceleration signal is eliminated. During the data processing process, the influence of time scale inconsistency, etc. hardly needs to be considered, which is beneficial to improving the elimination accuracy of the common interference effect in the electrostatic accelerometer and improving the effectiveness, accuracy, and measurement accuracy of the linear acceleration observation. This method is applicable to improving the signals of high-precision multi-degree-of-freedom synchronous observation accelerometers.

[0105] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for eliminating the interference effect of an electrostatic accelerometer, characterized in that, It includes the following steps: Compare the satellite angular acceleration signal measured by the electrostatic accelerometer's rotational degree of freedom with the satellite angular acceleration obtained from the observation data of the star sensor or inertial measurement unit. If there is an angular acceleration difference exceeding the preset range between the two, obtain the corresponding difference of the angular acceleration signal; Calculate the correlation coefficients between the differences of the angular acceleration signals corresponding to every two of the three rotational degrees of freedom. If there is a linear relationship exceeding the first preset correlation coefficient between the differences of the angular acceleration signals corresponding to at least two rotational degrees of freedom, extract the common-mode signal between the differences of the angular acceleration signals corresponding to the rotational degrees of freedom, and perform normalization processing on the common-mode signal to obtain the basic mode of the interference effect; Calculate the correlation coefficients between the linear acceleration signals measured by the three translational degrees of freedom and the basic mode respectively. If the correlation coefficient between the linear acceleration signal and the basic mode exceeds the second preset correlation coefficient, calculate the proportion of the basic mode in the linear acceleration signal; Eliminate the corresponding proportion of the basic mode from the linear acceleration signal measured by the electrostatic accelerometer to eliminate the interference effect.

2. The elimination method according to claim 1, characterized in that, The calculation formula for the correlation coefficient between the differences of the angular acceleration signals corresponding to every two rotational degrees of freedom is: Among them, β x and β y respectively represent the differences in angular acceleration signals corresponding to two rotational degrees of freedom; r(β x , β y ) is the correlation coefficient between β x and β y ; cov(β x , β y ) is the covariance between β x and β y ; var(β x ), var(β y ) are the variances of β x and β y respectively.

3. The elimination method according to claim 2, characterized in that, The method for extracting the basic mode is: Calculate the common-mode signal β using the difference of k angular acceleration signals CM ; For the common-mode signal β CM perform normalization processing to obtain the basic mode e0; Among them, the common-mode signal β CM is: Among them, represents the pseudo-inverse matrix of any one of the k angular acceleration signal differences, β1; β j represents the j-th angular acceleration signal.

4. The elimination method according to claim 3, wherein The calculation method for the correlation coefficient between the linear acceleration signals measured by the three translational degrees of freedom and the basic mode is: Among them, a i represents the linear acceleration signal of the translational degree of freedom, and r(a i , e0) is the correlation coefficient between a i and e0, and cov(a i , e0) is the covariance between a i and e0, and var(a i ) and var(e0) are the variances of a i and e0 respectively.

5. The elimination method according to claim 4, characterized in that, The calculation method for the proportion of the basic mode in the linear acceleration signal is: Among them, a i,sim represents the linear acceleration obtained by simulating the i-degree of freedom according to the non-conservative force model, and the non-conservative force model includes the solar radiation pressure, atmospheric drag, and earth radiation pressure received by the spacecraft; a i,out is the satellite linear acceleration signal measured by the electrostatic accelerometer.

6. An elimination system for the interference effect of an electrostatic accelerometer, characterized in that, It includes: A first subtractor, which is used to compare the satellite angular acceleration signal measured by the electrostatic accelerometer's rotational degree of freedom with the satellite angular acceleration obtained from the observation data of the star sensor or inertial measurement unit. If there is an angular acceleration difference exceeding the preset range between the two, obtain the corresponding difference of the angular acceleration signal; A first correlation coefficient calculation unit, which is used to calculate the correlation coefficients between the differences of the angular acceleration signals corresponding to every two of the three rotational degrees of freedom; A first discriminator, which is used to determine whether there is a linear relationship exceeding the first preset correlation coefficient between the differences of the angular acceleration signals corresponding to at least two rotational degrees of freedom; A common-mode signal extractor, which is used to extract the common-mode signal between the differences of the angular acceleration signals corresponding to the rotational degrees of freedom; A normalization processor, which is used to perform normalization processing on the common-mode signal to obtain the basic mode of the interference effect; A second correlation coefficient calculation unit, which is used to calculate the correlation coefficients between the linear acceleration signals measured by the three translational degrees of freedom and the basic mode respectively; A second discriminator, which is used to determine whether the correlation coefficient between the linear acceleration signal and the basic mode exceeds the second preset correlation coefficient; A proportional coefficient calculation unit, which is used to calculate the proportion of the basic mode in the linear acceleration signal; A second subtractor, which is used to eliminate the corresponding proportion of the basic mode from the linear acceleration signal measured by the electrostatic accelerometer to eliminate the interference effect.

7. The elimination system according to claim 6, wherein The calculation formula for the correlation coefficient between the differences of the angular acceleration signals corresponding to every two rotational degrees of freedom is: Among them, β x and β y respectively represent the differences in angular acceleration signals corresponding to two rotational degrees of freedom; r(β x , β y ) is the correlation coefficient between β x and β y ; cov(β x , β y ) is the covariance between β x and β y ; var(β x ), var(β y ) are the variances of β x and β y respectively.

8. The elimination system according to claim 7, characterized in that The method for extracting the basic mode is: Using the differences of k angular acceleration signals to calculate the common-mode signal β CM ; Normalize the common-mode signal β CM to obtain the basic mode e0; Among them, the common-mode signal β CM is as follows: Among them, represents the pseudoinverse matrix of any one of the k angular acceleration signal differences, β1; β j represents the jth angular acceleration signal.

9. The elimination system according to claim 8, wherein The calculation method for the correlation coefficient between the linear acceleration signals measured by the three translational degrees of freedom and the basic mode is: Among them, a i represents the linear acceleration signal of the translational degree of freedom, and r(a i , e0) is the correlation coefficient between a i and e0, and cov(a i , e0) is the covariance between a i and e0. var(a i ) and var(e0) are the variances of a i and e0 respectively.

10. The elimination system according to claim 9, wherein The calculation method for the proportion of the basic mode in the linear acceleration signal is: where a i,sim represents the linear acceleration obtained by simulating the non-conservative force model for the i-th degree of freedom, and the non-conservative force model includes the solar radiation pressure, atmospheric drag, and Earth's radiation pressure acting on the spacecraft; a i,out is the satellite linear acceleration signal measured by the electrostatic accelerometer.

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