CN112325885A - Factor graph co-location algorithm based on mathematical statistical characteristics - Google Patents

Factor graph co-location algorithm based on mathematical statistical characteristics Download PDF

Info

Publication number
CN112325885A
CN112325885A CN202011189329.9A CN202011189329A CN112325885A CN 112325885 A CN112325885 A CN 112325885A CN 202011189329 A CN202011189329 A CN 202011189329A CN 112325885 A CN112325885 A CN 112325885A
Authority
CN
China
Prior art keywords
information
node
factor graph
boat
function
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202011189329.9A
Other languages
Chinese (zh)
Inventor
张亚
王庆鑫
高伟
范世伟
佟明烨
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin Institute of Technology
Original Assignee
Harbin Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Harbin Institute of Technology filed Critical Harbin Institute of Technology
Priority to CN202011189329.9A priority Critical patent/CN112325885A/en
Publication of CN112325885A publication Critical patent/CN112325885A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Data Mining & Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • Automation & Control Theory (AREA)
  • Computing Systems (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Evolutionary Biology (AREA)
  • Operations Research (AREA)
  • Probability & Statistics with Applications (AREA)
  • Navigation (AREA)

Abstract

The invention designs a factor graph co-location algorithm based on mathematical statistical characteristics. Firstly, a co-location algorithm factor graph model based on mathematical statistical characteristics is established, a two-dimensional problem of a traditional co-location algorithm is converted into a one-dimensional problem, expectation and variance of position state variables are used as reliability information to be transmitted between variable nodes and function nodes in the factor graph model, and finally filtering fusion estimation of the position state information of the slave boat is achieved. Therefore, under the condition of not changing the measurement precision of an inertial device in the system, the cooperative positioning error is reduced and the positioning capability of the cooperative positioning system is improved by avoiding the linearization processing of the nonlinear distance observation equation, and meanwhile, the calculation complexity and the calculation amount can be reduced.

Description

Factor graph co-location algorithm based on mathematical statistical characteristics
(I) the technical field
The invention relates to an Autonomous Underwater Vehicle (AUV) cooperative positioning technology, in particular to AUV position state information estimation by utilizing mathematical statistical characteristics of related variables as iterative transfer solution of reliability information between variable nodes and function nodes on the basis of a factor graph and sum-product algorithm. When the method is used for AUV cooperative positioning, because the nonlinear distance observation equation does not need to be subjected to linearization processing, errors caused by linearization are avoided, the cooperative positioning errors are reduced, the positioning capability of a cooperative positioning system is improved, and meanwhile, because the two-dimensional problem of the traditional cooperative positioning algorithm is converted into the one-dimensional problem, the calculation complexity is reduced, and the calculation amount is reduced.
(II) background of the invention
In the face of increasingly complex operation environments and operation tasks, the navigation capacity and the load capacity of a single unmanned operation system are limited, and tasks such as information acquisition, regional monitoring, multi-target attack and the like are difficult to complete, so that the cooperative operation technology of a plurality of unmanned operation systems becomes an inevitable choice for the development of the unmanned operation systems. For the marine field, Autonomous Underwater Vehicles (AUVs) are a mainstream development trend and a development direction, and cooperative combat by using the AUVs can not only undertake complex tasks such as information collection, mine detection, coastal anti-submergence, relay communication and the like which are difficult to be performed by a single body, but also have the advantages of high efficiency, high reliability, high quality and the like. Therefore, AUV cooperative combat has wide application prospect.
Although the high-precision inertial navigation equipment can meet the AUV underwater positioning requirement, the high-precision inertial navigation equipment is high in cost; the speed of error accumulation along with time of the low-precision inertial navigation equipment is too high, and the AUV cannot be accurately positioned. For the acoustic navigation equipment, relative positioning is mainly realized through acoustic ranging, and due to the influence of underwater sound propagation speed, the update rate of the underwater sound navigation equipment is low, and the underwater sound navigation equipment cannot provide AUV position information in real time. Therefore, information interaction among multiple boats is realized, a small number of platforms are used for carrying high-precision inertial navigation equipment, and a cooperative positioning scheme for correcting positioning errors of an AUV (autonomous Underwater vehicle) provided with low-precision navigation equipment is significant on the basis of an underwater acoustic communication and distance measurement method.
Under the premise that the system is observable, the co-location algorithm is a key factor influencing the AUV location accuracy. However, in the conventional co-location algorithm, although the Extended Kalman Filter (EKF) algorithm successfully achieves co-location, when a non-linear problem is faced, the EKF actually linearizes the non-linear system by taking a taylor expansion first-order term, and a high-order truncation error caused by truncation may have a large influence on a system estimation result, thereby reducing the co-location accuracy. In addition, the Unscented Kalman Filter (Unscented Kalman Filter, UKF) algorithm is based on the idea that the probability density of an approximate nonlinear function is simpler than that of the approximate nonlinear function, and adopts deterministic sampling points to obtain relevant statistical parameters, so that the linearization process of the nonlinear function is avoided, the high-order truncation error generated by linearization of the nonlinear function is avoided, and the calculation precision can reach more than two orders. However, the UKF algorithm has large calculation amount and low efficiency, so that the application of the UKF algorithm in real-time navigation is limited, and the robustness of observation noise is still to be improved.
Aiming at the problems, the invention designs a factor graph cooperative positioning algorithm based on the expected variance. The invention adopts the factor graph to perform data fusion, realizes the updating of information in the factor graph by using a sum-product algorithm under the condition that the noise in the cooperative positioning system is Gaussian noise, converts complex operation into a plurality of simple operations by using the factor graph and the product algorithm, does not relate to Jacobian matrix operation in the algorithm, and reduces the complexity of the calculation. The distance observation equation does not need to be linearized in the factor graph, so that errors caused by linearization are avoided, the cooperative positioning errors are reduced, and the positioning capability of the cooperative positioning system is improved. The factor graph is non-directional, most of the problems based on the factor graph are solved by iterative transfer of 'reliability information' between variable nodes and function nodes, and in the invention, expectation and variance of related variables are used as reliability information.
(III) summary of the invention
The invention aims to design a factor graph co-location algorithm based on expected variance, and the complexity of the algorithm is reduced and the location accuracy of the system is improved by optimizing the co-location algorithm on the premise of not changing the accuracy of an inertial device.
The object of the present invention can be achieved by the following steps:
step 1: establishing a co-location algorithm factor graph model based on mathematical statistical characteristics;
step 2: and (4) taking the mathematical statistical characteristics of the position variable, namely expectation and variance as reliability information, and carrying out filtering updating on the position state information of the system.
In step 1, since the depth can be accurately measured by the depth meter mounted on the AUV, and the improvement of the accuracy of the depth information by the cooperative positioning is limited, the position information and the distance observation information of each AUV can be projected onto the horizontal plane, and the problem of the AUV cooperative positioning can be discussed in the two-dimensional plane. The factor graph contains two nodes: variable nodes and function nodes. As shown in fig. 1, circles in the graph represent variable nodes, rectangular shapes represent function nodes, and each edge in the graph connects one variable node and one function node. Based on this, the co-location model can be decomposed into two one-dimensional problems. Two one-dimensional problems are represented by two main node sets in the x-coordinate set and the y-coordinate set in the factor graph, respectively.
The established co-location algorithm factor graph model contains N groups of nodes, and N is the number of observation information received from the boat in the co-location system. Master-slave boat ranging information
Figure BDA0002752338890000021
Through node Fi(i-1 … N) into a factor graph, from an a priori estimate of the boat position through nodes a and B into the factor graph, through CiAnd DiThe node converts the position information of the master boat and the slave boat into the position difference between an x coordinate set and a y coordinate set, and then the position difference passes through a node EiAnd fusing the information of the x coordinate set and the y coordinate set.
In step 2, the expectation and variance of the initial position state of the AUV are initialized, the position state estimation of the next moment is obtained by dead reckoning, the nodes x and y are updated again, and the node Δ x is updatedn、ΔynAnd dnUpdate and then carry out the update on the node CnAnd DnUpdating and finally node EnAnd (6) updating.
The method comprises the following specific steps:
(1) initialization
Initial state is determined at the start of co-location:
Figure BDA0002752338890000031
Figure BDA0002752338890000032
in the formula (x)0,y0) In order to be in position from the time of boat initiation,
Figure BDA0002752338890000033
is the corresponding variance;
Figure BDA0002752338890000034
to predict the value of a step from the boat's k moment position state,
Figure BDA0002752338890000035
is the corresponding variance.
(2)
Figure BDA0002752338890000036
And
Figure BDA0002752338890000037
update of
At non-initial times, dead reckoning can be performed according to the following formula:
Figure BDA0002752338890000038
in the formula (I), the compound is shown in the specification,
Figure BDA0002752338890000039
representing the speed of flight from time k, expected to be muvVariance is
Figure BDA00027523388900000310
Figure BDA00027523388900000311
For the heading angle from time k of the boat, μ is expectedθVariance is
Figure BDA00027523388900000312
In addition, since the speed magnitude is independent of the heading, the covariance cov (v, θ) is 0.
Computing
Figure BDA00027523388900000313
And
Figure BDA00027523388900000314
expectation, variance of (c):
Figure BDA00027523388900000315
Figure BDA00027523388900000316
Figure BDA00027523388900000317
Figure BDA00027523388900000318
(3) updating of x and y
Firstly, the reliability information needs to follow the following criteria during iterative computation:
the information sent from the variable node x to the function node is the product of all information received at x from other function nodes except the function node;
the information transferred from the function node to the variable node is the product of the information transferred from all the neighbor variable nodes except the variable node to the function node and the function, and then the product is obtained by integrating all the relevant variables.
According to the above criteria, the following expression can be simplified:
Figure BDA00027523388900000319
Figure BDA00027523388900000320
thus, the final estimation results for nodes x and y can be expressed as:
Figure BDA0002752338890000041
Figure BDA0002752338890000042
the updated probability density functions of x and y are respectively:
Figure BDA0002752338890000043
Figure BDA0002752338890000044
in the formula, mx,my,
Figure BDA0002752338890000045
The calculation can be made by:
Figure BDA0002752338890000046
Figure BDA0002752338890000047
Figure BDA0002752338890000048
Figure BDA0002752338890000049
in the formula, N represents the number of distance information observed from the boat at the same time;
Figure BDA00027523388900000410
-an expectation of an x-coordinate representing a slave boat position estimated from the nth master boat observation information;
Figure BDA00027523388900000411
-an expectation of a y-coordinate representing a slave boat position estimated from the nth master boat observation information;
Figure BDA00027523388900000412
-to represent
Figure BDA00027523388900000413
A corresponding variance;
Figure BDA00027523388900000414
-to represent
Figure BDA00027523388900000415
A corresponding variance;
as known from belief information transfer criteria, x transfers its probability density function to nodes A and CnThe process is as follows:
Figure BDA00027523388900000416
Figure BDA00027523388900000417
similarly, y passes its probability density function to nodes B and DnThe process is as follows:
Figure BDA00027523388900000418
Figure BDA00027523388900000419
(4)Δxn、Δynand dnUpdate of
ΔxnPasses its probability density function to node CnAnd EnThe probability density function of its transfer is:
Figure BDA0002752338890000051
Figure BDA0002752338890000052
Δynpasses its probability density function to node DnAnd EnThe probability density function of its transfer is:
Figure BDA0002752338890000053
Figure BDA0002752338890000054
dnpasses its probability density function to node EnAnd FnThe probability density function of its transfer is:
Figure BDA0002752338890000055
Figure BDA0002752338890000056
(5)Cnand DnUpdate of
Function node CnAnd DnThe function of (a) is to convert relative position information to absolute position information. Thus, the slave node CnDelivery to node Δ xnThe probability density function of (a) can be expressed as:
Figure BDA0002752338890000057
in turn, the slave node CnThe probability density function delivered to node x can be expressed as:
Figure BDA0002752338890000058
for node DnFrom node DnDelivery to node aynThe probability density function of (a) can be expressed as:
Figure BDA0002752338890000059
in turn, the slave node DnThe probability density function delivered to node y can be expressed as:
Figure BDA00027523388900000510
(6)Enupdate of
Function node EnThe function of (a) is to combine the x set of coordinate systems with the y set. According to the Pythagorean theorem, variable nodesΔxnAnd Δ ynThe constraints in between can be described as:
Figure BDA00027523388900000511
slave function node EnTo variable node Δ ynThe probability density function of (a) can be expressed as:
Figure BDA00027523388900000512
in the formula (I), the compound is shown in the specification,
Figure BDA00027523388900000513
-representing the difference in x-coordinates of the master and slave boats during the last iteration;
Figure BDA0002752338890000061
-representing the corresponding variance.
Slave function node EnTo variable node Δ xnThe probability density function of (a) can be expressed as:
Figure BDA0002752338890000062
in the formula (I), the compound is shown in the specification,
Figure BDA0002752338890000063
-representing the difference in x-coordinates of the master and slave boats during the last iteration;
Figure BDA0002752338890000064
-representing the corresponding variance.
(IV) description of the drawings
FIG. 1 is a built co-location algorithm factor graph model.
Fig. 2 is a motion trail diagram of a master boat and a slave boat in a simulation experiment.
Fig. 3 is a diagram of positioning error of a simulation experiment.
(V) detailed description of the preferred embodiments
The present invention will be described in detail with reference to specific embodiments.
The invention provides a method which can reduce the complexity of calculation, reduce the calculation amount, avoid the linearization processing of a nonlinear distance observation equation, reduce the cooperative positioning error and improve the capability of a cooperative positioning system. The purpose of the invention is realized by the following steps:
1. establishing a co-location algorithm factor graph model based on mathematical statistical characteristics;
2. updating variable nodes and function nodes in the model;
3. and carrying out filtering fusion estimation on the position state of the system through the transferred probability density function.
In order to verify the effectiveness of the invention, a factor graph co-location algorithm based on mathematical statistical characteristics is simulated by using software.
FIG. 1 is a mathematical statistics characteristic-based co-location algorithm factor graph model established in the figure
Figure BDA0002752338890000065
Representing one-step prediction of position state, (x, y) representing position state after filtering fusion estimation, (deltax, deltay) representing relative position information between a master boat and a slave boat,
Figure BDA0002752338890000066
indicating measurement information between master and slave vessels, dNIs shown as
Figure BDA0002752338890000067
Fig. 2 is a diagram of the motion trajectories of the master boat and the slave boat in a simulation test, and the simulation conditions are as follows: initial position (x) of main boat 1m1,ym1) -2 m/s speed (-400m, -200m) with a 0 ° heading; initial position (x) of main boat 2m2,ym2) (-400m, -1800m), speed 2m/s, heading 0 °; the initial position of the boat is (0m, 0)m), a speed of 2m/s and a heading of 0 deg. In the simulation, the velocity noise σ from the boatv＝(0.5m/s)2Acceleration noise σa＝(0.01m/s2)2Gyroscope for measuring noise
Figure BDA0002752338890000068
Distance observation noise σh＝(1m)2All are uncorrelated additive noise. And updating the estimation of the position information by using a filtering algorithm, wherein the period of each filtering estimation is 1 s. In the positioning error diagram in the simulation experiment of fig. 3, it can be seen from the diagram that in the operation process, the positioning error of the slave boat motion trajectory obtained by using the EKF and UKF filtering algorithms is gradually increased, and the positioning error of the factor graph co-positioning algorithm based on the mathematical statistic characteristics provided by the invention can be gradually converged.
The effectiveness of the factor graph cooperative positioning algorithm based on the mathematical statistic characteristics is verified through the experiment, the aim of improving the overall positioning accuracy of the system can be achieved by avoiding the linearization processing of the nonlinear distance observation equation on the premise of not improving the measurement accuracy of the inertial components in the cooperative system, meanwhile, the complexity of calculation can be reduced, and the calculation amount is reduced.

Claims (3)

1. A factor graph co-location algorithm based on mathematical statistics features is characterized by comprising the following steps:
step 1: establishing a co-location algorithm factor graph model based on mathematical statistical characteristics;
step 2: and (4) taking the mathematical statistical characteristics of the position variable, namely expectation and variance as reliability information, and carrying out filtering updating on the position state information of the system.
2. The method for establishing the co-location algorithm factor graph model according to the step 1 of the mathematical statistics feature based factor graph co-location algorithm is characterized in that the conventional co-location two-dimensional problem is converted into a one-dimensional problem, and the two one-dimensional problems are respectively represented by two main node groups in an x coordinate group and a y coordinate group in the factor graph.
The specific idea is as follows: master-slave boat ranging information
Figure FDA0002752338880000017
Through node Fi(i-1 … N) into a factor graph, from an a priori estimate of the boat position through nodes a and B into the factor graph, through CiAnd DiThe node converts the position information of the master boat and the slave boat into the position difference between an x coordinate set and a y coordinate set, and then the position difference passes through a node EiAnd fusing the information of the x coordinate set and the y coordinate set.
3. The filter updating method for the position state information of the system in the step 2 of the mathematical statistics characteristic-based factor graph co-location algorithm according to claim 1 is characterized in that the mathematical statistics characteristics of the position variables, namely expectation and variance, are used as reliability information to be transferred between the variable nodes and the function nodes.
Firstly, a criterion expression followed by the credibility information in iterative computation is defined:
(1) the information sent from the variable node x to the function node is the product of all information received at x for function nodes other than this function node;
Figure FDA0002752338880000011
(2) the information transmitted to the variable node by the function node is obtained by multiplying the information transmitted to the function node by all the neighbor variable nodes except the variable node by the function and then integrating all the related variables.
Figure FDA0002752338880000012
And then, the expectation and the variance of the position variable are used as reliability information to be transmitted between the variable node and the function node, and finally, the filtering fusion estimation of x and y is realized.
The updated probability density function for x, y is:
Figure FDA0002752338880000013
Figure FDA0002752338880000014
in the formula, mx,my,
Figure FDA0002752338880000015
The calculation can be made by:
Figure FDA0002752338880000016
Figure FDA0002752338880000021
Figure FDA0002752338880000022
Figure FDA0002752338880000023
in the formula, N represents the number of distance information observed from the boat at the same time;
Figure FDA0002752338880000024
-an expectation of an x-coordinate representing a slave boat position estimated from the nth master boat observation information;
Figure FDA0002752338880000025
-an expectation of a y-coordinate representing a slave boat position estimated from the nth master boat observation information;
Figure FDA0002752338880000026
-to represent
Figure FDA0002752338880000027
A corresponding variance;
Figure FDA0002752338880000028
-to represent
Figure FDA0002752338880000029
The corresponding variance.
CN202011189329.9A 2020-10-30 2020-10-30 Factor graph co-location algorithm based on mathematical statistical characteristics Pending CN112325885A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011189329.9A CN112325885A (en) 2020-10-30 2020-10-30 Factor graph co-location algorithm based on mathematical statistical characteristics

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011189329.9A CN112325885A (en) 2020-10-30 2020-10-30 Factor graph co-location algorithm based on mathematical statistical characteristics

Publications (1)

Publication Number Publication Date
CN112325885A true CN112325885A (en) 2021-02-05

Family

ID=74297261

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011189329.9A Pending CN112325885A (en) 2020-10-30 2020-10-30 Factor graph co-location algorithm based on mathematical statistical characteristics

Country Status (1)

Country Link
CN (1) CN112325885A (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112946571A (en) * 2021-02-08 2021-06-11 西北工业大学 Three-dimensional co-location method based on factor graph
CN113156368A (en) * 2021-03-23 2021-07-23 哈尔滨工业大学 Error parameter identification cooperative positioning method based on factor graph
CN114577211A (en) * 2022-02-25 2022-06-03 哈尔滨工程大学 Factor graph-based master-slave AUV (autonomous Underwater vehicle) cooperative positioning method considering ocean current influence
CN114577211B (en) * 2022-02-25 2024-06-28 哈尔滨工程大学 Master-slave AUV cooperative positioning method based on factor graph considering ocean current influence

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108364014A (en) * 2018-01-08 2018-08-03 东南大学 A kind of multi-sources Information Fusion Method based on factor graph
CN108375782A (en) * 2018-01-18 2018-08-07 西北工业大学 Factor graph co-located method based on satellite navigation and location system
US20180304891A1 (en) * 2015-07-29 2018-10-25 Volkswagen Aktiengesellschaft Determining arrangement information for a vehicle
US20190219401A1 (en) * 2018-01-12 2019-07-18 The Trustees Of The University Of Pennsylvania Probabilistic data association for simultaneous localization and mapping
CN110274588A (en) * 2019-06-19 2019-09-24 南京航空航天大学 Double-layer nested factor graph multi-source fusion air navigation aid based on unmanned plane cluster information
CN110278525A (en) * 2019-05-21 2019-09-24 袁正道 A kind of high-precision indoor wireless positioning method
CN110837854A (en) * 2019-10-30 2020-02-25 东南大学 AUV multi-source information fusion method and device based on factor graph
CN111337020A (en) * 2020-03-06 2020-06-26 兰州交通大学 Factor graph fusion positioning method introducing robust estimation

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20180304891A1 (en) * 2015-07-29 2018-10-25 Volkswagen Aktiengesellschaft Determining arrangement information for a vehicle
CN108364014A (en) * 2018-01-08 2018-08-03 东南大学 A kind of multi-sources Information Fusion Method based on factor graph
US20190219401A1 (en) * 2018-01-12 2019-07-18 The Trustees Of The University Of Pennsylvania Probabilistic data association for simultaneous localization and mapping
CN108375782A (en) * 2018-01-18 2018-08-07 西北工业大学 Factor graph co-located method based on satellite navigation and location system
CN110278525A (en) * 2019-05-21 2019-09-24 袁正道 A kind of high-precision indoor wireless positioning method
CN110274588A (en) * 2019-06-19 2019-09-24 南京航空航天大学 Double-layer nested factor graph multi-source fusion air navigation aid based on unmanned plane cluster information
CN110837854A (en) * 2019-10-30 2020-02-25 东南大学 AUV multi-source information fusion method and device based on factor graph
CN111337020A (en) * 2020-03-06 2020-06-26 兰州交通大学 Factor graph fusion positioning method introducing robust estimation

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
范世伟等: "An Advanced Cooperative Positioning Algorithm Based on Improved Factor Graph and Sum-Product Theory for Multiple AUVs", 《IEEE ACCES》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112946571A (en) * 2021-02-08 2021-06-11 西北工业大学 Three-dimensional co-location method based on factor graph
CN112946571B (en) * 2021-02-08 2023-09-08 西北工业大学 Factor graph-based three-dimensional co-location method
CN113156368A (en) * 2021-03-23 2021-07-23 哈尔滨工业大学 Error parameter identification cooperative positioning method based on factor graph
CN113156368B (en) * 2021-03-23 2023-05-30 哈尔滨工业大学 Error parameter identification co-location method based on factor graph
CN114577211A (en) * 2022-02-25 2022-06-03 哈尔滨工程大学 Factor graph-based master-slave AUV (autonomous Underwater vehicle) cooperative positioning method considering ocean current influence
CN114577211B (en) * 2022-02-25 2024-06-28 哈尔滨工程大学 Master-slave AUV cooperative positioning method based on factor graph considering ocean current influence

Similar Documents

Publication Publication Date Title
CN107315171B (en) Radar networking target state and system error joint estimation algorithm
US20210373855A1 (en) Rotation Matrix-Based Factor Graph Cooperative Localization Algorithm
CN112325885A (en) Factor graph co-location algorithm based on mathematical statistical characteristics
CN110187337B (en) LS and NEU-ECEF space-time registration-based high maneuvering target tracking method and system
CN110209180B (en) Unmanned underwater vehicle target tracking method based on HuberM-Cubasic Kalman filtering
CN111257865A (en) Maneuvering target multi-frame detection tracking method based on linear pseudo-measurement model
CN111739066A (en) Visual positioning method, system and storage medium based on Gaussian process
Zhang et al. An integrated navigation method for small-sized AUV in shallow-sea applications
CN114137525A (en) Multi-target detection method and system based on vehicle-mounted millimeter wave radar
CN116929338B (en) Map construction method, device and storage medium
CN111736144B (en) Maneuvering turning target state estimation method only by distance observation
CN110728026B (en) Terminal trajectory target passive tracking method based on angular velocity measurement
CN116047495B (en) State transformation fusion filtering tracking method for three-coordinate radar
Song et al. Research on Target Tracking Algorithm Using Millimeter‐Wave Radar on Curved Road
CN116681733A (en) Near-distance real-time pose tracking method for space non-cooperative target
CN116734860A (en) Multi-AUV self-adaptive cooperative positioning method and system based on factor graph
CN116224320A (en) Radar target tracking method for processing Doppler measurement under polar coordinate system
CN113761662B (en) Generation method of trajectory prediction pipeline of gliding target
CN114993341A (en) Carrier rocket trajectory estimation method and device based on space-based measurement
CN114763998A (en) Unknown environment parallel navigation method and system based on micro radar array
Radhakrishnan et al. Continuous-discrete shifted Rayleigh filter for underwater passive bearings-only target tracking
Lu et al. A new performance index for measuring the effect of single target tracking with Kalman particle filter
CN113989327A (en) Single UUV target state estimation method based on convolutional neural network particle filter algorithm
Zhang et al. Seamless tracking of group targets and ungrouped targets using belief propagation
Zheng et al. An Imm-BP based algorithm for tracking maneuvering underwater targets by multistatic marine robot networks

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
WD01 Invention patent application deemed withdrawn after publication
WD01 Invention patent application deemed withdrawn after publication

Application publication date: 20210205