CN110501686A - A kind of method for estimating state based on NEW ADAPTIVE high-order Unscented kalman filtering - Google Patents
A kind of method for estimating state based on NEW ADAPTIVE high-order Unscented kalman filtering Download PDFInfo
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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Abstract
The present invention discloses the method for estimating state based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering, belongs to the state estimation field in passive radar tracking to high speed carrier.The present invention includes: to establish the state model and measurement model of the nonlinear discrete of Target Tracking System；Optimal free parameter κ is selected according to Target Tracking System state dimension；It establishes high-order UT and obtains state using point and weight；Sampled point is transmitted through nonlinear function；Optimal adaptive factor is brought into state one-step prediction covariance matrix；It establishes high-order UT and obtains measurement using point and weight；Sampled point is transmitted through nonlinear function；The calculating of gain matrix；The output of posteriority state estimation output and covariance matrix.The present invention restrained effectively the influence of strong nonlinearity maneuvering target and macromutation to filter, has good influence to different sampling intervals and different corner rates, reduces the influence of dynamic model error.
Description
Technical field
The invention belongs to, to the state estimation field of high speed carrier, be based on a kind of NEW ADAPTIVE in passive radar tracking
The method for estimating state of high-order Unscented kalman filtering.
Background technique
State estimation is aspect most basic in field of digital signals, is the problem of digital signal to nonlinear processing,
Nonlinear filter is the favorable method for handling dynamical system.People are to be made that many contributions to nonlinear processing.Its
In include most typical method extended Kalman filter (EKF), the method is approximately thought based on nonlinear function
Think, and require to guarantee nonlinear function continuously differentiable or can lead, Jacobi will be carried out in technological layer for the method
(Jacobian) solution of matrix.The solving complexity of Jacobian matrix is high in engineer application, is difficult to realize, and
Under the conditions of strong nonlinearity, the method can dissipate, or even failure.
In addition scholar solves the problems, such as by the approximate method proposition of probability density distribution nonlinear.Such as volume karr
Graceful filter (Cubature Kalman filter, CKF), centered difference Kalman filter (central difference
Filter, CDKF), Gauss-Hermite (Gauss-Hermite filter, GHF) etc..What these nonlinear transformations obtained
As a result the Posterior Mean and covariance of system state distribution, completion status estimation be can satisfy, and can achieve three rank Taylor's essences
Degree approaches any non-linear.Effect wants excellent and EKF.There are also the particle filter (Particle deduced under Bayesian frame
filter,PF).PF is unable to satisfy in engineering for a long time due to the problems such as can not solving sample degeneracy and calculation amount restriction
Demand is merely resting on theory analysis and analogue simulation stage.
Recent years the research of UKF is arisen spontaneously, UKF by the way of Unscented transform (UT), and
The transmitting of nonlinear function is carried out using 2n+1 symmetric points, as shown in Figure 1.Instead of EKF local linearization.Therefore it does not require
It function of state and measures the continuous of function and leads or can be micro-, estimated accuracy is positively retained at second order Taylor's precision.Computation complexity is small
In PF.A kind of (Aerospace Science and Technology, 2017,71:12-24.) method utilizes maximum a posteriori
Concept and random weighting criterion establish noise statistics data, propose a kind of new adaptive based on maximum a posteriori and random weighting
Answer UKF (MRAUKF) algorithm.However, the big impulse response for state mutation, filtering convergence is poor.Another is based on
The nonlinear dynamic system event trigger data transmission of UKF and packet loss nonlinear filtering algorithm (International Journal
Of Robust&Nonlinear Control, vol.27, no.18,2017.), and be applied in wireless sensor network,
The adequate condition of predicting covariance bounded convergence has been obtained, has obtained the adequate condition of filter Stochastic stable, but for
The biggish carrier of the speed of service, filter effect are poor.(Journal of the Franklin Institute,vol.354,
No.18,2017.) three rank UKF of three rank UKF and robust, though precision has promotion, computation complexity is higher.(IET Science
Measurement&Technology, vol.6, no.6, pp.502-509,2012.) utilize Huber-m estimation method raising UKF
Robustness, and by minimize Huber cost function, i.e. l1Norm and l2Norm improves the robustness of UKF.However,
The influence function of Huber will not be reduced, this may reduce the estimation performance of filtering algorithm.On the other hand High Order Moment is considered
It is lost with information, the improvement for also thering are many scholars to carry out, for example, quadravalence UKF (Proceedings of SPIE-The
International Society for Optical Engineering, 1997,3086:110-121.), five rank UKF
A kind of (IEEE Transactions on Signal Processing, 2006,54 (8): 2910-2921.) UKF of the degree of bias
(International Journal of Control, 2016,89 (12): 1-16.), another method are to match average side
The border degree of bias and the method for average marginal kurtosis prediction (Mathematical Theory of Networks and Systems,
June 2010).But improved from essential meaning, precision is still to be improved.
Summary of the invention
The purpose of the present invention is overcoming the limitation of above-mentioned filtering algorithm, UKF algorithm is inherently improved, and strong non-thread
Under the conditions of property, a kind of analytic solutions are obtained.The invention discloses the shapes based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering
State estimation method.
A kind of method for estimating state based on NEW ADAPTIVE high-order Unscented kalman filtering comprising the steps of:
Step 1: the state model and measurement model of the nonlinear discrete of Target Tracking System are established；
Step 2: optimal free parameter κ is selected according to Target Tracking System state dimension；
Step 3: it establishes high-order UT and obtains state using point and weight；
Step 4: sampled point is transmitted through nonlinear function, and is weighted processing and is obtained state one-step prediction and state
One-step prediction covariance matrix；
Step 5: optimal adaptive factor is brought into state one-step prediction covariance matrix；
Step 6: it establishes high-order UT and obtains measurement using point and weight；
Step 7: sampled point is transmitted through nonlinear function, and is weighted processing and is obtained measuring one-step prediction and measurement
One-step prediction covariance matrix and Cross-covariance；
Step 8: the calculating of gain matrix；
Step 9: the output of posteriority state estimation output and covariance matrix, into next iteration.
Step 1 includes:
Wherein state equation is xk=fk-1(xk-1)+wk-1, measurement equation zk=hk(xk)+vk, k expression kth step, k-1 table
Show -1 step of kth；xkIndicate the n dimension tracking target component state vector of kth step, zkFor the measurement of the m dimension tracking target of+1 step of kth
Vector, f () and h () are known nonlinear function, wk-1And vkRespectively represent k-1 step n dimension stochastic system noise and
Kth walks the measurement noise of m dimension；And it is Q that stochastic system noise obedience mean value, which is 0 variance,k-1Gaussian Profile, Qk-1Indicate kth-
The variance matrix of 1 step system noise；It is R that Stochastic Measurement Noises vector obedience mean value, which is 0 variance,kGaussian Profile, RkIndicate kth step
The variance matrix of noise is measured, and meets wk-1With vkIt is uncorrelated.
Step 2 includes:
According to cost function G(n,κ)=(n-1) κ2+(2n2-14n)κ+n3-13n2+ 60n-60, and minimize cost function
Obtain free parameter κ；When system is second-order system, free parameter is κ=0.835；The free parameter when system is third-order system
For κ=1.417；When system is fourth-order system, free parameter is κ=2.
Included by step 3:
Step 3.1: first kind sampled point and weight are established according to the following formula:
Step 3.2: the second class sampled point and weight are established according to the following formula:
Step 3.3: third class sampled point and weight are established according to the following formula:
WhereinWithMeet following formula:
ei1=[0 ... 0,1,0 ... 0]
Step 4 includes:
Step 4.1: the sampled point for calculating state equation according to the following formula is propagated
Step 4.2: estimated state one-step prediction according to the following formula
Step 4.3: estimated state one-step prediction covariance P according to the following formulak|k-1:
Step 5 includes:
Wherein
Step 6 includes:
Step 6.1: first kind sampled point and weight are established according to formula (14):
Step 6.2: the second class sampled point and weight are established according to formula (15):
Step 6.3: third class sampled point and weight are established according to formula (16):
Step 7 includes:
Step 7.1: the sampled point for calculating measurement equation according to the following formula is propagated
Step 7.2: estimation measures one-step prediction according to the following formula
Step 7.3: measuring one-step prediction covariance according to the following formulaAnd Cross-covariance
Step 8 includes:
The gain matrix of self-adaption high-order UKF is calculated according to the following formula:
Step 9 includes:
The output of kth step dbjective state output and covariance matrix is carried out with following formula according to the following formula:
Compared with the prior art, the advantages of the present invention are as follows:
1. the first two square can only be captured for general approximate Gaussian filtering algorithm.In order to capture high-order moment, improve
Estimated accuracy proposes a kind of high-order UT sampling policy with free parameter, and is brought under UKF frame.
2. being based on orthogonality principle, adaptive factor, further adjust gain square are introduced in state one-step prediction covariance
Battle array, restrained effectively the influence of strong nonlinearity maneuvering target and macromutation to filter, to different sampling intervals and different turns
Angle rate has good influence, reduces the influence of dynamic model error.
Detailed description of the invention
Fig. 1 is standard UT sampling point distributions figure,
Fig. 2 is high-order UT sampling point distributions figure,
Fig. 3 is the root mean square error curve of location estimation,
Fig. 4 is the root mean square error curve of velocity estimation,
Fig. 5 is algorithm flow chart.
Specific embodiment
The present invention is explained in detail with reference to the accompanying drawing:
The present invention relates to field of signal processing, it is therefore intended that needs to constantly update data letter in target following state estimation
Breath, and the presence of analytic solutions is had no in the target of high-speed cruising, under the conditions of strong nonlinearity, it will appear model under non-ideal condition
Mismatch and high-order moment are lost, to influence the precision and robust performance of state estimation.The present invention is filtered for Generalized Gaussian
Device proposes a kind of NEW ADAPTIVE high-order Unscented kalman filtering in the case where Model Matching difference and high-order moment are lost
The method for estimating state of (Adaptive High-order Unscented Kalman Filter, AHUKF).By introducing certainly
By parameter κ, a kind of method for obtaining high-order Unscented kalman filtering (high-order UKF, HUKF) with analytic solutions.And
Selection gist is analyzed in theory.It is based on orthogonality principle on this basis, proposes a kind of based on prediction residual estimation association side
The selection method of the optimal adaptive factor of poor matrix, and be introduced into state one-step prediction covariance, it reduces kinetic model and misses
The influence of difference.The present invention is verified in target following model using big sampling interval and big exploitation speed.Test knot
Fruit shows that method proposed by the present invention is higher than existing method precision.And binding time analysis of complexity has good
Practical application value.
By introducing free parameter κ, a kind of sampled point strategy of high-order UT transformation with analytic solutions is obtained, such as Fig. 2 institute
It states, and analyzes selection gist in theory.It is based on orthogonality principle on this basis, proposes a kind of based on prediction residual estimation
The selection method of the optimal adaptive factor of covariance matrix, and be introduced into state one-step prediction covariance, reduce kinetic simulation
The influence of type error.In particular under the non-ideal condition that strong nonlinearity, state mutation and high-order moment are lost.Specifically
Refer to the processing of the disturbance, different sampling interval and different running rate passive radar big to carrier state to signal, and
To the estimation method of carrier state.The present invention and standard UKF algorithm, adaptive UKF algorithm and high-order UKF algorithm are big
Compare under the non-ideal condition of state model mutation, different sampling intervals and different running rates, is verified by Monte Carlo
Showing the present invention has higher precision of state estimation and better robustness.And binding time analysis of complexity, this hair
It is bright that there is good practical application value.
Below in conjunction with attached drawing 5 to the shape proposed by the present invention based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering
State estimation method is described in further detail.Embodiment flow chart is shown in Fig. 5.
Specific implementation method one can be divided into the following steps:
Step 1: the state model and measurement model of target following nonlinear discrete are established；
Step 2: optimal free parameter κ is selected according to Target Tracking System state dimension；
Step 3: it establishes high-order UT and obtains state using point and weight；
Step 4: sampled point is transmitted through nonlinear function, and is weighted processing and is obtained state one-step prediction and state
One-step prediction covariance matrix；
Step 5: optimal adaptive factor is brought into state one-step prediction covariance matrix；
Step 6: it establishes high-order UT and obtains measurement using point and weight；
Step 7: sampled point is transmitted through nonlinear function, and is weighted processing and is obtained measuring one-step prediction and measurement
One-step prediction covariance matrix and Cross-covariance；
Step 8: the calculating of gain matrix；
Step 9: the output of posteriority state estimation output and covariance matrix, into next iteration.
The state model and measurement model of the established target following nonlinear discrete of step 1 are as follows:
Wherein state equation is xk=fk-1(xk-1)+wk-1, measurement equation zk=hk(xk)+vk, k expression kth step, k-1 table
Show -1 step of kth.xkIndicate the parameter state vector of the n dimension tracking target of kth step, zkFor the amount of the m dimension tracking target of+1 step of kth
Direction finding amount, f () and h () are known nonlinear function, wk-1And vkRespectively represent the n dimension stochastic system noise of k-1 step
With the measurement noise of kth step m dimension.And it is Q that stochastic system noise obedience mean value, which is 0 variance,k-1Gaussian Profile, Qk-1Indicate the
The variance matrix of k-1 step system noise.It is R that Stochastic Measurement Noises vector obedience mean value, which is 0 variance,kGaussian Profile, RkIndicate kth
Step measures the variance matrix of noise, and meets wk-1With vkIt is uncorrelated.
The detailed process of optimal free parameter k is selected described in step 2 according to the system mode dimension of tracking target are as follows:
According to cost function G(n,κ)=(n-1) κ2+(2n2-14n)κ+n3-13n2+ 60n-60, and minimize cost function
Obtain free parameter κ.When system is second-order system, free parameter is κ=0.835.The free parameter when system is third-order system
For κ=1.417.When system is fourth-order system, free parameter is κ=2.Method proposed by the present invention is than second order UKF not at this time
With under free parameter and high-order UKF and adaptive UKF has higher precision and performance.
Establishment high-order UT described in step 3 obtains state using point and the process of weight are as follows:
Given initial valuePk-1=P0, and utilize high-order UT constructing tactics sampled point and weight.
First kind sampled point and weight are determined according to formula (2):
The second class sampled point and weight are determined according to formula (3):
Third class sampled point and weight are determined according to formula (4):
WhereinWithAnd meet formula (5)-(7) following formula:
ei1=[0 ... 0,1,0 ... 0] (5)
Sampled point is transmitted through nonlinear function described in step 4, and be weighted processing obtain state one-step prediction and
The process of state one-step prediction covariance matrix are as follows:
It is propagated according to the sampled point that formula (8) calculate state equation
According to formula (9) estimated state one-step prediction
According to formula (10) estimated state one-step prediction covariance Pk|k-1:
Optimal adaptive factor is brought into the process of state one-step prediction covariance matrix described in step 5 are as follows: according to
Formula (11) and (12) calculate adaptive factor and are brought into (13)
Wherein, wherein
Establishment high-order UT described in step 6 obtains the process measured using point and weight are as follows:
First kind sampled point and weight are determined according to formula (14):
The second class sampled point and weight are determined according to formula (15):
Third class sampled point and weight are determined according to formula (16):
Step 7 transmits sampled point through nonlinear function, and is weighted processing and obtains measuring one-step prediction and measurement one
The process of step prediction covariance matrix and Cross-covariance are as follows:
It is propagated according to the sampled point that formula (17) calculate measurement equation
Estimated to measure one-step prediction according to formula (18)
One-step prediction covariance is measured according to formula (19)With formula (20) Cross-covariance
The calculating process of the gain matrix of step 8 are as follows:
The gain matrix of self-adaption high-order UKF is calculated according to formula (21):
The output of step 9 posteriority state estimation output and covariance matrix, into the process of next iteration are as follows:
The output of kth step state output and covariance matrix is carried out according to formula (22) and formula (23):
Data information constantly updates during tracking target and advancing, and radar station can obtain distance and the side of carrier
Position information.Method provided by the invention has higher estimated accuracy and robustness than existing method, below with specific example
To illustrate superiority of the invention.It is specific as follows:
According to maneuvering target track question, the state equation and measurement equation of Target Tracking System described below are established:
Wherein, the state equation of kth stepIndicate the mesh of (cartesian coordinate system) in x-axis and y-axis plane
Target position and speed.It is verified using big running rate and big sampling interval.Ω=- 9 ° of s-1Constant rate is indicated, between sampling
Every Δ T=3, Qk=diag [0.1 0.01 0.1 0.01] andIndicate system noise variance and measurement
Noise variance, wherein σr=100and σθ=100mrad.Given initial state value and initial covariance value are as follows: x0=[100m
20ms-1 500m 30ms-1]TAnd P0=[100m2 10m2s-2 100m2 10m2s-2]T。P0Characterize initial position and speed not
Certainty.
Performance indicator according to formula (26) root mean square error as measure algorithm position and speed.
Wherein M represents Monte Carlo number.WithRespectively represent really is position and estimative position.
It is smaller to the root square mean error amount of location estimation, represent that precision is higher, and effect is better.Simulation time 100 seconds, under the same conditions
Using second order UKF, high-order UKF, adaptive UKF and self-adaption high-order UKF proposed by the present invention, and carry out 100 Monte Carlos
L-G simulation test.
Implementation result: curve A represents the root mean square error curve of high-order UKF state estimation in Fig. 3 and Fig. 4, and curve B is represented
The root mean square error curve of second order UKF state estimation, curve C represent the root mean square error curve of adaptive UKF state estimation, bent
Line D represents the root mean square error curve of method state estimation provided by the invention, the root square mean error amount smaller generation of state estimation
Table estimated accuracy is higher, and performance is better.
From above embodiments, it is not difficult to find out that, opposite and other methods, method provided by the invention can obtain higher essence
Degree, can more accurately track carrier target.
Claims (10)
1. the method for estimating state based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering, which is characterized in that comprising following
Step:
Step 1: the state model and measurement model of the nonlinear discrete of Target Tracking System are established；
Step 2: optimal free parameter κ is selected according to Target Tracking System state dimension；
Step 3: it establishes high-order UT and obtains state using point and weight；
Step 4: sampled point is transmitted through nonlinear function, and is weighted processing and is obtained one step of state one-step prediction and state
Predict covariance matrix；
Step 5: optimal adaptive factor is brought into state one-step prediction covariance matrix；
Step 6: it establishes high-order UT and obtains measurement using point and weight；
Step 7: sampled point is transmitted through nonlinear function, and is weighted processing and is obtained measuring one-step prediction and measure a step
Predict covariance matrix and Cross-covariance；
Step 8: the calculating of gain matrix；
Step 9: the output of posteriority state estimation output and covariance matrix, into next iteration.
2. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, step 1 includes:
Wherein state equation is xk=fk-1(xk-1)+wk-1, measurement equation zk=hk(xk)+vk, k indicates kth step, and k-1 indicates the
K-1 step；xkIndicate the n dimension tracking target component state vector of kth step, zkThe measurement vector of target is tracked for the m dimension of+1 step of kth,
F () and h () is known nonlinear function, wk-1And vkRespectively represent the n dimension stochastic system noise and kth step of k-1 step
The measurement noise of m dimension；And it is Q that stochastic system noise obedience mean value, which is 0 variance,k-1Gaussian Profile, Qk-1Indicate -1 step system of kth
The variance matrix of system noise；It is R that Stochastic Measurement Noises vector obedience mean value, which is 0 variance,kGaussian Profile, RkIt indicates that kth step measures to make an uproar
The variance matrix of sound, and meet wk-1With vkIt is uncorrelated.
3. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, step 2 includes:
According to cost function G(n,κ)=(n-1) κ2+(2n2-14n)κ+n3-13n2+ 60n-60, and cost function is made to minimize to obtain
Free parameter κ；When system is second-order system, free parameter is κ=0.835；When system is third-order system, free parameter is κ
=1.417；When system is fourth-order system, free parameter is κ=2.
4. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, included by step 3:
Step 3.1: first kind sampled point and weight are established according to the following formula:
Step 3.2: the second class sampled point and weight are established according to the following formula:
Step 3.3: third class sampled point and weight are established according to the following formula:
Wherein ei1WithMeet following formula:
ei1=[0 ... 0,1,0 ... 0]
5. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, step 4 includes:
Step 4.1: the sampled point for calculating state equation according to the following formula is propagated
Step 4.2: estimated state one-step prediction according to the following formula
Step 4.3: estimated state one-step prediction covariance P according to the following formulak|k-1:
6. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, step 5 includes:
Wherein
7. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, step 6 includes:
Step 6.1: first kind sampled point and weight are established according to formula (14):
Step 6.2: the second class sampled point and weight are established according to formula (15):
Step 6.3: third class sampled point and weight are established according to formula (16):
8. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, step 7 includes:
Step 7.1: the sampled point for calculating measurement equation according to the following formula is propagated
Step 7.2: estimation measures one-step prediction according to the following formula
Step 7.3: measuring one-step prediction covariance according to the following formulaAnd Cross-covariance
9. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, step 8 includes:
The gain matrix of self-adaption high-order UKF is calculated according to the following formula:
10. the method for estimating state according to claim 1 based on a kind of NEW ADAPTIVE high-order Unscented kalman filtering,
It is characterized in that, step 9 includes:
The output of kth step dbjective state output and covariance matrix is carried out with following formula according to the following formula:
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| WEIDONG ZHOU等: ""A new adaptive high-order unscented kalman filter for improving the accuracy and robustness of target tracking"", 《IEEE ACCESS》 * |
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| CN110912535A (en) * | 2019-12-11 | 2020-03-24 | 云南大学 | Novel pilot-free Kalman filtering method |
| CN110912535B (en) * | 2019-12-11 | 2023-12-15 | 云南大学 | Novel non-pilot Kalman filtering method |
| CN111693984A (en) * | 2020-05-29 | 2020-09-22 | 中国计量大学 | Improved EKF-UKF moving target tracking method |
| CN111693984B (en) * | 2020-05-29 | 2023-04-07 | 中国计量大学 | Improved EKF-UKF moving target tracking method |
| CN113407909A (en) * | 2021-07-15 | 2021-09-17 | 东南大学 | Tasteless algorithm for non-analytic complex nonlinear system |
| CN113407909B (en) * | 2021-07-15 | 2024-01-09 | 东南大学 | Calculation method of odorless algorithm for non-analytic complex nonlinear system |
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