CN113077055A - Distributed multi-source fusion positioning method based on FBPF-EIKF-FastSLAM - Google Patents

Distributed multi-source fusion positioning method based on FBPF-EIKF-FastSLAM Download PDF

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CN113077055A
CN113077055A CN202110327231.3A CN202110327231A CN113077055A CN 113077055 A CN113077055 A CN 113077055A CN 202110327231 A CN202110327231 A CN 202110327231A CN 113077055 A CN113077055 A CN 113077055A
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胡燕祝
王松
贺琬婧
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Beijing University of Posts and Telecommunications
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Abstract

The invention relates to a distributed multi-source fusion positioning method based on FBPF-EIKF-FastSLAM, which is a method for fusion positioning of distributed self-adaptive multi-source information, belongs to the field of positioning and orientation and machine learning, and is characterized by comprising the following steps: (1) determining an average value and an envelope estimation value of adjacent extreme points; (2) determining a residual signal; (3) determining a frequency modulated signal and an envelope signal; (4) performing LMD decomposition to determine a first PF component; (5) establishing an ICA mathematical model; (6) constructing a PNN neural network; (7) a discriminant function of the output variable is determined. The invention effectively solves the problem of the influence of the background noise of the complex environment on the positioning accuracy, improves the filtering efficiency, effectively improves the system operation efficiency, reduces the system response time, improves the system operation speed and accelerates the target positioning updating frequency.

Description

Distributed multi-source fusion positioning method based on FBPF-EIKF-FastSLAM
Technical Field
The invention relates to the field of positioning and orientation and machine learning, in particular to a method for performing fusion positioning on distributed self-adaptive multi-source information.
Background
At present, for the positioning of a target in a complex environment, multiple data sources are mainly formed on the basis of multiple sensors, and the position information of the target is accurate through algorithm fusion. The traditional multi-source fusion algorithm generally adopts a high-order correction CKF multi-element fusion method and an NLOS algorithm. For the high-order correction CKF multi-element fusion algorithm, because the order of the self-adaptive high-order correction function is dynamically adjusted according to the positioning error, strict requirements are imposed on the extraction and the judgment of the error, and meanwhile, the noise of the environmental background is not easy to remove, and an interference source is easy to generate. For the NLOS algorithm, because the measurement noise of the fusion filter is dynamically adjusted according to the result settlement residual matrix, the initial value dependence on the feature point depth and the covariance matrix is large, and if the setting is not correct, or the estimated values are inconsistent, the deviation is generated. The complexity of the environment background and the continuous transformation of the target position cause that the technology has larger error deviation probability in practical application.
For the positioning of the target in the complex environment, the key point is the efficient and stable removal of the environmental background noise and the positioning. Therefore, higher requirements are put on the target positioning in complex environments. Aiming at the problems, a distributed self-adaptive multi-source fusion positioning method is provided, a strict interval boundary containing an accurate solution is obtained by adopting interval analysis operation, and the filtering of environmental background noise can be realized on the premise of not being constrained by a system model. Meanwhile, the performance advantages of few particles required by box particle filtering and high running speed are fully utilized, the firefly algorithm is integrated, the extended interval Kalman filtering is combined, the refreshing speed of system positioning information is improved, and the target positioning accuracy and robustness are improved.
Disclosure of Invention
Aiming at the problems in the prior art, the technical problem to be solved by the invention is to provide a distributed multi-source fusion positioning method based on FBPF-EIKF-FastSLAM, and the specific flow of the method is shown in FIG. 1.
The technical scheme comprises the following implementation steps:
(1) determining the weighted sum of the uniform PDFs p (x):
Figure BDA0002995109920000011
where x denotes a random variable, i denotes a count unit, N denotes the number of uniformly mixed PDFs, and wiIndicates the probability density, [ x ] corresponding to the ith bin particle]Represents a box particle, U[x]Represents PDF, [ x ] with bin particles as a support seti]The (i) th bin of particles is represented,
Figure BDA0002995109920000012
(2) predicting probability density p (x) at time k +1k+1|z1,k)：
At time k, assume xkThe PDF under the state is expressed as:
Figure BDA0002995109920000021
according to the time updating step, for the probability density at the k +1 moment:
Figure BDA0002995109920000022
in the formula, k represents time, xkIs a system state vector, zkIn order to observe the vector, the vector is,
Figure BDA0002995109920000023
the probability density of the ith bin particle at time k,
Figure BDA0002995109920000024
the state vector of the ith bin particle at time k,
Figure BDA0002995109920000025
the PDF for the support set at time k for the ith bin particle,
Figure BDA0002995109920000026
representing supporting header particles of
Figure BDA0002995109920000027
(ii) uniform PDF, [ f [)]To contain the function, [ V ]k]A bin particle corresponding to state transition noise at time k +1, [ Uk]To control the input bin particles.
(3) Determination of State posterior PDFp (x)k+1|z1,k+1)：
Figure BDA0002995109920000028
Figure BDA0002995109920000029
In the formula etak+1To normalize the coefficient, [ Z ]k+1]Representing the actual observation of the bin particle, SS, at time k +1ψiRepresented as a CSP, is shown to predict the bin particles and constrain them by the relationship of the observation function to the actual observed bin particles to eliminate the excess from the original bin particles.
Figure BDA00029951099200000210
The state value of the ith bin particle at the time k +1,
Figure BDA00029951099200000211
to be composed of
Figure BDA00029951099200000212
The constraint is carried out so that,
Figure BDA00029951099200000213
to be composed of
Figure BDA00029951099200000214
Confined box particle xk+1In order to support the PDF of the set,
Figure BDA00029951099200000215
for a new box of particles after constraint, | [ X ]]And | is the volume of the box particle.
Selecting a proper threshold value, executing random subdivision resampling, and randomly selecting a certain one-dimensional state subinterval of the box particles obtained at the current moment for uniform division according to the resampling times, so that the box particles keep a proper size.
(4) Updating the fluorescence intensity of the box particle
Figure BDA00029951099200000216
Figure BDA00029951099200000217
In the formula (I), the compound is shown in the specification,
Figure BDA0002995109920000031
the fluorescence intensity of the ith bin at time k +1,
Figure BDA0002995109920000032
for the predicted observation of the ith bin particle at time k +1, [ Z ]k+1]Is an actual observation. Instead of comparing the fluorescence intensity values between each bin of particles, a comparison is made using the actual observations and the predicted observations for each bin of particles.
(5) Updating global optimal box particle [ g ]k+1]：
Determining the degree of attraction β between the box particles:
Figure BDA0002995109920000033
wherein N (0,1) is a Gaussian distribution random vector having a mean value of 0 and a variance of 1,
Figure BDA0002995109920000034
as random weight terms, βmIs the maximum attraction, gamma is the light intensity absorption coefficient, diThe spatial distance between the bin particle at time k +1 and the globally optimal bin particle. When the position update is completed, the fluorescence brightness value of the box particle is calculated and compared, and the global optimal box particle [ g ] is updatedk+1]：
Figure BDA0002995109920000035
In the formula, I ([ X ]) is the fluorescent brightness of the box particle.
(6) Updating bin particle positions
Figure BDA0002995109920000036
Figure BDA0002995109920000037
Where rand is a random number that is subject to uniform distribution. By updating the positions of the box particles, the box particles are guided to move towards the positions of the globally optimal box particles by utilizing the guiding function exerted by the attraction degree in the updating process. And setting the maximum iteration number, stopping the iteration of the algorithm when the fluorescence brightness function value is larger than the set iteration termination threshold value, and otherwise, continuing the iteration until the maximum iteration number is reached.
(7) Determining innovation and interval Kalman gain:
Figure BDA0002995109920000038
Figure BDA0002995109920000039
in the formula (I), the compound is shown in the specification,
Figure BDA00029951099200000310
to be novel, I is the identity matrix,
Figure BDA00029951099200000311
for actual observation, an uncertain interval vector is observed before, a common vector is observed after,
Figure BDA00029951099200000312
in order to observe the inclusion of the function,
Figure BDA00029951099200000313
the interval Kalman gain is represented by the gain of the interval Kalman,
Figure BDA00029951099200000314
in order to carry out the interval polymerization operation,
Figure BDA00029951099200000315
is a Jacobian matrix of intervals,
Figure BDA00029951099200000316
representing the observed noise interval covariance matrix. Updating the environment map construction:
Figure BDA0002995109920000041
Figure BDA0002995109920000042
in the formula (I), the compound is shown in the specification,
Figure BDA0002995109920000043
is a constrained interval position vector. And completing environmental characteristic estimation, observing and correlating data collected by the sensor, updating by using EIKF, and perfecting map information.
Compared with the prior art, the invention has the advantages that:
(1) the influence of the background noise of the complex environment on the positioning accuracy is effectively solved, and the filtering efficiency is improved.
(2) The method effectively improves the system operation efficiency, reduces the system response time, improves the system operation speed and accelerates the target positioning update frequency.
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For a better understanding of the present invention, reference is made to the following further description taken in conjunction with the accompanying drawings.
FIG. 1 is a flow chart of the steps for establishing a distributed multi-source fusion positioning method based on FBPF-EIKF-FastSLAM;
FIG. 2 is a flow chart of a method for establishing a distributed multi-source fusion positioning method based on FBPF-EIKF-FastSLAM;
FIG. 3 is a result of locating four sets of distributed multi-source information using the present invention;
detailed description of the preferred embodiments
The present invention will be described in further detail below with reference to examples.
The data selected by the implementation case come from a typical demonstration area of an underground shielding space, 1000 groups of samples are shared in total, wherein 5 scenes including an underground tunnel, a railway tunnel, an underground mall, an underground parking lot and a subway station are provided, each scene has 200 groups of data, 140 groups of samples are extracted from each data in the 5 groups of scenes by adopting a random sampling method to serve as a training set, and the rest are used as a testing set. Finally, the total number of samples used as the training set is 700 and the total number of samples used as the test set is 300.
The overall flow of the distributed multi-source fusion positioning method provided by the invention is shown in figure 1, and the specific steps are as follows:
(1) determining the weighted sum of the uniform PDFs p (x):
Figure BDA0002995109920000044
in the formula, x represents a random variable, i represents a counting unit, N represents the number of uniformly mixed PDFs, the value is 20, and wiIndicates the probability density, [ x ] corresponding to the ith bin particle]Represents a box particle, U[x]Represents PDF, [ x ] with bin particles as a support seti]The (i) th bin of particles is represented,
Figure BDA0002995109920000045
(2) predicting probability density p (x) at time k +1k+1|z1,k)：
At time k, assume xkThe PDF under the state is expressed as:
Figure BDA0002995109920000051
according to the time updating step, for the probability density at the k +1 moment:
Figure BDA0002995109920000052
in the formula, k represents time, xkIs a system state vector, zkIn order to observe the vector, the vector is,
Figure BDA0002995109920000053
the probability density of the ith bin particle at time k,
Figure BDA0002995109920000054
the state vector of the ith bin particle at time k,
Figure BDA0002995109920000055
the PDF for the support set at time k for the ith bin particle,
Figure BDA0002995109920000056
representing supporting header particles of
Figure BDA0002995109920000057
(ii) uniform PDF, [ f [)]To contain the function, [ V ]k]A bin particle corresponding to state transition noise at time k +1, [ Uk]To control the input bin particles.
(3) Determination of State posterior PDFp (x)k+1|z1,k+1)：
Figure BDA0002995109920000058
Figure BDA0002995109920000059
In the formula etak+1To normalize the coefficient, [ Z ]k+1]Indicating that the bin particle was actually observed at time k +1,
Figure BDA00029951099200000510
expressed as a CSP, expressed as a predicted box particle passage observation function andthe relation of actual observation box particles is restrained and used for eliminating redundant parts in the original box particles.
Figure BDA00029951099200000511
The state value of the ith bin particle at the time k +1,
Figure BDA00029951099200000512
to be composed of
Figure BDA00029951099200000513
The constraint is carried out so that,
Figure BDA00029951099200000514
to be composed of
Figure BDA00029951099200000515
Confined box particle xk+1In order to support the PDF of the set,
Figure BDA00029951099200000516
for a new box of particles after constraint, | [ X ]]And | is the volume of the box particle.
Selecting a proper threshold value, executing random subdivision resampling, and randomly selecting a certain one-dimensional state subinterval of the box particles obtained at the current moment for uniform division according to the resampling times, so that the box particles keep a proper size.
(4) Updating the fluorescence intensity of the box particle
Figure BDA00029951099200000517
Figure BDA00029951099200000518
In the formula (I), the compound is shown in the specification,
Figure BDA0002995109920000061
the fluorescence intensity of the ith bin at time k +1,
Figure BDA0002995109920000062
for the predicted observation of the ith bin particle at time k +1, [ Z ]k+1]Is an actual observation. Instead of comparing the fluorescence intensity values between each bin of particles, a comparison is made using the actual observations and the predicted observations for each bin of particles.
(5) Updating global optimal box particle [ g ]k+1]：
Determining the degree of attraction β between the box particles:
Figure BDA0002995109920000063
wherein N (0,1) is a Gaussian distribution random vector having a mean value of 0 and a variance of 1,
Figure BDA0002995109920000064
as random weight terms, βmThe maximum attraction is 0.85, gamma is the light intensity absorption coefficient and is 1, and diThe spatial distance between the bin particle at time k +1 and the globally optimal bin particle. When the position update is completed, the fluorescence brightness value of the box particle is calculated and compared, and the global optimal box particle [ g ] is updatedk+1]：
Figure BDA0002995109920000065
In the formula, I ([ X ]) is the fluorescent brightness of the box particle.
(6) Updating bin particle positions
Figure BDA0002995109920000066
Figure BDA0002995109920000067
Where rand is a random number that is subject to uniform distribution. By updating the positions of the box particles, the box particles are guided to move towards the positions of the globally optimal box particles by utilizing the guiding function exerted by the attraction degree in the updating process. And setting the maximum iteration number, stopping the iteration of the algorithm when the fluorescence brightness function value is larger than the set iteration termination threshold value, and otherwise, continuing the iteration until the maximum iteration number is reached.
(7) Determining innovation and interval Kalman gain:
Figure BDA0002995109920000068
Figure BDA0002995109920000069
in the formula (I), the compound is shown in the specification,
Figure BDA00029951099200000610
to be novel, I is the identity matrix,
Figure BDA00029951099200000611
for actual observation, an uncertain interval vector is observed before, a common vector is observed after,
Figure BDA00029951099200000612
in order to observe the inclusion of the function,
Figure BDA00029951099200000613
the interval Kalman gain is represented by the gain of the interval Kalman,
Figure BDA00029951099200000614
in order to carry out the interval polymerization operation,
Figure BDA00029951099200000615
is a Jacobian matrix of intervals,
Figure BDA00029951099200000616
representing the observed noise interval covariance matrix. Updating the environment map construction:
Figure BDA0002995109920000071
Figure BDA0002995109920000072
in the formula (I), the compound is shown in the specification,
Figure BDA0002995109920000073
is a constrained interval position vector. And completing environmental characteristic estimation, observing and correlating data collected by the sensor, updating by using EIKF, and perfecting map information.
In order to verify the accuracy of the invention in positioning distributed multi-source information, four groups of multi-source information positioning experiments are carried out on the invention, and the experimental results are shown in fig. 3. As can be seen from fig. 3, the accuracy of the distributed multi-source fusion positioning method provided by the invention for positioning the distributed multi-source information is kept above 96%, and the method can achieve higher accuracy on the basis of ensuring stability, and has good positioning effect. The distributed multi-source fusion positioning method established by the invention is effective, provides a better method for establishing an accurate fusion positioning method model, and has certain practicability.

Claims (1)

1. The invention is characterized in that: (1) determining a weighted sum of the uniform PDFs; (2) predicting the probability density at the k +1 moment; (3) determining state posterior PDF; (4) updating the fluorescence brightness of the box particles; (5) updating global optimal box particles; (6) updating the bin particle position; (7) determining innovation and interval Kalman gain; the method specifically comprises the following seven steps:
the method comprises the following steps: determining the weighted sum of the uniform PDFs p (x):
Figure FDA0002995109910000011
where x denotes a random variable, i denotes a count unit, N denotes the number of uniformly mixed PDFs, and wiIndicates the summary corresponding to the ith bin particleSpecific density, [ x ]]Represents a box particle, U[x]Represents PDF, [ x ] with bin particles as a support seti]The (i) th bin of particles is represented,
Figure FDA0002995109910000012
step two: predicting probability density p (x) at time k +1k+1|z1,k)：
At time k, assume xkThe PDF under the state is expressed as:
Figure FDA0002995109910000013
according to the time updating step, for the probability density at the k +1 moment:
Figure FDA0002995109910000014
in the formula, k represents time, xkIs a system state vector, zkIn order to observe the vector, the vector is,
Figure FDA0002995109910000015
the probability density of the ith bin particle at time k,
Figure FDA0002995109910000016
the state vector of the ith bin particle at time k,
Figure FDA0002995109910000017
the PDF for the support set at time k for the ith bin particle,
Figure FDA0002995109910000018
representing supporting header particles of
Figure FDA0002995109910000019
(ii) uniform PDF, [ f [)]To contain the function, [ V ]k]A bin particle corresponding to state transition noise at time k +1, [ Uk]To control the input of bin particles;
step three: determination of State posterior PDFp (x)k+1|z1,k+1)：
Figure FDA00029951099100000110
In the formula etak+1To normalize the coefficient, [ Z ]k+1]Indicating that the bin particle was actually observed at time k +1,
Figure FDA0002995109910000021
expressed as a CSP, expressed as a predicted box particle, constrained by the relationship of the observation function and the actual observation box particle, and used for eliminating redundant parts in the original box particle;
Figure FDA0002995109910000022
the state value of the ith bin particle at the time k +1,
Figure FDA0002995109910000023
to be composed of
Figure FDA0002995109910000024
The constraint is carried out so that,
Figure FDA0002995109910000025
to be composed of
Figure FDA0002995109910000026
Confined box particle xk+1In order to support the PDF of the set,
Figure FDA0002995109910000027
for a new box of particles after constraint, | [ X ]]L is the volume of the box particle;
selecting a proper threshold value, executing random sub-division resampling, and randomly selecting a certain one-dimensional state subinterval of the box particles obtained at the current moment for uniform division according to the number of resampling times so that the box particles keep a proper size;
step four: updating the fluorescence intensity of the box particle
Figure FDA0002995109910000028
Figure FDA0002995109910000029
In the formula (I), the compound is shown in the specification,
Figure FDA00029951099100000210
the fluorescence intensity of the ith bin at time k +1,
Figure FDA00029951099100000211
for the predicted observation of the ith bin particle at time k +1, [ Z ]k+1]Is an actual observation; comparing the actual observation value with the predicted observation value of each box particle to replace the comparison of the fluorescence brightness value between each box particle;
step five: updating global optimal box particle [ g ]k+1]：
Determining the degree of attraction β between the box particles:
Figure FDA00029951099100000212
wherein N (0,1) is a Gaussian distribution random vector having a mean value of 0 and a variance of 1,
Figure FDA00029951099100000213
as random weight terms, βmIs the maximum attraction, gamma is the light intensity absorption coefficient, diThe spatial distance between the bin particles at the moment k +1 and the global optimal bin particles is taken as the distance; when the position update is completed, the fluorescence brightness value of the box particle is calculated and compared, and the global optimal box particle [ g ] is updatedk+1]：
Figure FDA00029951099100000214
Wherein I ([ X ]) is the fluorescent brightness of the box particle;
step six: updating bin particle positions
Figure FDA00029951099100000215
Figure FDA00029951099100000216
In the formula, rand is a random number which is subject to uniform distribution; updating the positions of the box particles, and guiding the box particles to move towards the positions of the globally optimal box particles by utilizing the guiding function exerted by the attraction degree in the updating process; setting the maximum iteration number, stopping the iteration of the algorithm when the value of the fluorescence brightness function is larger than the set iteration termination threshold, and otherwise, continuing the iteration until the maximum iteration number is reached;
step seven: determining innovation and interval Kalman gain:
Figure FDA0002995109910000031
Figure FDA0002995109910000032
in the formula (I), the compound is shown in the specification,
Figure FDA0002995109910000033
to be novel, I is the identity matrix,
Figure FDA0002995109910000034
for actual observation, there is an uncertainty before being observedAfter being observed, is a normal vector,
Figure FDA0002995109910000035
in order to observe the inclusion of the function,
Figure FDA0002995109910000036
the interval Kalman gain is represented by the gain of the interval Kalman,
Figure FDA0002995109910000037
in order to carry out the interval polymerization operation,
Figure FDA0002995109910000038
is a Jacobian matrix of intervals,
Figure FDA0002995109910000039
representing an observation noise interval covariance matrix; updating the environment map construction:
Figure FDA00029951099100000310
Figure FDA00029951099100000311
in the formula (I), the compound is shown in the specification,
Figure FDA00029951099100000312
the constrained interval position vector is obtained; and completing environmental characteristic estimation, observing and correlating data collected by the sensor, updating by using EIKF, and perfecting map information.
CN202110327231.3A 2021-03-26 2021-03-26 Distributed multi-source fusion positioning method based on FBPF-EIKF-FastSLAM Pending CN113077055A (en)

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Application publication date: 20210706