CN108444471A - A kind of accelerometer signal denoising method based on particle filter and wavelet transformation - Google Patents
A kind of accelerometer signal denoising method based on particle filter and wavelet transformation 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
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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
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Abstract
The invention discloses the accelerometer signal denoising methods based on particle filter and wavelet transformation, including：Particle is initialized, particle filter is applied to the preprocessing part of acceleration signal denoising, remains the low entropy of Wavelet Denoising Method；According to the relationship between observation and predicted value, the weight for obtaining each particle is calculated, the state of particle according to a preliminary estimate, give up weight smaller particless, overcome sample degeneracy phenomenon according to the weight after normalization；The preliminary state estimation of acceleration signal is transformed into wavelet field, chooses the number of plies of suitable wavelet basis and wavelet decomposition, the preliminary state estimation of acquisition is subjected to wavelet decomposition：Threshold value quantizing is carried out to the high frequency coefficient of wavelet decomposition, status signal is reconstructed using each layer coefficients of wavelet decomposition, the signal after reconstruct is the acceleration signal after noise reduction；The method is not required to consider accelerometer noise profile condition, by increasing the number of particles of particle filter, improves denoising degree.
Description
Technical field
The present invention relates to signal processing and autonomous positioning fields, more particularly to one kind being based on particle filter and wavelet transformation
Accelerometer signal denoising method.
Background technology
As the improvement of people's living standards, the demand for services based on location information such as navigation and path planning increases year by year
At present.Different from outdoor positioning, the solution that indoor positioning is widely accepted and is applied as GPS not yet at present.Phase
Than in such as RFID technologies for needing to dispose high hardware device, inertial sensor technology of low cost and easy to maintain is current
Obtain more and more concerns.But the measurement error of the accelerometer signal caused by noise can rapidly increase with accumulated time
Add, often result in that positioning accuracy is barely satisfactory, so the denoising to accelerometer signal is essential.It is common to be applied to practical work
Acceleration denoising method in journey has following several：
1, low-pass filtering method
The rule that low-pass filtering denoising is statistical property and spectrum distribution based on noise is carried out to accelerometer[1-2].With
For Butterworth LPF, the high fdrequency component in frequency domain is corresponded to according to noise, and acceleration signal spectrum distribution is one
Signal is transformed to frequency domain by the characteristics of a finite interval first with Fourier transformation by time domain, is then being designed suitably
Signal is reached into denoising effect using low-pass filtering after filter parameter.However noise of this method in filtering off high frequency is simultaneously
Some detailed information can be lost.
2, Wavelet noise-eliminating method
Wavelet noise-eliminating method[3-4]It can be summarized as three steps：Signals and associated noises are transformed to first with multi-scale wavelet transformation small
Wave zone chooses wavelet basis function appropriate, wavelet transformation is carried out to acceleration signal after determining the number of plies of wavelet decomposition.Then
By the threshold value quantizing of high-frequency wavelet coefficient, threshold value is carried out to wavelet coefficient using the threshold value of selection and is blocked.Finally by what is obtained
Wavelet coefficient completes wavelet inverse transformation, and reconstruction signal is then the signal after noise reduction.Wavelet noise-eliminating method has low entropy, can be very
The non-stationary property of signal is described well, and is simply easily achieved, therefore is used widely.
3, kalman filter method
Kalman filtering is the filter designed based on state equation and recurrence method, including time update equation and measurement
Renewal equation two parts[5], concrete model can be described as：
xk+1=Axk+Buk+wk (1)
yk=Cxk+vk (2)
Wherein, A is state-transition matrix, and B is the matrix of the certainty input and k+1 moment states that contact the k moment, and C is
Calculation matrix.xk+1And ykRespectively state and measured value, vkAnd wkRespectively process noise and measurement noise.Formula (1) is for pushing away
Current time state variable and error covariance estimated value are calculated to obtain the prior estimate of subsequent time state, formula (2) be used for by
The State Viewpoint measured value at prior estimate and current time can carry out optimal estimation to the state at current time.
Kalman filtering is to optimize autoregression data processing method, is merged in recent years in information[6], location navigation[7]Deng
Aspect is widely applied.But under inaccurate signal model, Kalman filtering can bring large error even to dissipate, and
It is only applicable to linear system and zero-mean, Gaussian Profile standard noise under the conditions of.And the particle filter side that the present invention utilizes
Method is non-parametrization wave filter, be can be used under the conditions of nonlinear and non-Gaussian.
Bibliography：
[1] Guo Xing defends filtering technique research [J] scientific and technical innovation Leaders of accelerometer signals, 2008 (22):4-5.
[2] once inertial track tracking [D] South China Normal Universitys of the snow coin based on 3-axis acceleration sensor, 2013.
[3]Wang H,Cheng Z,Yang J,et al.Research on wavelet de-noising method
based MEMS accelerator signal[C]//IEEE International Conference on
Information and Automation.IEEE, 2010:2001-2004.
[4] Jing Zhen, Zhao Luyang, He Wei wait the Wavelet Denoising Method in indoor location fingerprint positioning methods to apply [J] information skills
Art, 2016 (3):41-44.
[5]Fu Mengyin,Deng Zhihong,Zhang Jiwei.Kalman filter theory and its
applications in navigationsystem[M].Beijing:Science Press,2003
[6]Mahmood A,Baig A,Ahsan Q.Real time localization of mobile robotic
platform via fusion of Inertial and Visual Navigation System[C]//
International Conference on Robotics and Artificial Intelligence.IEEE,2013:
40-44.
[7] Wang Shuai, application [J] war industry automation of Wei state's Kalman filterings in quadrotor attitude measurement,
2011, 30(1):73-74.
Invention content
The accelerometer signal denoising method based on particle filter and wavelet transformation that the present invention provides a kind of, the present invention without
Accurately system model is needed, good denoising can be carried out to nonlinear and non-Gaussian system, it is described below：
Accelerometer signal denoising method based on particle filter and wavelet transformation, the described method comprises the following steps：
Particle is initialized, particle filter is applied to the preprocessing part of acceleration signal denoising, is remained small
The low entropy of wave denoising features the non-stationary property of acceleration signal, and good denoising is carried out to nonlinear and non-Gaussian system；
According to the relationship between observation and predicted value, the weight for obtaining each particle is calculated, according to the power after normalization
Again the state of particle according to a preliminary estimate, give up weight smaller particless, overcome sample degeneracy phenomenon；
The preliminary state estimation of acceleration signal is transformed into wavelet field, chooses suitable wavelet basis and the layer of wavelet decomposition
The preliminary state estimation of acquisition is carried out wavelet decomposition by number：
Threshold value quantizing is carried out to the high frequency coefficient of wavelet decomposition, status signal is carried out using each layer coefficients of wavelet decomposition
Reconstruct, the signal after reconstruct is the acceleration signal after noise reduction；
The method is not required to consider accelerometer noise profile condition, by increasing the number of particles of particle filter, carries
High denoising degree.Further, the method further includes：
Based on bayesian criterion, accelerometer is described as including the discrete dynamic system of state equation and observational equation；
According to system state equation, state value is predicted, obtains predicted value.
Wherein, described to be specially by the preliminary state estimation progress wavelet decomposition of acquisition：
Wherein, c is used for the coefficient of the approximate quantity and details coefficients according to certain sequential storage wavelet decomposition signal, and l is used for
The length of each approximation component and details coefficients coefficient is stored,For utilization ' db6' small echos pairCarry out 5
Layer decomposes.
Further, the method carries out autonomous inertial positioning using the acceleration signal after denoising, and positioning accuracy obtains
It is promoted.
The advantageous effect of technical solution provided by the invention is：
1, denoising method provided by the invention had both remained the low entropy of Wavelet Denoising Method, featured acceleration signal well
Non-stationary property, and be not required to be limited to linear Gaussian system as Kalman filter；
2, this method is not required to consider accelerometer noise profile condition, and application range is more extensive, by increasing particle filter
Denoising degree can be improved in the number of particles of device, and the denoising effect than being based only upon wavelet method is more preferable.
Description of the drawings
Fig. 1 is a kind of flow chart of the accelerometer signal denoising method based on particle filter and wavelet transformation；
Fig. 2 is the acceleration signal denoising effect figure for taking different populations；
Wherein, (a) population is 400；(b) population is 600；(c) population is 800；(d) population is 1000.
Fig. 3 is the denoising effect figure for taking different wavelet basis；
Fig. 4 is the Wavelet Denoising Method design sketch for taking the different decomposition number of plies.
Specific implementation mode
To make the object, technical solutions and advantages of the present invention clearer, embodiment of the present invention is made below further
It is described in detail on ground.
The service industry based on location information was fast-developing in recent years, and people increasingly increase accurately indoor positioning demand
It is more.Autonomous positioning technology based on inertial sensor is easy to maintain and receive more and more attention because required at low cost.And it is straight
The accelerometer output signal obtained often has been superimposed serious noise jamming, and the deviation accumulation of noise analyzes motion state
Prodigious deviation is caused with the precision of autonomous positioning, so it is most important to carry out denoising to accelerometer signal.
The embodiment of the present invention aims at a kind of accelerometer signal denoising method based on particle filter and wavelet transformation.
So-called particle filter refers to：The random sample propagated in state space by one group is to probability density function p (xk|zk) (wherein,
xkFor state value, zkBy measured value) it carries out approximation integral operation is replaced with sample average, to obtain state minimum variance estimate
Process, these samples i.e. be known as " particle ".
Particle filter is now widely used for the fields such as target following, but because its should not modulus Linear and Gauss, so
The embodiment of the present invention applies it to the stage that noise suppression preprocessing is carried out to acceleration signal.
Embodiment 1
Based on particle filter and wavelet transformation, the embodiment of the present invention propose it is a kind of based on particle filter and wavelet transformation plus
Speedometer signal denoising method.Since high-precision accelerometer is expensive, be not suitable for popularization and application, so poor to precision
The optimization processing that low cost acceleration meter signal carries out noise reduction becomes realistic plan.The embodiment of the present invention, which uses, combines grain
Son filtering and the thought of wavelet transformation achieve the purpose that optimize denoising to signal, described below referring to Fig. 1：
101：Particle is initialized, particle filter is applied to the preprocessing part of acceleration signal denoising, is retained
The low entropy of Wavelet Denoising Method, features the non-stationary property of acceleration signal, is well gone to nonlinear and non-Gaussian system
It makes an uproar；
102：According to the relationship between observation and predicted value, the weight for obtaining each particle is calculated, after normalization
Weight the state of particle according to a preliminary estimate, give up weight smaller particless, overcome sample degeneracy phenomenon；
103：The preliminary state estimation of acceleration signal is transformed into wavelet field, chooses suitable wavelet basis and wavelet decomposition
The number of plies, the preliminary state estimation of acquisition is subjected to wavelet decomposition：
104：Threshold value quantizing is carried out to the high frequency coefficient of wavelet decomposition, using each layer coefficients of wavelet decomposition to status signal
It is reconstructed, the signal after reconstruct is the acceleration signal after noise reduction.
In conclusion 101- steps 104 devise one kind without accurately system to the embodiment of the present invention through the above steps
Model, so that it may to the method that nonlinear and non-Gaussian system carries out good denoising, this method had both remained the low entropy of Wavelet Denoising Method,
The non-stationary property of acceleration signal is featured well, and is not required to be limited to linear Gaussian system as Kalman filter.
Embodiment 2
With reference to Fig. 1, specific calculation formula, the scheme in embodiment 1 is further introduced, it is as detailed below
Description：
201：Based on bayesian criterion, accelerometer can be described as moving comprising state equation and the discrete of observational equation as follows
State system；
xk=f (xk-1)+vk-1 (3)
zk=hk(xk)+wk (4)
Wherein, formula (3) is state equation, for indicating that discrete dynamic system state changes with time；Formula (4) is observation
Equation describes the relationship of certain moment state and observed quantity.K is index, xkAnd zkRespectively state variable and measurand, vkWith
wkRespectively process noise and measurement noise.F () state transition equation, h () are observational equation.
202：Particle is initialized；
Sample particlesInitialization obtained by following formula：
Wherein,For i-th of primary, sqrt is sqrt function, and P is covariance, and randn is random number
Function.In addition it is 1/N by each sample particles weight assignment (N is population).
Particle filter is applied to the preprocessing part of acceleration signal denoising, without accurately system model.Current grain
The sub- widest field of filtering application is target following, and in addition in digital communicating field, the fields such as image procossing also obtain extensively
Using.The embodiment of the present invention is not only restricted to the constraint that model is linear, Gauss assumes based on particle filter, applies it to accelerating
It spends signal and carries out the pretreated stage.So being different from Kalman filtering, the embodiment of the present invention, can without accurately system model
Good denoising is carried out to nonlinear and non-Gaussian system.
203：According to system state equation (i.e. formula (3)), state value is predicted, obtains predicted value；
K=2,3 ..., tf (tf is state total number).
Wherein,For i-th of predicted value, N is total number of particles, i=1,2 ..., N.
204：According to the relationship between observation and predicted value, the weight for obtaining each particle is calculated by following equation；
Wherein, vhat is the difference of observation and predicted value, and R is measurement noise covariance matrix,For i-th particle
Weight, pi are pi, and exp is the exponential function using e the bottom of as.
205：Weight is normalized；
206：State is according to a preliminary estimate：
207：Give up the smaller particle of weight, is replaced with the particle that weight is larger, sample degeneracy can be overcome in this way
Phenomenon；
208：The preliminary state estimation of acceleration signal is transformed into wavelet field, chooses suitable wavelet basis and wavelet decomposition
Number of plies K, the preliminary state estimation of acquisition is subjected to wavelet decomposition：
Wherein, c is used for the coefficient of the approximate quantity and details coefficients according to certain sequential storage wavelet decomposition signal, and l is used for
The length of each approximation component and details coefficients coefficient is stored,For utilization ' db6' small echos pairCarry out 5
Layer decomposes.
In practical application, common wavelet basis has Daubechies, Coiflets, Symlets, orthogonal wavelet and biorthogonal
Small echo, the part is known to those skilled in the art, and the embodiment of the present invention does not repeat this.
209：Threshold value quantizing is carried out to the high frequency coefficient of wavelet decomposition；
Wherein, common threshold function table has soft-threshold function and hard threshold function, calculates as shown in formula (11) and (12)：
Adoptable two kinds of processing modes when being the threshold value quantizing to wavelet decomposition high frequency coefficient of formula 11,12, respectively soft-threshold are divided
Divide with hard -threshold, when concrete application answers alternative.
Wherein, fT(wjk) be threshold value block after wavelet coefficient, wjkFor the coefficient of k-th of high fdrequency component of jth layer, sgn is
Jump function.TjkFor k-th of high fdrequency component coefficient threshold of jth layer, for calculation formula such as shown in (13), N is that acceleration signal is long
Degree.
210：Status signal is reconstructed using each layer coefficients of wavelet decomposition, after the signal after reconstruct is noise reduction
Acceleration signal：
Wherein,Acceleration signal after optimizing for noise reduction, waverec (c5, l, ' db6') it is based on 5 layers of decomposition texture
And ' db6' small echos rebuild acceleration signal.
Referring to Fig. 2, it is shown that this method is more preferable compared with the denoising degree for being based only upon particle filter method, and effect is smoother；And
This method further can optimize acceleration signal, overcome and be based only upon Wavelet Denoising Method side by the adjustment to population
Method after wavelet basis and Decomposition order determine the shortcomings that cannot be adjusted.
Embodiment 3
The feasibility of scheme in Examples 1 and 2 is verified with reference to Fig. 3-Fig. 4 and table 1- tables 2, is referred to down
Text description：
Quantitative aspect, table 1 show the increase with population, denoising root-mean-square error of this method to acceleration signal
It continuously decreases.And the denoising effect for choosing default threshold is better than and takes soft-threshold and hard -threshold.Table 2 be to using particle filter,
Acceleration signal after wavelet transformation and this method denoising carries out double integral, to the example to real trace length for 3.8m
The error result positioned.Position error the result shows that, using this method to acceleration signal carry out denoising after positioning accurate
Degree is substantially better than other denoising methods.
When being pre-processed to acceleration signal using particle filter, to obtain best denoising effect, in the reality of table 2
Population is chosen for 1000 in the application of border, but this parameter needs suitably to be adjusted under different application conditions, as acceleration is believed
Number dynamic change it is larger, selected population also can accordingly increase.In the resampling stage, judgment criterion that this method is taken
For the random number for generating in (0,1) range at random, it is compared with the normalized weight of the particle, if normalized weight is big
In random number, then the particle is retained to following iteration, otherwise is given up the particle for replacing with big weight.
Table 1 blocks the denoising root-mean-square error (RMSE) under mode in different populations and threshold value
Table 2 utilizes the acceleration position error after different filtering method denoisings
Fig. 3 shows that, in the denoising effect for choosing different wavelet basis, by comparing analyzing, the embodiment of the present invention exists
Daubechies wavelet basis is used in the selection of wavelet basis.Meanwhile Fig. 4 presents the effect of denoising when taking the different decomposition number of plies
Fruit, it can be seen that in Decomposition order K=6, be not only effectively maintained useful accelerometer signal, but also very to noise remove
It is good.
The step of taking the embodiment of the present invention to describe is configured each parameter as above-mentioned, can obtain good denoising
Effect, and the experimental results showed that, the embodiment of the present invention shows good in qualitative analysis and quantitative objective indicator evaluation
Effect.Autonomous inertial positioning is carried out using the acceleration signal after this method denoising, positioning accuracy has obtained significantly being promoted,
Each service field based on location information has certain actual application value.
To the model of each device in addition to doing specified otherwise, the model of other devices is not limited the embodiment of the present invention,
As long as the device of above-mentioned function can be completed.
It will be appreciated by those skilled in the art that attached drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
Serial number is for illustration only, can not represent the quality of embodiment.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all the present invention spirit and
Within principle, any modification, equivalent replacement, improvement and so on should all be included in the protection scope of the present invention.
Claims (4)
1. the accelerometer signal denoising method based on particle filter and wavelet transformation, which is characterized in that the method includes with
Lower step：
Particle is initialized, particle filter is applied to the preprocessing part of acceleration signal denoising, small echo is remained and goes
The low entropy made an uproar features the non-stationary property of acceleration signal, and good denoising is carried out to nonlinear and non-Gaussian system；
According to the relationship between observation and predicted value, the weight for obtaining each particle is calculated, according to the weight pair after normalization
The state of particle according to a preliminary estimate, give up weight smaller particless, overcome sample degeneracy phenomenon；
The preliminary state estimation of acceleration signal is transformed into wavelet field, chooses the number of plies of suitable wavelet basis and wavelet decomposition,
The preliminary state estimation of acquisition is subjected to wavelet decomposition：
Threshold value quantizing is carried out to the high frequency coefficient of wavelet decomposition, weight is carried out to status signal using each layer coefficients of wavelet decomposition
Structure, the signal after reconstruct are the acceleration signal after noise reduction；
The method is not required to consider accelerometer noise profile condition, and by increasing the number of particles of particle filter, raising is gone
It makes an uproar degree.
2. the accelerometer signal denoising method according to claim 1 based on particle filter and wavelet transformation, feature
It is, the method further includes：
Based on bayesian criterion, accelerometer is described as including the discrete dynamic system of state equation and observational equation；
According to system state equation, state value is predicted, obtains predicted value.
3. the accelerometer signal denoising method according to claim 1 based on particle filter and wavelet transformation, feature
It is, the preliminary state estimation by acquisition carries out wavelet decomposition and is specially：
Wherein, c is used for the coefficient of the approximate quantity and details coefficients according to certain sequential storage wavelet decomposition signal, and l is for storing
The length of each approximation component and details coefficients coefficient,For utilization ' db6' small echos pairCarry out 5 layers points
Solution.
4. the accelerometer signal denoising method according to claim 1 based on particle filter and wavelet transformation, feature
It is, the method carries out autonomous inertial positioning using the acceleration signal after denoising, and positioning accuracy is improved.
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| CN113049202A (en) * | 2021-03-08 | 2021-06-29 | 中国地震局工程力学研究所 | Local weighted regression correction method and system for acceleration integral displacement |
| CN113360840A (en) * | 2021-05-25 | 2021-09-07 | 北京北电科林电子有限公司 | Special vehicle positioning correction method based on data preprocessing |
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