MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENSE ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY PHAM VAN PHUC DESIGN THE ALGORITHMS TO DETECT THE POSITION, STATUS AND CONTROL THE MOVEMENT OF UNDERWATER VEHICLES Major: Control Engineering and Automation Code: 52 02 16 SUMMARY OF PhD THESIS IN ENGINEERING HA NOI – 2019 The thesis was completed at ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY Scientific Supervisors: Assoc Prof Dr Tran Duc Thuan Dr Nguyen Quang Vinh Review 1: Assoc Prof Dr Pham Tuan Thanh Military Technical Academy Review 2: Assoc Prof Dr Luu Kim Thanh Vietnam Maritime University Review 3: Assoc Prof Dr Nguyen Quang Hung Academy of Military Science and Technology The thesis was defended in front of the Doctoral Evaluating Committee at Academy level held at Academy of Military Science and Technology at ………/………, 2019 The thesis can be found at: - The Library of Academy of Military Science and Technology - Vietnam National Library THE SCIENTIFIC PUBLICATIONS Pham Van Phuc, Nguyen Quang Vinh, Nguyen Đuc Anh, (2015), “ A system for positioning underwater vehivles based on combination of IMU and Doppler speed measument enquipment”, The 3rd Vietnam Conference on Control and Automation, pp 37-42 Pham Van Phuc, Truong Duy Trung, Nguyen Quang Vinh, (2016), “ Control of the motion orientation and the depth of underwater vehicles by use of the neural network”, JMST, Academy of Military Science and Technology, Special number of Rocket, pp.15-22 Pham Van Phuc, Nguyen Quang Vinh, (2017), “The nonlinear control of underwater vehicles using hedge algebras”, JMST, Academy of Military Science and Technology, Vol 51, pp.40-45 Pham Van Phuc, Tran Duc Thuan, Nguyen Viet Anh, Nguyen Quang Vinh, (2018), “An algorithm for determination the location and position for underwater vehicles”, JMST, Academy of Military Science and Technology, Vol 56, pp.03-13 Pham Van Phuc, Tran Duc Thuan, Nguyen Quang Vinh, (2018), “A dynamics model of underwater vehicle” JMST, Academy of Military Science and Technology, Vol 58, pp 14-20 Nguyen Quang Vinh, Pham Van Phuc, (2018), “Control of the motion orientation of autonomous underwater vehicle” XIIIth International Symposium «Intelligent Systems», INTELS’18, 22-24 October 2018, St Petersburg, Russia Procedia Computer Science 2018, pp.192-198 Pham Van Phuc, Nguyen Quang Vinh (2019), “Construction of a backstepping controller for controlling the depth motion of an automatic underwater vehicle” The 4th International Conference on Research in Intelligent and Computing in Engineering, 8-9 August 2019, Hanoi, VietNam ( Đã có xác nhận đăng) INTRODUCTION The necessity of the thesis Vietnam is a country with long maritime border and the East Sea region plays a strategic role especially in marine combat and defense, as well as connecting with international maritime routes Nowadays, exploration and exploitation of marine resources is highly concerned in many countries That makes the maritime disputes among countries becom complicated and consequently threatening the sovereignty, country security and maritime safety of the region and the world Therefore, it is an urgent requirement to develop combined weapons that effectively counteract sea attacks in our marintime territory It is also nessesary to equip underwater vehicles that effectively serve the reconnaissance and guard mission as well as, the exploration, exploitation of our marine resources Underwater Vehicles (UV) in the official force of the Navy are mainly submarines and anti-submarine weapons such as torpedoes, anti-submarine missiles There are also small underwater robots that are used for search rescue and ocean exploration The essential components of the UV's control structure are the navigation system and the control system The navigation system conducts the positioning and navigation functions to determine the position and posture of the UV and then create desired trajectory for the UV to follow The control system sends instant control signals that allow the UV to move in the desired trajectory Until now, there are many reports on the studying and developing the Autonomous Underwater Vehicle (AUV) navigation and control systems for both military and civilian purposes, as in [3], [16], [17] These studies have solved some problems in dynamics, motion control of AUV and Remotely Operated Underwater Vehilce (ROV) using traditional control theory The results of the study [17] suggested the addition the inertial guidance equipment as well as design an adaptive neuron controller to guide and control anti- submarine weapons However, in order to efficiently apply the above results on solving the stability and control problems for AUV, it is necessary to develop better appropriate controllers and algorithms Over the world, there are many countries interested in developing AUVs with devices for navigation and control However, it is difficult for local researchers and system integrators to access this resource, if any, it is in an improper form with implicit algorithms The above analysis shows the complication of the AUV navigation and control problem and the urgency to solve those problem, especially for the military applications The requirement of having a modern People's Navy force demands, deep understaning of the armed weapons and the ablity to repair, improve, upgrade and manufacture new weapons and underground vehicles Therefore, the thesis:''Design the algorithms to detect the position, status and control the movements of underwater vehicles '' is conducted in order to contribute to solve the practical problems of the exploitation and manufacture of underwater vehicles Research objectives of the thesis Summarize the algorithms to determine position, status and the algorithms to control motion trajectories for an underwater vehicle category Subjects and scope of research Research object of the thesis: Control system of an Autonomus Underwater Vehicle (AUV) with basic specifications as follows: the total weight of AUV is 20 kg; 1600mm length; 300mm width; velocity 0.2m/s;100m diving depth; operation time is 10 hours Research methodology Research methodology of the thesis: The research combines the theoretical method and the numerical method Scientific significance and practical meaning of the thesis - The research result of the thesis contributes to provide the scientific knowledge for other research and education in the stability system, controlling the movement trajectory of the underwater vehicle and the related fields - The results of the thesis can be applied to improve and modernize the existing underwater vehicles as well as design and manufacture new underwater vehicles The structure of the thesis The whole thesis is 109 pages divided in to chapters along with the Introduction, Conclusion, List of published scientific works, References and Appendix CHAPTER 1: OVERVIEW OF THE UNDERWATER DEVICES AND RESEARCH PROBLEMS ON KINEMATICS, POSITIONING AND CONTROL OF UNDERWATER DEVICES 1.1 Overview of the underwater vehicle The underwater vehicles began to appear in the early 19th century at the University of Washington and have made great achievements during the past decades Currently, the underwater vehicles are widely used in many different civilian and military tasks such as objective monitoring, exploration and exploitation of marine resources, oceanographic survey, disaster warning, search and rescue, handling landmines, cleaning contaminated water environment [3] Based on the degree of man involve menton the conduction of underwater vehicles, the underwater vehicles are divided into two catergories, unmanned underwater vehicles and the unmanned underwater vehicles, in which the unmanned underwater vehicles are divided into remotely underwater vehicle (ROV) and autonomous underwater vehicle (AUV) [14] The difference between AUV and ROV is: ROV is connected to the control center with cable or an audio link in the form of sound waves Connecting cables ensure the providing of information and control signals, in this way the operator can continuously grip and control the vehicle using to the predictable programs The underwater vehicle mentioned in this thesis is an AUV that move three-dimensional space in the water by a pushing system This AUV can be used in ocean research and exploration, reconnaissance, guard mission in the defined sea region 1.2 Kinetics and dynamics for underwater vehicles 1.2.1 Reference systems 1.2.1.1 N-frame system N-frame system is a reference system associated with the earth; the selected reference origin coincides with the starting point of the underwater vehicle Attached to this n-frame system, a Decartes coordinate system deals with the origin of the coordinate with the reference root, the axis xof the N-frame system to the geographic Northern direction, the axis yof the N-frame system to the geographic Eastern direction, axis xand axisy form a tangent plane to the Earth's surface 1.2.1.2 B-frame system B-frame system is a reference system attached to the selected reference object and the origin coincides with the center root of the gravity of the underwater vehicle Attached to the b-frame system, the coordinate system with the origin of the coordinate coincides with the reference origin, the vertical axis 0b X b is directed vertically of the underwater vehicle, the axis 0b X b is directed downwards and the axis 0b Yb is directed horizontally that forms the positive triangle 1.2.1.3 Converting the coordinate system by Ơle corner method Performing coordinate rotations to convert from the coordinate system linked to the geographical coordinate system with the direction Cbn of the Cosin matrix shown in the following form: n Cb  RZ , RY , RX , (1.5) The corners  , , are called the Ơle corners Matrix Cbn is an orthogonal matrix so it can convert a vector from a geographic coordinate system to a linked coordinate system by a transfer matrix: n 1 Cn  (Cb )  (Cb ) b n T  RTX , RYT , RZT , (1.6) 1.2.2 Kinetic model of AUV The movement of AUV is 6-free-degree movement including vertical movements along orthogonal axes X , Y , Z and rotational movements around each axis   (V T ,  T )T  (u , v, w, p , q , r )T ;  (1T , 2T )T  ( x, y , z , ,  ,  )T The relationship between the vector components in the linked coordinate system and the geographic coordinate system for the AUV is [6]: (1.9)   J ( ) 1.2.3 Dynamics of AUV The nonlinear dynamical equation of AUV in 6-free-degree of the coordinate system is described as follows [20], [32]: (1.11) M  C ( )  D( )  g ( )   , in which: M  M RB  M A is an inertial matrix  consisting of AUV mass M RB and additional mass M A ; C ( )  CRB ( )  CA ( ) is the Coriolis matrix and the radial force for moving the solid object and the additional mass; D ( )  Dl ( )  Dq ( ) is a hydrodynamic damping matrix  ; Dl ( ) represents linear damping quantity; Dq ( ) is nonlinear damping quantity; g ( ) is vector 1 of gravitational force; are forces and floating moments  is the control force vector / torque of the input 1.3 The positioning and status for moving vehicles In water, the electromagnetic wave is absorbed; UV can not receive the signal directly from the GPS to deal the drift of the measuring elements for the INS device Therefore, it is necessary to use additional information from fixed or mobile buoys on the sea surface to determine the exact position and status of AUV (in case of using mobile buoys, a satellite navigation device must be attached on the buoy to determine the location and information of coordinates updated for UV) 1.4 Studies on control for underwwater vehicles It had been known, designing control systems for AUV faces many difficulties because it must be closely connected with dynamic models So far, there are many different control methods to design precise motion control system for AUV such as PID control, adaptive, sliding mode, neural network… 1.5 Conclusion of Chapter Through the overview of UV, kinetic descriptions and studies of determining position, status and control, some conclusions are shown as follows: UVs are increasingly used in economy, security and defense They are many types of in many types of Uvs with diverse functions Navigation and motion control are fundamental for UVs, however this is issuesare new in Vietnam, especially in the military In order to efficiently exploit the existing UVs (mainly the imported) and even manufacture and design new UV, it is necessary to investigate the problems related to UV including Navigation and movement control of underwater vehicles Navigation of UV differs from that of others in space, on the ground, and in water (rivers, lakes and ocean) Therefore, in-depth research is required to provide the scientific infomation for futher the exploitation and design as well as manufacture the navigation and motion control systems for underwater vehicles In order to improve the quality of motion control for UV, it is important to study the control nature of UV, new equipments in Vietnam and to use the modern the oretical control tools to design the control algorithms for UV This will serve as basis infomation to develop softwares for UV control system CHAPTER 2: DESIGN THE ALGORYTHM TO DETECT THE POSITION AND STATUS FOR UV 13 2     (3.7) Setup Lyapunov function for dynamical system (1.13) as follows: V1  1T 1 (3.8) The input control parameter vector  needs to be defined so that the following equation is satisfied: c2  M 1 (  C ( )  D ( )  g ( ))    0, (3.23) to make this change (3.23) as follows: M 1 (  C ( )  D( )  g ( ))    c2 hoặc: M 1 (  C ( )  D( )  g ( ))  c2   (3.24) multiply the two equations (3.32) with the matrix M received:   C ( )  D( )  g ( )  M (c2  ) (3.25) From (3.25) we have:   M (c2   )  C ( )  D( )  g ( ), (3.26) It is the control rule required to satisfy equation (3.31) From the expression (3.26), it is necessary to determine the control law vector  in addition to the information  ,  ,  ,  and also need the coefficient c2 To determine  , it needs for a series of data about vectors  according to the expression (3.14) that is to have information about  and must have a coefficient c2 Then determine c1 and c2 per the formula (3.51) Thus, only the rule of c1 and c2 has been defined to satisfy the requirement under the condition (3.37), ie, V2  In this case, according to the theory of dynamical stability Lyapunov (3.15), (3.22) will be asymptotic, ie: 1  0,   (3.54) This shows that the posture and position of the underwater vehicle block approach to the set values (desired values) 14 3.3 Design fuzzy controller and hedge algebra controller for movement of underwater vehicle 3.3.1 Design fuzzy controller 3.3.1.1 Structure of fuzzy control system for the AUV AUV control system consists of four modules: - Speed control module is responsible for controlling the speed of AUV by setting the motor speed - Direction control system isused to control direction and output for vertical steering wheels - The depth control module performs AUV control in the vertical plane - The waterflow module is used to calibrate AUV position when the waterflow appears 3.3.1.2 Design fuzzy controller for stable depth for AUV -The deviation variable has the following forms: Noise Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Ze), Positive Small (PS), Positive Medium (PM), Positive Big (PB ) - Variable "deviation speed" has the following forms: Normal Big (NB), Normal Medium (NM), Zero (Ze), Positive Medium (PM), Positive Big (PB) - It turns out that the control voltage has the following forms: Noise Big (NB), Normal Medium (NM), Normal Sound (NS), zero (ZE), Positive Small (PS), Positive Medium (PM), Positive Big (PB) The control law consists of 35 format rules: if the deviation is NB and the deviation rate is NB, the voltage is NB Select MIN-MAX rule, defuzzification by Wtaver method (average value) 3.3.2 Design the controller for the underwater vehicle to apply hedge algebra 3.3.2.1 Hedge algebra and its application in control 3.3.2.2.Method of design the controller using hedge algebra The steps to design controllers per hedge algebras as follows: Step 1: Determine the input and output variables, their variation domain and the control rule system with language elements in HA 15 Step 2: Select the structure AX i (i   m) and Ay for the variables and X i y Determine the fuzzy parameters of the and the hedge Step 3: Calculate quantitative semantic value for language labels in m 1 the law system Setup real super S real m 1 Step 4: Select the interpolation method on the super S real and optimize the parameters of the controller 3.2.2.2 Controller design using hedge algebra for movement of AUV to the depth The controller has two input variables and one variable as follows: + The first input variable of the controller is the difference between the current depth and the set depth and is denoted E as the range of variation of [-1, 1] + The second input variable is the rate of variation of the depth (the derivative of the discrepancy) and is denoted IE as the variable range IE of [-1, 1] + The output variable of the controller is the control unit u to control the voltage of the power source and is denoted U as the variable range in the range [-2, 2] Select the element G = 0,N,W,P,1 and the set of hedge H - =  L ; H + = V  Select the degree of fuzzy measurement of elements and the degree of fuzzy measurement of hedges as follows: v(W)  W  0,5; fm( N )  W  0,5; fm( P)   0,5  0,5 With the fuzzy parameters selected in Table 3.2 and the relationship between the hedges, between the hedges with the elements as shown in Table 3.3, using quantitative semantics, we calculate the quantitative value of the term the meaning of language elements in the law table  (N)  W   fm(N)  0,5  0, 45*0,5  0, 275 16 l   (VN)   (N)  sign(VN)  fm(VN)  0.5 1  sign(VN ) sign(VVN)(    )  fm(VN)   i 1   0, 275  (1) 0,55.0,5  0,5 1  (1).1.(1).(0,55  0, 45)  0,55.0,5  0, 261 l   (VVN)   (V N)  sign(VVN)  fm(VVN)  0.5 1  sign(VN ) sign(VVVN)(    )  fm(VVN)   i 1  1   0, 261  (1)  0,55.0,55.0,5  0.5 1  (1).(1).( 1)(0,55  0, 45).0,55.0,55.0,5  0,194  i1   1   ( LN)   (N)  sign( LN)   fm( LN)  0.5 1  sign( LN) sign(VLN)(    )  fm( LN)  i     0, 275  1.0, 45.0,5  0,5 1  1.( 1).1.(0,55  0, 45)  0, 45.0,5  0, 298  (P)  W   fm(P)  0,5  0,5*0, 45  0,725 ;  1   (VP)   (P)  sign(VP)   fm(VP)  0.5 1  sign(VP) sign(VVP)(    )  fm(VP)  i 1  0, 725  (1) 0,55.0,5  0,5 1  1.1.1.(0,55  0, 45)  0,55.0,5  0,849   1   (VVP)   (VP)  sign(VVP)   fm(VVP)  0.5 1  sign(VVP) sign(VVVP)(    )  fm(VVP)  i 1   0,849  (1) 0,55.0,55.0,5  0,5 1  1.1.1.(0,55  0,45).0,55.0,55.0,5  0,916 1   ( LP)   (P)  sign( LP)  fm( LP)  0.5 1  sign( LP) sign(VLP)(    )  fm( LP)   i 1   0,849  0, 45.0,5  0,5 1  (1).(1).(1).(0,55  0, 45)  0, 45.0,5  0, 707 Design the quantitative semantic curve: from the values in table 3.7, using the connection AND = MIN to the meaning Es AND IEs  MIN(Es , IEs ), that each point (Es , IEs Us ) of table 3.7 brings a point from which the points MIN((Es , IEs ),Us ), of the quantitative semantic curve above on the basic principles of average point on table 3.8 Solve semantic value control u s to get control value u Assuming the linguistic variable X belongs to the real range [x0 x1 ] and its linguistic labels receive quantitative values in the 17 corresponding semantic quantitative range [s0 s1 ] , then the problem of quantifying the real value and the quantitative solution is done with defined intervals and the semantic interval of the variables E, IE, U given by Figure 3.9 per the following formula [61] 3.4 Conclusion of Chapter In case the parameters in the model which is used to describe the underground vehicle are clearly defined, the control rules will rely on the backstepping algorithm By demonstrating the additional clause, it has come up with an explicit formula for choosing the c1 , c2 coefficients in the backstepping control law to ensure that underground vehicles follow the desired trajectory and posture In case the controllers were design using hedge algebras, it can create an algebraic structure in the form of functional relations which allows the formation of a large arbitrarily set of linguistic values to describe in and out relationships Thus the quality of the control system is better than the fuzzy control The content of chapter is published in the work [02], [03], [06], [07] and this is the new contribution of the thesis CHAPTER 4: THE SIMULATION OF ALGORITHMS FOR DETECT THE POSITION STATUS AND CONTROL UNDERWATER VEHICLES 4.1 The simulation determining the position and status for underwater vehicles 4.1.1 Setup simulation parameters In order to perform the simulation, it is necessary to create two vectors, the acceleration vector and the velocity vector Acceleration is established with consideration of noise measurement with white noise (Gauss noise) Suppose the correct initial corners are valid  (0)  500 ;  (0)  400 ;  (0)  200 4.1.2 Results of simulation 18 Figure 4.1.Elements a11 , a12 , a13 of the directional Cosine matrix 4.2 The Simulation of the back-stepping motion control of AUV 4.2.1 Simulation of the input control signals In order to verify the performance of the controller, the thesis uses model parameters as in documents [21] and [25] Scenario 1: The law of control is implemented under (3.106) with c1 , c2 coefficients that are under (3.105) Figure 4.4 and 4.5.Input force control signals by axis X , Y Scenario 2: The law of control is implemented under (3.106) but c1 , c2 coefficients are not under (3.105), we choose c2  cos 19 Figure 4.8 and 4.9 Input force control signals by axis X , Y Between the two scenarios shows that the movement of underground vehicles is still stable, but fluctuates with large amplitude and time transits Thus, when choosing the factors that not meet the condition (3,105), the control quality of the system decreases significantly This shows that proving additional clause and giving the condition (3.105) is scholarly valid 4.2.2 The simulation of motion control in depth The simulation carried out during the period 80s with the inlet angle of the rudder steering wheel controlled in a pre-set angle  s so that the output system is the angle  changed to a lower angle of inclination Depth diagram is shown in Figure 4.12 Figure 4.12.Response system to the control in depth 20 The results show that the pitch angle, in this case, oscillates around the corner of 900 for seconds and stabilizes at the angle of 900 4.3 AUV control simulations applying fuzzy controller The input data is shown as follows: the values of AUV are taken from a category of underground vehicles (Appendix 1) Figure 4.15 Result of AUV control in the direction of using FC The fuzzy controller has the advantage of resisting external influences as well as the changes in internal parameters which ensure maintaining the reference trajectory, but time for AUV to stay in orbit for 8.5s 4.4 AUV control simulation applying the hedge algebra With simulation data in cases where the value of AUV is taken from a category of the underwater vehicles (Appendix 1), the parameters of the hedge algebra controller are taken as item 3.2: v(W)  W  0,5; fm( N )  W  0,5; fm( P)   0,5  0,5,   0, 45,   0,55 4.4.1 Simulation of AUV control in the direction of HA Assuming that the moment of 50(s) has white noise impacting the AUV, then the direction angle shall be deflected from the orbit angle, since the system uses a hedge algebra controller so it quickly adapts and after the time of 7.8s, it shall return to the reference trajectory 21 Figure 4.17 Response of AUV control in the direction of using HA 4.4.2 Simulation AUV control per the angle HA application Figure 4.19 Response of AUV control per the angle using hedge algebra The simulation results shown in Figure 4.19 show that at the start of the simulation, the AUV angle does not coincide with the desired pitch angle, so there is an error of the trajectory, but the trajectory of the system quickly resists the desired trajectory response, especially when the moment 50(s) is affected by the noise due to the HAC controller and the system quickly adheres to the desired trajectory 4.4.3 Control simulation shaking angle of hedge algebra Figure 4.21 Result of AUV control per the angle using HAC 22 4.4.4 Control simulation of hedge algebra application for AUV in the direction, angle and shaking angle Figure 4.23.AUV control results applying hedge algebra per the directional angle, angle and shaking angle Figure 4.24 Angle deviation at AUV control applying hedge algebra HA controller for AUV form 6-free-degree has done close asymptoically to the predetermined trajectory The proximity cability 23 based on the adaptation to the nonlinear model of AUV is very good, from 28 seconds onwards; the system almost clings completely to orbit HA algorithm allows AUV to follow a continuous trajectory 4.5 Comparing the simulation result of the motion control AUV between fuzzy method and HA application With the input data as Appendix 1, after many times of experimenting with fuzzy control method and method of controlling the use of hedge algebra on the same model, the same parameters get the following results: Figure 4.26 Simulation of HA/FLC control for AUV 4.6 Conclusion of Chapter Backstepping control technique showed the efficiency of controlling AUV motion according to the reference trajectory The fuzzy controller satisfied the kinematic requirements However, when the parameters of the subject change, the quality of the system also changes The controller using hedge algebra to stabilize the motion angle of AUV, responded effectively to the effects of the external noise, maintained th orbital deviation and rapid convergence force 24 CONCLUSION - Navigation and control to operate underwater vehicles (in the water environment) is different to navigation and control the vehicle that operate in space, on land and on the water surface (sea surface, the surface of rivers and lakes) Therefore, special solutions on both equipment and scientific research are required for navigation and control in underwater vehicles In Vietnam, this field is relatively new - In the case where the parameters of the underwater vehicle are updated, the backstepping control solution has provided the trajectory and the position of the vehicle is well set, when selecting a reasonable coefficient in the control law By proving additional clauses, there sults suggested a solution; that helps to determine the rational coefficients in the backstepping control law For cases where the model parameters of the underwater vehicles are not fully updated, it is possible to use hedge algebra to develop control algorithms for the movement of the underwater vehicle - The simulation results showed the efficiency of the proposed algorithms: the algorithm to determine the position and status of underwater vehicles based on negative buoys; the algorithm for controlling the motion of the underwater vehicles by backstepping, fuzzy control, and algebraic algebra control * New contributions of the thesis - Had designed an algorithm to determine the position and status of underwater vehicles using information from the hydroacoustic navigation buoys - Had designed an algorithm to control the movement of underwater vehicles using backstepping method and hedge algebras * Further direction Deploying experimental algorithms for different types and gradually develop the theoretical results of the thesis into applications into implementation especially when improving and modernizing underwater vehicles ... Thuan Dr Nguyen Quang Vinh Review 1: Assoc Prof Dr Pham Tuan Thanh Military Technical Academy Review 2: Assoc Prof Dr Luu Kim Thanh Vietnam Maritime University Review 3: Assoc Prof Dr Nguyen... B-frame system is a reference system attached to the selected reference object and the origin coincides with the center root of the gravity of the underwater vehicle Attached to the b-frame system,... Vietnam National Library THE SCIENTIFIC PUBLICATIONS Pham Van Phuc, Nguyen Quang Vinh, Nguyen Đuc Anh, (2015), “ A system for positioning underwater vehivles based on combination of IMU and Doppler