CN103472259A - Method for silicon micro-resonant type accelerometer temperature compensation - Google Patents

Abstract

The invention discloses a method for silicon micro-resonant type accelerometer temperature compensation. The method comprises the steps that firstly, under the condition that the accelerated speed does not exist, a singular change relation curve of a direct current drive voltage maintaining the constant resonant amplitude of a resonant beam and the resonant frequency of the resonant beam is calibrated; secondly, under the condition that the accelerated speed exists, the direct current drive voltage and the resonant frequency are measured; thirdly, combined with the previously obtained relation curve, the resonant frequency caused by the temperature is subtracted from the resonant frequency obtained through measurement and the temperature compensation operation is completed. According to the method for silicon micro-resonant type accelerometer temperature compensation, the defect that large deviation of a compensation result is caused by the non-determinacy of temperature field distribution in a traditional direct temperature compensation method and heat conduction delay is overcome, and real-time and high-accuracy temperature compensation is achieved. According to the method, the cost of temperature compensation is low, sensors do not need to be additionally arranged, and temperature compensation can be achieved through existing circuit devices.

Description

A kind of silicon micro-resonance type accelerometer temperature compensation

Technical field

The present invention relates to a kind of silicon micro-resonance type accelerometer temperature compensation, relate in particular to and a kind ofly utilize accelerometer self drive voltage signal but not directly measure temperature signal and silicon micro-resonance type accelerometer is carried out to the method for temperature compensation.

Background technology

Silicon micro-resonance type accelerometer is based on MEMS technique, and two resonance beam that are forced to flexural vibrations of take are the power sensing unit, the poor size that characterizes suffered acceleration of vibration frequency of two resonance beam (resonance beam 1 and resonance beam 2).Because the elastic modulus temperature influence of resonance beam, and the silicon micro element is different from the substrate thermal expansivity, so silicon micro-resonance type accelerometer measuring accuracy temperature influence is remarkable.For the impact of compensation temperature on measurement result, common method is measure the environment temperature of silicon micro element and set up model of temperature compensation by outside temperature probe.Due to uncertainty and the heat conducting time delay that temperature field distributes, this compensation method poor effect and lag-effect is arranged.

Summary of the invention

Goal of the invention: in order to overcome the deficiencies in the prior art, the invention provides a kind of accelerometer self drive voltage signal of utilizing and silicon micro-resonance type accelerometer is carried out to the method for temperature compensation, by backoff algorithm, the accelerometer resonance frequency is exported and carried out accurate compensation in real time.

Technical scheme: for achieving the above object, the technical solution used in the present invention is:

A kind of silicon micro-resonance type accelerometer temperature compensation, comprise the steps:

(1) under without the acceleration signal input condition, in ℃ variation range of environment temperature-40～60, resonance frequency and driving DC voltage to silicon micro-resonance type accelerometer are measured, and obtain the temperature variant monotonic relationshi curve of resonance frequency and the temperature variant monotonic relationshi curve of driving DC voltage of resonance beam 1 and resonance beam 2; Described silicon micro-resonance type accelerometer has two resonance beam, is designated as respectively resonance beam 1 and resonance beam 2;

(2), under without the acceleration signal input condition, demarcate the monotone variation relation curve that resonance beam 1 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency; Now the resonance frequency changing value of resonance beam 1 is the deviation frequency that temperature causes;

(3), under without the acceleration signal input condition, demarcate the monotone variation relation curve that resonance beam 2 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency; Now the resonance frequency changing value of resonance beam 2 is the deviation frequency that temperature causes;

(4) use described silicon micro-resonance type accelerometer to carry out acceleration analysis, obtain the resonance frequency f of resonance beam 1 ₁resonance frequency f with resonance beam 2 ₂, and the driving DC voltage V of resonance beam 1 now _d1driving DC voltage V with resonance beam 2 _d2;

(5) because the voltage signal antijamming capability is low, driving DC voltage is subject to noise, therefore to the driving DC voltage V of resonance beam 1 and resonance beam 2 _d1and V _d2carry out filtering, the driving DC voltage after filtering noise is respectively

with the monotone variation curve obtained according to step (3) obtains driving DC voltage

corresponding temperature drift frequency f _t1, the monotone variation curve obtained according to step (4) obtains driving DC voltage

corresponding temperature drift frequency f _t2;

(6) resonance frequency of resonance beam is the frequency f caused by acceleration signal _awith the frequency shift (FS) f caused by temperature _ttwo parts addition forms, that is:

f ₁=f _a1+f _T1

f ₂=f _a2+f _T2

Resonance beam 1 after the accounting temperature compensation and the difference on the frequency of resonance beam 2 are:

f _a1-f _a2=(f ₁-f _T1)-(f ₂-f _T2)=(f ₁-f ₂)-(f _T1-f _T2)

(7) calculate measured acceleration signal a _ccfor:

a _cc=(f _a1-f _a2)/S _F

S wherein _fconstant multiplier for accelerometer.

Described step (1) specifically comprises the steps:

(11), in ℃ variation range of environment temperature-40～60, demarcate s temperature spot;

(12) under without the acceleration signal input condition, test as follows: resonance frequency and the driving DC voltage of the resonance frequency of collection resonance beam 1 and driving DC voltage, collection resonance beam 2 on each temperature spot;

(13) experiment of repeated execution of steps (12), the experiment number of accumulative total execution step (12) is t time;

(14) resonance frequency under each temperature spot and driving DC voltage are made even and are:

$f_{1i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{f}_{1i,j},f_{2i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{f}_{2i,j}$

$V_{d1i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{V}_{d1i,j},V_{d2i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{V}_{d2i,j}$

Wherein, i=1,2 ..., s, j=1,2 ..., t; f _{1i, j}for the resonance frequency that resonance beam 1 records during the j time repeated experiments on i temperature spot, f _{2i, j}for the resonance frequency that resonance beam 2 records during the j time repeated experiments on i temperature spot, V _{d1i, j}for the driving DC voltage that resonance beam 1 records during the j time repeated experiments on i temperature spot, V _{d2i, j}the driving DC voltage recorded during the j time repeated experiments on i temperature spot for resonance beam 2;

(15), according to the corresponding relation of resonance frequency mean value, driving DC voltage mean value and temperature, obtain the temperature variant monotonic relationshi curve of resonance frequency and the temperature variant monotonic relationshi curve of driving DC voltage of resonance beam 1 and resonance beam 2.

Described step (2) specifically comprises the steps:

(21) to resonance beam 1, the average resonance frequencies under each temperature spot and average driving DC voltage data are used the cubic polynomial model of fit to carry out matching, obtain the monotone variation relation curve that resonance beam 1 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency:

f _T1=a ₀+a ₁V _d1+a ₂V _d1 ²+a ₃V _d1 ³

(22) use the principle of least square, obtain the coefficient a of above formula _n, n=0,1,2,3.

Described step (3) specifically comprises the steps:

(31) to resonance beam 2, the average resonance frequencies under each temperature spot and average driving DC voltage data are used the cubic polynomial model of fit to carry out matching, obtain the monotone variation relation curve that resonance beam 2 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency:

f _T2=b ₀+b ₁V _d2+b ₂V _d2 ²+b ₃V _d2 ³

(32) use the principle of least square, obtain the coefficient b of above formula _n, n=0,1,2,3.

The described measurement data V to driving DC voltage _dcarry out filtering to obtain

concrete grammar be:

At first, set up as drag:

${\hat{V}}_d\left(k\right)=a{\hat{V}}_d(k-1)+\mathrm{\ω}(k-1)$

$V_d\left(k\right)=c{\hat{V}}_d\left(k\right)+\mathrm{\υ}\left(k\right)$

Same driving DC voltage under same temperature spot is carried out to m actual value and measure, k=1,2 ..., m; V _d(k) be the driving DC voltage actual measured value measured for the k time,

for V _d(k) filtered value, ω (k) is the dynamic noise while measuring for the k time, υ (k) is the measurement noise of introducing in the k time measuring process, a, c is measuring system and the definite parameter of method of testing;

Secondly, by V _d(k) be expressed as V _d,k, will

be expressed as

variance yields according to following formula statistics dynamic noise ω (k) and measurement noise υ (k)

with

${\mathrm{\σ}}_{\mathrm{\ω}}^2=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{({\hat{V}}_{d,k}-{\stackrel{\stackrel{\‾}{^}}{V}}_d)}^2,{\stackrel{\stackrel{\‾}{^}}{V}}_d=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\hat{V}}_{d,k}$

${\mathrm{\σ}}_{\mathrm{\υ}}^2=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{(V_{d,k}-{\stackrel{\‾}{V}}_d)}^2,{\stackrel{\‾}{V}}_d=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{V}_{d,k}$

Then, use following recursion iterative, the measurement data of driving DC voltage carried out to filtering:

$\left\{\begin{array}{c}{\hat{V}}_d\left(k\right)=a{\hat{V}}_d(k-1)+b\left(k\right)[V_d\left(k\right)-\mathrm{ac}{\hat{V}}_d(k-1)]\\ b\left(k\right)=\frac{c{P}_1\left(k\right)}{c^2{P}_1\left(k\right)-{\mathrm{\σ}}_{\mathrm{\υ}}^2}\\ P_1\left(k\right)=a^{2}P(k-1)+{\mathrm{\σ}}_{\mathrm{\ω}}^2\\ P\left(k\right)=P_1\left(k\right)-\mathrm{cb}\left(k\right)P_1\left(k\right)\end{array}\right.$

Wherein, b (k) is the time-variable filtering gain, and P (k) is equal square evaluated error.

Beneficial effect: silicon micro-resonance type accelerometer temperature compensation provided by the invention, overcome uncertainty and the hot conduction delay that in traditional direct temperature compensation method, temperature field distributes and brought the defect of relatively large deviation to compensation result, can realize real-time, high-precision temperature compensation; The temperature compensation cost of the inventive method is low, does not need additionally to increase sensor, only utilizes existing circuit devcie to realize.

The accompanying drawing explanation

Fig. 1 is structured flowchart of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further described.

A kind of silicon micro-resonance type accelerometer temperature compensation, comprise the steps:

(1) under without the acceleration signal input condition, in ℃ variation range of environment temperature-40～60, resonance frequency and driving DC voltage to silicon micro-resonance type accelerometer are measured, and obtain the temperature variant monotonic relationshi curve of resonance frequency and the temperature variant monotonic relationshi curve of driving DC voltage of resonance beam 1 and resonance beam 2; Described silicon micro-resonance type accelerometer has two resonance beam, is designated as respectively resonance beam 1 and resonance beam 2; Specifically comprise the steps:

(11), in ℃ variation range of environment temperature-40～60, demarcate s temperature spot; Such as, take 10 ℃ as temperature interval, p-40～60 ℃ of temperature ranges are divided, and obtain 11 temperature spots, i.e. s=11;

(12) under without the acceleration signal input condition, test as follows: resonance frequency and the driving DC voltage of the resonance frequency of collection resonance beam 1 and driving DC voltage, collection resonance beam 2 on each temperature spot; When gathering, can use temperature control device that the environment temperature of silicon micro-resonance type accelerometer is controlled on corresponding temperature spot;

(13) experiment of repeated execution of steps (12), the experiment number of accumulative total execution step (12) is t time;

(14) resonance frequency under each temperature spot and driving DC voltage are made even and are:

$f_{1i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{f}_{1i,j},f_{2i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{f}_{2i,j}$

$V_{d1i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{V}_{d1i,j},V_{d2i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{V}_{d2i,j}$

Wherein, i=1,2 ..., s, j=1,2 ..., t; f _{1i, j}for the resonance frequency that resonance beam 1 records during the j time repeated experiments on i temperature spot, f _{2i, j}for the resonance frequency that resonance beam 2 records during the j time repeated experiments on i temperature spot, V _{d1i, j}for the driving DC voltage that resonance beam 1 records during the j time repeated experiments on i temperature spot, V _{d2i, j}the driving DC voltage recorded during the j time repeated experiments on i temperature spot for resonance beam 2;

(15), according to the corresponding relation of resonance frequency mean value, driving DC voltage mean value and temperature, obtain the temperature variant monotonic relationshi curve of resonance frequency and the temperature variant monotonic relationshi curve of driving DC voltage of resonance beam 1 and resonance beam 2.

(2), under without the acceleration signal input condition, demarcate the monotone variation relation curve that resonance beam 1 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency; Now the resonance frequency changing value of resonance beam 1 is the deviation frequency that temperature causes; Specifically comprise the steps:

(21) to resonance beam 1, the average resonance frequencies under each temperature spot and average driving DC voltage data are used the cubic polynomial model of fit to carry out matching, obtain the monotone variation relation curve that resonance beam 1 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency:

f _T1=a ₀+a ₁V _d1+a ₂V _d1 ²+a ₃V _d1 ³

(22) use the principle of least square, obtain the coefficient a of above formula _n, n=0,1,2,3;

When inputting without acceleration, temperature is the reason that causes frequency shift, therefore be from the frequency of calculating of falling into a trap with above formula the deviation frequency that temperature causes.

(3), under without the acceleration signal input condition, demarcate the monotone variation relation curve that resonance beam 2 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency; Now the resonance frequency changing value of resonance beam 2 is the deviation frequency that temperature causes; Specifically comprise the steps:

(31) to resonance beam 2, the average resonance frequencies under each temperature spot and average driving DC voltage data are used the cubic polynomial model of fit to carry out matching, obtain the monotone variation relation curve that resonance beam 2 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency:

f _T2=b ₀+b ₁V _d2+b ₂V _d2 ²+b ₃V _d2 ³

(32) use the principle of least square, obtain the coefficient b of above formula _n, n=0,1,2,3;

When inputting without acceleration, temperature is the reason that causes frequency shift, therefore be from the frequency of calculating of falling into a trap with above formula the deviation frequency that temperature causes.

(4) use described silicon micro-resonance type accelerometer to carry out acceleration analysis, obtain the resonance frequency f of resonance beam 1 ₁resonance frequency f with resonance beam 2 ₂, and the driving DC voltage V of resonance beam 1 now _d1driving DC voltage V with resonance beam 2 _d2.

(5) because the voltage signal antijamming capability is low, driving DC voltage is subject to noise, therefore to the driving DC voltage V of resonance beam 1 and resonance beam 2 _d1and V _d2carry out filtering, the driving DC voltage after filtering noise is respectively

with the monotone variation curve obtained according to step (3) obtains driving DC voltage

corresponding temperature drift frequency f _t1, the monotone variation curve obtained according to step (4) obtains driving DC voltage

corresponding temperature drift frequency f _t2.

(6) resonance frequency of resonance beam is the frequency f caused by acceleration signal _awith the frequency shift (FS) f caused by temperature _ttwo parts addition forms, that is:

f ₁=f _a1+f _T1

f ₂=f _a2+f _T2

Resonance beam 1 after the accounting temperature compensation and the difference on the frequency of resonance beam 2 are:

f _a1-f _a2=(f ₁-f _T1)-(f ₂-f _T2)=(f ₁-f ₂)-(f _T1-f _T2)。

(7) calculate measured acceleration signal a _ccfor:

a _cc=(f _a1-f _a2)/S _F

S wherein _fconstant multiplier for accelerometer.

Because the voltage signal antijamming capability is low, driving DC voltage is subject to noise, for fear of in frequency signal pointwise compensation process, by excessive voltage noise pull-in frequency measurement result, need to carry out filtering to the voltage signal collected in actual use procedure in step (4).This case is used following mode to carry out filtering, i.e. the described measurement data V to driving DC voltage _dcarry out filtering to obtain

concrete grammar be:

At first, set up as drag:

${\hat{V}}_d\left(k\right)=a{\hat{V}}_d(k-1)+\mathrm{\ω}(k-1)$

$V_d\left(k\right)=c{\hat{V}}_d\left(k\right)+\mathrm{\υ}\left(k\right)$

Same driving DC voltage under same temperature spot is carried out to m actual value and measure, k=1,2 ..., m; V _d(k) be the driving DC voltage actual measured value measured for the k time,

for V _d(k) filtered value, ω (k) is the dynamic noise while measuring for the k time, υ (k) is the measurement noise of introducing in the k time measuring process, a, c is measuring system and the definite parameter of method of testing;

Secondly, by V _d(k) be expressed as V _d,k, will

be expressed as

variance yields according to following formula statistics dynamic noise ω (k) and measurement noise υ (k)

with

${\mathrm{\σ}}_{\mathrm{\ω}}^2=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{({\hat{V}}_{d,k}-{\stackrel{\stackrel{\‾}{^}}{V}}_d)}^2,{\stackrel{\stackrel{\‾}{^}}{V}}_d=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\hat{V}}_{d,k}$

${\mathrm{\σ}}_{\mathrm{\υ}}^2=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{(V_{d,k}-{\stackrel{\‾}{V}}_d)}^2,{\stackrel{\‾}{V}}_d=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{V}_{d,k}$

Then, use following recursion iterative, the measurement data of driving DC voltage carried out to filtering:

$\left\{\begin{array}{c}{\hat{V}}_d\left(k\right)=a{\hat{V}}_d(k-1)+b\left(k\right)[V_d\left(k\right)-\mathrm{ac}{\hat{V}}_d(k-1)]\\ b\left(k\right)=\frac{c{P}_1\left(k\right)}{c^2{P}_1\left(k\right)-{\mathrm{\σ}}_{\mathrm{\υ}}^2}\\ P_1\left(k\right)=a^{2}P(k-1)+{\mathrm{\σ}}_{\mathrm{\ω}}^2\\ P\left(k\right)=P_1\left(k\right)-\mathrm{cb}\left(k\right)P_1\left(k\right)\end{array}\right.$

Wherein, b (k) is the time-variable filtering gain, and P (k) is equal square evaluated error.

The above is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (4)

1. a silicon micro-resonance type accelerometer temperature compensation, is characterized in that: comprise the steps:

(1) under without the acceleration signal input condition, in ℃ variation range of environment temperature-40～60, resonance frequency and driving DC voltage to silicon micro-resonance type accelerometer are measured, and obtain the temperature variant monotonic relationshi curve of resonance frequency and the temperature variant monotonic relationshi curve of driving DC voltage of resonance beam 1 and resonance beam 2; Described silicon micro-resonance type accelerometer has two resonance beam, is designated as respectively resonance beam 1 and resonance beam 2;

(2), under without the acceleration signal input condition, demarcate the monotone variation relation curve that resonance beam 1 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency; Now the resonance frequency changing value of resonance beam 1 is the deviation frequency that temperature causes;

(3), under without the acceleration signal input condition, demarcate the monotone variation relation curve that resonance beam 2 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency; Now the resonance frequency changing value of resonance beam 2 is the deviation frequency that temperature causes;

(4) use described silicon micro-resonance type accelerometer to carry out acceleration analysis, obtain the resonance frequency f of resonance beam 1 ₁resonance frequency f with resonance beam 2 ₂, and the driving DC voltage V of resonance beam 1 now _d1driving DC voltage V with resonance beam 2 _d2;

(5) to the driving DC voltage V of resonance beam 1 and resonance beam 2 _d1and V _d2carry out filtering, the driving DC voltage after filtering noise is respectively

with the monotone variation curve obtained according to step (3) obtains driving DC voltage

corresponding temperature drift frequency f _t1, the monotone variation curve obtained according to step (4) obtains driving DC voltage

corresponding temperature drift frequency f _t2;

(6) resonance frequency of resonance beam is the frequency f caused by acceleration signal _awith the frequency shift (FS) f caused by temperature _ttwo parts addition forms, that is:

f ₁=f _a1+f _T1

f ₂=f _a2+f _T2

Resonance beam 1 after the accounting temperature compensation and the difference on the frequency of resonance beam 2 are:

f _a1-f _a2=(f ₁-f _T1)-(f ₂-f _T2)=(f ₁-f ₂)-(f _T1-f _T2)

(7) calculate measured acceleration signal a _ccfor:

a _cc=(f _a1-f _a2)/S _F

S wherein _fconstant multiplier for accelerometer.

2. silicon micro-resonance type accelerometer temperature compensation according to claim 1, it is characterized in that: described step (1) specifically comprises the steps:

(11), in ℃ variation range of environment temperature-40～60, demarcate s temperature spot;

(12) under without the acceleration signal input condition, test as follows: resonance frequency and the driving DC voltage of the resonance frequency of collection resonance beam 1 and driving DC voltage, collection resonance beam 2 on each temperature spot;

(13) experiment of repeated execution of steps (12), the experiment number of accumulative total execution step (12) is t time;

(14) resonance frequency under each temperature spot and driving DC voltage are made even and are:

$f_{1i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{f}_{1i,j},f_{2i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{f}_{2i,j}$

$V_{d1i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{V}_{d1i,j},V_{d2i}=\frac{1}{t}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}{V}_{d2i,j}$

Wherein, i=1,2 ..., s, j=1,2 ..., t; f _{1i, j}for the resonance frequency that resonance beam 1 records during the j time repeated experiments on i temperature spot, f _{2i, j}for the resonance frequency that resonance beam 2 records during the j time repeated experiments on i temperature spot, V _{d1i, j}for the driving DC voltage that resonance beam 1 records during the j time repeated experiments on i temperature spot, V _{d2i, j}the driving DC voltage recorded during the j time repeated experiments on i temperature spot for resonance beam 2;

(15), according to the corresponding relation of resonance frequency mean value, driving DC voltage mean value and temperature, obtain the temperature variant monotonic relationshi curve of resonance frequency and the temperature variant monotonic relationshi curve of driving DC voltage of resonance beam 1 and resonance beam 2.

3. silicon micro-resonance type accelerometer temperature compensation according to claim 2 is characterized in that:

Described step (2) specifically comprises the steps:

(21) to resonance beam 1, the average resonance frequencies under each temperature spot and average driving DC voltage data are used the cubic polynomial model of fit to carry out matching, obtain the monotone variation relation curve that resonance beam 1 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency:

f _T1=a ₀+a ₁V _d1+a ₂V _d1 ²+a ₃V _d1 ³

(22) use the principle of least square, obtain the coefficient a of above formula _n, n=0,1,2,3;

Described step (3) specifically comprises the steps:

(31) to resonance beam 2, the average resonance frequencies under each temperature spot and average driving DC voltage data are used the cubic polynomial model of fit to carry out matching, obtain the monotone variation relation curve that resonance beam 2 maintains the constant driving DC voltage of resonance amplitude and its resonance frequency:

f _T2=b ₀+b ₁V _d2+b ₂V _d2 ²+b ₃V _d2 ³

(32) use the principle of least square, obtain the coefficient b of above formula _n, n=0,1,2,3.

4. silicon micro-resonance type accelerometer temperature compensation according to claim 3, is characterized in that: the described measurement data V to driving DC voltage _dcarry out filtering to obtain

concrete grammar be:

At first, set up as drag:

${\hat{V}}_d\left(k\right)=a{\hat{V}}_d(k-1)+\mathrm{\ω}(k-1)$

$V_d\left(k\right)=c{\hat{V}}_d\left(k\right)+\mathrm{\υ}\left(k\right)$

Same driving DC voltage under same temperature spot is carried out to m actual value and measure, k=1,2 ..., m; V _d(k) be the driving DC voltage actual measured value measured for the k time,

for V _d(k) filtered value, ω (k) is the dynamic noise while measuring for the k time, υ (k) is the measurement noise of introducing in the k time measuring process, a, c is measuring system and the definite parameter of method of testing;

Secondly, by V _d(k) be expressed as V _d,k, will

be expressed as

variance yields according to following formula statistics dynamic noise ω (k) and measurement noise υ (k)

with

${\mathrm{\σ}}_{\mathrm{\ω}}^2=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{({\hat{V}}_{d,k}-{\stackrel{\stackrel{\‾}{^}}{V}}_d)}^2,{\stackrel{\stackrel{\‾}{^}}{V}}_d=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{\hat{V}}_{d,k}$

${\mathrm{\σ}}_{\mathrm{\υ}}^2=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{(V_{d,k}-{\stackrel{\‾}{V}}_d)}^2,{\stackrel{\‾}{V}}_d=\frac{1}{m}\underset{k=1}{\overset{m}{\mathrm{\Σ}}}{V}_{d,k}$

Then, use following recursion iterative, the measurement data of driving DC voltage carried out to filtering:

$\left\{\begin{array}{c}{\hat{V}}_d\left(k\right)=a{\hat{V}}_d(k-1)+b\left(k\right)[V_d\left(k\right)-\mathrm{ac}{\hat{V}}_d(k-1)]\\ b\left(k\right)=\frac{c{P}_1\left(k\right)}{c^2{P}_1\left(k\right)-{\mathrm{\σ}}_{\mathrm{\υ}}^2}\\ P_1\left(k\right)=a^{2}P(k-1)+{\mathrm{\σ}}_{\mathrm{\ω}}^2\\ P\left(k\right)=P_1\left(k\right)-\mathrm{cb}\left(k\right)P_1\left(k\right)\end{array}\right.$

Wherein, b (k) is the time-variable filtering gain, and P (k) is equal square evaluated error.

Images