CN113156368B - Error parameter identification co-location method based on factor graph - Google Patents

Error parameter identification co-location method based on factor graph Download PDF

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CN113156368B
CN113156368B CN202110306773.2A CN202110306773A CN113156368B CN 113156368 B CN113156368 B CN 113156368B CN 202110306773 A CN202110306773 A CN 202110306773A CN 113156368 B CN113156368 B CN 113156368B
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error
parameter identification
speed
factor graph
location
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CN113156368A (en
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张亚
范世伟
王庆鑫
魏健雄
高伟
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Harbin Institute of 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
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves

Abstract

The invention provides a factor graph-based error parameter identification co-location method. Firstly, an error parameter identification factor graph model is established, then error parameter identification is carried out on process errors comprising speed errors and course errors, information is transmitted between function nodes and variable nodes in the factor graph by utilizing the maximum relevant entropy criterion, error compensation on the speed and the course of the slave boat is achieved, and finally filtering fusion estimation on position state information of the slave boat is achieved. Under the condition that the measurement accuracy of an inertial device in the system is not changed, the process error is identified and compensated, the co-location error is reduced, and the location capability of the co-location system is improved.

Description

Error parameter identification co-location method based on factor graph
Technical Field
The invention relates to an autonomous underwater vehicle (Autonomous Underwater Vehicle, AUV) co-location technology, in particular to a method for transmitting information between function nodes and variable nodes of a factor graph by adopting a maximum relevant entropy criterion, identifying a process error containing speed error and course error of a slave boat in the operation process of a co-location system, restraining the increase of the location error by compensating the process error, and improving the autonomous location capability of the slave boat.
Background
AUV has advantages such as the movable range is big, mobility is strong, intelligent degree is high, has great value in fields such as marine investigation, marine resource exploration, search and rescue under water, diving support, military investigation. For the ocean field, AUV related technology is a mainstream trend and development direction, and AUV cooperative operation can not only bear complex tasks which are difficult to compete with monomers, such as information collection, mine detection, coastal anti-diving, relay communication and the like, but also has the advantages of high efficiency, high reliability, high quality and the like. Therefore, AUV cooperative operation has wide application prospect.
The AUV cooperative positioning technology is a positioning mode based on a network, utilizes the underwater acoustic communication technology, fuses the relative position relation among AUVs by using the measurement information of the shared sensor to improve the positioning precision, and can effectively inhibit the influence of autonomous navigation positioning errors of dead reckoning on the cooperative positioning precision, so that the overall positioning error of a cooperative positioning system is bounded.
In an AUV co-location system, a common mode is a master-slave co-location structure comprising a master boat and a slave boat. The main boat is usually provided with high-precision navigation positioning equipment with high price, the high-precision position information of the main boat can be obtained, the precision of the navigation positioning equipment carried by the slave boat is low, the position estimation is firstly carried out by using a dead reckoning algorithm of the main boat, and then the correction is carried out by using the distance information between the main boat and the slave boat.
In an AUV co-location system, since ranging and communication are achieved using underwater acoustic devices, they are inevitably affected by characteristics of underwater acoustic signals. In an actual underwater environment, the phenomena of multipath propagation and abnormal measured value usually occur in underwater acoustic ranging and communication, and the influence of the multipath and abnormal value can cause the characteristic of non-Gaussian distribution to be presented in the underwater acoustic ranging, so that heavy tail noise with the tail part of probability distribution heavier than the Gaussian distribution occurs. However, the estimation performance of the traditional nonlinear co-location positioning methods, such as an extended kalman filtering method and an unscented kalman filtering method, when processing heavy-tail non-gaussian noise can be greatly reduced, and even the filter can be unstable.
In addition, for dead reckoning algorithms from boats, the key factors affecting autonomous positioning accuracy are speed error and heading error. Under the condition that the lateral movement of the AUV is not considered, when the position is calculated by using the measured speed and heading according to a mathematical model of the system, the speed error and the heading error have larger influence on the position estimation of the AUV, so that the error of self-positioning is increased.
Aiming at the problems, the invention designs an error parameter identification co-location method based on a factor graph, and the maximum correlation entropy criterion is adopted to transfer information between the function node and the variable node of the factor graph, so that the situation of heavy-tail non-Gaussian noise can be better processed. Meanwhile, an error parameter identification method is designed, the process error of the slave boat including the speed error and the course error in the operation process of the co-location system is identified, the increase of the location error is restrained through the compensation of the process error, the autonomous location capability of the slave boat is improved, and the purpose of improving the location precision of the co-location system is achieved.
Disclosure of Invention
The invention aims to design an error parameter identification co-location method based on a factor graph, and on the premise of not changing the precision of an inertial device, the information is transferred between a function node and a variable node of the factor graph by adopting a maximum relevant entropy criterion, so that the process error of a slave boat including a speed error and a course error in the operation process of a co-location system is identified, the increase of the location error is restrained by compensating the process error, and the autonomous location capability of the slave boat is improved.
The object of the invention can be achieved by the following steps:
step 1: establishing an error parameter identification co-location method factor graph model;
step 2: identifying the speed error and the course error of the system by utilizing the maximum correlation entropy criterion;
step 3: and compensating the speed error and the heading error, and further filtering and updating the state information of the system.
In step 1, since depth can be accurately measured by using the depth gauge mounted on the AUV, and accuracy improvement of depth information by co-positioning is limited, position information and distance observation information of each AUV can be projected into a horizontal plane, and the problem of co-positioning of the AUV in a two-dimensional plane can be discussed, namely, only horizontal coordinates (x, y) of the AUV need to be filtered. The factor graph contains two nodes: variable nodes and function nodes. As shown in figure 1, in order to consider an ideal factor graph model of speed error and heading error, a circle in the graph represents a variable node, a rectangle shape represents a function node, and each edge in the graph is connected with a variable node and a function node.
In an ideal case, the self-positioning according to FIG. 1 requires the use of measurementThe obtained speed
Figure BDA0002988016870000021
And heading
Figure BDA0002988016870000022
Subtracting the identified speed error +.>
Figure BDA0002988016870000023
And heading error->
Figure BDA0002988016870000024
Obtaining a speed and a course which are closer to the reality and participating in calculation; when the observation information is received from the boat to perform co-location to obtain posterior position estimation, the information is reversely transmitted to obtain the speed +.>
Figure BDA0002988016870000025
And heading->
Figure BDA0002988016870000026
And further estimate the corresponding error. But when the time k (k>l+1) receiving again the observation information and no observation information during the period l to k, the recognized speed error +_ is caused by the difficulty in obtaining a posterior position estimate during the period l to k>
Figure BDA0002988016870000027
And heading error->
Figure BDA0002988016870000028
And become complex. Typically the l-to-k time is short, so the following assumptions are made about speed error and heading error:
Figure BDA0002988016870000029
Figure BDA00029880168700000210
the positioning error at time l can be written as:
Figure BDA00029880168700000211
Figure BDA00029880168700000212
since no observation information is received from time l to time k, the position update adopts a priori estimation value, and the a priori estimation of x is as follows:
Figure BDA0002988016870000031
a priori estimates of y as
Figure BDA0002988016870000032
And (3) finishing to obtain:
Figure BDA0002988016870000033
Figure BDA0002988016870000034
then the positioning error at time k can be written as:
Figure BDA0002988016870000035
in the formula
Figure BDA0002988016870000036
-representation (Deltat cos theta l+1 +…Δt cosθ k )；
Figure BDA0002988016870000037
-representation (v) l+1 Δt sinθ l+1 -…v k Δt sinθ k )。
Figure BDA0002988016870000038
in the formula
Figure BDA0002988016870000039
-representation (Deltatsin theta l+1 +…Δt sinθ k )；
Figure BDA00029880168700000310
-representation (v) l+1 Δt cosθ l+1 +…v k Δt cosθ k )。
The factor graph model for identifying the speed error and the heading error can be redesigned according to the two formulas, and the factor graph model is shown in the figure 2. Meanwhile, the two formulas can be rewritten as follows:
Figure BDA00029880168700000311
when (when)
Figure BDA0002988016870000041
When the following formula is established:
Figure BDA0002988016870000042
further written as:
Figure BDA0002988016870000043
Figure BDA0002988016870000044
when (when)
Figure BDA0002988016870000045
When the coefficient matrix is not full of rank, it is impossible to determine +.>
Figure BDA0002988016870000046
and />
Figure BDA0002988016870000047
But the manoeuvre of the AUV is small and the direction of travel does not change much during the co-location period, so the matrix is typically full rank.
In step 2, the invention designs a factor graph-based error parameter identification co-location method, and adopts the related entropy of variables to transfer information between variable nodes and function nodes of the factor graph. The solid line box in fig. 2 is a time update stage, that is, when the observed quantity sent by the master boat is not received from the slave boat; the part of the dashed box is the observation update phase, when the observations sent by the master are received from the boats and the posterior estimate of the position (x k ,y k ) And carrying out parameter identification on the speed error and the heading error of the slave boat as observation information. The specific update procedure is as follows.
(1) Time update
(1) Time update of speed error and heading error
Figure BDA0002988016870000048
Figure BDA0002988016870000049
(2) Time update of position estimate
Figure BDA00029880168700000410
Figure BDA00029880168700000411
in the formula
Figure BDA00029880168700000412
wherein />
Figure BDA00029880168700000413
and />
Figure BDA00029880168700000414
As shown below, and has->
Figure BDA00029880168700000415
and />
Figure BDA00029880168700000416
Is 0.
Figure BDA00029880168700000417
Figure BDA00029880168700000418
In the calculation process, if no observed quantity is received at the time n, the time update of the position is utilized as the position estimation result at the current time, as follows:
x n ＝x′ n
y n ＝y′ n
(3) temporal updating of coefficients
Figure BDA0002988016870000051
Figure BDA0002988016870000052
Figure BDA0002988016870000053
Figure BDA0002988016870000054
(2) Observation update
In order to reduce the influence of heavy tail noise in observed quantity on speed and course error parameter identification, the method selects relevant entropy as a cost function in the error parameter identification co-location method based on the factor graph. In the observation update phase, the variable node is firstly used for
Figure BDA0002988016870000055
Through the function node R k To variable node->
Figure BDA0002988016870000056
The transfer information may be expressed specifically as a process of maximizing the following expression.
Figure BDA0002988016870000057
wherein ,
Figure BDA0002988016870000058
representing the relative entropy, and representing the second norm.
Slave variable node
Figure BDA0002988016870000059
Through the function node S k To variable node->
Figure BDA00029880168700000510
The transfer of information can be expressed in particular as a process that maximizes the following formula:
Figure BDA00029880168700000511
then there is at this time:
Figure BDA00029880168700000512
Figure BDA00029880168700000513
when the above is established, it is obvious that
Figure BDA00029880168700000514
Figure BDA00029880168700000515
Slave function node I k To variable node delta x k Can be expressed as:
Figure BDA00029880168700000516
slave function node L k To variable node delta y k Can be expressed as:
Figure BDA00029880168700000517
slave function node N k Delivery to variable nodes
Figure BDA00029880168700000518
Can be expressed as:
Figure BDA0002988016870000061
slave function node N k Delivery to variable nodes
Figure BDA0002988016870000062
Can be expressed as:
Figure BDA0002988016870000063
variable node δx k Can be expressed as:
Figure BDA0002988016870000064
when the correlation entropy in the above equation takes the maximum value, there are:
Figure BDA0002988016870000065
when the above formula is satisfied, it is apparent that:
Figure BDA0002988016870000066
variable node delta y k Can be expressed as:
Figure BDA0002988016870000067
when the correlation entropy in the above equation takes the maximum value, there are:
Figure BDA0002988016870000068
when the above formula is satisfied, it is apparent that:
Figure BDA0002988016870000069
variable node
Figure BDA00029880168700000610
Can be expressed as:
Figure BDA00029880168700000611
when the correlation entropy in the above equation takes the maximum value, there are:
Figure BDA00029880168700000612
the method can be obtained after the above steps are unfolded:
Figure BDA0002988016870000071
the method can be obtained after finishing the above steps and phase shifting:
Figure BDA0002988016870000072
dividing both sides of the equation simultaneously by
Figure BDA0002988016870000073
The method can obtain: />
Figure BDA0002988016870000074
Can be obtained after phase shift
Figure BDA0002988016870000075
The estimated values of (2) are:
Figure BDA0002988016870000081
due to the right side of the equation
Figure BDA0002988016870000082
At this point, no update is made, and the calculation is replaced with a priori values, so there are:
Figure BDA0002988016870000083
thus, there may be:
Figure BDA0002988016870000084
variable node
Figure BDA0002988016870000085
Can be expressed as:
Figure BDA0002988016870000086
when the correlation entropy in the above equation takes the maximum value, there are:
Figure BDA0002988016870000087
the method can be obtained after the above steps are unfolded:
Figure BDA0002988016870000091
the phase shift and arrangement can be achieved:
Figure BDA0002988016870000092
and (3) with
Figure BDA0002988016870000093
Similarly, get->
Figure BDA0002988016870000094
The estimated values of (2) are:
Figure BDA0002988016870000095
due to the right side of the equation
Figure BDA0002988016870000096
At this point, there is no update, and the calculation is replaced with a priori value, so there is:
Figure BDA0002988016870000097
thus, there may be:
Figure BDA0002988016870000101
when the error parameter identification co-location method based on the factor graph provided by the invention is used for error identification, two free parameters in the algorithm need to be determined, namely calculation
Figure BDA0002988016870000102
Value and->
Figure BDA0002988016870000103
Core width in the equation of value. In the method of the invention, since the speed error and heading error change in a short time are small, and the influence of the position error on the method of the invention is large, the large kernel width will cause the result of the algorithm to have large fluctuation, so the small kernel width should be selected, and the calculation is not needed>
Figure BDA0002988016870000104
The kernel width of the value may be designed as:
Figure BDA0002988016870000105
calculation of
Figure BDA0002988016870000106
The kernel width of the value may be designed as:
Figure BDA0002988016870000107
drawings
FIG. 1 is a schematic diagram of an idealized factor graph model of an established error parameter identification co-location method.
FIG. 2 is a factor graph model of an established error parameter identification co-location method.
Fig. 3 is a diagram of the motion trajectories of the master and slave boats in a simulation experiment.
Fig. 4 is a range error in a simulation experiment.
FIG. 5 shows the speed and heading error recognition results in simulation experiments.
FIG. 6 shows the positioning errors of different algorithms in the simulation experiment.
Detailed Description
The present invention will be described in detail with reference to specific examples.
The invention provides an error parameter identification co-location method based on factor graphs, which adopts the maximum relevant entropy criterion to transfer information between function nodes and variable nodes of the factor graphs, identifies the process error containing speed error and course error of a slave boat in the operation process of a co-location system, inhibits the increase of the location error through the compensation of the process error, and improves the autonomous location capability of the slave boat. The invention aims at realizing the following steps:
1. establishing an error parameter identification co-location method factor graph model;
2. identifying the speed error and the course error of the system by utilizing the maximum correlation entropy criterion;
3. and compensating the speed error and the heading error, and further filtering and updating the state information of the system.
In order to verify the effectiveness of the invention, software is utilized to simulate the error parameter identification co-location method based on the factor graph.
The simulation conditions are as follows: in the simulation, errors of 0.1m/s and 3 degrees are respectively added to an electromagnetic log and a magnetic compass, gaussian white noise interference with standard deviation of 2m is added to underwater sound equipment, and 20m of error simulation heavy tail noise is added to 10% probability. The simulation time is set to 2000s, the cooperative positioning is carried out in the first 1000s in the experiment, and the positioning is carried out in the last 1000s from the boat only by means of self navigation equipment.
In the simulation, two main boats are shared, one secondary boat, the starting points of the two main boats are respectively 450m and 0m and 450m, and the starting points of the secondary boats are 0m and 450m, and the heading of each boat is 90 degrees and the speed is 2m/s. The actual running track of each boat is shown in figure 3. The range error in the simulation is shown in fig. 4, the identification result of the error parameter identification factor graph co-locating method in the simulation on the speed error and the course error is shown in fig. 5, and it can be seen from fig. 5 that the speed error and the course error are effectively identified in the system co-locating period by the method provided by the invention.
Fig. 6 shows positioning errors estimated by using different co-positioning methods, wherein a first method is a factor graph co-positioning method without error parameter identification, and a second method is a factor graph-based error parameter identification co-positioning method according to the present invention. As can be seen from the figure, the positioning error estimated by the method does not diverge with time before 1000s, but when the slave boat cannot receive the observed quantity sent by the master boat after 1000s, the slave boat performs autonomous positioning by means of the navigation equipment of the slave boat, and the positioning error diverges rapidly with the increase of time; and the second method recognizes and compensates the speed error and the course error, so that the positioning error of the ship after 1000s is far smaller than the positioning error estimated by the first method.
The effectiveness of the error parameter identification co-location method based on the factor graph provided by the invention is verified through the experiment, and the purpose of improving the overall location accuracy of the system can be achieved by identifying and compensating the speed error and the course error in the running process of the system on the premise of not improving the measurement accuracy of the inertial components in the co-location system.

Claims (2)

1. The error parameter identification co-location method based on the factor graph is characterized by comprising the following steps of:
step 1: establishing an error parameter identification co-location method factor graph model;
step 2: identifying the speed error and the course error of the system by utilizing the maximum correlation entropy criterion;
step 3: compensating the speed error and the course error, further filtering and updating the state information of the system,
in the step 2, in the process of identifying the speed error and heading error of the system by using the maximum correlation entropy criterion, information is transmitted in a factor graph by using the correlation entropy of the variable to obtain the speed error
Figure FDA0004200678850000011
As shown in the formula:
Figure FDA0004200678850000012
wherein ,
Figure FDA0004200678850000013
representing a priori estimates of the velocity error, the kernel width σ is chosen as follows:
Figure FDA0004200678850000014
heading error
Figure FDA0004200678850000015
As shown in the formula:
Figure FDA0004200678850000016
wherein ,
Figure FDA0004200678850000017
representing a priori estimates of heading error, the kernel width σ is selected as follows:
Figure FDA0004200678850000018
wherein ,δxk -representing the positioning error in the x-direction at time k;
δy k -representing the positioning error in the y-direction at time k;
Figure FDA0004200678850000019
-representation (Δtcosθ) l+1 +...Δtcosθ k )；
Figure FDA00042006788500000110
-representation (v) l+1 Δtsinθ l+1 -...v k Δtsinθ k )。
2. The error parameter identification co-location method as defined in claim 1, wherein in the error parameter identification co-location method established in step 1, the measured velocity is used in an ideal factor graph model
Figure FDA0004200678850000021
And heading->
Figure FDA0004200678850000022
Subtracting the identified speed error +.>
Figure FDA0004200678850000023
And heading error->
Figure FDA0004200678850000024
Obtaining the speed and heading which are closer to the true and participating in calculation, further filtering to obtain the position state information of the carrier,
in the factor model used in the design, the speed and the course after compensation obtained by theoretical derivation are shown in the following formula:
Figure FDA0004200678850000025
/>
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