CN114485724A - Method for rapidly evaluating scale nonlinear error of MEMS gyroscope - Google Patents
Method for rapidly evaluating scale nonlinear error of MEMS gyroscope Download PDFInfo
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- G—PHYSICS
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
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Abstract
The invention provides a method for rapidly evaluating scale nonlinear error of an MEMS gyroscope, which is characterized in that the MEMS gyroscope is arranged on a turntable; the turntable rotates continuously at uniform acceleration, and the speed of the turntable and the corresponding output quantity of the gyroscope are detected; and performing global fitting and piecewise regression fitting on the output quantity of the gyroscope and the rate of the turntable, and evaluating the scale nonlinear error of the gyroscope according to the maximum deviation of the global fitting and the piecewise regression fitting. The invention places the MEMS gyroscope on a rate turntable which rotates at a uniform acceleration, measures the output of the MEMS gyroscope at a constant sampling frequency and transmits the data to a receiving and processing system, thereby greatly shortening the error test and evaluation time.
Description
Technical Field
The invention relates to the technical field of gyroscopes, in particular to a method for rapidly evaluating scale nonlinear errors of an MEMS gyroscope.
Background
A gyroscope is an inertial device that can autonomously detect angular rate or angular velocity. With the development of the MEMS technology, the MEMS gyroscope has also been widely researched and applied, and has a wide development and application prospect due to its advantages of small size, light weight, low cost, and the like. Since the precision of the MEMS gyroscope is relatively low at present, the evaluation of the nonlinear error of the scale plays a very important role in improving the precision.
The scale factor is an important index of the gyroscope, and is the ratio of the output quantity of the gyroscope to the input angular rate, and is expressed by the slope of a specific straight line, and the straight line is obtained by least square fitting according to the input and output data measured in the whole input angular rate range. The scale nonlinear error is another main index reflecting the performance of the gyroscope, and refers to the ratio of the maximum deviation value and the maximum output value of the output quantity of the gyroscope relative to a least square method fitting straight line in the input angular velocity range.
The traditional scale nonlinear error testing method is to install a gyroscope on a rate turntable, then set the turntable to rotate at a plurality of different constant angular rates, acquire the output values of a plurality of gyroscopes after the turntable is stabilized, take the average value of the output values to represent the output value of the gyroscope when the turntable is input at the constant rate, and then perform fitting processing on each angular rate and the corresponding gyroscope output value, such as a least square method, a segmentation method, a nonlinear interpolation method and the like, to test the scale nonlinear error of the gyroscope. The methods need to set the working mode of the rotary table for many times, and can acquire data only when the rotary table is stable, so that the testing precision is high, but the testing time is long, the steps are more, and rapid evaluation cannot be realized.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for rapidly evaluating the scale nonlinear error of an MEMS gyroscope.
In order to achieve the above object, the present invention provides a method for rapidly evaluating a nonlinear error of a MEMS gyroscope scale, comprising:
mounting the MEMS gyroscope on a turntable;
the turntable rotates continuously at uniform acceleration, and the speed of the turntable and the corresponding output quantity of the gyroscope are detected;
and performing global fitting and piecewise regression fitting on the output quantity of the gyroscope and the rate of the turntable, and evaluating the scale nonlinear error of the gyroscope according to the maximum deviation of the global fitting and the piecewise regression fitting.
Further, the method also comprises the steps of setting the rotating speed range of the rotary table according to the range of the MEMS gyroscope, so that the range of the gyroscope is fully covered; and setting the uniform acceleration according to the required detection time.
Further, performing the global fit includes:
calculating a fitting calculation slope K and a fitting zero position F by adopting a total data least square method 0：
Calculating a global fitting function:
wherein Ω isiIs the ith turret velocity detected.
Further, the least square method calculates the fitting calculation slope K and the fitting zero position F0The method comprises the following steps:
wherein FiFor the turntable with a velocity of omegaiThe output value of the time gyroscope; k is a scaling factor; f0Is a fitting zero position; n is the number of fitting points. .
Further, piecewise regression fitting includes:
dividing all data into p segments according to the speed of the rotary table, and calculating the slope K of the mth segment by respectively adopting a least square method for the p segments of dataLmAnd fitting null F(Lm)0；
The fitting function for the mth segment is calculated as:
further, the slope K of the mth segment is calculatedLmAnd fitting null F(Lm)0The method comprises the following steps:
wherein FiFor the turntable with a velocity of omegaiThe output value of the time gyroscope; m is1Is the first data point of the mth segment, mhThe last data point of the mth segment, and h is the number of sample fitting points included in the mth segment.
Further, estimating the gyroscope scale non-linearity error from the maximum deviation of the global fit and the piecewise regression fit, comprising:
for the m-th segment
To obtain omegaL1、ΩL2…ΩLm…ΩLnRespectively substituting the global fitting function and the fitting function of the mth section to obtain a fitting value
And
calculating a deviation value
Find emMaximum value of (d): e.g. of the typemax＝max{e1,e2...en}；
And calculating the scale nonlinear error estimated value of the gyroscope as follows:
In the formula FmaxThe maximum value is output for the gyroscope in all data.
The technical scheme of the invention has the following beneficial technical effects:
(1) the invention places the MEMS gyroscope on a rate turntable which rotates at a uniform acceleration, measures the output of the MEMS gyroscope at a constant sampling frequency and transmits the data to a receiving and processing system, thereby greatly shortening the error test and evaluation time.
(2) The method carries out global fitting and segmented local fitting on data respectively, takes the mean value of two end points of each segmented interval as an input rate and brings the mean value into a fitting function to obtain a global fitting value and a segmented fitting value, then obtains the maximum difference value of two different fitting values, evaluates the gyroscope scale nonlinear error, and is simple in calculation and short in time consumption.
Drawings
FIG. 1 is a flow chart of fast estimation of nonlinear error of a MEMS gyroscope;
FIG. 2 is a schematic of a global fit;
FIG. 3 is a schematic of a piecewise fit.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
The MEMS gyroscope scale nonlinear error rapid evaluation flow based on uniform acceleration continuous rotation, as shown in FIG. 1, comprises the following steps:
(1) rate table state settings.
And setting the magnitude of the uniform acceleration and the rotating speed range of the rate turntable according to the evaluated MEMS gyroscope measuring range and the evaluated time. The rotation speed range covers the range of the MEMS gyroscope.
The traditional test mode needs at least 2 hours, but the mode of the invention can finish the test in the process of one-time uniform acceleration, and the uniform acceleration is set according to the required detection time to finish the test quickly. The method is particularly suitable for scenes which do not need high-precision calibration but have higher requirements on calibration speed.
(2) And (4) installing the MEMS gyroscope on the rotary table, and starting the rotary table and the gyroscope.
(3) The rotary table rotates continuously at uniform acceleration, and the speed of the rotary table and the corresponding output quantity of the gyroscope are detected.
When the rotary table rotates continuously with uniform acceleration, the MEMS gyroscope can automatically detect the angular rate of the rotary table, and the data acquisition system connected with the rotary table can acquire the rate of the rotary table at different moments and the corresponding gyroscope output quantity. The output of the MEMS gyroscope is measured at a constant sampling frequency, corresponding to the angular rate of the turntable.
(4) And carrying out global fitting and piecewise regression fitting on the output quantity of the gyroscope and the rate of the turntable, and evaluating the scale nonlinear error of the gyroscope according to the maximum deviation of the global fitting and the piecewise regression fitting.
And acquiring output values of the rate turntable and the gyroscope by using a data acquisition system, obtaining a model of the input-output relation of the gyroscope through global and segmented least square fitting, and finally, integrating the global and segmented models to evaluate the nonlinear error of the gyroscope. Taking a global least squares fit as an example:
the output-to-input relation typical model of the MEMS gyroscope can be expressed as
Fi＝KΩi+F0+εi
FiFor turntable with speed of omegaiThe output value of the time gyroscope; k is a scaling factor; omegaiInputting the speed of the turntable, namely the angular speed; f0Is a fitting zero position; epsiloniIs the fitting error.
K, F can be obtained by least squares0:
Where n is the number of fitting points. .
K, F is obtained0Then a fitting function can be obtained:
piecewise regression fitting includes:
the test curve is segmented by the equal-step angular velocity, the test curve is set to be divided into p segments, and the p segments are respectively subjected to local fitting like the aforementioned least square method, so that p fitting functions can be obtained, wherein the fitting function expression of the mth segment (m is 1,2, … n) interval is as follows:
Calculating the slope K of the mth segmentLmAnd fitting null F(Lm)0The method comprises the following steps:
wherein FiFor the turntable with a velocity of omegaiThe output value of the time gyroscope; m is1Is the first data point of the mth segment, mhThe last data point of the mth segment, and h is the number of sample fitting points included in the mth segment.
Estimating gyroscope scale non-linearity errors from the maximum deviation of the global fit and the piecewise regression fit, comprising:
let the mth angular rate measurement interval be [ m ]l,mh]Taking the average value of the two end points as the input angular velocity omegaLmI.e. omegaLm＝(ml+mh) And/2, performing the processing on the n sections to obtain n input angular velocities, wherein the n input angular velocities are respectively omegaL1、ΩL2…ΩLm…ΩLnWill be omegaL1Substituting a global fitting function
Fitting a function to the first interval
Fitting values can be obtained
And
the same can be obtained
By dividing each segment
And
making a difference and taking the absolute value, i.e.
Find the maximum value of e:
emax＝max{e1,e2...en}
the scale nonlinear error estimate for the gyroscope is:
in the formula KnEvaluation of scaled non-linearity errors for a gyroscope, FmaxAnd outputting the maximum value for the gyroscope in the full test section.
The scale nonlinear error is a main index reflecting the performance of the gyroscope, and represents the performance quality of the gyroscope. The number of the segmented intervals can be increased according to requirements, and the scale nonlinear error evaluation value is improved.
In summary, the invention provides a method for rapidly evaluating the scale nonlinear error of an MEMS gyroscope, which comprises the steps of mounting the MEMS gyroscope on a turntable; the turntable rotates continuously in a uniformly accelerated manner, and the speed of the turntable and the corresponding output quantity of the gyroscope are detected; and carrying out global fitting and piecewise regression fitting on the output quantity of the gyroscope and the rate of the turntable, and evaluating the scale nonlinear error of the gyroscope according to the maximum deviation of the global fitting and the piecewise regression fitting. According to the invention, the MEMS gyroscope is placed on the rate turntable which uniformly accelerates to rotate, the output of the MEMS gyroscope is measured at a constant sampling frequency, and the data of the output is transmitted to the receiving and processing system, so that the error test and evaluation time is greatly shortened.
It should be understood that the above-described embodiments of the present invention are merely illustrative of or explaining the principles of the invention and are not to be construed as limiting the invention. Therefore, any modifications, equivalents, improvements and the like which are made without departing from the spirit and scope of the present invention shall be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundary of the appended claims, or the equivalents of such scope and boundary.
Claims (7)
1. A method for rapidly evaluating a nonlinear error of a MEMS gyroscope scale is characterized by comprising the following steps:
mounting the MEMS gyroscope on a turntable;
the turntable rotates continuously at uniform acceleration, and the speed of the turntable and the corresponding output quantity of the gyroscope are detected;
and performing global fitting and piecewise regression fitting on the output quantity of the gyroscope and the rate of the turntable, and evaluating the scale nonlinear error of the gyroscope according to the maximum deviation of the global fitting and the piecewise regression fitting.
2. The method for rapidly assessing the nonlinear error in the scaling of the MEMS gyroscope of claim 1, further comprising setting a range of the rotation speed of the turntable according to the range of the MEMS gyroscope so that the range of the gyroscope is fully covered; and setting the uniform acceleration according to the required detection time.
3. The method for rapid estimation of MEMS gyroscope scale nonlinearity errors according to claim 1 or 2, wherein performing a global fit comprises:
calculating a fitting calculation slope K and a fitting zero position F by adopting a total data least square method0：
Calculating a global fitting function:
wherein omegaiIs the ith turret velocity detected.
4. The method of claim 3 wherein the least squares method calculates the fit calculation slope K and the fit zero F 0The method comprises the following steps:
wherein FiFor the turntable with a velocity of omegaiThe output value of the time gyroscope;k is a scaling factor; f0Is a fitting zero position; n is the number of fitting points.
5. The method of claim 3, wherein piecewise regression fitting comprises:
dividing all data into p segments according to the speed of the rotary table, and calculating the slope K of the mth segment by respectively adopting a least square method for the p segments of dataLmAnd fitting null F(Lm)0；
The fitting function for the mth segment is calculated as:
6. the MEMS gyroscope scale nonlinear error rapid assessment method of claim 5, characterized in that the slope K of the mth segment is calculatedLmAnd fitting null F(Lm)0The method comprises the following steps:
wherein FiFor the turntable with a velocity of omegaiThe output value of the time gyroscope; m is1Is the first data point of the mth segment, mhThe last data point of the mth segment, and h is the number of sample fitting points included in the mth segment.
7. The method of claim 6, wherein estimating the gyroscope scale non-linearity error from the maximum deviation of the global fit and the piecewise regression fit comprises:
for the m-th segment
To obtain omegaL1、ΩL2…ΩLm…ΩLnRespectively substituting the global fitting function and the fitting function of the mth section to obtain a fitting value 
And with
Calculating a deviation value
Find emMaximum value of (c): e.g. of a cylindermax＝max{e1,e2...en}；
And calculating the scale nonlinear error estimated value of the gyroscope as follows:
in the formula FmaxThe maximum value is output for the gyroscope in the whole data.
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