CN108801252A - A kind of online noise-reduction method of MEMS gyroscope based on Normalized LMS Algorithm - Google Patents
A kind of online noise-reduction method of MEMS gyroscope based on Normalized LMS Algorithm Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/18—Stabilised platforms, e.g. by gyroscope
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- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
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Abstract
The invention belongs to field of navigation systems, disclose a kind of online noise-reduction method of the MEMS gyroscope based on Normalized LMS Algorithm, comprise the following steps：Step (1)：The faster Normalized LMS Algorithm of design closure speed；Step (2)：The relationship for deriving convergence factor and instantaneous square error determines the value of convergence factor, and introduces fixed convergence factor in the renewal equation of Normalized LMS Algorithm and control misalignment rate, introduces parameter alpha and controls step-length；Step (3)：Determine the range of the value and fixed convergence factor of α.The present invention solves the problems, such as that the expectation of the real-time output valve of MEMS gyroscope is unpredictable, realizes the online noise reduction of gyroscope signal；The accuracy of Low-cost Strapdown Inertial Navigation System MEMS gyroscope output angle movable information can be improved, excellent noise reduction effect, real-time is high, and calculation amount is reduced.
Description
Technical field
The invention belongs to field of navigation systems more particularly to a kind of MEMS gyroscope based on Normalized LMS Algorithm are online
Noise-reduction method.
Background technology
Inertial measurement component is directly installed in the navigation such as the needs such as aircraft, naval vessels, guided missile posture, speed, course letter
In the main body of breath, measuring signal is transformed to computer a kind of airmanship of navigational parameter.Hyundai electronics computer technology
Rapid development be strap-down inertial navigation system create condition.It begins one's study this novel navigation system from people at the end of the fifties
Since system, it has been successfully used to the flight of guiding Spacecraft reentry atmosphere.Strap-down inertial navigation system is in the U.S. " A Bo
On sieve " number airship effect had once been played as back-up system.
Strap-down inertial navigation system does not depend on external information at work, not outwardly radiation energy yet, is not easily susceptible to
It hinders and damage, is a kind of autonomic navigation system.Strap-down inertial navigation system relatively has two with gimbaled inertial navigation system
A main difference：(1) inertial platform is eliminated, gyroscope and accelerometer are mounted directly on board the aircraft, make system bulk
It is small, light weight and cost is low, easy to maintain.But gyroscope and accelerometer directly bear vibration, impact and the angle fortune of aircraft
It is dynamic, thus will produce additional dynamic error.This just has higher requirement to gyroscope and accelerometer.(2) needs calculate
Machine is coordinately transformed the aircraft acceleration signal that accelerometer measures, then carries out the navigation ginseng that needs are calculated in navigation
Number course, ground velocity, distance to go and geographical location etc..This system needs are coordinately transformed and it is necessary to be counted in real time
It calculates, thus requires computer that there is very high arithmetic speed and larger capacity.
With the raising of the expansion and application demand of inexpensive strap-down inertial application field, strapdown inertial navigation system
It is higher and higher to the required precision of MEMS gyroscope.Gyroscope is the important sensing element of strapdown inertial navigation system, it is exported
The angular movement information of carrier coordinate system relative inertness coordinate system, the positioning accuracy of the measurement accuracy of gyroscope to inertial navigation system
There is direct influence.Because the interference of the unique aufbauprinciples of MEMS itself and its installation environment causes MEMS gyroscope to export
Noise is larger, there is certain influence to the working performance of strapdown inertial navigation system, it is therefore necessary to make an uproar to MEMS gyroscope
Sound is inhibited.
Currently, scholars are just making great efforts to seek effective online data noise-reduction method.Document《Digital filter is in micromechanics top
Application in spiral shell system》, sensor and micro-system, 2003,22 (9):56-57 can filter out signal using conventional digital filters
High frequency noise components, however for the signal of non-stationary and narrower bandwidth, traditional digital filter Shortcomings drawn game
It is sex-limited；Document《MEMS sensor random error Allan variance analyses》, Chinese journal of scientific instrument, 2011,32 (12):2863-2868
It proposes that the method using Allan variances determines the random noise type and its source and characteristic of MEMS gyroscope, uses curve matching
Every error coefficient is found out, the online noise reduction technology of Kalman filtering is then utilized, white noise can be effectively inhibited or coloured made an uproar
Sound, but due to filtering restrictive condition it is harsher, the priori statistical property of data wants accurately known, thus its there are certain offices
It is sex-limited.Document《A kind of Real-time Wavelet De-noising algorithm》, Chinese journal of scientific instrument, 2004,25 (6):781-783 is dropped using interval wavelet
Make an uproar algorithm, construct Real-time Wavelet De-noising algorithm, noise reduction is preferable, however this method real-time is not strong and calculation amount compared with
Greatly, therefore this method is not particularly suited for inertial navigation system.
Invention content
It is an object of the invention to open fast convergence rate, a kind of output noise small is based on Normalized LMS Algorithm
The online noise-reduction method of MEMS gyroscope.
The object of the present invention is achieved like this：
A kind of online noise-reduction method of MEMS gyroscope based on Normalized LMS Algorithm, comprises the following steps：
Step (1)：The faster Normalized LMS Algorithm of design closure speed：Using output from Gyroscope as adaptive filter
The input vector x (k) of wave device passes through normalizing using gyroscope current sample values as the desired signal y (k) of sef-adapting filter
Change the renewal equation update convergence factor μ of LMS algorithmkWith coefficient vector w (k), last output factor vector and input vector
Product y ' (k).
X (k)=[x1(k),x2(k)L xN(k)]T；
W (k)=[w0(k),w1(k)L wN(k)]T；
In above formula, k is the newer number of algorithm, and N is the number of vector element；xi(k) it is i-th yuan of input vector
Element, 1≤i≤N；wj(k) it is j-th of element of coefficient vector, 1≤j≤N；
The renewal equation of Normalized LMS Algorithm is expressed as：
In above formula, μkFor convergence factor；E (k) is the error in Normalized LMS Algorithm renewal process：E (k)=y (k)-w
(k)Tx(k)；It is related error gradient vector with coefficient vector w (k),It substitutes into?：
W (k+1)=+ 2 μ of w (k)kE (k) x (k)=w (k)+Δ wT(k)；
Step (2)：Derive μkWith the relationship of instantaneous square error, μ is determinedkValue, and in the update of Normalized LMS Algorithm
Fixed convergence factor μ is introduced in equationnMisalignment rate is controlled, parameter alpha is introduced and controls step-length：
Instantaneous square error e2(k)：
e2(k)=y2(k)+wT(k)x(k)xT(k)w(k)-2y(k)wT(k)x(k)；
As w (k)=w (k)+Δ w (k), instantaneous square error is：
e2(k)=e2(k)+2ΔwT(k)x(k)x(k)Tw(k)+ΔwT(k)x(k)xT(k)Δw(k)-2y(k)ΔwT(k)x
(k)；Then
By the μ of Δ w (k)=2kE (k) x (k) substitute into Δ e2(k) in：
It enablesIt solves
It willThe renewal equation for substituting into Normalized LMS Algorithm obtains：
Fixed convergence factor μ is introduced in the renewal equation of Normalized LMS AlgorithmnMisalignment rate is controlled, parameter alpha control is introduced
Step-length：
Step (3)：Determine the value of α and fixed convergence factor μnRange：
Enable α=0.0005；
R is the autocorrelation matrix of input vector x (k)：
E[xT(k) x (k)]=tr [R], tr [R] represents the mark of matrix R；
The renewal equation of the renewal equation of more traditional LMS algorithm and Normalized LMS Algorithm again, then：
AbbreviationObtain 0 < μn< 2.
Beneficial effects of the present invention are：
The present invention replaces desired value to solve the expectation of the real-time output valve of MEMS gyroscope not with gyroscope current sample values
Predictable problem；Using the relevant convergence factor of input vector come continuous correction factor vector, finally by coefficient vector with it is defeated
The product of incoming vector realizes the online noise reduction of gyroscope signal as the output after noise reduction；The present invention can improve inexpensive victory
Join the accuracy of inertial navigation system MEMS gyroscope output angle movable information, excellent noise reduction effect, real-time is high, and calculation amount is reduced.
Description of the drawings
Fig. 1 is a kind of online noise-reduction method schematic diagram of the MEMS gyroscope based on Normalized LMS Algorithm；
Fig. 2 is the online noise-reduction method flow chart of MEMS gyroscope of LMS algorithm；
Fig. 3 is a kind of online noise-reduction method flow chart of the MEMS gyroscope based on Normalized LMS Algorithm；
Fig. 4 is data comparison figure before and after MEMS static state measured data noise reductions；
Fig. 5 is data comparison figure before and after MEMS Actual metering on kinetic state Noise reducing of data；
Fig. 6 is MEMS dynamic data spectrograms；
Fig. 7 is the spectrogram after MEMS Actual metering on kinetic state Noise reducing of data.
Specific implementation mode
Further describe the present invention below in conjunction with the accompanying drawings：
A kind of online noise-reduction method of MEMS gyroscope based on Normalized LMS Algorithm, comprises the following steps：
Such as Fig. 1, Fig. 2 and Fig. 3, step (1)：Normalized LMS Algorithm is the error made between output signal and expected response
Mean-square value is the adaptive-filtering of minimum, has good effect to the elimination of MEMS gyroscope noise.But it is run in navigation system
In the process, the desired value of gyroscope output is unforeseen, and the present invention proposes to substitute desired value with gyroscope current sample values
Method solves the problems, such as it is expected unforeseen.The faster Normalized LMS Algorithm of design closure speed：By output from Gyroscope
As the input vector x (k) of sef-adapting filter, using gyroscope current sample values as the desired signal y of sef-adapting filter
(k), convergence factor μ is updated by the renewal equation of Normalized LMS AlgorithmkWith coefficient vector w (k), last output factor vector
With the product y ' (k) of input vector.
X (k)=[x1(k),x2(k)L xN(k)]T；
W (k)=[w0(k),w1(k)L wN(k)]T；
In above formula, k is the newer number of algorithm, and N is the number of vector element, and N is bigger, and algorithm noise reduction is more ideal,
But the problem of also increasing the complexity of algorithm simultaneously and lag output can be caused.To ensure the real-time of noise reduction and noise reduction
Property, the usual values of N are 50 < N < 200；xi(k) it is i-th of element of input vector, 1≤i≤N；wj(k) it is coefficient vector
J-th of element, 1≤j≤N；
The renewal equation of traditional LMS algorithm is
W (k+1)=+ 2 μ e (k) x (k) of w (k)；
In above formula, μ values are changeless constant, and after μ values determine, algorithm will be restrained with set speed,
Its converged paths is simultaneously non-optimal.Because the value of μ is only related with the mark of input signal correlation matrix R, value range isTr [R] represents the mark of matrix R, shows that μ will not be with the change of each element of input signal from the above analysis
And change, so optimal converged paths can not be determined, it is not well positioned to meet the requirement of real-time noise-reducing.R is input in formula
The autocorrelation matrix of signal vector x (k), autocorrelation matrix R are：
In order to improve convergence rate, transformable receipts are utilized in the renewal equation of Normalized LMS Algorithm proposed by the present invention
Hold back factor muk.The renewal equation of Normalized LMS Algorithm is expressed as：
In above formula, μkFor convergence factor；E (k) is the error in Normalized LMS Algorithm renewal process：E (k)=y (k)-w
(k)Tx(k)；It is related error gradient vector with coefficient vector w (k), from error expressionIt substitutes into?：
W (k+1)=+ 2 μ of w (k)kE (k) x (k)=w (k)+Δ wT(k)；
Step (2)：Derive μkWith the relationship of instantaneous square error, μ is determinedkValue, and in the update of Normalized LMS Algorithm
Fixed convergence factor μ is introduced in equationnMisalignment rate is controlled, parameter alpha is introduced and controls step-length：
Instantaneous square error e2(k)：
e2(k)=y2(k)+wT(k)x(k)xT(k)w(k)-2y(k)wT(k)x(k)；
As w (k)=w (k)+Δ w (k), instantaneous square error is：
e2(k)=e2(k)+2ΔwT(k)x(k)x(k)Tw(k)+ΔwT(k)x(k)xT(k)Δw(k)-2y(k)ΔwT(k)x
(k)；
Then
In order to improve convergence rate, by selecting suitable μkValue, makes Δ e2(k) it is negative value, and reaches minimum.It will
The μ of Δ w (k)=2kE (k) x (k) substitute into Δ e2(k) in：
It enablesIt solves
It willThe renewal equation for substituting into Normalized LMS Algorithm obtains：
In the renewal equation of Normalized LMS Algorithm, it is generally the case that in order to control misalignment rate in renewal equation, also
Fixed convergence factor μ need to be introducedn.In addition, in order to avoid working as xT(k) occur prodigious step-length when x (k) very littles, should also include one
A parameter alpha：
Step (3)：Determine the value of α and fixed convergence factor μnRange：
By multigroup experiment it is found that α selects the constant of a very little that can meet the requirements, α=0.0005 is enabled；
R is the autocorrelation matrix of input vector x (k)：
E[xT(k) x (k)]=tr [R], tr [R] represents the mark of matrix R；
In view of LMS direction 2e (k) x (k) actually use the average value of convergence factor forMore traditional LMS again
The renewal equation of algorithm and the renewal equation of Normalized LMS Algorithm, then：
AbbreviationObtain 0 < μn< 2.Actually in MEMS gyroscope noise reduction process, convergence factor takes
0 < μ of valuenNoise reduction is relatively good when < 1.The range is only the premise of algorithmic stability, does not ensure that the best performance of algorithm,
Specific optimal performance also needs to obtain by testing.And through known to multigroup experimental result：In the MEMS gyro of Strapdown Inertial Navigation System
Instrument output frequency is more than or equal to 100Hz and parameter N, μnWith α within the above range in the case of, be substantially not present lag output
The problem of.
Embodiment 1：Handle static data：
It is placed on MEMS gyroscope is static on single axle table, sample frequency 100Hz, acquires 20000 static datas.
Dimension N chooses 150, fixed convergence factor μnChoose 0.001, parameter alpha chooses 0.0005, coefficient vector and input vector be zero to
Amount, other initializaing variables are zero.Such as Fig. 4, it can be seen that noise reduction is more apparent, exports and there is no lag.It is logical
Cross the analysis to data, the root-mean-square value of data noise is respectively 0.9236 and 0.2793 before and after noise reduction, and noise reduction is apparent.
Embodiment 2：Handle dynamic data：
MEMS gyroscope is placed on single axle table, setting turntable rotating speed is 6 °/s, sample frequency 100Hz, acquisition
20000 dynamic datas.Parameter N chooses 150, fixed convergence factor μn0.001 is chosen, parameter alpha chooses 0.0005, coefficient vector
It is null vector with input vector, other initializaing variables are zero.Such as Fig. 5, it can be seen that it is fine using the effect of noise reduction of the present invention, it is defeated
Go out the problem of there is no lag.Fig. 5 shows that gyro output valve is slightly less than the 6 °/s of reference true value of turntable output, this is because gyro
Constant error caused by, show that the present invention can effectively inhibit the random error of MEMS gyroscope from noise reduction, but can not
Inhibit constant error, it is follow-up that the calibration algorithm of MEMS only need to be added just due to inhibiting MEMS gyroscope constant error to be easier
It can inhibit, the emphasis discussed not as the present invention.The present invention is in order to preferably analyze data, such as Fig. 6 and Fig. 7, it can be seen that this
Invention can effectively reject the noise information other than useful signal, to realize the noise reduction to MEMS gyroscope signal, improve
The accuracy of MEMS gyroscope output.
Compared with prior art, the present invention with gyroscope current sample values replaces desired value to solve MEMS gyroscope real-time
Output valve it is expected unpredictable problem；Using the relevant convergence factor of input vector come continuous correction factor vector, finally
Using the product of coefficient vector and input vector as the output after noise reduction, the online noise reduction of gyroscope signal is realized；Energy of the present invention
The accuracy of Low-cost Strapdown Inertial Navigation System MEMS gyroscope output angle movable information is enough improved, excellent noise reduction effect, real-time is high,
Calculation amount is reduced.
The above is not intended to restrict the invention, and for those skilled in the art, the present invention can have various
Change and variation.All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should all include
Within protection scope of the present invention.
Claims (4)
1. a kind of online noise-reduction method of MEMS gyroscope based on Normalized LMS Algorithm, it is characterised in that：It comprises the following steps：
Step (1)：The faster Normalized LMS Algorithm of design closure speed：Using output from Gyroscope as sef-adapting filter
Input vector x (k) pass through Normalized LMS using gyroscope current sample values as the desired signal y (k) of sef-adapting filter
The renewal equation update convergence factor μ of algorithmkWith coefficient vector w (k), the product y ' of last output factor vector and input vector
(k)；
Step (2)：Derive μkWith the relationship of instantaneous square error, μ is determinedkValue, and in the renewal equation of Normalized LMS Algorithm
The fixed convergence factor μ of middle introducingnMisalignment rate is controlled, parameter alpha is introduced and controls step-length；
Step (3)：Determine the value of α and fixed convergence factor μnRange.
2. the online noise-reduction method of a kind of MEMS gyroscope based on Normalized LMS Algorithm according to claim 1, feature
It is：The product y ' (k) of coefficient vector and input vector in the step (1) is：
Y ' (k)=wT(k)x(k)；
Input vector x (k) is：
X (k)=[x1(k),x2(k)L xN(k)]T；
Coefficient vector w (k) is：
W (k)=[w0(k),w1(k)L wN(k)]T；
In above formula, k is the newer number of algorithm, and N is the number of vector element；xi(k) it is i-th of element of input vector, 1≤i
≤N；wj(k) it is j-th of element of coefficient vector, 1≤j≤N；
The renewal equation of Normalized LMS Algorithm is：
In above formula, μkFor convergence factor；E (k) is the error in Normalized LMS Algorithm renewal process：E (k)=y (k)-w (k)Tx
(k)；It is related error gradient vector with coefficient vector w (k),It substitutes into?：
W (k+1)=+ 2 μ of w (k)kE (k) x (k)=w (k)+Δ wT(k)。
3. the online noise-reduction method of a kind of MEMS gyroscope based on Normalized LMS Algorithm according to claim 1, feature
It is：The step (2) is specially：
Instantaneous square error e2(k)：
e2(k)=y2(k)+wT(k)x(k)xT(k)w(k)-2y(k)wT(k)x(k)；
As w (k)=w (k)+Δ w (k), instantaneous square error is：
e2(k)=e2(k)+2ΔwT(k)x(k)x(k)Tw(k)+ΔwT(k)x(k)xT(k)Δw(k)-2y(k)ΔwT(k)x(k)；
Then
By the μ of Δ w (k)=2kE (k) x (k) substitute into Δ e2(k) in：
It enablesIt solves
It willThe renewal equation for substituting into Normalized LMS Algorithm obtains：
Fixed convergence factor μ is introduced in the renewal equation of Normalized LMS AlgorithmnMisalignment rate is controlled, parameter alpha is introduced and controls step-length：
4. the online noise-reduction method of a kind of MEMS gyroscope based on Normalized LMS Algorithm according to claim 1, feature
It is：The step (3) is specially：
Enable α=0.0005；
Matrix R is the autocorrelation matrix of input vector x (k)：
E[xT(k) x (k)]=tr [R], tr [R] represents the mark of matrix R；
The renewal equation of more traditional LMS algorithm and the renewal equation of Normalized LMS Algorithm obtain again：
AbbreviationObtain 0 < μn< 2.
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