CN116431981A - Distributed group member filtering method based on mobile robot positioning system - Google Patents

Distributed group member filtering method based on mobile robot positioning system Download PDF

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CN116431981A
CN116431981A CN202211566212.7A CN202211566212A CN116431981A CN 116431981 A CN116431981 A CN 116431981A CN 202211566212 A CN202211566212 A CN 202211566212A CN 116431981 A CN116431981 A CN 116431981A
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mobile robot
matrix
positioning system
sensor node
robot positioning
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CN116431981B (en
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胡军
李佳兴
张红旭
武志辉
徐龙
杜君花
高培夏
董睿杰
周奥展
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Heilongjiang Yuheng Technology Innovation Development Co ltd
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Harbin University of Science and Technology
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Abstract

The invention discloses a distributed group member filtering method based on a mobile robot positioning system, which comprises the following steps: step one, establishing a dynamic model of a mobile robot positioning system with state saturation under an encryption and decryption mechanism; step two, designing a distributed set member filter in the sense of minimizing a filtering error ellipsoid; step three,Calculating an intermediate matrix P of each node in the sensor network at k time i,k+1|k The method comprises the steps of carrying out a first treatment on the surface of the Step four, calculating a filter gain matrix of each sensor node
Figure DDA0003986176860000012
Step five, designing a distributed collector filter of the ith sensor node at the moment k+1
Figure DDA0003986176860000011
Judging whether k+1 reaches the total duration M, if k+1 is less than M, executing step six, and if k+1 is more than or equal to M, ending operation; step six, calculating a filter error limited matrix P of each sensor node i,k+1|k+1 The method comprises the steps of carrying out a first treatment on the surface of the Let k=k+1, execute step two until k+1 is satisfied. The invention solves the problem that the existing distributed filtering method can not process the distributed filtering of the sensor network with state saturation under the encryption and decryption mechanism.

Description

Distributed group member filtering method based on mobile robot positioning system
Technical Field
The invention relates to a filtering method, in particular to a distributed member collecting filtering method of a mobile robot positioning system under a sensor network with state saturation under an encryption and decryption mechanism.
Background
The mobile robot system is a comprehensive system capable of sensing the surrounding environment and simultaneously having the functions of planning, decision making, control and the like, and has wide application prospects in various fields of military, agriculture, medical treatment, civil aviation, logistics storage industry and the like. The problem of positioning of mobile robot systems is a hotspot problem in current research, and the handling of this problem helps to increase the level of automation of mobile robots.
Because of rapid development of information technology, in order to ensure the security of data, an encryption and decryption mechanism is introduced in the signal transmission process to schedule the data, so that the data can be effectively prevented from being damaged, and the data signal can be ensured to be transmitted safely. Meanwhile, considering that in practical situations, a mobile robot generally moves in a limited space, for example, an indoor mobile robot, the position information, the speed information and the like of the mobile robot are constrained, and therefore, considering a state saturation phenomenon in system modeling has practical significance.
Because the existing filtering method rarely considers state saturation and encryption and decryption mechanisms at the same time, especially for unknown but bounded system noise, the existing filtering method cannot handle the problems, and further the problems of damaged filtering algorithm performance, reduced estimation accuracy and the like are caused.
Disclosure of Invention
The invention provides a distributed group member filtering method based on a mobile robot positioning system, which aims to solve the problem of distributed group member filtering with saturated state under an encryption and decryption mechanism based on the mobile robot positioning system. The method can reflect the actual situation more truly, and is easy to execute and apply on line by adopting a recurrence method.
The invention aims at realizing the following technical scheme:
a distributed group member filtering method based on a mobile robot positioning system comprises the following steps:
step one, based on a Cartesian coordinate system, selecting position and direction information of a mobile robot positioning system as state variables, and establishing a mobile robot positioning system dynamic model with state saturation under an encryption and decryption mechanism;
step two, designing a distributed collector filter for the dynamic model of the mobile robot positioning system established in the step one under the meaning of minimizing a filtering error ellipsoid;
step three, calculating an intermediate matrix P of each node in the sensor network at the moment k i,k+1|k ；
Step four, according to the intermediate matrix P obtained in the step three i,k+1|k Calculation ofFilter gain matrix for each sensor node
Figure BDA0003986176840000021
Step five, according to the filter gain matrix obtained in the step four
Figure BDA0003986176840000022
Substituting the filter into the distributed group member filter designed in the second step to design the distributed group member filter of the ith sensor node at the moment k+1>
Figure BDA0003986176840000023
Judging whether k+1 reaches the total duration M, if k+1 is less than M, executing step six, and if k+1 is more than or equal to M, ending operation;
step six, according to the filter gain matrix of each sensor node obtained in the step four
Figure BDA0003986176840000024
Calculating a filter error limiting matrix P for each sensor node i,k+1|k+1 The method comprises the steps of carrying out a first treatment on the surface of the Let k=k+1, execute step two until k+1 is satisfied.
Compared with the prior art, the invention has the following advantages:
1. the invention considers the encryption and decryption mechanism and the influence of state saturation on the performance of the filtering algorithm, comprehensively considers the effective information of the filtering error limited matrix by using the distributed type member filtering method, and compared with the existing distributed type filtering method, the invention designs the distributed type member filter for the mobile robot positioning system and considers the state saturation and encryption and decryption mechanism, thereby completing the design process of the distributed type member filtering algorithm based on the mobile robot positioning system, improving the anti-interference capability of the filtering and being easy to apply on line.
2. The invention adopts a random analysis technology and related knowledge of matrix theory, obtains a specific expression of the limited matrix by considering the available information of the limited matrix of the filtering errors, and then ensures that the filtering errors are positioned in an ellipsoid by designing a proper distributed filter gain matrix. The method ensures the minimization of the filtered error ellipsoid domain, and completes the better performance of the filtering algorithm under the condition that the state saturation and the encryption and decryption mechanism occur simultaneously. From the simulation experiment result, it can be seen that the reduction of the quantization interval length reduces the average filtering error of the node 1 by 0.51, the average filtering error of the node 2 by 0.9, the average filtering error of the node 3 by 0.82 and the average filtering error of the node 4 by 0.96.
3. The distributed recursive collector filtering algorithm designed by the invention can effectively estimate the state information of the mobile robot positioning system.
4. The distributed recursive collector filtering algorithm designed by the invention is easy to solve on line, and solves the problem that the existing distributed filtering method can not process the distributed filtering of the sensor network with state saturation under the encryption and decryption mechanism.
Drawings
FIG. 1 is a flow chart of a distributed crew filtering method based on a mobile robot positioning system of the present invention;
FIG. 2 is a first component of the actual state trajectory of the mobile robotic positioning system
Figure BDA0003986176840000031
And filtering it by the first node>
Figure BDA0003986176840000032
And filtering it by the second node>
Figure BDA0003986176840000033
FIG. 3 is a first component of the actual state trajectory of the mobile robotic positioning system
Figure BDA0003986176840000034
And the third node filters it>
Figure BDA0003986176840000035
And a fourth node to itFiltering->
Figure BDA0003986176840000036
FIG. 4 is a second component of the actual state trajectory of the mobile robotic positioning system
Figure BDA0003986176840000037
And filtering it by the first node>
Figure BDA0003986176840000038
And filtering it by the second node>
Figure BDA0003986176840000039
FIG. 5 is a second component of the actual state trajectory of the mobile robotic positioning system
Figure BDA00039861768400000310
And the third node filters it>
Figure BDA0003986176840000041
And the fourth node filters it +.>
Figure BDA0003986176840000042
FIG. 6 is a third component of the actual state trajectory of the mobile robotic positioning system
Figure BDA0003986176840000043
And filtering it by the first node>
Figure BDA0003986176840000044
And filtering it by the second node>
Figure BDA0003986176840000045
FIG. 7 is a third component of the actual state trajectory of the mobile robotic positioning system
Figure BDA0003986176840000046
And the third node filters it>
Figure BDA0003986176840000047
And the fourth node filters it +.>
Figure BDA0003986176840000048
FIG. 8 is a trace plot of the trace of the filter error and the constrained matrix for the first sensor node and the second sensor node;
FIG. 9 is a trace plot of the trace of the filter error and the constrained matrix for the third and fourth sensor nodes;
FIG. 10 is a graph of filtered errors at different quantization interval lengths for a first sensor node and a second sensor node;
FIG. 11 is a graph of filtered errors at different quantization interval lengths for a third sensor node and a fourth sensor node;
fig. 2 to 7: "represents the actual state trajectory of the mobile robot positioning system,
Figure BDA0003986176840000049
a filter trajectory representing the state of the mobile robot positioning system based on the measured value of the first sensor node, a>
Figure BDA00039861768400000410
A filtered trajectory representing the state of the mobile robot positioning system based on the measurements of the second sensor node,
Figure BDA00039861768400000411
a filter trajectory representing the state of the mobile robot positioning system based on the measurement value of the third sensor node,/for the mobile robot positioning system>
Figure BDA00039861768400000412
Representing a status of the mobile robot positioning system based on the measurements of the fourth sensor nodeFiltering the track;
fig. 8 to 9: "-means the filtering error of the mobile robot positioning system,
Figure BDA00039861768400000413
an upper bound representing a filtering error;
fig. 10 to 11:
Figure BDA00039861768400000414
representing the filtering error of each node at d=0.01,/->
Figure BDA00039861768400000415
Representing the filtering error for each node at d=0.05.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
The invention provides a distributed collector filtering method based on a mobile robot positioning system. Based on the measurable information, a novel distributed set member saturation filter is designed to estimate the state of the system. Next, a distributed filter gain matrix is calculated. And finally, substituting the designed gain matrix of the distributed filter into a distributed set member filter to construct a distributed set member filter algorithm with state saturation under an encryption and decryption mechanism. As shown in fig. 1, the method comprises the steps of:
step one, based on a Cartesian coordinate system, selecting position and direction information of a mobile robot positioning system as state variables, and establishing a mobile robot positioning system dynamic model with state saturation under an encryption and decryption mechanism.
In the step, the established dynamic model of the mobile robot positioning system with state saturation is as follows:
Figure BDA0003986176840000051
Figure BDA0003986176840000052
wherein x is k ＝[π k τ k θ k ] T T represents the transpose, (pi) k ,τ k ) Representing position information, θ, of a mobile robot in a Cartesian coordinate system at a kth time k Indicating direction information of the mobile robot under a Cartesian coordinate system at the kth moment; x is x k+1 ＝[π k+1 τ k+1 θ k+1 ] T ，(π k+1 ,τ k+1 ) Representing position information, θ, of a mobile robot in a Cartesian coordinate system at time k+1 k+1 Indicating direction information of the mobile robot in a Cartesian coordinate system at the k+1th moment;
Figure BDA0003986176840000053
information indicating the speed of a mobile robot, w k Process noise, y, for mobile robot positioning system i,k For measuring and outputting information of mobile robot positioning system, v i,k Measuring noise for a mobile robot positioning system; i is a sensor node label, and N represents the number of nodes in the sensor network researched by the invention; sigma (·) represents a saturation function, specifically defined by the following formula:
σ(s)＝[σ 1 (s 1 )σ 2 (s 2 )σ 3 (s 3 )] T
σ i (s i )＝sign(s i )min{s i,max ,|s i }(i＝1,2,3)
wherein s is i,max Representing saturation level s max Is the i-th element of (a); sign (·) is a sign function, min (·) is a minimum function, |·| represents taking the absolute value of "·", and [ (·)] T Representation of matrix "[. Cndot.]"transpose.
In order to improve the safety of data and the communication efficiency, the invention adopts an encryption and decryption mechanism to schedule the transmission condition of the measured value. Specifically, the quantization function Q (v) = [ Q (v) 1 )q(υ 2 )] T The quantization level of (2) is expressed as:
Figure BDA0003986176840000061
in the formula, v l (l=1, 2) represents the value to be quantized, q (v) l ) Represents the quantized measured value, where κ=0, 1,2, …, L is the number of quantization intervals, and l=max i,k ||s i,k /d|| ∞ Represents the maximum number of quantization intervals, and d represents the length of each quantization interval. Further, note that the quantization error can be expressed as:
Figure BDA0003986176840000062
in order to improve the security of data, the invention introduces an encryption and decryption mechanism, and the specific process is described as follows:
encryption policy: for data information y i,k The encrypted measurement data are:
Figure BDA0003986176840000063
wherein y is i,k Representing information to be encrypted s i,k Representing the encrypted information, Q (·) being the encryption criterion,>
Figure BDA0003986176840000064
is an encryption key.
Decryption policy: based on secret keys
Figure BDA0003986176840000065
The obtained encrypted information s i,k The decrypted measurement value may be expressed as:
Figure BDA0003986176840000066
wherein s is i,k Representing encrypted data information +_>
Figure BDA0003986176840000067
Representing the decrypted data information.
Based on the above analysis, the decryption error generated by the measurement output after passing through the encryption and decryption mechanism is defined as
Figure BDA0003986176840000068
Quantization error is +.>
Figure BDA0003986176840000069
Therefore, it is not difficult to obtain->
Figure BDA00039861768400000610
And step two, designing a distributed set member filter under the meaning of minimizing a filtering error ellipsoid domain based on the dynamic model of the mobile robot positioning system with state saturation under the encryption and decryption mechanism established in the step one. The method comprises the following specific steps:
to facilitate the following theoretical derivation, the present invention introduces the following notations:
Figure BDA0003986176840000071
based on the measurable information, a distributed set membership filter is constructed as follows:
Figure BDA0003986176840000072
Figure BDA0003986176840000073
in phi, phi k Indicating that the moment k is based on the state transition matrix of the mobile robot positioning system,
Figure BDA0003986176840000074
non-linearities based on mobile robot positioning system at the kth moment for the ith sensor nodeFiltered version of the function,/>
Figure BDA0003986176840000075
Representing the actual measurement output information of the ith sensor node after the encryption and decryption mechanism at the (k+1) th moment, H i,k+1 Based on the measurement matrix of the mobile robot positioning system at the k+1 time for the ith sensor node, sigma (·) is a saturation function, +.>
Figure BDA0003986176840000076
For one-step prediction of the ith sensor node at the kth time,/for the ith sensor node>
Figure BDA0003986176840000077
For one-step prediction of the jth sensor node at the kth time,/for example>
Figure BDA0003986176840000078
For the filtering of the ith sensor node at time k+1,/for example>
Figure BDA0003986176840000079
Filtering at the kth time for the ith sensor node,/->
Figure BDA00039861768400000710
E is the filter gain matrix of the ith sensor node at time k+1 i,k+1 Represents decryption error epsilon of ith sensor node at k+1 moment i For the i-th sensor node's unity gain parameter,/for the i-th sensor node>
Figure BDA00039861768400000711
For the connection weight between the ith sensor node and the jth sensor node,/and->
Figure BDA00039861768400000712
Representing the set of adjacent nodes associated with the ith sensor node, Σ represents the summing function.
Step three, calculating the middle of each sensor node in the sensor network at the k momentMatrix P i,k+1|k 。
In this step, an intermediate matrix P i,k+1|k The calculation formula of (2) is as follows:
Figure BDA00039861768400000713
in phi, phi k State transition matrix of mobile robot positioning system at time k, P i,k+1|k For the intermediate matrix of the ith node at the moment k, P i,k|k For the filter error limited matrix of the ith node at time k,
Figure BDA0003986176840000081
for the process noise limited matrix at time k, F k Is a nonlinear function parameter matrix based on a mobile robot positioning system, lambda k For the upper scaling factor based on the non-linear function of the mobile robot positioning system +.>
Figure BDA0003986176840000082
Representing the square of the first component of the saturation level, < ->
Figure BDA0003986176840000083
Representing the square of the second component of the saturation level, < >>
Figure BDA0003986176840000084
Representing the square of the third component of the saturation level, < ->
Figure BDA0003986176840000085
For the first parameter, ++>
Figure BDA0003986176840000086
Is->
Figure BDA0003986176840000087
Is the reverse of (1)>
Figure BDA0003986176840000088
For the second parameter, ++>
Figure BDA0003986176840000089
Is->
Figure BDA00039861768400000810
Is the reverse of (1)>
Figure BDA00039861768400000811
For the third parameter, ++>
Figure BDA00039861768400000812
Is->
Figure BDA00039861768400000813
In, (a, b) represents taking "a, b" as the minimum, tr {. Cndot. } "represents taking the trace" {. Cndot. } ", and I is the three-dimensional identity matrix.
Step four, according to the intermediate matrix P obtained in the step three i,k+1|k Calculating a filter gain matrix at time k+1
Figure BDA00039861768400000814
In this step, the filter gain matrix
Figure BDA00039861768400000815
The calculation formula of (2) is as follows:
Figure BDA00039861768400000816
in E-shape 1 E is an intermediate variable number one 2 Is an intermediate variable number two, epsilon 3 Is the third intermediate variable, E 4 Is the fourth intermediate variable, E 5 Is five intermediate variables, E 6 Is an intermediate variable number six, which is a variable number,
Figure BDA00039861768400000817
representation E s Is inverse (s=1, 2, …, 6). I is a two-dimensional identity matrix,>
Figure BDA00039861768400000818
is the filter gain matrix of the ith sensor node at time k+1, P i,k+1|k Intermediate matrix representing the ith sensor node at time k,/>
Figure BDA00039861768400000819
A key at time k+1, d is the quantization interval length, H i,k+1 Is the measurement matrix of the mobile robot positioning system of the ith sensor node at time k+1,/for the mobile robot positioning system>
Figure BDA00039861768400000820
Is H i,k+1 Transpose of->
Figure BDA00039861768400000821
Measurement noise limited matrix for mobile robot positioning system, [ ·] -1 Representing matrix "[. Cndot.]"inverse of (a).
Step five, according to the filter gain matrix of each sensor node obtained in the step four
Figure BDA00039861768400000822
Substituting the filter into a distributed member filter designed in the second step to obtain the filter of the ith sensor node at the k+1 moment ∈>
Figure BDA00039861768400000823
Judging whether k+1 reaches the total duration M, if k+1 is less than M, executing step six, and if k+1 is more than or equal to M, ending the operation.
Step six, according to the calculation in the step four
Figure BDA0003986176840000091
Calculating a filter error limited matrix P i,k+1|k+1 The method comprises the steps of carrying out a first treatment on the surface of the Let k=k+1, execute step two until k+1 is satisfied.
In this step, the filter error limited matrix P i,k+1|k+1 The calculation formula of (2) is as follows:
Figure BDA0003986176840000092
in E-shape 1 E is an intermediate variable number one 2 Is an intermediate variable number two, epsilon 3 Is the third intermediate variable, E 4 Is the fourth intermediate variable, E 5 Is five intermediate variables, E 6 Is an intermediate variable number six, which is a variable number,
Figure BDA0003986176840000093
representation E s Inverse (s=1, 2, …, 6), P i,k+1|k For the intermediate matrix of the ith node at the moment k, P i,k+1|k+1 For the filter error limited matrix of the ith node at time k+1,/for the filter error limited matrix at time k+1>
Figure BDA0003986176840000094
Is the filter gain matrix of the ith node at time k+1,/for the time of day>
Figure BDA0003986176840000095
Is a one-step prediction of the ith node at time k,/for example>
Figure BDA0003986176840000096
Is a one-step prediction of the jth node at time k,>
Figure BDA0003986176840000097
measurement noise limited matrix for mobile robot positioning system, H i,k+1 Is the measurement matrix of the mobile robot positioning system of the ith sensor node at time k+1,/for the mobile robot positioning system>
Figure BDA0003986176840000098
A key representing the time k+1, d being the quantization interval length, < >>
Figure BDA0003986176840000099
For matrix->
Figure BDA00039861768400000910
Is transposed of epsilon i For the consistency gain of the ith node, < +.>
Figure BDA00039861768400000911
For the connection weight between the ith sensor node and the jth sensor node,/and->
Figure BDA00039861768400000912
Representing the set of contiguous nodes of the ith sensor node, Σ represents the summing function, and I is the three-dimensional identity matrix.
P calculated according to this step i,k+1|k+1 By minimizing tr { P i,k+1|k+1 Design of the number of filter gains
Figure BDA00039861768400000913
Examples:
in this embodiment, taking a mobile robot positioning system with state saturation under an encryption and decryption mechanism as an example, the method of the present invention is adopted for simulation:
the invention selects the sensor network with four sensor nodes to carry out numerical simulation, and the edge set can be expressed as:
Figure BDA0003986176840000101
wherein each ordered number represents an interactive behavior of information between nodes, such as: (1, 3) means that the 3 rd node can transmit information to the 1 st node.
The following parameters were selected:
Figure BDA0003986176840000102
in the method, in the process of the invention,
Figure BDA0003986176840000103
a filtered initial value for the first sensor node, wherein the first component, the second component of the vectorThe component and the third component respectively represent the position and direction information of the first sensor node to the horizontal and vertical directions of the mobile robot at the initial time,/for the mobile robot>
Figure BDA0003986176840000104
The first component, the second component and the third component of the vector represent the position and direction information of the second sensor node to the horizontal and vertical directions of the mobile robot at the initial time, respectively, (-)>
Figure BDA0003986176840000105
The first component, the second component and the third component of the vector represent the position and direction information of the third sensor node to the horizontal and vertical directions of the mobile robot at the initial time, respectively, (-)>
Figure BDA0003986176840000106
The first component, the second component and the third component of the vector represent the position and direction information of the fourth sensor node to the horizontal and vertical directions of the mobile robot at the initial moment respectively, and the encryption and decryption key is set as->
Figure BDA0003986176840000107
The process noise of the mobile robot positioning system is w k ＝[0.3sin(0.1k)0.3cos(0.3k)0.4cos(0.2k)] T Measurement noise of mobile robot positioning system is v i,k ＝[1.2sin(0.1k)1.2sin(0.1k)] T The saturation levels of the horizontal, vertical positions and directions are respectively psi 1,max ＝20、ψ 2,max =30 and ψ 3,max ＝20，F k ＝I 3 Representing a non-linear function parameter matrix based on a mobile robot positioning system, lambda k =3 denotes an upper scaling factor based on a nonlinear function of the mobile robot positioning system, d=0.01 denotes a quantization interval length,
Figure BDA0003986176840000108
restricted matrix representing process noise of mobile robot positioning system,/->
Figure BDA0003986176840000111
Measurement noise limited matrix representing mobile robot positioning system, I 3 Representing a three-dimensional identity matrix, P i,0|0 ＝2I 3 Represents a filtered error limited matrix, where i=1, 2,3,4 represents the number of sensor nodes. The invention adopts filtering error to evaluate algorithm performance, and the calculation method comprises the following steps:
Figure BDA0003986176840000112
in particular, an average filtering error is introduced to further measure the filtering performance change condition under different quantization interval lengths, and the calculation method comprises the following steps: />
Figure BDA0003986176840000113
M=40 in the present invention.
Distributed filter effect:
as can be seen from fig. 2 to fig. 7, the inventive distributed collector filtering method can effectively estimate the target state for the mobile robot positioning system with state saturation under the encryption and decryption mechanism, and the system state is always kept below the known saturation level, which accords with the theoretical result of the present invention.
As can be seen from fig. 8 and 9, the trace of the filtering error is always kept below the trace of the filtering error limited matrix for each sensor node, which verifies the correctness of the present invention.
As can be seen from fig. 10 and 11, the filtering error gradually increases as the quantization interval length increases. Further, as can be seen from table 1, the average filter error of nodes 1,2,3 and 4 is reduced by 0.51, 0.9, 0.82 and 0.96, respectively.
TABLE 1
Figure BDA0003986176840000114

Claims (6)

1. The distributed group member filtering method based on the mobile robot positioning system is characterized by comprising the following steps of:
step one, based on a Cartesian coordinate system, selecting position and direction information of a mobile robot positioning system as state variables, and establishing a mobile robot positioning system dynamic model with state saturation under an encryption and decryption mechanism;
step two, designing a distributed collector filter for the dynamic model of the mobile robot positioning system established in the step one under the meaning of minimizing a filtering error ellipsoid;
step three, calculating an intermediate matrix P of each node in the sensor network at the moment k i,k+1|k ；
Step four, according to the intermediate matrix P obtained in the step three i,k+1|k Calculating a filter gain matrix for each sensor node
Figure FDA0003986176830000011
Step five, according to the filter gain matrix obtained in the step four
Figure FDA0003986176830000012
Substituting the filter into the distributed group member filter designed in the second step to design the distributed group member filter of the ith sensor node at the moment k+1>
Figure FDA0003986176830000013
Judging whether k+1 reaches the total duration M, if k+1 is less than M, executing step six, and if k+1 is more than or equal to M, ending operation;
step six, according to the filter gain matrix of each sensor node obtained in the step four
Figure FDA0003986176830000014
Calculating a filter error limiting matrix P for each sensor node i,k+1|k+1 The method comprises the steps of carrying out a first treatment on the surface of the Order thek=k+1, and step two is performed until k+1+.m is satisfied.
2. The distributed member filtering method based on the mobile robot positioning system according to claim 1, wherein in the first step, the dynamic model of the mobile robot positioning system with state saturation under the encryption and decryption mechanism is as follows:
Figure FDA0003986176830000021
Figure FDA0003986176830000022
Figure FDA0003986176830000023
wherein x is k ＝[π k τ k θ k ] T T represents the transpose, (pi) k ,τ k ) Representing position information, θ, of a mobile robot in a Cartesian coordinate system at a kth time k Representing direction information of the mobile robot in a Cartesian coordinate system at a kth moment, sigma (·) representing a saturation function, x k+1 ＝[π k+1 τ k+1 θ k+1 ] T ，(π k+1 ,τ k+1 ) Representing position information, θ, of a mobile robot in a Cartesian coordinate system at time k+1 k+1 Indicating direction information of the mobile robot in a Cartesian coordinate system at the k+1th moment;
Figure FDA0003986176830000024
information indicating the speed of a mobile robot, w k Process noise, y, for mobile robot positioning system i,k For measuring and outputting information of mobile robot positioning system, v i,k For measurement noise of a mobile robot positioning system, i is a sensor node index, i=1, 2,..The number of nodes in the sensor network, +.>
Figure FDA0003986176830000025
Representing decrypted data information e i,k Is the decryption error.
3. The mobile robot positioning system-based distributed group member filtering method according to claim 1, wherein in the second step, the distributed group member filter is:
Figure FDA0003986176830000026
Figure FDA0003986176830000027
in phi, phi k Indicating that the moment k is based on the state transition matrix of the mobile robot positioning system,
Figure FDA0003986176830000028
for the ith sensor node, at the kth moment, based on a filtered version of the nonlinear function of the mobile robot positioning system, +.>
Figure FDA0003986176830000029
Representing the actual measurement output information of the ith sensor node after the encryption and decryption mechanism at the (k+1) th moment, H i,k+1 Based on the measurement matrix of the mobile robot positioning system at the k+1 time for the ith sensor node, sigma (·) is a saturation function, +.>
Figure FDA00039861768300000210
For one-step prediction of the ith sensor node at the kth time,/for the ith sensor node>
Figure FDA00039861768300000211
For the j-th sensor nodeOne-step prediction of the point at the kth moment, < >>
Figure FDA00039861768300000212
For the filtering of the ith sensor node at time k+1,/for example>
Figure FDA00039861768300000213
Filtering at the kth time for the ith sensor node,/->
Figure FDA00039861768300000214
E is the filter gain matrix of the ith sensor node at time k+1 i,k+1 Represents decryption error epsilon of ith sensor node at k+1 moment i For the i-th sensor node's unity gain parameter,/for the i-th sensor node>
Figure FDA0003986176830000031
For the connection weight between the ith sensor node and the jth sensor node,/and->
Figure FDA0003986176830000032
Representing the set of adjacent nodes associated with the ith sensor node, Σ represents the summing function.
4. The method for filtering distributed group members based on mobile robot positioning system according to claim 1, wherein in said step three, an intermediate matrix P i,k+1|k The calculation formula of (2) is as follows:
Figure FDA0003986176830000033
in phi, phi k Representing state transition matrix based on mobile robot positioning system at time k, P i,k+1|k For the intermediate matrix of the ith node at the moment k, P i,k|k For the filter error limited matrix of the ith node at time k,
Figure FDA0003986176830000034
for the process noise limited matrix at time k, F k Is a nonlinear function parameter matrix based on a mobile robot positioning system, lambda k For the upper scaling factor based on the non-linear function of the mobile robot positioning system +.>
Figure FDA0003986176830000035
Representing the square of the first component of the saturation level, < ->
Figure FDA0003986176830000036
Representing the square of the second component of the saturation level, < >>
Figure FDA0003986176830000037
Representing the square of the third component of the saturation level, < ->
Figure FDA0003986176830000038
For the first parameter, ++>
Figure FDA0003986176830000039
Is->
Figure FDA00039861768300000310
Is the inverse of the (a) and (b),
Figure FDA00039861768300000311
for the second parameter, ++>
Figure FDA00039861768300000312
Is->
Figure FDA00039861768300000313
Is the reverse of (1)>
Figure FDA00039861768300000314
For the third parameter, ++>
Figure FDA00039861768300000315
Is->
Figure FDA00039861768300000316
In, (a, b) represents taking "a, b" as the minimum, tr {. Cndot. } "represents taking the trace" {. Cndot. } ", and I is the three-dimensional identity matrix.
5. The method for filtering distributed group members based on mobile robot positioning system according to claim 1, wherein in the fourth step, a filter gain matrix is used
Figure FDA00039861768300000317
The calculation formula of (2) is as follows:
Figure FDA00039861768300000318
in E-shape 1 E is an intermediate variable number one 2 Is an intermediate variable number two, epsilon 3 Is the third intermediate variable, E 4 Is the fourth intermediate variable, E 5 Is five intermediate variables, E 6 Is an intermediate variable number six, which is a variable number,
Figure FDA00039861768300000319
representation E s Is the inverse of (s=1, 2, …, 6), I is a two-dimensional identity matrix,/->
Figure FDA00039861768300000320
Is the filter gain matrix of the ith sensor node at time k+1, P i,k+1|k Intermediate matrix representing the ith sensor node at time k,/>
Figure FDA0003986176830000041
A key at time k+1, d is the quantization interval length, H i,k+1 Is the mobile machine of the ith sensor node at the moment k+1Measurement matrix of a robot positioning system, +.>
Figure FDA0003986176830000042
Is H i,k+1 Transpose of->
Figure FDA0003986176830000043
Measurement noise limited matrix for mobile robot positioning system, [ ·] -1 Representing matrix "[. Cndot.]"inverse of (a).
6. The method for filtering distributed group members based on mobile robot positioning system according to claim 1, wherein in said step six, the error limiting matrix P is filtered i,k+1|k+1 The calculation formula of (2) is as follows:
Figure FDA0003986176830000044
in E-shape 1 E is an intermediate variable number one 2 Is an intermediate variable number two, epsilon 3 Is the third intermediate variable, E 4 Is the fourth intermediate variable, E 5 Is five intermediate variables, E 6 Is an intermediate variable number six, which is a variable number,
Figure FDA0003986176830000045
representation E s Inverse (s=1, 2, …, 6), P i,k+1|k For the intermediate matrix of the ith node at the moment k, P i,k+1|k+1 For the filter error limited matrix of the ith node at time k+1,/for the filter error limited matrix at time k+1>
Figure FDA0003986176830000046
Is the filter gain matrix of the ith node at time k+1,/for the time of day>
Figure FDA0003986176830000047
Is a one-step prediction of the ith node at time k,/for example>
Figure FDA0003986176830000048
Is a one-step prediction of the jth node at time k,>
Figure FDA0003986176830000049
measurement noise limited matrix for mobile robot positioning system, H i,k+1 Is the measurement matrix of the mobile robot positioning system of the ith sensor node at time k+1,/for the mobile robot positioning system>
Figure FDA00039861768300000410
A key representing the time k+1, d being the quantization interval length, < >>
Figure FDA00039861768300000415
For matrix->
Figure FDA00039861768300000412
Is transposed of epsilon i For the consistency gain of the ith node, < +.>
Figure FDA00039861768300000413
For the connection weight between the ith sensor node and the jth sensor node,/and->
Figure FDA00039861768300000414
Representing the set of contiguous nodes of the ith sensor node, Σ represents the summing function, and I is the three-dimensional identity matrix.
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