CN103558415A - MEMS accelerometer with temperature compensation function - Google Patents

Abstract

The invention relates to an MEMS accelerometer with the temperature compensation function. The MEMS accelerometer with the temperature compensation function comprises an acceleration sensor, a temperature sensor and a temperature compensation chip, wherein the acceleration sensor and the temperature sensor are connected with the temperature compensation chip. A temperature compensation method adopted by the temperature compensation chip comprises the steps that (1), zero biases and a set of output values of a scale factor are measured under a plurality of temperature points, the zero biases and the output values are fitted to be a fitting surface, and a series of fitting coefficients are obtained and arranged to be a coefficient matrix; (2), modeling is carried out on output signals of the acceleration sensor and the output signals of the temperature sensor so as to be expressed as a model matrix; (3), dot product is carried out on the coefficient matrix and the model matrix so as to obtain an output formula after the acceleration sensor obtains the temperature compensation; (4), the fitting coefficients and the output formula are written into the temperature compensation chip to be calculated. Through three-dimensional fitting of the surface and compensation after calculation, influence on a system from errors generated when the accelerometer is assembled and installed is reduced effectively.

Description

Mems accelerometer with temperature compensation

Technical field

The present invention relates to a kind of mems accelerometer, especially a kind of mems accelerometer with temperature compensation function.

Background technology

MEMS(Micro Electro-Mechanical System) accelerometer is one of sensor important in microminiature inertial navigational system, and the quality of its performance has directly affected the navigation accuracy of inertial navigation system.Mems accelerometer is measured output error and is mainly derived from the several respects such as manufacturing process, installation method, external environment condition, the impact that wherein environment temperature is measured output to mems accelerometer is particularly outstanding, and it also becomes a key issue in the application of micro-acceleration gauge engineering.

At present, conventional local temperature control and software approach are realized temperature compensation.Local temperature control conventionally need change inner structure, the material of accelerometer or increase temperature control system, realizes complexity, so more employing software scenarios compensate in engineering, can make acceleration analysis stability improve 5-20 doubly after compensation.Software compensation scheme be take and obtained ACTE model as prerequisite, conventionally need temp. controlling box or the complicated testing apparatus of design specialized to carry out Model Distinguish experiment, as designed independently high precision temperature control box, and by the temperature model of circular dividing table identification accelerometer; Or adopt temperature model of temperature control turntable and circular dividing table identification accelerometer etc.

For example, the static model of accelerometer are as the formula (1):

y=K ₀+K ₁a _i+K ₂a _i ²+K ₃a _ia ₀ （1）

Wherein, y: accelerometer output (V); K ₀: the zero-bit output (V) of accelerometer; K ₁: the scaling factor of accelerometer (V/gn); K ₂: second order nonlinear coefficient (V/g _n ²); K ₃cross-coupling coefficient (V/g _n ²); a _i: the acceleration (g that is parallel to input axis of accelerometer _n); a ₀: transverse acceleration (g _n).The accelerometer adopting for test, due to K ₂and K ₃be generally 10 ^-4magnitude, its caused nonlinearity erron is less than 0.5%, therefore can ignore the nonlinear terms in accelerometer output and the distracter that intersects, and then can adopt formula (2) to export and obtain real accekeration according to accelerometer measures:

a _i=（y－K ₀）/K ₁ （2）

Traditional temperature compensation, the essence of accelerometer being carried out to Temperature Modeling is exactly the zero-bit output K of determination of acceleration meter ₀with scaling factor K ₁and the relation between temperature.If obtain the K of accelerometer under different temperatures ₀and K ₁, can adopt the method for a curve to obtain temperature model, as the formula (3):

K ₀=K ₀₀+K ₀₁T K ₁=K ₁₀+K ₁₁T （3）

Wherein, T is environment temperature, K ₀₀, K ₀₁, K ₁₀, K ₁₁for undetermined coefficient.

From formula (3), we can find out, traditional temperature compensation is that the zero-bit of accelerometer and scaling factor are separately compensated.

So traditional accelerometer is not only higher to accelerometer assembling and installation requirement when temperature compensation, and need to separately compensate the zero-bit of accelerometer and scaling factor.

Summary of the invention

The object of this invention is to provide a kind of without zero-bit and scaling factor are separated to the mems accelerometer with temperature compensation of considering.

For achieving the above object, the technical solution used in the present invention is:

A kind of mems accelerometer with temperature compensation, comprise MEMS acceleration transducer, it also comprises temperature sensor, temperature-compensated chip, the output terminal of the output terminal of described MEMS acceleration transducer and described temperature sensor is connected with the input end of described temperature-compensated chip through A/D passage respectively, and the output terminal of described temperature-compensated chip is the output terminal of the described mems accelerometer with temperature compensation;

The temperature compensation that described temperature-compensated chip adopts is: (1) circulates in zero output valve inclined to one side and scaling factor of the MEMS acceleration transducer described in measurement under a plurality of temperature spots by high low temperature and obtains one group of data, this group data fitting is obtained to its fitting surface, by described fitting surface, obtain and meet the required a series of fitting coefficients of matching order, and described a series of fitting coefficients are arranged in to matrix of coefficients; (2) by the output signal N of described MEMS acceleration transducer _rbe modeled as with the output signal T of described temperature sensor and be expressed as model matrix, wherein n is matching order; (3) described matrix of coefficients and described model matrix are done to dot product and obtained the output formula of MEMS acceleration transducer described within the scope of total temperature after temperature compensation; (4) by MEMS acceleration transducer described within the scope of described a series of fitting coefficients and total temperature, the output formula after temperature compensation writes in described temperature-compensated chip, by the output signal N of described MEMS acceleration transducer _rafter calculating, formula obtains the accekeration of the described output of the mems accelerometer with temperature compensation with the output signal T of described temperature sensor.

Preferably, by one group of data described in least square fitting, obtain its fitting surface.

Preferably, described matching order is 5 rank.

Preferably, described a series of fitting coefficients are 21, are respectively C ₀-C ₂₀, the matrix of coefficients that its arrangement forms is

$\left(\begin{array}{cccccc}{C}_0& C_2& C_5& C_9& C_{14}& C_{20}\\ C_1& C_4& C_8& C_{13}& C_{19}& 0\\ C_3& C_7& C_{12}& {\mathrm{<figure-callout\; id="18"\; label="C"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_{18}& 0& 0\\ C_6& C_{11}& C_{17}& 0& 0& 0\\ C_{10}& C_{16}& 0& 0& 0& 0\\ {\mathrm{<figure-callout\; id="15"\; label="C"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_{15}& 0& 0& 0& 0& 0\end{array}\right);$

Described model matrix is

$\left(\begin{array}{cccccc}1& T& T^2& T^3& T^4& T^5\\ N_R& N_{R}T& N_R{T}^2& N_R{T}^3& {\mathrm{<figure-callout\; id="4"\; label="N\; R\; T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">N</figure-callout>}}_R{T}^{}{}^4& 0\\ N_R^2& N_R^{2}T& N_R^2{T}^2& N_R^2{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3& 0& 0\\ N_R^3& N_R^{3}T& N_R^3{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2& 0& 0& 0\\ N_R^4& N_R^4\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}& 0& 0& 0& 0\\ N_R^5& 0& 0& 0& 0& 0\end{array}\right);$

The output formula of MEMS acceleration transducer described within the scope of described total temperature after temperature compensation is

$\begin{array}{c}g\left(T\right)={\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_0+C_1{N}_R+C_{2}T+C_3{\mathrm{<figure-callout\; id="2"\; label="N\; R"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">N</figure-callout>}}_R^{}+C_4{N}_{R}T+\\ C_5{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+C_6{\mathrm{<figure-callout\; id="3"\; label="N\; R"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">N</figure-callout>}}_R^{}+C_7{N}_R^{2}T+C_8{N}_R{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+\\ C_9{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3+C_{10}{N}_R^4+C_{11}{N}_R^{3}T+C_{12}{N}_R^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+\\ C_{13}{N}_R{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3+C_{14}{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3+C_{15}{N}_R^5+C_{16}{N}_R^{4}T+\\ C_{17}{N}_R^3{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+C_{18}{N}_R^2{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3+C_{19}{N}_R{\mathrm{<figure-callout\; id="4"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^4+C_{20}{T}^5\end{array}.$

Preferably, described MEMS acceleration transducer, described temperature sensor are in same heat field.

Because technique scheme is used, the present invention compared with prior art has following advantages: mems accelerometer of the present invention is not separately considered its zero-bit and scaling factor when compensation, but by curved surface 3 D Quasi and and calculate after compensate, effectively reduced the impact on system of error that accelerometer produces in assembling and installation process.

Accompanying drawing explanation

Accompanying drawing 1 is the schematic block circuit diagram of the mems accelerometer with temperature compensation of the present invention.

Accompanying drawing 2 is the curved surface schematic diagram of the mems accelerometer with temperature compensation of the present invention institute's matching in compensation method.

Accompanying drawing 3 is the data plot of the lower output-1g～+ 1g of the full temperature of the mems accelerometer before compensating.

Accompanying drawing 4 is the data plot of the lower output-30g～+ 30g of the full temperature of the mems accelerometer before compensating.

Accompanying drawing 5 is the graph of a relation of the lower output-1g～+ 1g of the full temperature of the mems accelerometer after compensating and temperature.

The magnitude of voltage figure that the g value that accompanying drawing 6 is the lower output of the full temperature of the mems accelerometer after compensating is converted into and the graph of a relation of temperature.

Embodiment

Below in conjunction with embodiment shown in the drawings, the invention will be further described.

Embodiment mono-: shown in accompanying drawing 1.With a mems accelerometer for temperature compensation, comprise MEMS acceleration transducer, temperature sensor and temperature-compensated chip.The output terminal of MEMS acceleration transducer is connected with the input end of temperature-compensated chip through A/D passage respectively with the output terminal of temperature sensor, and the output terminal of temperature-compensated chip is the output terminal with the mems accelerometer of temperature compensation.MEMS acceleration transducer adopts temperature sensors of high precision LM20, in temperature-compensated chip, the acceleration information collecting is processed and temperature compensation, and compensation result is exported.Meanwhile, for the ease of demarcating, guarantee that MEMS acceleration transducer and temperature sensor are in a heat field, after temperature sensor and MEMS acceleration transducer are bonded on a pcb board, then be assembled in an aluminium alloy shell.This main performance index with the mems accelerometer of temperature compensation is: operating voltage is 5V; Working current is 10mA; Range is variable, and maximum measurement range is ± 30g.

The temperature compensation that temperature-compensated chip adopts is as follows:

(1) in experiment, by high low temperature circulate under a plurality of temperature spots, measure MEMS acceleration transducer zero partially and the output valve of scaling factor obtain one group of data, utilize least square fitting to obtain its fitting surface these group data.By fitting surface, obtain and meet the required a series of fitting coefficients of matching order, and a series of fitting coefficients are arranged in to matrix of coefficients.

With 5 rank, fit to example, a series of fitting coefficients are 21, are respectively C ₀-C ₂₀, be arranged as matrix of coefficients

$\left(\begin{array}{cccccc}{C}_0& C_2& C_5& C_9& C_{14}& C_{20}\\ C_1& C_4& C_8& C_{13}& C_{19}& 0\\ C_3& C_7& C_{12}& {\mathrm{<figure-callout\; id="18"\; label="C"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_{18}& 0& 0\\ C_6& C_{11}& C_{17}& 0& 0& 0\\ C_{10}& C_{16}& 0& 0& 0& 0\\ {\mathrm{<figure-callout\; id="15"\; label="C"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_{15}& 0& 0& 0& 0& 0\end{array}\right)---\left(4\right)$

Visible, in above-mentioned matrix of coefficients, each fitting coefficient is arranged in the counter-diagonal of matrix and divides in the upper triangle forming.

(2) by the output signal N of MEMS acceleration transducer _rbe modeled as with the output signal T of temperature sensor

and be expressed as model matrix, wherein n is matching order.

Still with 5 rank, fit to example, the model matrix of formation is

$\left(\begin{array}{cccccc}1& T& T^2& T^3& T^4& T^5\\ N_R& N_{R}T& N_R{T}^2& N_R{T}^3& {\mathrm{<figure-callout\; id="4"\; label="N\; R\; T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">N</figure-callout>}}_R{T}^{}{}^4& 0\\ N_R^2& N_R^{2}T& N_R^2{T}^2& N_R^2{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3& 0& 0\\ N_R^3& N_R^{3}T& N_R^3{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2& 0& 0& 0\\ N_R^4& N_R^4\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}& 0& 0& 0& 0\\ N_R^5& 0& 0& 0& 0& 0\end{array}\right)---\left(5\right)$

This model matrix has the structure corresponding with matrix of coefficients, and wherein each element is also arranged in the counter-diagonal of matrix and divides in the upper triangle forming.

(3) matrix of coefficients formula (4) and model matrix formula (5) are done to dot product and obtain the output formula of MEMS acceleration transducer after temperature compensation within the scope of total temperature;

$\begin{array}{c}g\left(T\right)={\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_0+C_1{N}_R+C_{2}T+C_3{\mathrm{<figure-callout\; id="2"\; label="N\; R"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">N</figure-callout>}}_R^{}+C_4{N}_{R}T+\\ C_5{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+C_6{\mathrm{<figure-callout\; id="3"\; label="N\; R"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">N</figure-callout>}}_R^{}+C_7{N}_R^{2}T+C_8{N}_R{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+\\ C_9{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3+C_{10}{N}_R^4+C_{11}{N}_R^{3}T+C_{12}{N}_R^2{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+\\ C_{13}{N}_R{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3+C_{14}{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3+C_{15}{N}_R^5+C_{16}{N}_R^{4}T+\\ C_{17}{N}_R^3{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000417007570000013.png,HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^2+C_{18}{N}_R^2{\mathrm{<figure-callout\; id="3"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^3+C_{19}{N}_R{\mathrm{<figure-callout\; id="4"\; label="T"\; filenames="HDA0000417007570000021.png"\; state="\{\{state\}\}">T</figure-callout>}}^4+C_{20}{T}^5\end{array}---\left(6\right)$

The curved surface of its matching is illustrated as accompanying drawing 2, the output signal (N that wherein X-axis is accelerometer _r), the output that Y-axis is temperature sensor (T), the accekeration that Z axis is actual measurement (g).After the data of the accelerometer total temperature scope gamut with collected fit, this accelerometer has all been included in the curved surface fitting at any arbitrary accekeration of temperature spot in theory, and the calculating by formula (6) just can show that accelerometer is at the true accekeration of any temperature spot.

(4) by MEMS acceleration transducer within the scope of a series of fitting coefficients and total temperature, the output formula after temperature compensation writes in temperature-compensated chip, by the output signal N of MEMS acceleration transducer _rafter calculating, formula obtains the accekeration with the mems accelerometer output of temperature compensation with the output signal T of temperature sensor.

To the mems accelerometer not carrying out after the assembling of temperature compensation, adopt NI6281 data collecting card respectively at-40 ℃,-10 ℃, + 25 ℃, + 55 ℃, + 85 ℃ gather it-data of 1g～+ 1g, data plot after collection is shown in accompanying drawing 3, wherein horizontal ordinate is time (S), ordinate is magnitude of voltage (V), the output that the curve of series 2 is temperature sensor, temperature sensor is negative temperature coefficient, therefore the curve of series 2 represents respectively-40 ℃ by left-to-right 5 ladders,-10 ℃, + 25 ℃, + 55 ℃, + 85 ℃, the curve of series 1 represents by left-to-right 5 ladders that respectively accelerometer is at-40 ℃,-10 ℃, + 25 ℃, + 55 ℃, at+85 ℃ of temperature, the output of-1g～+ 1g.As seen from the figure, under low temperature condition, the output shift amount of accelerometer is still larger, because temporarily do not have the equipment can the output of testing acceleration meter within the scope of full temperature gamut, therefore the output of accelerometer within the scope of full temperature gamut only has zero-bit and scaling factor derivation by different temperature points to go out, and the data plot after derivation is shown in accompanying drawing 4.

And carrying out least square fitting by software, the fitting coefficient being compensated is

$\left[\begin{array}{cccccc}-203.222& 845.874& -1029.087& 615.967& -183.663& 21.671\\ 12.289& -105.471& 100.329& -40.267& 5.93& 0\\ 0.736& -0.645& 0.319& -0.061& 0& 0\\ -0.128& 0.025& -0.003& 0& 0& 0\\ 0.015& 0& 0& 0& 0& 0\\ -0.001& 0& 0& 0& 0& 0\end{array}\right]$

This coefficient is write in temperature-compensated chip, in temperature-compensated chip, by computing, the accekeration after final output is calculated, Output rusults is shown in accompanying drawing 5 and accompanying drawing 6.

From the contrast of accompanying drawing 6 and accompanying drawing 3, can find out, before temperature compensation in the situation of-40 ℃, accelerometer zero drift 500mV nearly, be converted into g value and be 10g nearly, and after temperature compensation, zero drift narrows down to 1g left and right, being converted into magnitude of voltage is the about 50mV that drifted about, as can be seen here, the temperature of accelerometer has floated an order of magnitude reduced.

Above-described embodiment is only explanation technical conceive of the present invention and feature, and its object is to allow person skilled in the art can understand content of the present invention and implement according to this, can not limit the scope of the invention with this.All equivalences that Spirit Essence is done according to the present invention change or modify, within all should being encompassed in protection scope of the present invention.

Claims (5)

1. the mems accelerometer with temperature compensation, comprise MEMS acceleration transducer, it is characterized in that: it also comprises temperature sensor, temperature-compensated chip, the output terminal of the output terminal of described MEMS acceleration transducer and described temperature sensor is connected with the input end of described temperature-compensated chip through A/D passage respectively, and the output terminal of described temperature-compensated chip is the output terminal of the described mems accelerometer with temperature compensation;

The temperature compensation that described temperature-compensated chip adopts is: (1) circulates in zero output valve inclined to one side and scaling factor of the MEMS acceleration transducer described in measurement under a plurality of temperature spots by high low temperature and obtains one group of data, this group data fitting is obtained to its fitting surface, by described fitting surface, obtain and meet the required a series of fitting coefficients of matching order, and described a series of fitting coefficients are arranged in to matrix of coefficients; (2) by the output signal N of described MEMS acceleration transducer _rbe modeled as with the output signal T of described temperature sensor

and be expressed as model matrix, wherein n is matching order; (3) described matrix of coefficients and described model matrix are done to dot product and obtained the output formula of MEMS acceleration transducer described within the scope of total temperature after temperature compensation; (4) by MEMS acceleration transducer described within the scope of described a series of fitting coefficients and total temperature, the output formula after temperature compensation writes in described temperature-compensated chip, by the output signal N of described MEMS acceleration transducer _rafter calculating, formula obtains the accekeration of the described output of the mems accelerometer with temperature compensation with the output signal T of described temperature sensor.

2. the mems accelerometer with temperature compensation according to claim 1, is characterized in that: by one group of data described in least square fitting, obtain its fitting surface.

3. the mems accelerometer with temperature compensation according to claim 1, is characterized in that: described matching order is 5 rank.

4. the mems accelerometer with temperature compensation according to claim 3, is characterized in that: described a series of fitting coefficients are 21, are respectively C ₀-C ₂₀, the matrix of coefficients that its arrangement forms is

$\left(\begin{array}{cccccc}{C}_0& C_2& C_5& C_9& C_{14}& C_{20}\\ C_1& C_4& C_8& C_{13}& C_{19}& 0\\ C_3& C_7& C_{12}& C_{18}& 0& 0\\ C_6& C_{11}& C_{17}& 0& 0& 0\\ C_{10}& C_{16}& 0& 0& 0& 0\\ C_{15}& 0& 0& 0& 0& 0\end{array}\right);$

Described model matrix is

$\left(\begin{array}{cccccc}1& T& T^2& T^3& T^4& T^5\\ N_R& N_{R}T& N_R{T}^2& N_R{T}^3& N_R{T}^4& 0\\ N_R^2& N_R^{2}T& N_R^2{T}^2& N_R^2{T}^3& 0& 0\\ N_R^3& N_R^{3}T& N_R^3{T}^2& 0& 0& 0\\ N_R^4& N_R^{4}T& 0& 0& 0& 0\\ N_R^5& 0& 0& 0& 0& 0\end{array}\right);$

The output formula of MEMS acceleration transducer described within the scope of described total temperature after temperature compensation is

$\begin{array}{c}g\left(T\right)=C_0+C_1{N}_R+C_{2}T+C_3{N}_R^2+C_4{N}_{R}T+\\ C_5{T}^2+C_6{N}_R^3+C_7{N}_R^{2}T+C_8{N}_R{T}^2+\\ C_9{T}^3+C_{10}{N}_R^4+C_{11}{N}_R^{3}T+C_{12}{N}_R^2{T}^2+\\ C_{13}{N}_R{T}^3+C_{14}{T}^3+C_{15}{N}_R^5+C_{16}{N}_R^{4}T+\\ C_{17}{N}_R^3{T}^2+C_{18}{N}_R^2{T}^3+C_{19}{N}_R{T}^4+C_{20}{T}^5\end{array}.$

5. the mems accelerometer with temperature compensation according to claim 1, is characterized in that: described MEMS acceleration transducer, described temperature sensor are in same heat field.

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