CN104793182B - Indoor positioning method based on particle filtering under condition of non-Gaussian noises - Google Patents
Indoor positioning method based on particle filtering under condition of non-Gaussian noises Download PDFInfo
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- CN104793182B CN104793182B CN201510190763.1A CN201510190763A CN104793182B CN 104793182 B CN104793182 B CN 104793182B CN 201510190763 A CN201510190763 A CN 201510190763A CN 104793182 B CN104793182 B CN 104793182B
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- G—PHYSICS
- G01—MEASURING; TESTING
- 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
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/10—Position of receiver fixed by co-ordinating a plurality of position lines defined by path-difference measurements, e.g. omega or decca systems
Abstract
The invention discloses an indoor positioning method based on particle filtering under the condition of non-Gaussian noises. The indoor positioning method comprises the following steps of modeling movement accelerated speed of an object and measurement noises into random vectors which obey Gaussian mixture distribution in a training stage by using a particle filtering method based on a suboptimum important function; and performing local linearization on a non-linear observation equation in a positioning state so as to obtain a suboptimum important function and a weight coefficient, change a degradation phenomenon in particle filtering and implement optimum estimation on state vectors. The indoor positioning method has the advantages that on one hand, compared with Gaussian noises, modeling of the Gaussian mixture model is close to actual conditions, and errors caused by model approximation can be reduced effectively; and on the other hand, the degradation speed of the weight coefficient in the particle filtering process can be increased through the solved suboptimum important function, the algorithm efficiency and the algorithm precision are improved, and the positioning precision is improved effectively.
Description
Technical field
The invention belongs to the technical field of wireless location.
Background technology
How indoors under environment, mobile realization of goal is accurately positioned and is followed the trail of be indoor positioning research emphasis it
One.In existing location technology, ultra broadband (UWB) technology can realize the range accuracy of Centimeter Level.Due to indoor environment pair
The impact of electromagnetic transmission, actual distance measurement value can be affected by non-Gaussian noise, so as to produce larger deviation, existing
Method assumes that noise Normal Distribution, and the result to measuring carries out Kalman filtering, but the measurement noise of reality is often not
It is to obey unimodal normal distribution, and multi-modal situation can be presented.So, observation noise is approximately into normal distribution, although can
To reduce amount of calculation, it can be difficult to virtual condition is accurately estimated, therefore, said method is high by mixing by distance measuring noises
This variable is approached.
Additionally, what legacy ultra-wideband (UWB) location algorithm obtained using trilateration is the least square that meets condition
Solution, but when small deviation occur in some anchor nodes, its positioning result can produce larger deviation；And mobile target exists
Can there is acceleration, deceleration, the kinestate such as at the uniform velocity during motion, so the acceleration of object of which movement will not also obey unimodal
Normal distribution.
The particle filter algorithm of standard selects priori probability density as importance density function, but due to not accounting for working as
Front measured value, the sample for obtaining is sampled from importance density function to be had with the sample obtained from the sampling of true posterior probability density
Very large deviation.The variance of weights of importance also can random increase over time so that the weight of particle focuses on minority particle
On, there is degenerate problem.In order to overcome degradation phenomena, the importance density function for choosing is needed, but is seen in real process
It is non-linear to survey equation, it is impossible to directly obtains optimum density function, therefore cannot ensure the efficiency and precision of calculating.
The content of the invention
Goal of the invention：Indoor orientation method under the conditions of a kind of non-Gaussian noise of present invention offer based on particle filter, should
Method improves sample degeneracy phenomenon in particle filter, realizes the optimal estimation to state vector, improves positioning precision.
Technical scheme：Indoor orientation method under the conditions of a kind of non-Gaussian noise based on particle filter, by state equation
Acceleration and observational equation in measurement noise be modeled as mixed Gaussian stochastic variable, and local linear is carried out to observational equation
Change, try to achieve suboptimum importance function, so as to carry out particle filter, draw the optimal estimation of quantity of state, the concrete steps of the method
For：
(1) state equation and observational equation of mobile target motion are set up, by the general of the vector acceleration in state equation
Rate is distributed by Gaussian mixtures to be approached, and the distance measuring noises in observational equation and inertia measurement noise profile are also led to
Cross Gaussian mixtures approximate；
(2) local linearization is carried out to nonlinear observational equation, the suboptimum importance function and power of any time is obtained
Coefficient, two parameters therein, the i.e. value of average and variance are obtained by recursion；
(3) the distance between mobile target current time and observer nodes, the motion side at mobile target current time are measured
Parallactic angle, and the distance with upper moment position, to measured value using the particle filter based on suboptimum importance function, obtain most
Excellent estimation；
(4) location tracking is carried out to mobile target according to mobile target after filtering and the distance and bearing angle of observation station, together
Two parameters of Shi Gengxin, i.e. average and variance.
Further, in the step (1) by the acceleration item of state equation be modeled as obey Gaussian mixtures with
Machine vector, by range error and the statistics of azimuth measurement error, being also modeled as the noise item in observational equation in advance
Obey the random vector of Gaussian mixtures.
Further, mobile target carried terminal in the step (1), including ultra broadband (UWB) and inertial sensor list
First (ISU) two parts, compare actual value and measured value according to actual scene, draw measurement error, and according to measurement error
Statistical property is using Gaussian mixtures come approximate.
Further, the acceleration of the state equation according to the acceleration in normal person's walking process, slow down and at the uniform velocity
Kinestate be modeled, adopt set number for 3 Gaussian mixtures approaching.
Further, the average and variance are the statistic in weight coefficient during particle filter, with Memorability, can
With the value needed for obtaining current time according to the value iteration of previous moment, recursive procedure is linear operation.
Further, ultra broadband (UWB) anchor node is single, and unique user is positioned.
Beneficial effect：Compared with prior art, it is an advantage of the current invention that：
1st, using the particle filter method based on suboptimum importance function, by the acceleration of object of which movement and measurement are made an uproar
Sound is modeled as the random vector for obeying Gaussian mixtures, is more nearly real case.
2nd, by local linearization being carried out to observational equation, so as to obtain suboptimum importance density function, improve particle filter
Degradation phenomena, improve computational efficiency and precision, realize high-precision positioning and following function under indoor environment.
3rd, by the comprehensive metrical information for using ultra broadband (UWB) ranging technology and inertial sensor unit (ISU), a side
Face can reduce anchor node number needed for ultra broadband (UWB) positioning, and dependence of the reduction to ultra broadband (UWB) is greatly reduced into
This；The error of another aspect inertial sensor measured value is also modeled as mixed Gaussian variable, can improve positioning precision.
Description of the drawings
Fig. 1 realizes block diagram for overall plan；
Fig. 2 is positioning scene figure；
Fig. 3 carries mobile terminal schematic diagram for needed for mobile target；
Fig. 4 is the particle filter algorithm flow chart based on suboptimum importance function.
Specific embodiment
With reference to the accompanying drawings and detailed description, further elucidate the present invention.
As shown in Figure 1-2, the indoor orientation method under the conditions of a kind of non-Gaussian noise based on particle filter, using single super
Broadband (UWB) anchor node is positioned to unique user.The method is by the survey in the acceleration and observational equation in state equation
Amount noise modeling is mixed Gaussian stochastic variable, and carries out local linearization to observational equation, tries to achieve suboptimum importance function, from
And particle filter is carried out, draw the optimal estimation of quantity of state, the concrete steps of the method：
(1) state equation and observational equation of mobile target motion are set up, by the general of the vector acceleration in state equation
Rate is distributed by Gaussian mixtures to be approached, and the distance measuring noises in observational equation and inertia measurement noise profile are also led to
Cross Gaussian mixtures approximate；
Wherein, the acceleration item of state equation is modeled as the random vector for obeying Gaussian mixtures, by advance to surveying
Away from error and the statistics of azimuth measurement error, also by the noise item in observational equation be modeled as obeying Gaussian mixtures with
Machine vector；
Mobile target carried terminal, including two parts of ultra broadband (UWB) and inertial sensor unit (ISU), according to reality
Border scene compares actual value and measured value, draws measurement error, and according to the statistical property of measurement error using mixed Gaussian point
Cloth comes approximate；
In state equation, the statistical property of acceleration can be modeled according to the speed of normal person's walking, as people is expert at
Exist during walking accelerate, slow down, the kinestate such as at the uniform velocity, therefore set number can be adopted for 3 mixed Gaussian point
Cloth is approaching.
(2) local linearization is carried out to nonlinear observational equation, the suboptimum importance function and power of any time is obtained
Coefficient, two parameters therein, the i.e. value of average and variance are obtained by recursion；
(3) the distance between mobile target current time and observer nodes, the motion side at mobile target current time are measured
Parallactic angle, and the distance with upper moment position, to measured value using the particle filter based on suboptimum importance function, obtain most
Excellent estimation；
(4) location tracking is carried out to mobile target according to mobile target after filtering and the distance and bearing angle of observation station, together
Two parameters of Shi Gengxin, i.e. average and variance.
Wherein, observational equation is nonlinear function, and state variable its statistical property after observational equation is difficult to analyze, because
This and causes importance function universal false by carrying out local linearization to observational equation so as to obtain importance function
If under the conditions of asymptotic convergence be distributed to required filtering.
Particle filter is using the particle filter algorithm based on importance function, the suboptimum importance as obtained by adopting and derive
Function and weight coefficient, can improve the degradation phenomena in particle filter, improve the efficiency and precision of algorithm.
As shown in Figure 3-4, make further concrete analysis to technical solution of the present invention and describe.
Set up the state equation and observational equation of mobile target motion：
ηk=F ηk-1+Γwk (1)
ξk=h (ηk)+vk(2) in state equation (1),
Wherein, ηkFor state variable, xp(k) and ypK () is k moment x-axis directions and the distance measurement value in y-axis direction, xv(k) and yv
K () is k moment x-axis directions and the movement velocity in y-axis direction；F is state-transition matrix, wkFor acceleration, wxp(k) and wyp(k)
The respectively distance measuring noises in k moment x directions and y directions, wxv(k) and wyvK () is respectively k moment x-axis directions and y-axis direction
Velocity noise；Coefficient matrixes of the Γ for acceleration item, vkFor measurement error；ξkFor observed quantity.
In observational equation (2),
Wherein,
As shown in figure 3, angle measurements of the α (k) for inertial sensor unit (ISU), is the k moment directions of motion and positive north
The angle in direction, α (k) ∈ [0,2 π]；Distance measurement values of the L (k) for ultra broadband (UWB)；vkFor measurement error, wherein, vθK () is boat
To the noise at angle, vLThe noise of (k) for distance measurement value.By measurement error vkWith acceleration w in (1)kStatistical property it is high using mixing
This distribution comes approximate.
Described observational equation (2) is related to solve the nonlinear operations such as anticosine, the extraction of square root of angle, therefore in order to obtain
Stochastic variable needs to be carried out local linearization, so as to both reduce calculating by the statistical property under the conditions of nonlinear system
Amount, can obtain importance function again, be that efficient particle filter lays the foundation.Linearisation is carried out to (2),
Wherein, constant h (F η are rememberedk-1) for Ck, noteFor Dk, then (3) be
Remember againThen (4) are
Assume that observation noise obeys Gaussian mixtures, i.e.,
Relationship modeling by adjacent moment acceleration is：
wk=wk-1+ek (7)
During user normally walks, there is the state of acceleration, deceleration, uniform motion.Different states its increment
Different distributions are presented, by the increment e of adjacent moment accelerationkModeling is also mixed Gauss model, i.e.,
So as to push away weight coefficient is,
Wherein,
Suboptimum density function is：
Wherein,
The weight coefficient pushed away according to (9), (10) and suboptimum density function, carry out optimum to measured value using particle filter and estimate
Meter, so as to show that current time moves the coordinate of target.Renewal is iterated to important statistic according to (11)～(14) simultaneously.
Described average and variance are the statistic during particle filter in weight coefficient, and which has Memorability, can according to it is previous when
The value iteration at quarter obtains the value needed for current time, and recursive procedure is linear operation, so as to greatly reduce amount of calculation.Meanwhile,
Using the particle filter algorithm based on importance function, which can improve the degradation phenomena in particle filter, carry for described filtering
The efficiency and precision of high algorithm.
The present invention using particle filter method based on suboptimum importance function, by by the acceleration of object of which movement and survey
Amount noise modeling is the random vector for obeying Gaussian mixtures, and carries out local linearization to nonlinear observational equation, is obtained
Go out suboptimum importance function and weight coefficient, and then improve sample degeneracy phenomenon in particle filter, realize to state vector most
Excellent estimation, improves positioning precision.
The better embodiment of the present invention is the foregoing is only, protection scope of the present invention with above-mentioned embodiment is not
Limit, as long as the equivalent modification made according to disclosed content of those of ordinary skill in the art or change, should all include power
In protection domain described in sharp claim.
Claims (6)
1. the indoor orientation method under the conditions of a kind of non-Gaussian noise based on particle filter, it is characterised in that：By in state equation
Acceleration and observational equation in measurement noise be modeled as mixed Gaussian stochastic variable, and local linear is carried out to observational equation
Change, try to achieve suboptimum importance function, so as to carry out particle filter, draw the optimal estimation of quantity of state, the concrete steps of the method
For：
(1) state equation and observational equation of mobile target motion are set up, by the probability of the vector acceleration in state equation point
Cloth is approached by Gaussian mixtures, by the distance measuring noises in observational equation and inertia measurement noise profile also by mixed
Close Gauss distribution and come approximate；
(2) local linearization is carried out to nonlinear observational equation, the suboptimum importance function and weight coefficient of any time is obtained,
Two parameters therein, the i.e. value of average and variance are obtained by recursion；
(3) the distance between mobile target current time and observer nodes are measured, the motion azimuth at target current time is moved,
And the distance with upper moment position, to measured value using the particle filter based on suboptimum importance function, obtain optimum and estimate
Meter；
(4) location tracking is carried out to mobile target according to mobile target after filtering and the distance and bearing angle of observation station, while more
New two parameters, i.e. average and variance.
2. the indoor orientation method under the conditions of a kind of non-Gaussian noise according to claim 1 based on particle filter, which is special
Levy and be：The acceleration item of state equation is modeled as obeying the random vector of Gaussian mixtures in the step (1), is passed through
In advance to range error and the statistics of azimuth measurement error, also the noise item in observational equation is modeled as obeying mixed Gaussian
The random vector of distribution.
3. the indoor orientation method under the conditions of a kind of non-Gaussian noise according to claim 1 based on particle filter, which is special
Levy and be：Mobile target carried terminal in the step (1), including ultra broadband (UWB) and inertial sensor unit (ISU) two
Part, compares actual value and measured value according to actual scene, draws measurement error, and is adopted according to the statistical property of measurement error
Gaussian mixtures come approximate.
4. the indoor orientation method under the conditions of a kind of non-Gaussian noise according to claim 1 and 2 based on particle filter, its
It is characterised by：The acceleration of the state equation according to the acceleration in normal person's walking process, slow down and kinestate at the uniform velocity
Be modeled, adopt set number for 3 Gaussian mixtures approaching.
5. the indoor orientation method under the conditions of a kind of non-Gaussian noise according to claim 1 based on particle filter, which is special
Levy and be：The average and variance are the statistic in weight coefficient during particle filter, with Memorability, can be according to previous
The value iteration at moment obtains the value needed for current time, and recursive procedure is linear operation.
6. the indoor orientation method under the conditions of a kind of non-Gaussian noise according to claim 3 based on particle filter, which is special
Levy and be：Ultra broadband (UWB) anchor node is single, and unique user is positioned.
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| CN109117965B (en) * | 2017-06-22 | 2022-03-01 | 毫末智行科技有限公司 | System state prediction device and method based on Kalman filter |
| US11474486B2 (en) * | 2019-03-11 | 2022-10-18 | Mitsubishi Electric Research Laboratories, Inc. | Model-based control with uncertain motion model |
| CN110440794B (en) * | 2019-07-26 | 2021-07-30 | 杭州微萤科技有限公司 | Positioning correction method for IMU navigation |
| CN110567441B (en) * | 2019-07-29 | 2021-09-28 | 广东星舆科技有限公司 | Particle filter-based positioning method, positioning device, mapping and positioning method |
| CN111761583B (en) * | 2020-07-08 | 2022-04-08 | 温州大学 | Intelligent robot motion positioning method and system |
| CN114077245A (en) * | 2020-08-21 | 2022-02-22 | 苏州三六零机器人科技有限公司 | SLAM method and device for multiple data sources, sweeping robot and readable medium |
| CN114040325B (en) * | 2021-11-05 | 2022-08-19 | 西北工业大学 | Single-anchor node network cooperative positioning method under inertial navigation assistance |
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