CN111427007B - Mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement - Google Patents

Mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement Download PDF

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CN111427007B
CN111427007B CN202010330263.4A CN202010330263A CN111427007B CN 111427007 B CN111427007 B CN 111427007B CN 202010330263 A CN202010330263 A CN 202010330263A CN 111427007 B CN111427007 B CN 111427007B
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ellipsoid
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CN111427007A (en
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白星振
张金昌
宋保业
刘洋
郑鑫磊
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Shandong University of Science and Technology
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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
    • G01S5/12—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 by co-ordinating position lines of different shape, e.g. hyperbolic, circular, elliptical or radial

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Abstract

The invention discloses a mine personnel safety state estimation method based on collective filtering under incomplete measurement, which fully considers the incomplete measurement of a wireless sensor and unknown but bounded noise in a mine environment and constructs a collective filter based on the incomplete measurement. In order to effectively process the nonlinear error in the positioning system of the mine workers, the system measurement equation is subjected to linearization processing, a scaling matrix and an unknown matrix are adopted to represent the linearization error, and the scaling matrix is processed by utilizing a particle swarm algorithm, so that the problem of linearization of the system is effectively solved, and the accurate positioning of the mine workers is realized. In addition, the invention determines various filtering parameters through semi-positive planning, and provides a recursive filtering algorithm to calculate the minimum state estimation ellipsoid containing the real state of the mine operator, thereby improving the reliability of the positioning system of the mine operator.

Description

Mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement
Technical Field
The invention relates to a mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement.
Background
In the technical field of mine industrial safety, a wireless positioning system has important application and has important practical significance for guaranteeing the safety of mine operators. The wireless positioning system generally adopts advanced wireless transmission network information facilities, and the wireless intelligent node senses data locally and cooperates with other sensors to exchange relevant information of a monitored object.
In actual engineering, a wireless positioning system is used for tracking and positioning personnel on an industrial site, so that the sensing capability of the industrial monitoring system on safety information is improved. However, the energy supply of wireless sensors is rather limited. If the wireless sensor periodically transmits the measured signal according to the traditional time-based communication scheme, a large amount of unnecessary transmission on a wireless network can be caused, so that the energy consumption of the wireless sensor is overlarge, and the service life of the wireless sensor is greatly shortened.
In addition, the wireless communication environment of the mine site is relatively complex, and various measurement noises and interferences exist. And the distance between the wireless sensor and the target is usually modeled by a certain nonlinear function. Therefore, various non-linear filters (e.g., extended kalman filter, unscented kalman filter) have emerged to address the estimation problem in wireless positioning systems. However, these filters need to assume that the noise sources are random white noise and gaussian noise. However, in the practical application of the wireless positioning system, the probability assumption of the system noise sometimes does not meet the real situation, and the more reasonable assumption is that the system noise is unknown but bounded.
In summary, it is more practical to consider the incomplete measurement of the wireless sensor and the unknown but bounded noise in the mine environment.
Disclosure of Invention
The invention aims to provide a mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement, so that the position positioning of mine operation personnel can be accurately realized under the condition of incomplete measurement.
In order to achieve the purpose, the invention adopts the following technical scheme:
the mine personnel safety state estimation method based on centralized personnel filtering under incomplete measurement comprises the following steps:
I. arranging a plurality of wireless sensors above a mine working area, and collecting position and speed information of mine operators;
II, establishing a mine worker positioning system model;
the system model establishment process is as follows:
the state quantity x of the mine worker moving in the mine working areakIncluding position and velocity, expressed as the following vector:
xk＝[x1,k v1,k x2,k v2,k]T (1)
wherein x iskThe vector is a 4-dimensional vector and represents the state of the mine worker; (x)1,k,x2,k) Indicating mine operator at time tkPosition coordinates of time; (v)1,k,v2,k) Indicating mine operator at time tkA velocity coordinate of time;
giving out a dynamic state equation x of mine operatorsk+1The following were used:
xk+1＝Akxk+Bkuk+ωk (2)
wherein the content of the first and second substances,
Figure GDA0002926095510000021
wherein, Δ tk＝tk+1-tkThe time interval between two continuous sampling moments in the mine worker positioning system consisting of the plurality of wireless sensors is shown; vector ukRepresenting the variation trend of the state track; omegakIs process noise;
defining the number of the wireless sensors as m, wherein m is a natural number greater than 0; wherein the ith wireless sensor is at time tkIs measured as yi,kI is more than 0 and less than or equal to m; the expression of the measurement equation is:
Figure GDA0002926095510000022
wherein the content of the first and second substances,
Figure GDA0002926095510000023
for measuring noise vkA component of (a); gi(xk) As a function of distance, gi(xk) The expression of (a) is:
Figure GDA0002926095510000024
wherein the content of the first and second substances,
Figure GDA0002926095510000025
representing the position coordinates of the ith wireless sensor; to simplify the expression, let:
Figure GDA0002926095510000026
the measurement results were then rewritten as:
yk＝g(xk)+vk (6)
wherein, yk∈RmIs an m-dimensional vector, an
Figure GDA0002926095510000027
Wherein the process noise omegak∈RnFor n-dimensional vectors, n is taken to be 4, and the noise v is measuredk∈RmIs an m-dimensional vector;
process noise omegak∈RnAnd the measurement noise vk∈RmBelong to the following ellipsoid sets W and V, respectively:
Figure GDA0002926095510000028
wherein Q iskAnd RkIs a known positive definite symmetric matrix describing the size and shape of an ellipsoid;
constructing a centralized filter based on incomplete measurement according to the mine operator positioning system model;
III.1, constructing a transmission mechanism under incomplete measurement;
the wireless sensors are mutually independent and respectively adopt a transmission mechanism under incomplete measurement to transmit information; the transmission time sequence of the information defining the ith wireless sensor under incomplete measurement is expressed as:
Figure GDA0002926095510000031
wherein the content of the first and second substances,
Figure GDA0002926095510000032
the information is transmitted for the t +1 th time at the k moment by the wireless sensor i; t is 0,1,2 …;
the following formula is defined:
Figure GDA0002926095510000033
wherein σi,kQuantity measurement representing previous transmission of ith wireless sensor
Figure GDA0002926095510000034
Measure y from the current quantityi,kA difference of (d);
thus, the information transfer function fi(-) is defined as follows:
Figure GDA0002926095510000035
wherein, deltaiDetermining a parameter for transmission of a wireless sensor i; according to the transmission scheme under incomplete measurement, the wireless sensor i sends the measurement to the ensemble filter only when equation (10) holds:
fi(σi,k,δi)＞0 (10)
therefore, the transmission timing under incomplete measurement is shown in equation (11):
Figure GDA0002926095510000036
wherein the content of the first and second substances,
Figure GDA0002926095510000037
the information is transmitted for the t +2 th time at the k moment by the wireless sensor i; inf { } represents the minimum value satisfying the constraint in brackets, and N represents a natural number; in addition, the signal received by the collector filter from the wireless sensor iInformation representation
Figure GDA0002926095510000038
Comprises the following steps:
Figure GDA0002926095510000039
thus, σi,kThe values are shown in formula (13):
Figure GDA00029260955100000310
order to
Figure GDA00029260955100000311
Then:
Figure GDA00029260955100000312
wherein the content of the first and second substances,
Figure GDA00029260955100000313
III.2, constructing a centralized member filter based on incomplete measurement;
according to the transmission mechanism under incomplete measurement constructed in step iii.1, in combination with the formula (2) -formula (6) mentioned in step II, the structure of the membership filter based on incomplete measurement is proposed as follows:
Figure GDA0002926095510000041
wherein, among others,
Figure GDA0002926095510000042
representing the center of the estimated ellipsoid at time k +1,
Figure GDA0002926095510000043
representing the center of an estimated ellipsoid at the moment k;
Figure GDA0002926095510000044
representing a predicted quantity measurement;
Figure GDA0002926095510000045
Kka filter gain matrix required to be solved for the collector filter;
then the state quantity x at the moment k +1k+1In that
Figure GDA0002926095510000046
In the indicated ellipsoid;
Pk+1estimating a shape matrix of the ellipsoid for the state;
IV, carrying out linear processing on a measurement equation of the mine operator positioning system;
the estimated error e is obtained from the equations (2) and (15)k+1Expressed as:
Figure GDA0002926095510000047
wherein the content of the first and second substances,
Figure GDA0002926095510000048
according to equation (8), the amount of measurements received by the ensemble filter from the wireless sensor is expressed as:
Figure GDA0002926095510000049
and, using Taylor's expansion, the non-linear measurement equation g (x)k) The linear representation is:
Figure GDA00029260955100000410
wherein the content of the first and second substances,
Figure GDA00029260955100000411
Lαis a scaling matrix, ΔαIs an unknown matrix, and|Δα||≤1；
then, the formula (18) is substituted into the formula (6) to obtain:
Figure GDA00029260955100000412
in conjunction with equations (16) and (17), the estimation error is expressed as:
Figure GDA00029260955100000413
scaling matrix LαThe method is obtained by a particle swarm optimization method, and comprises the following specific steps:
obtaining a scaling matrix by analyzing a linearization error
Figure GDA00029260955100000414
Wherein E iskFrom PkIs decomposed to obtain
Figure GDA0002926095510000051
PkEstimate the shape matrix of the ellipsoid, | | E for the statekI is EkEuclidean norm of;
1,2, N for all iiSatisfy the requirement of
Figure GDA0002926095510000052
Wherein the content of the first and second substances,
Figure GDA0002926095510000053
is composed of
Figure GDA0002926095510000054
Euclidean norm of gi(xk) Is g (x)k) The ith component of (a);
if present
Figure GDA0002926095510000055
And the parameter z is present to ensure that the < I < Z > is less than or equal to 1, and the < I < Z > is zA Euclidean norm;
then equation (21) holds:
Figure GDA0002926095510000056
obviously, NiIs influenced by z; thus, scaling the matrix LαTranslates into the following optimization problem:
Figure GDA0002926095510000057
wherein the content of the first and second substances,
Figure GDA0002926095510000058
is composed of
Figure GDA00029260955100000512
Euclidean norm of;
in order to obtain the optimal solution of the formula (22) when the condition of < I < Z > is less than or equal to 1, solving by adopting a particle swarm algorithm;
in the particle swarm algorithm, the particles move according to a position and speed formula to obtain an optimal solution, wherein the position and speed formula is as follows:
Figure GDA0002926095510000059
wherein x isl(s)＝[xl1(s),...,xld(s)]Is the location of the ith particle in the s iteration;
vl(s)＝[vl1(s),...,vld(s)]the velocity of the l-th particle in the s-th iteration; w is the inertial weight;
two acceleration coefficients c1And c2Referred to as cognitive parameters and social parameters, respectively;
r1and r2Are respectively uniformly distributed in [0,1 ]]A random number in between;
pl(s) and pg(s) local optimal position and global optimal position of the population in the s-th iteration, respectively;
setting an initial time at
Figure GDA00029260955100000510
A particles exist in a region expressed by | z | | < 1 at random;
the particles move according to the position and speed formula shown in the formula (23), and the obtained global optimal position p is subjected to b times of iterative movementg(b) Substituting in formula (22) to obtain NiTo obtain a scaling matrix L at time kα；
While
Figure GDA00029260955100000511
Represents g (x)k) The high-order item in the Taylor expansion process completes the linearization of the measurement equation of the positioning system of the mine operating personnel; wherein a and b are both constants;
v, determining various filtering parameters of the collector filter;
v.1, determining constraint conditions met by various filtering parameters of the collector filter;
for the mine worker positioning system, the initial state of the system is set to be x0The estimated value thereof
Figure GDA0002926095510000061
Satisfies the following conditions:
Figure GDA0002926095510000062
wherein, P0Is a given positive definite symmetric matrix;
and at time k, the state quantity xkBelongs to the state estimation ellipsoid
Figure GDA0002926095510000063
Then, if there is a filter parameter Pk+1＞0，Kk，λ1＞0，λ2＞0，λ3＞0，λ4> 0 and lambda5If > 0, the linear matrix inequality shown in the formula (25) is satisfied; then:
state quantity x at time k +1k+1Belongs to the state estimation ellipsoid
Figure GDA0002926095510000064
Figure GDA0002926095510000065
Wherein the content of the first and second substances,
Figure GDA0002926095510000066
i denotes an identity matrix, Πk＝[0 (Ak-KkGk)Ek 1 -KkLα -Kk -Kk]；
Each filtering parameter satisfies the constraint shown in formula (25); in addition, the center of the state estimation ellipsoid is determined by equation (15);
v.2, determining each filtering parameter of the collector filter according to a semi-positive planning method;
determining an optimum state ellipsoid by applying a semi-positive definite programming method, and determining each filtering parameter by solving the following optimization problems:
Figure GDA0002926095510000067
wherein trace (P)k+1) Representing the shape matrix Pk+1Each filter parameter of the trace (1) meets the constraint shown in the formula (25); obtaining the P through a semi-positive definite programming methodk+1The value of each filtering parameter when the trace of (A) is minimum;
substituting each filtering parameter into the step III to obtain a centralized filter based on incomplete measurement;
VI, positioning the mine operating personnel by using a centralized filter;
recursion of the collector filter is used for obtaining the positioning ellipsoid center at the k +1 moment
Figure GDA0002926095510000068
And positioning the ellipsoid-shaped matrix Pk+1The state quantity x of the mine workerk+1In that
Figure GDA0002926095510000069
In the represented ellipsoid, a person position fix is achieved.
The invention has the following advantages:
as described above, the present invention provides a mine personnel safety state estimation method based on incomplete measurement centralized filtering, which fully considers the incomplete measurement of a wireless sensor and unknown but bounded noise in a mine environment, and constructs a centralized filter based on incomplete measurement according to a mine operator positioning system model. In order to effectively process nonlinear errors in the mine operator positioning system, the measurement equation of the mine operator positioning system is subjected to linearization processing, a scaling matrix and an unknown matrix are adopted to express the linearization errors in the linearization processing, and the scaling matrix is processed by using a particle swarm algorithm, so that the linearization problem of the system is effectively solved, and the accurate positioning of the position of the mine operator is realized; in addition, the method determines various filtering parameters through semi-positive definite planning, and provides a recursive filtering algorithm to calculate a minimum state estimation ellipsoid containing the real state of the mine operator, so that the reliability of the positioning system of the mine operator is improved.
Drawings
Fig. 1 is a flowchart of a mine personnel safety state estimation method based on incomplete measurement centralized filtering in the invention.
Fig. 2 is a schematic layout diagram of wireless sensors according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of transmission timings of the sensors when the transmission determination parameter is 0.6 according to the embodiment of the present invention.
FIG. 4 is a schematic diagram showing a comparison between a real trajectory and an estimated trajectory of a mine operator in an embodiment of the invention.
FIG. 5 is a schematic diagram illustrating a comparison between the real state coordinate value and the estimated state coordinate value of the mine operator according to an embodiment of the present invention.
FIG. 6 is a diagram illustrating a comparison of the actual status and estimated boundaries of mine workers in an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
as shown in fig. 1, the mine personnel safety state estimation method based on collective filtering under incomplete measurement includes the following steps:
I. a plurality of wireless sensors are arranged above a mine working area, and position and speed information of mine operators is collected.
As shown in fig. 2, in order to improve the safety monitoring capability of the mine workers, for example, 6 wireless sensors may be deployed above the mine working area, so as to perform safety monitoring on the workers in the area.
The wireless sensors are respectively used for collecting information such as the position and the speed of mine workers. And this information will be transmitted to the filter for personnel (security status or) location estimation, in selected parts, by means of a transmission mechanism under incomplete measurement.
Of course, the number of wireless sensors in the present embodiment is not limited to the above 6, and is only exemplified here.
And II, after receiving the position and speed information of the mine operating personnel, establishing a mine operating personnel positioning system model.
The system model establishment process is as follows:
setting the state quantity x of the mine operator when the mine operator moves in the mine working areakIncluding position and velocity, expressed as the following vector:
xk＝[x1,k v1,k x2,k v2,k]T (1)
wherein x iskThe vector is a 4-dimensional vector and represents the state of the mine worker; (x)1,k,x2,k) Indicating mine operator at time tkOf the hourA position coordinate; (v)1,k,v2,k) Indicating mine operator at time tkThe velocity coordinate of time.
Giving out a dynamic state equation x of mine operatorsk+1The following were used:
xk+1＝Akxk+Bkuk+ωk (2)
wherein the content of the first and second substances,
Figure GDA0002926095510000081
wherein, Δ tk＝tk+1-tkThe time interval between two continuous sampling moments in the mine worker positioning system consisting of the plurality of wireless sensors is shown; vector ukRepresenting the variation trend of the state track; omegakIs process noise.
The number of the wireless sensors is defined as m, and m is a natural number greater than 0. Wherein the ith wireless sensor is at time tkIs measured as yi,kI is more than 0 and less than or equal to m; the expression of the measurement equation is:
Figure GDA0002926095510000082
wherein the content of the first and second substances,
Figure GDA0002926095510000083
for measuring noise vkA component of (a); gi(xk) As a function of distance, gi(xk) The expression of (a) is:
Figure GDA0002926095510000084
wherein the content of the first and second substances,
Figure GDA0002926095510000085
indicating the location coordinates of the ith wireless sensor. To simplify the expression, let:
Figure GDA0002926095510000086
the measurement results were then rewritten as:
yk＝g(xk)+vk (6)
wherein, yk∈RmIs an m-dimensional vector, an
Figure GDA0002926095510000087
Wherein the process noise omegak∈RnFor n-dimensional vectors, n is taken to be 4, and the noise v is measuredk∈RmIs an m-dimensional vector; process noise omegak∈RnAnd the measurement noise vk∈RmBelong to the following ellipsoid sets W and V, respectively:
Figure GDA0002926095510000088
wherein Q iskAnd RkIs a known positive definite symmetric matrix describing the size and shape of the ellipsoid.
And III, constructing a centralized filter based on incomplete measurement according to the mine operator positioning system model.
The construction process of the membership filter based on incomplete measurement proposed in the embodiment can be divided into the following two steps:
and III.1, constructing a transmission mechanism under incomplete measurement.
After the wireless sensor collects the position and speed equivalent measurement information of the mine operation personnel, the measurement information needs to be transmitted to the filter for personnel positioning processing. In order to achieve the purpose of energy saving, the measured signals on the wireless sensors cannot be transmitted completely. In the case of such incomplete measurement, a special information transmission mechanism is proposed.
And each wireless sensor judges whether the current measurement is sent to the filter or not according to the difference value between the previous transmitted measurement and the current measurement. In this way, the wireless sensor can adjust its own transmission rate according to the dynamic change of the sensing signal, thereby reducing the data amount transmitted to the filter. In addition, in order to improve the energy efficiency of the sensors and ensure the estimation performance of the positioning system, each wireless sensor can independently execute the transmission strategy without considering the consistency with other sensors in the cluster.
The transmission mechanism under the incomplete measurement can effectively reduce energy consumption and obviously prolong the service life of the wireless sensor.
The transmission time sequence of the information defining the ith wireless sensor under incomplete measurement is expressed as:
Figure GDA0002926095510000091
wherein the content of the first and second substances,
Figure GDA0002926095510000092
the information is transmitted for the t +1 th time at the k moment by the wireless sensor i; t is 0,1,2 ….
The following formula is defined:
Figure GDA0002926095510000093
wherein σi,kQuantity measurement representing previous transmission of ith wireless sensor
Figure GDA0002926095510000094
Measure y from the current quantityi,kThe difference of (a).
Thus, the information transfer function fi(-) is defined as follows:
Figure GDA0002926095510000095
wherein, deltaiThe parameters are judged for the transmission of the wireless sensor i. Based on the transmission mechanism under incomplete measurement, the wireless sensor i is only in the formula (1)0) The measurements are sent to the collector filter when it is established:
fi(σi,k,δi)＞0 (10)
therefore, the transmission timing under incomplete measurement is shown in equation (11):
Figure GDA0002926095510000096
wherein the content of the first and second substances,
Figure GDA0002926095510000097
the wireless sensor i transmits information for the t +2 th time at the k moment, inf { } represents the minimum value meeting the constraint in brackets, and N represents a natural number. In addition, the information received by the collective filter from the wireless sensor i represents
Figure GDA0002926095510000098
Comprises the following steps:
Figure GDA0002926095510000101
thus, σi,kThe values are shown in formula (13):
Figure GDA0002926095510000102
order to
Figure GDA0002926095510000103
Then:
Figure GDA0002926095510000104
wherein the content of the first and second substances,
Figure GDA0002926095510000105
the transmission mechanism in this embodiment can adjust the transmission frequency of the information according to the variation characteristic of the measurement, thereby ensuring the transmission performance. Compared with the traditional time-based transmission scheme, the transmission mechanism in the embodiment improves the resource utilization efficiency by reasonably reducing redundant transmission, and simultaneously ensures the required filtering performance.
And III.2, constructing a membership filter based on incomplete measurement.
The collective filtering is to describe the true state of the system by a collection of outer bounding ellipsoids that contain the model structure, measurement data, and noise boundaries of the system, resulting in a set of feasible states for the state information.
The set of feasible states consists of the state and measurement equations of the system, noise boundaries, measurement outputs and initial state values.
Compared with methods such as Kalman filtering and the like which need to know the statistical characteristics of the noise, the method adopts the centralized filtering which only needs to know the boundary of the noise, so that the method is more suitable for processing unknown bounded noise in the mine environment.
According to the transmission mechanism under incomplete measurement constructed in step iii.1, in combination with the formula (2) -formula (6) mentioned in step II, the structure of the membership filter based on incomplete measurement is proposed as follows:
Figure GDA0002926095510000106
wherein the content of the first and second substances,
Figure GDA0002926095510000107
representing the center of the estimated ellipsoid at time k +1,
Figure GDA0002926095510000108
representing the center of an estimated ellipsoid at the moment k;
Figure GDA0002926095510000109
representing a predicted quantity measurement;
Figure GDA00029260955100001010
Kkthe filter gain matrix that needs to be solved for the ensemble filter.
And IV, carrying out linearization processing on the measurement equation of the mine operator positioning system.
In the embodiment, the measurement equation of the system mine operator positioning system is a nonlinear function, and if the nonlinear terms involved are processed according to the traditional extended kalman filter algorithm, the high-order terms generated by the taylor expansion are simply ignored, and the conservatism is inevitably caused in some cases, so that the precision is reduced.
When the measurement equation of the positioning system of the mine workers is subjected to linearization processing, the embodiment adopts the scaling matrix and the unknown matrix to express the linearization error, and utilizes the particle swarm algorithm to process the scaling matrix, so that the linearization problem of the positioning system of the mine workers is effectively solved, and the positioning accuracy of the mine workers is improved.
The estimated error e is obtained from the equations (2) and (15)k+1Expressed as:
Figure GDA0002926095510000111
wherein the content of the first and second substances,
Figure GDA0002926095510000112
according to equation (8), the amount of measurements received by the ensemble filter from the wireless sensor is expressed as:
Figure GDA0002926095510000113
and, using Taylor's expansion, the non-linear measurement equation g (x)k) The linear representation is:
Figure GDA0002926095510000114
wherein the content of the first and second substances,
Figure GDA0002926095510000115
Lαis an indeterminate scaling matrix, ΔαIs an unknown matrix, and | | | Δα||≤1。
Then, the formula (18) is substituted into the formula (6) to obtain:
Figure GDA0002926095510000116
in conjunction with equations (16) and (17), the estimation error is expressed as:
Figure GDA0002926095510000117
scaling matrix LαThe method is obtained by a particle swarm optimization method, and comprises the following specific steps:
obtaining a scaling matrix by analyzing a linearization error
Figure GDA0002926095510000118
Wherein E iskFrom PkIs decomposed to obtain
Figure GDA0002926095510000119
PkEstimate the shape matrix of the ellipsoid, | | E for the statekI is EkEuclidean norm of.
1,2, N for all iiSatisfy the requirement of
Figure GDA00029260955100001110
Wherein the content of the first and second substances,
Figure GDA00029260955100001111
is composed of
Figure GDA00029260955100001112
Euclidean norm of gi(xk) Is g (x)k) The ith component of (a).
If present
Figure GDA00029260955100001113
And the parameter z is present to ensure that the | z | is less than or equal to 1, and the | z | is the Euclidean norm of z.
Then equation (21) holds:
Figure GDA00029260955100001114
obviously, NiIs influenced by z. Thus, scaling the matrix LαTranslates into the following optimization problem:
Figure GDA0002926095510000121
wherein the content of the first and second substances,
Figure GDA0002926095510000122
is composed of
Figure GDA0002926095510000128
Euclidean norm of.
In order to obtain the optimal solution of the formula (22) when the condition of < i > z < i > is less than or equal to 1, a particle swarm algorithm is adopted for solving.
In the particle swarm algorithm, the particles move according to a position and speed formula to obtain an optimal solution, wherein the position and speed formula is as follows:
Figure GDA0002926095510000123
wherein x isl(s)＝[xl1(s),...,xld(s)]Is the location of the ith particle in the s iteration;
vl(s)＝[vl1(s),...,vld(s)]the velocity of the l-th particle in the s-th iteration; w is the inertial weight;
two acceleration coefficients c1And c2Referred to as cognitive parameters and social parameters, respectively;
r1and r2Are respectively uniformly dividedIs distributed on [0,1 ]]A random number in between;
pl(s) and pg(s) are the local optimal location and global optimal location of the population in the s-th iteration, respectively.
Setting an initial time at
Figure GDA0002926095510000124
A particles exist in a region expressed by | z | | < 1 at random;
the particles move according to the position and speed formula shown in (23), and after b times of iterative movement, the obtained global optimal position pg(b) Into formula (22) to obtain NiThe value is obtained.
Wherein a and b are constants, and the values of a and b are determined according to time and precision requirements and actual conditions.
By means of particle swarm algorithm, obtaining accurate NiA value; further, a scaling matrix L at the time k is obtainedαTo do so
Figure GDA0002926095510000125
Represents g (x)k) And (4) completing linearization of a measurement equation of the positioning system of the mine workers by using a high-order term in the Taylor expansion process.
In the embodiment, the measurement equation of the positioning system of the mine workers is subjected to linear processing, which is determined by the accurate positioning requirement of the mine environment on the mine workers, so that the safety of the mine workers is ensured.
Conventionally, the higher order terms of the Taylor expansion are ignored, which inevitably reduces the accuracy of the state estimation, and the embodiment of the present invention takes this point into account, and uses the higher order terms
Figure GDA0002926095510000126
And (4) showing.
Albeit ΔαIs unknown, but it satisfies | | | Δα| | < 1, i.e. ΔαIs bounded, and then gets
Figure GDA0002926095510000127
Is bounded.
The embodiment makes full use of the boundedness of the high-order item, can more accurately obtain the filtering parameters of the collector filter, further improves the filtering performance of the filter, and finally is beneficial to improving the positioning accuracy of mine workers.
V. determining the filter parameters of the ensemble filter. The determination of the filter parameters can be divided into the following two steps:
and V.1, determining the constraint conditions met by each filtering parameter of the member filter.
For the mine worker positioning system, the initial state of the system is set to be x0The estimated value thereof
Figure GDA0002926095510000131
Satisfies the following conditions:
Figure GDA0002926095510000132
wherein, P0Is a given positive definite symmetric matrix.
And at time k, the state quantity xkBelongs to the state estimation ellipsoid
Figure GDA0002926095510000133
Then, if there is a filter parameter Pk+1＞0，Kk，λ1＞0，λ2＞0，λ3＞0，λ4> 0 and lambda5If > 0, the linear matrix inequality shown in the formula (25) is satisfied; then:
state quantity x at time k +1k+1Belongs to the state estimation ellipsoid
Figure GDA0002926095510000134
Figure GDA0002926095510000135
Wherein the content of the first and second substances,
Figure GDA0002926095510000136
i denotes an identity matrix, Πk＝[0 (Ak-KkGk)Ek 1 -KkLα -Kk -Kk]。
Each filtering parameter satisfies the constraint shown in formula (25); in addition, the center of the state estimation ellipsoid is determined by equation (15).
V.2, determining each filtering parameter of the collector filter according to a semi-positive planning method;
determining an optimal state estimation ellipsoid by applying a semi-positive definite programming method, and determining each filtering parameter by solving the following optimization problems:
Figure GDA0002926095510000137
wherein trace (P)k+1) Representing the shape matrix Pk+1Each filter parameter of the trace (1) meets the constraint shown in the formula (25); obtaining the P through a semi-positive definite programming methodk+1The value of each filtering parameter when the trace of (A) is minimum;
and substituting each filtering parameter into the step III to obtain the centralized filter based on incomplete measurement.
VI, positioning mine operating personnel according to the filter algorithm;
recursion of the collector filter is used for obtaining the positioning ellipsoid center at the k +1 moment
Figure GDA0002926095510000138
And positioning the ellipsoid-shaped matrix Pk+1The state quantity x of the mine workerk+1In that
Figure GDA0002926095510000139
In the represented ellipsoid, a person position fix is achieved.
Compared with the traditional Kalman filtering method and the like which need to know the statistical characteristics of the noise, the centralized filtering adopted by the embodiment of the invention only needs to know the boundary of the noise, so that the method and the device are more suitable for processing the unknown bounded noise in the mine environment.
In addition, considering that the energy supply of the wireless sensor is quite limited, the information obtained by the wireless sensor is not sent to the filter completely, but is transmitted through a transmission mechanism under incomplete measurement, so that the limited energy of the wireless sensor is saved, the service life of the sensor is longer, the filter obtains useful information as much as possible, and the estimation precision is ensured.
In addition, in consideration of the nonlinearity of the system measurement equation, the embodiment of the invention adopts the scaling matrix and the unknown matrix to express the high-order item in the linearization process of the measurement equation instead of simply neglecting the high-order item, thereby reducing the linearization error, improving the estimation precision of the collective filter, further being beneficial to improving the positioning precision of the mine operators and ensuring the safety of the mine operators.
Fig. 3 shows the times when the six wireless sensors S1 to S6 transmit data when the transmission determination parameter is 0.6. As can be seen from fig. 3, the wireless sensor does not transmit all the information to the collector filter, but selectively transmits the information, so that the energy consumption is reduced, and the service life of the wireless sensor is effectively prolonged. The six wireless sensors are mutually independent and adopt a transmission mechanism under incomplete measurement to transmit information, so the information transmission moments of the six wireless sensors are different, the information transmitted to the filter by each wireless sensor can be effectively complemented, and the situation that the 6 wireless sensors cannot transmit the information to the filter at a certain moment is avoided as much as possible.
Fig. 4 is a schematic diagram comparing the real track and the estimated track of the mine worker. By comparison, the centralized member filter can well estimate the track of the mine worker. FIG. 5 is a schematic diagram showing the comparison between the real state coordinate value and the estimated state coordinate value of the mine operator. Wherein (x1, x2) represents the position coordinates of the mine worker, and the coordinates are compared when the sampling time is from 0 to 200. As can be seen from fig. 5, the state coordinate values estimated by the ensemble filter are very different from the true state coordinate values. Through the comparison, the method disclosed by the invention has a good effect on the estimation of the safety state of the mine personnel. This is because although the information obtained by the membership filter is reduced in the case of incomplete measurement, the wireless sensor selects more effective information for transmission by the transmission mechanism under incomplete measurement proposed by the present invention. Therefore, the invention can reasonably reduce redundant transmission and improve the resource utilization efficiency on the basis of ensuring the required filtering performance.
Fig. 6 is a schematic diagram comparing the actual state and estimated boundaries of the mine operator. Where (x1, x2) represents the position coordinates of the mine worker. As can be seen from fig. 6, when the sampling time is from 0 to 200, the real state of the mine worker is always between the estimated boundaries obtained by the membership filter constructed in the embodiment of the present invention, and it is ensured that the real value is always within the estimated range, thereby facilitating more reasonable and effective safety management for the mine worker.
It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A mine personnel safety state estimation method based on incomplete measurement centralized filtering is characterized in that,
the method comprises the following steps:
I. arranging a plurality of wireless sensors above a mine working area, and collecting position and speed information of mine operators;
II, establishing a mine worker positioning system model;
the system model establishment process is as follows:
the state quantity x of the mine worker moving in the mine working areakIncluding position and velocity, expressed as the following vector:
xk＝[x1,k v1,k x2,k v2,k]T (1)
wherein x iskIs a 4-dimensional vector and is a vector,indicating the state of the mine operator; (x)1,k,x2,k) Indicating mine operator at time tkPosition coordinates of time; (v)1,k,v2,k) Indicating mine operator at time tkA velocity coordinate of time;
giving out a dynamic state equation x of mine operatorsk+1The following were used:
xk+1＝Akxk+Bkuk+ωk (2)
wherein the content of the first and second substances,
Figure FDA0002926095500000011
wherein, Δ tk＝tk+1-tkThe time interval between two continuous sampling moments in the mine worker positioning system consisting of the plurality of wireless sensors is shown; vector ukRepresenting the variation trend of the state track; omegakIs process noise;
defining the number of the wireless sensors as m, wherein m is a natural number greater than 0; wherein the ith wireless sensor is at time tkIs measured as yi,kI is more than 0 and less than or equal to m; the expression of the measurement equation is:
Figure FDA0002926095500000012
wherein the content of the first and second substances,
Figure FDA0002926095500000013
for measuring noise vkA component of (a); gi(xk) As a function of distance, gi(xk) The expression of (a) is:
Figure FDA0002926095500000014
wherein the content of the first and second substances,
Figure FDA0002926095500000015
representing the position coordinates of the ith wireless sensor; to simplify the expression, let:
Figure FDA0002926095500000021
the measurement results were then rewritten as:
yk＝g(xk)+vk (6)
wherein, yk∈RmIs an m-dimensional vector, an
Figure FDA0002926095500000022
Wherein the process noise omegak∈RnFor n-dimensional vectors, n is taken to be 4, and the noise v is measuredk∈RmIs an m-dimensional vector;
process noise omegak∈RnAnd the measurement noise vk∈RmBelong to the following ellipsoid sets W and V, respectively:
Figure FDA0002926095500000023
wherein Q iskAnd RkIs a known positive definite symmetric matrix describing the size and shape of an ellipsoid;
constructing a centralized filter based on incomplete measurement according to the mine operator positioning system model;
III.1, constructing a transmission mechanism under incomplete measurement;
the wireless sensors are mutually independent and respectively adopt a transmission mechanism under incomplete measurement to transmit information; the transmission time sequence of the information defining the ith wireless sensor under incomplete measurement is expressed as:
Figure FDA0002926095500000024
wherein the content of the first and second substances,
Figure FDA0002926095500000025
the information is transmitted for the t +1 th time at the k moment by the wireless sensor i; t is 0,1,2 …;
the following formula is defined:
Figure FDA0002926095500000026
wherein σi,kQuantity measurement representing previous transmission of ith wireless sensor
Figure FDA0002926095500000027
Measure y from the current quantityi,kA difference of (d);
thus, the information transfer function fi(-) is defined as follows:
Figure FDA0002926095500000028
wherein, deltaiDetermining a parameter for transmission of a wireless sensor i; according to the transmission scheme under incomplete measurement, the wireless sensor i sends the measurement to the ensemble filter only when equation (10) holds:
fi(σi,k,δi)＞0 (10)
therefore, the transmission timing under incomplete measurement is shown in equation (11):
Figure FDA0002926095500000031
wherein the content of the first and second substances,
Figure FDA0002926095500000032
denotes the t + of wireless sensor i at the moment k2 times of information transmission; inf { } represents the minimum value satisfying the constraint in brackets, and N represents a natural number; in addition, the information received by the collective filter from the wireless sensor i represents
Figure FDA0002926095500000033
Comprises the following steps:
Figure FDA0002926095500000034
thus, σi,kThe values are shown in formula (13):
Figure FDA0002926095500000035
order to
Figure FDA0002926095500000036
Then:
Figure FDA0002926095500000037
wherein the content of the first and second substances,
Figure FDA0002926095500000038
III.2, constructing a centralized member filter based on incomplete measurement;
according to the transmission mechanism under incomplete measurement constructed in step iii.1, in combination with the formula (2) -formula (6) mentioned in step II, the structure of the membership filter based on incomplete measurement is proposed as follows:
Figure FDA0002926095500000039
wherein, among others,
Figure FDA00029260955000000310
representing the k +1 time estimateThe center of the ellipsoid is the center of the ellipsoid,
Figure FDA00029260955000000311
representing the center of an estimated ellipsoid at the moment k;
Figure FDA00029260955000000312
representing a predicted quantity measurement;
Figure FDA00029260955000000313
Kka filter gain matrix required to be solved for the collector filter;
then the state quantity x at the moment k +1k+1In that
Figure FDA00029260955000000314
In the indicated ellipsoid;
wherein, Pk+1Estimating a shape matrix of the ellipsoid for the state;
IV, carrying out linear processing on a measurement equation of the mine operator positioning system;
the estimated error e is obtained from the equations (2) and (15)k+1Expressed as:
Figure FDA00029260955000000315
wherein the content of the first and second substances,
Figure FDA00029260955000000316
according to equation (8), the amount of measurements received by the ensemble filter from the wireless sensor is expressed as:
Figure FDA00029260955000000317
and, using Taylor's expansion, the non-linear measurement equation g (x)k) The linear representation is:
Figure FDA0002926095500000041
wherein the content of the first and second substances,
Figure FDA0002926095500000042
Lαis a scaling matrix, ΔαIs an unknown matrix, and | | | Δα||≤1；
Then, the formula (18) is substituted into the formula (6) to obtain:
Figure FDA0002926095500000043
in conjunction with equations (16) and (17), the estimation error is expressed as:
Figure FDA0002926095500000044
scaling matrix LαThe method is obtained by a particle swarm optimization method, and comprises the following specific steps:
obtaining a scaling matrix by analyzing a linearization error
Figure FDA0002926095500000045
Wherein E iskFrom PkIs decomposed to obtain
Figure FDA0002926095500000046
PkEstimate the shape matrix of the ellipsoid, | | E for the statekI is EkEuclidean norm of;
1,2, N for all iiSatisfy the requirement of
Figure FDA0002926095500000047
Wherein the content of the first and second substances,
Figure FDA0002926095500000048
is composed of
Figure FDA0002926095500000049
Euclidean norm of gi(xk) Is g (x)k) The ith component of (a);
if present
Figure FDA00029260955000000410
And the existence of the parameter z ensures that the < I < Z > is less than or equal to 1, and the < I > z < I > is the Euclidean norm of z;
then equation (21) holds:
Figure FDA00029260955000000411
obviously, NiIs influenced by z; thus, scaling the matrix LαTranslates into the following optimization problem:
Figure FDA00029260955000000412
wherein the content of the first and second substances,
Figure FDA00029260955000000413
is composed of
Figure FDA00029260955000000414
Euclidean norm of;
in order to obtain the optimal solution of the formula (22) when the condition of < I < Z > is less than or equal to 1, solving by adopting a particle swarm algorithm;
in the particle swarm algorithm, the particles move according to a position and speed formula to obtain an optimal solution, wherein the position and speed formula is as follows:
Figure FDA00029260955000000415
wherein x isl(s)＝[xl1(s),...,xld(s)]Is the location of the ith particle in the s iteration;
vl(s)＝[vl1(s),...,vld(s)]the velocity of the l-th particle in the s-th iteration; w is the inertial weight;
two acceleration coefficients c1And c2Referred to as cognitive parameters and social parameters, respectively;
r1and r2Are respectively uniformly distributed in [0,1 ]]A random number in between;
pl(s) and pg(s) local optimal position and global optimal position of the population in the s-th iteration, respectively;
setting an initial time at
Figure FDA0002926095500000051
A particles exist in a region expressed by | z | | < 1 at random;
the particles move according to the position and speed formula shown in the formula (23), and the obtained global optimal position p is subjected to b times of iterative movementg(b) Substituting in formula (22) to obtain NiTo obtain a scaling matrix L at time kα；
While
Figure FDA0002926095500000052
Represents g (x)k) The high-order item in the Taylor expansion process completes the linearization of the measurement equation of the positioning system of the mine operating personnel; wherein a and b are both constants;
v, determining various filtering parameters of the collector filter;
v.1, determining constraint conditions met by various filtering parameters of the collector filter;
for the mine worker positioning system, the initial state of the system is set to be x0The estimated value thereof
Figure FDA0002926095500000053
Satisfies the following conditions:
Figure FDA0002926095500000054
wherein, P0Is a given positive definite symmetric matrix;
and at time k, the state quantity xkBelongs to the state estimation ellipsoid
Figure FDA0002926095500000055
Then, if there is a filter parameter Pk+1＞0，Kk，λ1＞0，λ2＞0，λ3＞0，λ4> 0 and lambda5If > 0, the linear matrix inequality shown in the formula (25) is satisfied; then:
state quantity x at time k +1k+1Belongs to the state estimation ellipsoid
Figure FDA0002926095500000056
Figure FDA0002926095500000057
Wherein the content of the first and second substances,
Figure FDA0002926095500000058
i denotes an identity matrix, Πk＝[0 (Ak-KkGk)Ek 1 -KkLα -Kk -Kk]；
Each filtering parameter satisfies the constraint shown in formula (25); in addition, the center of the state estimation ellipsoid is determined by equation (15);
v.2, determining each filtering parameter of the collector filter according to a semi-positive planning method;
determining an optimum state ellipsoid by applying a semi-positive definite programming method, and determining each filtering parameter by solving the following optimization problems:
Figure FDA0002926095500000061
wherein trace (P)k+1) Representing the shape matrix Pk+1Each filter parameter of the trace (1) meets the constraint shown in the formula (25); obtaining the P through a semi-positive definite programming methodk+1The value of each filtering parameter when the trace of (A) is minimum;
substituting each filtering parameter into the step III to obtain a centralized filter based on incomplete measurement;
VI, positioning the mine operating personnel by using a centralized filter;
recursion of the collector filter is used for obtaining the positioning ellipsoid center at the k +1 moment
Figure FDA0002926095500000062
And positioning the ellipsoid-shaped matrix Pk+1The state quantity x of the mine workerk+1In that
Figure FDA0002926095500000063
In the represented ellipsoid, a person position fix is achieved.
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