Aerospace and marine instrumentmaking sensors, devices and systems under thermal actions
V.E. Dzhashitov, V.M. Pankratov // Under the general editorship of the RAS Academician V.G. Peshekhonov St. Petersburg: SRC of Russia  CSRI "Elektropribor", 2005.  404 p. Price  70 RUR © SRC of Russia  CSRI "Elektropribor", 2005 © V.E. Dzhashitov, V.M. Pankratov, 2005 ISBN 5900780570
Mathematical models of classical and promising aerospace and marine sensors, devices and systems have been considered with regard to external and internal, deterministic and random thermal actions. Mathematical models of thermal processes and thermal drift of floated, dynamically tuned, electrostatic, hemispherical resonator, fiberoptic, micromechanical gyros and accelerometers, sensors and other physical parameters, electronics service units have been constructed and investigated. Particular attention has been given to construction of the new mathematical models enabling to investigate the nonlinear dynamics of thermally disturbed sensors, devices and systems.
The monograph presents a developed, generalized and significantly enhanced version of the book "Mathematical models of thermal drift of gyroscopic sensors of inertial systems", 2001, on the basis of the recent research conducted by its authors. Quite detailed extracts from it have been quoted here. It provides logical coherence of the material presentation not only for specialists and designers but also for students and postgraduates. Besides, such an approach makes it possible to get to know the current status of thermal disturbance issues of highprecision measurement instrumentation. The book contains systematic parts revealing the essence of interconnectivity of physical processes under operation of aerospace and marine articles.
The book is intended for scientists, engineers and technicians. Also it can be useful for postgraduates and students of higher education institutes. Bibliography: 53 references. 162 illustrations. 10 tables. 
Introduction  3 
Chapter 1. Laws of motion of AES center of mass in the nearEarth space  14 
1.1. General motion equation of material point in the outer space   
1.2. Motion equation of AES center of mass near the Earth  16 
1.3. Solution of motion equations of AES center of mass in the central gravitational field  23 
1.4. Peculiarities of AES disturbed motion  33 
1.5. Equations of mutual motion of SV in the nearEarth space  39 
1.6. Influence of deviations in initial conditions on AES motion trajectory  42 
1.7. General statement and solution principles of AES navigation problem using onboard measurements  54 
Chapter 2. Statement and solution methods of AES orientation problems  62 
2.1. General statement of AES orientation problems and selection of coordinate systems   
2.2. Orientation parameters and kinematic equations of AES motion around the center of mass  67 
2.3. Possible solution algorithms for orientation kinematic equations  74 
Chapter 3. Sources of primary navigation information for solution of AES navigation and orientation problems  80 
3.1. General characteristic of primary navigation information sources   
3.2. Inertial sources of primary navigation information  85 
3.3. Astronomical sources of primary navigation information  92 
3.4. Possibilities to use some physical fields for AES navigation and orientation  105 
3.5. Satellite navigation systems  109 
3.6. Land commandandmeasurement complexes  117 
Chapter 4. Methods for determining AES orbit parameters at minimum amount of primary navigation information  121 
4.1. Problems of determining orbit parameters with the use of minimum amount of information   
4.2. Determining position vector by measurements of zenith distances of two stars and flight altitude  127 
4.3. Refinement of the position vector by measurements of primary navigation parameters  131 
4.4. Determination of orbit parameters by measurements of the vector in several points  137 
Chapter 5. Statistical methods for estimation of AES orbit parameters and orientation  146 
5.1. General statement of determination problems for AES orbit parameters and orientation in statistical methods of information processing   
5.2. General procedure of information processing by statistical methods  151 
5.3. Peculiarities of statistical processing methods application at estimating orbit parameters  172 
Chapter 6. AES inertial navigation and orientation systems  178 
6.1. Construction principles and classification of AES inertial navigation and orientation systems   
6.2. Functioning algorithms of AES strapdown inertial navigation systems in orientation mode (on passive flight phases)  206 
6.3. Operation algorithms of AES strapdown inertial systems in navigation and orientation problem solution mode on active flight phases  222 
Chapter 7. AES integrated onboard navigation and orientation systems  228 
7.1. Structure, arrangement and composition of integrated onboard navigation and orientation systems for AES   
7.2. Astroinertial measuring unit  234 
7.3. Functioning algorithms of integrated strapdown inertial navigation and orientation systems (SINOS) in orientation mode  249 
7.4. Algorithms of SINOS drift astrocorrection in orientation mode  263 
7.5. Algorithms for solution of navigation and orientation problems in emergency conditions  270 
Chapter 8. Methods for accuracy estimation of AES navigation and orientation problems solution by onboard autonomous systems  276 
8.1. Problems and possible ways of accuracy estimation of AES navigation and orientation problems solution   
8.2. General procedure for navigation accuracy estimation at processing by the method of least squares  280 
8.3. Ways and possibilities of obtaining analytical accuracy estimates by using the results of statistical processing of discrete measurements  283 
8.4. Methods for accuracy estimation of AES navigation and orientation problems solution by imitation mathematical simulation  307 
Conclusions  319 
References  320 
Foreword  3 
Introduction  5 
Chapter 1. Foundations of General Reliability Theory for Technical Systems  14 
1.1. Technical System Hardware Reliability. Probabilistic Assessment  14 
1.2. Simple Flow of Events and Markov Models for Technical System Operation  19 
1.3. Reliability of Redundant Technical Systems  26 
1.4. Monitoring and Diagnostics of Technical Systems  35 
Chapter 2. Error Model and Information Reliability Assessment of Navigation Systems  42 
2.1. Characteristics of Scalar Random Processes  44 
2.2. Vector Markov Processes  52 
2.3. Stochastic Error Models of Navigation System  56 
2.4. Runs of Random Markov Processes. FokkerPlanckKolmogorov Equations  68 
2.5. NS Information Reliability Assessment under Diffusion Error Models  74 
2.6. NS Information Reliability Assessment under Jump Error Models  81 
Chapter 3. Information Failures and Malfunctions in Navigation Systems. Monitoring and Diagnostics Methods  89 
3.1. Monitoring and Diagnostics of Information Failures and Malfunctions as a Decision Problem  89 
3.2. Review of Known Approaches to Solving Monitoring and Diagnostics Problems for Information Failures and Malfunctions  96 
3.3. Estimation of Determined Dynamic System State  100 
3.4. Optimal Estimation of Stochastic Dynamic System State  107 
3.5. Monitoring and Diagnostics of Information Failures and Malfunctions in NS by Optimal Methods for MultipleChoice Filtration  115 
3.6. Monitoring and Diagnostics of Information Failures and Malfunctions in NS by Suboptimal Methods for MultipleChoice Filtration  129 
Chapter 4. Information Failures and Malfunctions of Navigation Systems. Examples of Monitoring and Diagnostics  137 
4.1. Monitoring of Satellite Navigation System Integrity  137 
4.2. Monitoring and Diagnostics of Information Failures in Redundant Autonomous System of Marine Navigation  146 
4.3. Monitoring and Diagnostics of Information Failures in Low Redundant Autonomous System of Marine Navigation  157 
Appendix 1. General Concepts of Probability Theory  175 
Appendix 2. Riccati Equation Solution  181 
Appendix 3. Probability of 1st Order Markov Process NonExceedance of a Specified Level at Interval  185 
Appendix 4. Kalman Filter Ratio Derivation  193 
References  200 
On behalf of the Organizing Committee of the 4^{th} Conference of Young Scientists Navigation and Motion Control  5 
Session "Smart control systems"  
S.N.Vasiliev
Logical approach to dynamic systems control (L e c t u r e) 
7 
E.A.Cherkashin
Using artificial intelligence for informationcontrol systems 
24 
T.I.Madzhara
A computeraided system for solving optimal control problems 
31 
Session "Gyroscopic systems"  
A.A.Stolbov
On increasing the calibration accuracy of the inertial navigation system based on attitude gyros 
38 
A.M.Boronakhin
The use of analytical gyro vertical for navigation on the railway track 
45 
V.V.Pchelin, A.V.Uskov
A stabilized gyro compass based on a strapdown shortperiod vertical 
53 
N.V.Goncharov, Yu.V.Filatov
Development of goniometric methods and means for monitoring the vehicle attitude 
58 
Session "Data processing"  
L.A.Mironovsky
The theory of invariants and its application in diagnosis (L e c t u r e) 
64 
Yu.A.Litvinenko
Kalman filter sensitivity to uncertainty of water current when solving the problem of inertial navigation system damping by the log 
83 
A.P.Aleshkin, T.O.Myslivtsev
Adaptive empirical estimation of the state vector for a spacecraft under measurement shortage 
89 
M.S.Koryukin
The use of neuronet algorithms for processing data from redundant sensors 
97 
G.V.Bezmen
The possibility analysis for using neural networks in solving filtering problems 
103 
K.Yu.Petrova
Optimization of defect distinguishability in test diagnosis 
107 
I.S.Kayutin
Study of digital data processing algorithms for an acceleration sensor 
115 
D.P.Loukianov, A.Ya.Maizelis
Investigation of speed variations for highspeed gas flows in variable crosssection nozzles 
121 
V.A.Smirnov
Algebraic synthesis of controllers of gyroscopic stabilization and control systems 
129 
A.V.Bobkov
A system of positioning by the terrain image on the basis of line set analysis 
137 
Session "Sensors of navigation and control systems"  
M.I.Evstifeev, M.F.Smirnov, A.A.Untilov
The analysis of mechanical, electrical and thermal characteristics in designing a micromechanical gyro 
142 
D.P.Loukianov, I.Yu.Ladychuk
Study of microaccelerometers using surface acoustic waves 
149 
Yu.V.Shadrin, S.G.Kucherkov
Dynamic characteristics of a ring micromechanical gyro with the open loop 
155 
Yu.V.Povodyrev, S.M.Dyugurov
Development of methods and means to increase the accuracy of the angular data pickup system of a strapdown electrostatic gyro 
160 
V.N.Khodurov
Experimental investigation into the thermal drift of fiberoptic gyros 
165 
D.I.Lychev, S.G.Kucherkov
A precision rotary test bench for testing a micromechanical gyro 
171 
Session "Control theory and systems"  
V.O.Nikiforov
Control of vehicles with roughly known characteristics: roughness, adaptation and robustness (L e c t u r e) 
177 
V.O.Rybinsky
Robust stabilization of linear periodic systems 
188 
K.Yu.Polyakov
Ultimate possibilities of smoothing random processes using continuousdigital filters 
196 
O.E.Yakupov
An adaptive electrohydraulic servo drive of the aircraft 
203 
T.V.Turenko
A hybrid model of the direct digital control system with a unitarycode sensor 
211 
A.G.Klimenkov, A.L.Starichenkov, T.S.Chernysheva
The software of the simulator for hydrofoil ship motion control 
218 
Session "Electronic and electromechanical devices of navigation and control systems"  
V.D.Aksenenko, S.I.Matveev
Synchronous demodulation using the digital signal processing technique 
225 
Ya.V.Belyaev, Ya.A.Nekrasov
The methods for estimating the accuracy of a temperature stabilization system using the software for thermal fields calculation 
229 
A.M.Richnyak
A superconductive geomagnetic motor for spacecraft orientation and stabilization systems 
233 
Session "Computer technologies in navigation and control"  
A.A.Belash, S.S.Gurevich
The central computer of the strapdown inertial attitude system and its software 
241 
D.A.Tomchin
The virtual laboratory for study and control of a singlerotor vibration bench 
246 
S.N.Turusov, O.Yu.Lukomskaya
The system of informational support for organizational readiness of the ship's crew 
253 
Session "Ship navigation"  
A.V.Ulanov
The analysis of alternative approaches to managing the controlled motion of an underwater gliding vehicle 
261 
I.F.Shishkin, A.G.Sergushev
Using the science about tracks in water areas 
268 
A.G.Shpektorov, V.A.Zuev
Stabilization of a highspeed vehicle at the prescribed route 
274 
N.V.Kuzmina
Contrasting color of auxiliary information in the marine directionfinder 
280 
Session "Integrated navigation and orientation systems"  
A.M.Boronakhin, A.V.Kazantsev. S.A.Karpasov
The results of experimental investigations of the navigation system on the railway as a part of the track measurement car CSRI4 
286 
S.V.Ignatiev
A stabilized gyrocompass based on fiberoptic gyros with rotating sensor unit 
291 
A.A.Pisarevsky, A.N.Doronin
The integrated system for aircraft 
299 
Yu.V.Gavrilenko, N.A.Zaitseva, E.V.Kochneva
Suboptimal doublestep filter for special navigation problems 
303 
Round table "The results and forms of holding a conference using the Internet"  
Yu.A.Litvinenko, O.A.Stepanov, D.O.Taranovsky
The experience in holding the conference of young scientists Navigation and Motion Control using the Internet 
309 
L i s t o f a u t h o r s

315 
Foreword 5 Gravimetry L.K. Zheleznyak, V.N. Koneshov
Uptodate methods for studying gravity field of the World ocean9 L.K. Zheleznyak
The Russian marine gravimetric system14 A.V. Sokolov, S.V. Usov, L.S. Elinson
Gravity survey in conditions of marine seismic work21 B.A. Blazhnov, L.P. Nesenjuk, V.G. Peshekhonov, A.V. Sokolov, L.S. Elinson, L.K. Zheleznyak
An integrated mobile gravimetric system. Development and test results33 V.N. Ilyin, Yu.L. Smoller, S.Sh. Yurist
A mobile groundbased gravity meter. Development and test results45 V.N. Berzhitzky , V.N. Ilyin , E.B.Saveliev, Y.L. Smoller, Yu.V. Bolotin, A.A.Golovan, N.A.Parusnikov, G.V. Popov, M.V. Chichinadze
GT1A inertial gravimeter system design experience and results of flight tests48 O.A. Stepanov, B.A. Blazhnov, D.A. Koshaev
The efficiency of using velocity and coordinate satellite measurements in determining gravity aboard an aircraft61 Yu.I. Nikolsky
Problems of reduction in highaccuracy gravity measurements in geodesy and geology75
Gravity gradiometryG.B. Volfson
State and prospects of gravity gradiometry development90 A.B. Manukin
Design of a measuring system for a highly sensitive gravity gradiometer using vertical pendulums105 M.S. Petrovskaya, G.B. Volfson
Construction of geopotential models by the satellite gradiometry data111 V.G. Peshekhonov, G.B. Volfson
Problem solution for design of a gravity variometer operating on a moving base118 G.B. Volfson, M.I. Evstifeev, V.G. Rozentsvein, M.P. Semenova, Yu.I. Nikolsky, E.V. Rokotyan, S.F. Bezrukov
A new generation of gravity variometers for geophysical investigations122
Borehole navigationA.A. Molchanov, G.S. Abramov
Navigation in investigation of underground space in searching, exploring and developing mineral deposits136 V.G. Rozentsvein
State of the art of borehole gyroscopic navigation systems146 E.V. Freiman, S.V. Krivosheyev, V.V. Losev
Peculiarities of attitude algorithm construction for gyroscopic inclinometers based on a singleaxis gyrostabilizer168 N.P. Rogatykh
Methodical aspects of inclinometer design178 V.M. Suminov, D.V. Galkin, A.A. Maslov
A mathematical error model of a gyro inclinometer190