CN109871508A - There are the centralized two stages kalman estimate methods of correlated measurement noise - Google Patents
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Abstract
There are the centralized two stages kalman estimate methods of correlated measurement noise the present invention relates to a kind of.For the filtering problem for the multi-sensor measurement system that there is the correlated measurement noise for influencing measured value, the present invention is by introducing decorrelation technique, it re-establishes a kind of measurement noise incoherent measurement equation and the optimal estimation value of system mode is obtained by two-stage Kalman filter device.Method proposed by the invention is compared with directly utilizing two stages Kalman method, although data fusion result is identical, computation complexity is substantially reduced.
Description
Technical field
The invention belongs to wave filter technology field, in particular to a kind of there are cards of the centralized two stages of correlated measurement noise
Germania estimation method.
Background technique
Kalman Filter Technology needs accurate process dynamics and measurement model.In many actual conditions, deviation shadow
Acoustic system dynamics and observation may cause performance decline if deviation is not included in model.Dual stage process is unknown inclined to handling
The state estimation of poor system is highly effective, because it can be improved calculated performance and prevents the generation of dimension disaster.
In the 1960s, Friedland is proposed two-stage Kalman filter device (TKF), basic thought be by
Strengthened condition filter (ASKF) is decoupled into two filters, i.e. low-dimensional " zero deflection " filter and " deviation " filter, and
Best estimate can be counted as the output of the zero deflection filter by the output calibration of deviation filter.Hsieh is proposed most
Excellent two-stage Kalman filter device.
Unfortunately, current two-stage Kalman filter in application field there is apparent limitation, such as not phase
Close noise and linear system etc..But in a practical situation, noise correlation system is often existing.Such as: (1) due to
System is influenced by from internal component and external environment variation, and the noise that may result in system has correlation, (2)
It is coloured noise system for measurement noise, after its noise is extended for state, can also converts original system to noise phase relation
System.(3) field of Multi-sensor Fusion is needed in maneuvering target tracking etc., often there is also noise correlation circumstances.
Multisensor Data Fusion technology is used widely in target following, and reason is that it can be provided than single
The more accurate Combined estimator information of sensor.Multi-sensor information fusion is as a kind of informix and processing technique, also referred to as
Fusion is the New borderline subjects occurred the 1980s, the information that each sensor is provided
Fusion, which is carried out, by certain Optimality Criteria generates new fusion results.Fusion results estimate more effective utilize relative to single-sensor
The information of each sensor, estimation is more accurate and complete, and the precision for merging estimation is higher than the precision of each sensor estimation.It is more
Sensor data fusion improves the reliability and robustness of system, extends the observation of observation information temporally and spatially
Dimension enhances the resolution capability of system, enhances the confidence level and precision of information fusion.It is many due to Multi-sensor Fusion
Advantage, in recent years, multi-sensor information fusion technology are all obtained in many high-tech areas such as military field and civil field
Extensive development and application.
Since the derivation of conventional two-stage Kalman filter algorithm is to be based on the incoherent linear Gaussian system of noise
It unites between noise and measurement noise, measures incoherent white Gaussian noise between noise.But in a practical situation, noise is related
System is often existing.
Summary of the invention
In order to cope with measurement noise correlation and dynamic deviation situation above-mentioned, present invention introduces square root factorization and ask
Inverse approach obtains the two-stage Kalman filter device under measurement noise correlated condition, proposes the collection there are correlated measurement noise
Chinese style two stages kalman estimate method.
The present invention can be generally divided into four parts.
First part is that system model is established.
Second part introduces square root factorization and inversion technique, re-establishes a kind of incoherent measurement side of measurement noise
Journey.
Part III to target it is all observe come when, based on system previously oneself information for having had to the moment dbjective state
Predictive estimation is carried out, then the target state estimator value is updated using Kalman filter and each local observation, thus
Fusion estimated value to the moment target based on global information.
Part IV is combined the estimated information of zero deflection state and deviation by linear combination.
Beneficial effects of the present invention: measurement noise correlation can be handled, relatively single two-stage Kalman filter
Device, the present invention can obtain the more fine estimation to zero deflection state and deviation.The method of proposition with directly utilize two stages
Kalman's method is compared, although data fusion result is identical, computation complexity is substantially reduced.
Detailed description of the invention
Fig. 1 is flow chart of the present invention.
Specific embodiment
Specific implementation step of the invention can be found in Fig. 1, comprising the following steps:
Step 1. system modelling
Considering a kind of common band deviation multisensor syste is model, and system mode noise statistics are it is known that deposit
It is described as follows in the state equation of the system of correlated measurement noise, deviation equation and measurement equation:
In formula, k indicates time series；xk,bkAnd yi,kRespectively system n ties up the p of state, m dimension deviation and i-th of sensor
Dimension observation；And vi,kThe respectively measurement noise of system mode noise, system deviation noise and i-th of sensor；Ak+1,k
∈Rn×nFor state-transition matrix；Ci,k∈Rp×nFor the state matrix of i-th of sensor.State-noise, deviation noise and measurement
Noise is zero mean Gaussian white noise sequence:
And the correlation of i-th of sensor and the measurement noise of j-th of sensor is as follows:
Step 2. introduces square root factorization and inversion technique, re-establishes a kind of incoherent measurement equation of noise
For the band deviation multisensor syste that step 1 provides, i-th of sensor and j-th of sensor must measure noise
There are correlations, can not directly use two-stage Kalman filter device.Therefore, noise decorrelation technique is introduced, to measurement equation
It is converted, is obtained and the measurement incoherent new system mode noise of noise.Reconstruction process is as described below: considering based on all
Measured value { the y of sensor1,k,y2,k,...,yN,k}。
It enables
Then fusion center is represented by corresponding to the broad sense measurement equation of this N number of sensor
yk=Ckxk+Dkbk+vk (3)
The variance matrix of the measurement noise of multiple sensors is
In practice, the nonlinear system with correlated noise often exists, if traditional two-stage Kalman filter
Algorithm is still applied to these systems, and complexity will be improved inevitably.Multisensor measurement relevant for measurement noise
Model is translated into the irrelevant broad sense of measurement noise using the inversion technique of square root factorization and unit lower triangular matrix
Multisensor measures equation.
Due to Rk=[rij,k] be a positive definite real symmetric matrix, according to the Cholesky of matrix decompose it is found that RkIt can be unique
It resolves on ground
Wherein, Lk=[lij,k] it is unit inferior triangular flap, D=diag (d1,d2,...,dNm) and positive definite,
For unit lower triangular matrix Lk, inverse matrix presence, and be still unit inferior triangular flap, note
By MkCarry out Partitioning Expression of A
In formula measurement equation both sides premultiplication with Mk, then the broad sense measurement equation of multisensor can be converted to
zk=Gkxk+Pkbk+ηk (4)
Wherein,
zk=Mkyk, Gk=MkCk, Pk=MkDk,
The measurement equation of original system is rewritten as
Step 3. measures equation according to broad sense and obtains zero deflection state using two-stage Kalman filter deviceAnd deviation
bkEstimated informationSpecifically:
The known k-1 moment is to system zero deflection stateEstimated valueThen k moment zero deflection statePrediction
Value is
The known k-1 moment is to system zero deflection stateEstimation error variance battle arrayThe then zero deflection at k moment
StatePrediction varivance matrix be
The zero deflection state at k momentGain matrix be
The zero deflection state at k momentEstimation error variance matrix be
The zero deflection state at k momentEstimated value be
If deviation bkIt is ignored, zero deflection state filter is exactly the Kalman filter based on equation 1.Its
In it is noted that the varivance matrix of noise of state equation becomesIt is not
The known k-1 moment is to system deviation bkEstimated value bk-1/k-1, then k Time of day offsets bkPredicted value be
bk/k-1=bk-1/k-1 (11)
The known k-1 moment is to system deviation bkEstimation error variance battle arrayThe then deviation b at k momentkPrediction miss
Poor variance matrix is
The deviation b at k momentkGain matrix be
The deviation b at k momentkEstimated value be
The deviation b at k momentkEstimation error variance matrix be
Wherein, I is unit matrix.
Residual error is
Sensitivity matrix 1 is
Sensitivity matrix 2 is
Uk=Ak,k-1Vk+Bk,k-1 (18)
Noise adaptive error covariance matrix is
Step 4. passes through linear combination for zero deflection stateWith deviation bkEstimated informationIt combines, obtains system mode xkEstimated information
In formula, VkIt is fusion factor.
Claims (1)
1. there are the centralized two stages kalman estimate methods of correlated measurement noise, it is characterised in that this method includes following step
It is rapid:
Step 1. system modelling
Considering a kind of common band deviation multisensor syste is model, and system mode noise statistics are it is known that there are phases
The state equation, deviation equation and measurement equation for closing the system of measurement noise are described as follows:
In formula, k indicates time series；xk,bkAnd yi,kRespectively system n ties up the p Wei Guan of state, m dimension deviation and i-th of sensor
It surveys；And vi,kThe respectively measurement noise of system mode noise vector, system deviation noise vector and i-th of sensor
Vector；Ak+1,k∈Rn×nFor state-transition matrix；Ci,k∈Rp×nFor the state matrix of i-th of sensor；State-noise, deviation are made an uproar
Sound and measurement noise are zero mean Gaussian white noise sequences: vi,k~N (0,
Ri,k), and the correlation of i-th of sensor and the measurement noise of j-th of sensor is as follows:
Step 2. introduces square root factorization and inversion technique, re-establishes a kind of incoherent measurement equation of noise；
Noise decorrelation technique is introduced, measurement equation is converted, is obtained and the measurement incoherent new system mode of noise
Noise；Reconstruction process is as follows: in view of the measured value { y based on all the sensors1,k,y2,k,...,yN,k}
It enables
Then fusion center is expressed as corresponding to the broad sense measurement equation of this N number of sensor
yk=Ckxk+Dkbk+vk (3)
The variance matrix of the measurement noise of multiple sensors
Multisensor measurement model relevant for measurement noise, utilizes the side of inverting of square root factorization and unit lower triangular matrix
Method is translated into the irrelevant broad sense multisensor measurement equation of measurement noise；
Due to Rk=[rij,k] be a positive definite real symmetric matrix, according to the Cholesky of matrix decompose it is found that RkCan uniquely it divide
Xie Cheng
Wherein, Lk=[lij,k] it is unit inferior triangular flap, D=diag (d1,d2,...,dNm) and positive definite,
For unit lower triangular matrix Lk, inverse matrix presence, and be still unit inferior triangular flap, note
By MkCarrying out Partitioning Expression of A is
In measurement equation both sides premultiplication with Mk, then multisensor broad sense measurement it is equations turned at
zk=Gkxk+Pkbk+ηk (4)
Wherein,
zk=Mkyk, Gk=MkCk, Pk=MkDk,
The measurement equation of original system is rewritten as
Step 3. measures equation according to broad sense and obtains zero deflection state using two-stage Kalman filter deviceWith deviation bk's
Estimated informationSpecifically:
The known k-1 moment is to system zero deflection stateEstimated valueThen k moment zero deflection statePredicted value be
The known k-1 moment is to system zero deflection stateEstimation error variance battle arrayThe then zero deflection state at k momentPrediction varivance matrix be
The zero deflection state at k momentGain matrix be
The zero deflection state at k momentEstimation error variance matrix be
The zero deflection state at k momentEstimated value be
The known k-1 moment is to system deviation bkEstimated value bk-1/k-1, then k Time of day offsets bkPredicted value be
bk/k-1=bk-1/k-1 (11)
The known k-1 moment is to system deviation bkEstimation error variance battle arrayThe then deviation b at k momentkPrediction error side
Poor matrix is
The deviation b at k momentkGain matrix be
The deviation b at k momentkEstimated value be
The deviation b at k momentkEstimation error variance matrix be
Wherein, I is unit matrix；
Residual error is
Sensitivity matrix 1 is
Sensitivity matrix 2 is
Uk=Ak,k-1Vk+Bk,k-1 (18)
Noise adaptive error covariance matrix is
Step 4. passes through linear combination for zero deflection stateWith deviation bkEstimated informationGroup
Altogether, system mode x is obtainedkEstimated information
In formula, VkIt is fusion factor.
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| CN110710981A (en) * | 2019-09-23 | 2020-01-21 | 浙江工业大学 | Blood oxygen content estimation method based on binary sensor Kalman fusion |
| CN110720929A (en) * | 2019-09-23 | 2020-01-24 | 浙江工业大学 | Blood oxygen content estimation method based on binary sensor bounded recursive optimization fusion |
| CN111062359A (en) * | 2019-12-27 | 2020-04-24 | 广东海洋大学深圳研究院 | Two-stage Kalman filtering fusion method based on noise sequential decorrelation |
| CN112649804A (en) * | 2020-12-21 | 2021-04-13 | 杭州电子科技大学 | Centralized multi-sensor fusion filtering method based on characteristic function |
| CN114046785A (en) * | 2021-11-10 | 2022-02-15 | 广东微电科技有限公司 | Magnetic detection signal linear noise filtering method and system, computer readable storage medium, magnetic navigation sensor and AGV trolley |
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Cited By (6)
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|---|---|---|---|---|
| CN110710981A (en) * | 2019-09-23 | 2020-01-21 | 浙江工业大学 | Blood oxygen content estimation method based on binary sensor Kalman fusion |
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| CN111062359A (en) * | 2019-12-27 | 2020-04-24 | 广东海洋大学深圳研究院 | Two-stage Kalman filtering fusion method based on noise sequential decorrelation |
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| CN114046785A (en) * | 2021-11-10 | 2022-02-15 | 广东微电科技有限公司 | Magnetic detection signal linear noise filtering method and system, computer readable storage medium, magnetic navigation sensor and AGV trolley |
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