CN108732380A - A kind of trigonometric function temperature-compensation method - Google Patents
A kind of trigonometric function temperature-compensation method Download PDFInfo
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- CN108732380A CN108732380A CN201810560713.1A CN201810560713A CN108732380A CN 108732380 A CN108732380 A CN 108732380A CN 201810560713 A CN201810560713 A CN 201810560713A CN 108732380 A CN108732380 A CN 108732380A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
- G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
- G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
- G06F7/544—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices for evaluating functions by calculation
- G06F7/548—Trigonometric functions; Co-ordinate transformations
Abstract
The invention discloses a kind of trigonometric function temperature-compensation method, the method includes：To needing the system of temperature-compensating to carry out warm circulation experiment in incubator；Experimental data is pre-processed, N groups wait for fitting data；Fitting data point, which is fitted, to be waited for N groups with trigonometric function, obtains trigonometric function expression formula：Initial data is compensated using trigonometric function expression formula and is compensated result；The fitting of a polynomial effect of high exponent number can be reached by realizing, and also can overcome the disadvantages that double-exponential function to complex curve fitting effect poor, while the technique effect that calculation amount is small.
Description
Technical field
The present invention relates to temperature-compensation method fields, and in particular, to a kind of trigonometric function temperature-compensation method.
Background technology
With the development of MEMS technology, inertial sensor becomes most widely used MEMS in the past few years
One of device, wherein micro-acceleration gauge have become the inertial device for being widely used in measuring object acceleration.But environment temperature
The variation of degree is one of the most important reason that mems accelerometer generates error, and it causes the performance of mems accelerometer big
The reduction of amplitude.
Existing temperature compensation software method is to use polynomial function mostly：
Such as y=a0+a1×x+a2×x2+a3×x3..., since polynomial function calculates simply, may be used linearly most
Therefore small square law fitting is widely used.However there is also certain limitations for polynomial function, since temperature curve has
Nonlinear feature needs to use higher order when in face of more complicated temperature curve.Therefore parameter is more, calculates
Amount increases.Neural network and Kalman filtering scheduling algorithm can also effectively compensate temperature curve, but algorithm comparison
Complexity is only limitted to theoretical research, it is difficult to be integrated into sensor chip.
Invention content
The present invention provides a kind of trigonometric function temperature-compensation methods, solve existing temperature-compensation method calculation amount
Greatly, complicated technical problem is calculated, the fitting of a polynomial effect that can reach high exponent number is realized, also can overcome the disadvantages that double-exponential function
To complex curve fitting effect poor, while the technique effect that calculation amount is small.
For achieving the above object, this application provides a kind of trigonometric function temperature-compensation method, the method includes：
To needing the system of temperature-compensating to carry out warm circulation experiment in incubator；
Experimental data is pre-processed, N groups wait for fitting data；
Fitting data point, which is fitted, to be waited for N groups with trigonometric function, obtains trigonometric function expression formula：
Y=a0+a1×sin(x)+a2×cos(x)；Wherein, N is the positive integer more than or equal to 2, a0For linear coefficient；a1For
Sinusoidal coefficients；a2For cosine coefficient；X is function argument, that is, corresponding temperature value；
Initial data is compensated using trigonometric function expression formula and is compensated result.
Further, this method waits for that fitting data point is fitted using trigonometric function least square method to N groups, specific to wrap
It includes：
Initial data is pre-processed, scatter plot (X is obtainedi Yi), XiFor temperature voltage value, YiFor output voltage values；
Determine fitting function expression formula：Y=a0+a1×sin(x)+a2×cos(x)；
Using linear least square design factor；
1. needing to construct one group of coefficient now, it is set to meet minimum with the extent of deviation of raw data points, i.e.,
2. a pair function is replaced, as follows
3. I be coefficient a0,a1,...,anThe function of many variables, so the above problem, which can be converted to, solves function of many variables I
The problem of extreme value.The necessary condition that extreme value is solved according to the function of many variables, seeks partial derivative, making it equal to 0 can obtain to each coefficient
4. normal equation system can be obtained after abbreviation
By data (Xi Yi) bring normal equation system into, normal equation system is solved, coefficient and function expression are obtained.
Further, carrying out pretreatment to data includes：Using wavelet analysis carry out noise reduction process, smoothing processing, etc. between
Every sampling abnormal value elimination.
One or more technical solution provided by the present application, has at least the following technical effects or advantages：
The Taylor expansion of trigonometric function in the application has infinite exponent number, when coping with nonlinear temperature curve,
The fitting of a polynomial effect that high exponent number can be reached also can overcome the disadvantages that double-exponential function to complex curve fitting effect poor.
Expression formula coefficient ratio in this method is less, only a0, a1, a2Three coefficients, are counted using least square method
It calculates, calculation amount is smaller.
The compensation circuit easy of integration in mems accelerometer is designed if necessary, can use cordic algorithm or is looked into
Look for the methods of table design compensation circuit module, it is only necessary to which addition and subtraction iteration can calculate trigonometric function, and hardware resource is few.
Description of the drawings
Attached drawing described herein is used for providing further understanding the embodiment of the present invention, constitutes one of the application
Point, do not constitute the restriction to the embodiment of the present invention；
Fig. 1 is the application intermediate cam function temperature-compensation method block schematic illustration；
Fig. 2 is the application intermediate cam function least square method flow diagram；
Fig. 3 is the application intermediate cam Function Fitting effect diagram；
Fig. 4 is effect temperature compensation schematic diagram in the application.
Specific implementation mode
The present invention provides a kind of trigonometric function temperature-compensation methods, solve existing temperature-compensation method calculation amount
Greatly, complicated technical problem is calculated, the fitting of a polynomial effect that can reach high exponent number is realized, also can overcome the disadvantages that double-exponential function
To complex curve fitting effect poor, while the technique effect that calculation amount is small.
To better understand the objects, features and advantages of the present invention, below in conjunction with the accompanying drawings and specific real
Mode is applied the present invention is further described in detail.It should be noted that in the case where not conflicting mutually, the application's
Feature in embodiment and embodiment can be combined with each other.
Many details are elaborated in the following description to facilitate a thorough understanding of the present invention, still, the present invention may be used also
Implemented with being different from the other modes being described herein in range using other, therefore, protection scope of the present invention is not by under
The limitation of specific embodiment disclosed in face.
A kind of trigonometric function temperature-compensation method, flow diagram is as shown in Figure 1, detailed process is as follows：
To needing the system of temperature-compensating to carry out warm circulation experiment in incubator；
Experimental data is pre-processed, including the use of wavelet analysis, smoothing processing, equal interval sampling；
N group data points are fitted with trigonometric function, obtain trigonometric function expression formula；
Initial data is compensated using trigonometric function expression formula and is compensated result.
Trigonometric function fitting algorithm flow chart is as shown in Figure 2.
Algorithm includes trigonometric function model y=a0+a1×sin(x)+a2×cos(x)。
Fitting coefficient is a0, a1, a2。
Backoff algorithm mainly uses least square method, obtains pretreated N groups first and waits for fitting data (Xi, Yi) (i=
1,2,3,4 ... N)；Secondly fitting function expression formula, that is, y=a is determined0+a1×sin(x)+a2×cos(x)；Next it calculates
To the system of linear equations about coefficient, i.e. normal equation system；Finally bring N groups data (Xi, Yi) (i=1,2,3,4 ... N) into method
Equation group solves coefficient and obtains function expression.
A kind of compensation system realization may be used in specific embodiment：
MEMS sensor containing temperature sensor is subjected to warm circulation experiment, obtains the temperature in certain temperature range
Degree-output data.
Data are used into MATLAB processing, and is obtained sampling at equal intervals and obtains the data point for needing to be fitted.
It determines trigonometric function and is fitted using least square method, obtain fitting coefficient.
A compensation circuit being integrated into MEMS sensor is designed, cordic algorithm or lookup may be used in trigonometric function
The methods of table is realized, rom packing coefficients are used in compensation circuit, are directly compensated to output.
The present invention is used and is compensated to the temperature curve of mems accelerometer using the function feature of trigonometric function, due to
Final compensation result (following Fig. 3, shown in 4), fitting precision reaches RSME=4.7024E-05, Rsquare=0.9947, compensation
Temperature curve peak-to-peak value reduces an order of magnitude or more afterwards.
Although preferred embodiments of the present invention have been described, it is created once a person skilled in the art knows basic
Property concept, then additional changes and modifications may be made to these embodiments.So it includes excellent that the following claims are intended to be interpreted as
It selects embodiment and falls into all change and modification of the scope of the invention.
Obviously, various changes and modifications can be made to the invention without departing from essence of the invention by those skilled in the art
God and range.In this way, if these modifications and changes of the present invention belongs to the range of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to include these modifications and variations.
Claims (3)
1. a kind of trigonometric function temperature-compensation method, which is characterized in that the method includes：
To needing the system of temperature-compensating to carry out warm circulation experiment in incubator；
Experimental data is pre-processed, N groups wait for fitting data；
Fitting data point, which is fitted, to be waited for N groups with trigonometric function, obtains trigonometric function expression formula：
Y=a0+a1×sin(x)+a2×cos(x)；Wherein, N is the positive integer more than or equal to 2, a0For linear coefficient；a1For sine
Coefficient；a2For cosine coefficient；X is function argument, that is, corresponding temperature value；
Initial data is compensated using trigonometric function expression formula and is compensated result.
2. trigonometric function temperature-compensation method according to claim 1, which is characterized in that this method uses trigonometric function most
Small square law waits for that fitting data point is fitted to N groups, specifically includes：
Initial data is pre-processed, scatter plot (X is obtainedi Yi), XiFor temperature voltage value, YiFor output voltage values；
Determine fitting function expression formula：Y=a0+a1×sin(x)+a2×cos(x)；
The system of linear equations about coefficient is calculated；
By data (Xi Yi) bring system of linear equations into, system of linear equations is solved, coefficient and function expression are obtained.
3. trigonometric function temperature-compensation method according to claim 1 or 2, which is characterized in that pre-processed to data
Including：Utilize wavelet analysis, smoothing processing, equal interval sampling.
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Cited By (2)
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| CN111271810A (en) * | 2020-01-08 | 2020-06-12 | 宁波奥克斯电气股份有限公司 | Air conditioner control method, control system, air conditioner and computer storage medium |
| CN113063964A (en) * | 2021-03-23 | 2021-07-02 | 西安微电子技术研究所 | Temperature compensation type quartz flexible accelerometer servo circuit and quartz flexible accelerometer |
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