CN116431981B - Distributed group member filtering method based on mobile robot positioning system - Google Patents
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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 the moment k 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 nodeStep five, designing a distributed collector filter of the ith sensor node at the moment k+1Judging 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 prior distributed filtering method can not process the state under the encryption and decryption mechanismDistributed filtering of saturated sensor networks.
Description
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 Calculating a filter gain matrix for each sensor node
Step five, according to the filter gain matrix obtained in the step fourSubstituting 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>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 fourCalculating 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 systemAnd filtering it by the first node>And filtering it by the second node>
FIG. 3 is a first component of the actual state trajectory of the mobile robotic positioning systemAnd the third node filters it>And the fourth node filters it +.>
FIG. 4 is a second component of the actual state trajectory of the mobile robotic positioning systemAnd filtering it by the first node>And filtering it by the second node>
FIG. 5 is a second component of the actual state trajectory of the mobile robotic positioning systemAnd the third node filters it>And the fourth node filters it +.>
FIG. 6 is a third component of the actual state trajectory of the mobile robotic positioning systemAnd filtering it by the first node>And filtering it by the second node>
FIG. 7 is a third component of the actual state trajectory of the mobile robotic positioning systemAnd the third node filters it>And the fourth node filters it +.>
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,a filter trajectory representing the state of the mobile robot positioning system based on the measured value of the first sensor node, a>A filtered trajectory representing the state of the mobile robot positioning system based on the measurements of the second sensor node,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>A filtered trajectory representing a state of the mobile robot positioning system based on the measurements of the fourth sensor node;
fig. 8 to 9: "-means the filtering error of the mobile robot positioning system,an upper bound representing a filtering error;
fig. 10 to 11:representing the filtering error of each node at d=0.01,/->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:
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;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:
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: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:wherein y is i,k Representing information to be encrypted s i,k Representing the encrypted information, Q (·) being the encryption criterion,>is an encryption key.
Decryption policy: based on secret keysThe obtained encrypted information s i,k The decrypted measurement value may be expressed as:wherein s is i,k Representing encrypted data information +_>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 asQuantization error is +.>Therefore, it is not difficult toTo->
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:
based on the measurable information, a distributed set membership filter is constructed as follows:
in phi, phi k Indicating that the moment k is based on the state transition matrix of the mobile robot positioning system,for the ith sensor node, at the kth moment, based on a filtered version of the nonlinear function of the mobile robot positioning system, +.>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, +.>For the ith sensorOne-step prediction of the node at the kth moment, < >>For one-step prediction of the jth sensor node at the kth time,/for example>For the filtering of the ith sensor node at time k+1,/for example>Filtering at the kth time for the ith sensor node,/->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>For the connection weight between the ith sensor node and the jth sensor node,/and->Representing the set of adjacent nodes associated with the ith sensor node, Σ represents the summing function.
Step three, calculating an intermediate matrix P of each sensor node in the sensor network at the moment k i,k+1|k 。
In this step, an intermediate matrix P i,k+1|k The calculation formula of (2) is as follows:
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 ith nodeA filter error limited matrix at time k,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 +.>Representing the square of the first component of the saturation level, < ->Representing the square of the second component of the saturation level, < >>Representing the square of the third component of the saturation level, < ->For the first parameter, ++>Is->Is the reverse of (1)>For the second parameter, ++>Is->Is the reverse of (1)>For the third parameter, ++>Is->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
In this step, the filter gain matrixThe calculation formula of (2) is as follows:
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,representation E s Is inverse (s=1, 2, …, 6). I is a two-dimensional identity matrix,>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,/>A key at time k+1, d is the quantization interval length, H i,k+1 Is the measurement moment of the mobile robot positioning system of the ith sensor node at the moment k+1Array (S)>Is H i,k+1 Transpose of->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 fourSubstituting 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 ∈>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 fourCalculating 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:
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,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>Is the filter gain matrix of the ith node at time k+1,/for the time of day>Is a one-step prediction of the ith node at time k,/for example>Is a one-step prediction of the jth node at time k,>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>A key representing the time k+1, d being the quantization interval length, < >>For matrix->Is transposed of epsilon i For the consistency gain of the ith node, < +.>For the connection weight between the ith sensor node and the jth sensor node,/and->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
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:
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:
in the method, in the process of the invention,the first sensor node is the initial value of the filtering, wherein the first component, the second component and the third component of the vector respectively represent the position and the direction information of the first sensor node to the horizontal and the vertical directions of the mobile robot at the initial moment, (-)>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, (-)>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, (-)>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->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,restricted matrix representing process noise of mobile robot positioning system,/->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 performanceThe calculation method comprises the following steps: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: />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
Claims (1)
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, wherein the mobile robot positioning system dynamic model with state saturation under the encryption and decryption mechanism is as follows:
in the method, in the process of the invention,t represents the transpose, (pi) k ,τ k ) Representing the position information of the mobile robot in the k-th moment Cartesian coordinate system, +.>Representing directional information of the mobile robot in a Cartesian coordinate system at a kth moment, sigma (·) representing a saturation function, < ->，(π k+1 ,τ k+1 ) Representing the position information of the mobile robot in the Cartesian coordinate system at time k+1,/for the mobile robot>Indicating direction information of the mobile robot in a Cartesian coordinate system at the k+1th moment; />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 measuring noise of the mobile robot positioning system, i is a sensor node label, i=1, 2,..n, N represents the number of nodes in the sensor network,/for the mobile robot positioning system>Representing decrypted data information e i,k Is a decryption error;
step two, designing a distributed group member 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 domain, wherein the distributed group member filter is as follows:
in phi, phi k Indicating that the moment k is based on the state transition matrix of the mobile robot positioning system,for the ith sensor node, at the kth moment, based on a filtered version of the nonlinear function of the mobile robot positioning system, +.>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, +.>For one-step prediction of the ith sensor node at the kth time,/for the ith sensor node>For one-step prediction of the jth sensor node at the kth time,/for example>Is the ithFiltering of the individual sensor nodes at time k+1,>filtering at the kth time for the ith sensor node,/->For the filter gain matrix, ε, of the ith sensor node at time k+1 i For the i-th sensor node's unity gain parameter,/for the i-th sensor node>For the connection weight between the ith sensor node and the jth sensor node,/and->Representing a set of adjacent nodes associated with the ith sensor node, Σ representing a summing function;
step three, calculating an intermediate matrix P of each node in the sensor network at the moment k i,k+1|k The intermediate matrix P i,k+1|k The calculation formula of (2) is as follows:
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,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 +.>Representing the square of the first component of the saturation level, < ->Representing the square of the second component of the saturation level, < >>Representing the square of the third component of the saturation level, < ->For the first parameter, ++>Is->Is the inverse of the (a) and (b),for the second parameter, ++>Is->Is the reverse of (1)>For the third parameter, ++>Is->In, (a, b) represents taking "a, b" as the minimum, tr { · } represents taking the trace of "{ · }", and I is a 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 for each sensor nodeThe filter gain matrix->The calculation formula of (2) is as follows:
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,representation E s S=1, 2,..6, i is a two-dimensional identity matrix, +.>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,/>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>Is H i,k+1 Transpose of->Measurement noise limited matrix for mobile robot positioning system, [ ·] -1 Representing matrix "[. Cndot.]"inverse;
step five, according to the filter gain matrix obtained in the step fourSubstituting 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>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 fourCalculating 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 greater than or equal to M, the filtering error limited matrix P i,k+1|k+1 The calculation formula of (2) is as follows:
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,representation E s 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>Is the filter gain matrix of the ith node at time k+1,/for the time of day>Is one of the ith node at time kStep prediction (I)>Is a one-step prediction of the jth node at time k,>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>A key representing the time k+1, d being the quantization interval length, < >>For matrix->Is transposed of epsilon i For the consistency gain of the ith node, < +.>For the connection weight between the ith sensor node and the jth sensor node,/and->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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