State Research Center of the Russian Federation
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Fundamentals of the Estimation Theory with Applications to the Problems of Navigation Information Processing.

O.A. Stepanov
Part 1. Introduction to the Estimation Theory
Part 2. Fundamentals of the Applied Filtering Theory
Published in 2009 and 2012 correspondingly

    Price: 440 RUR per volume.

Part 1 covers the general principles and approaches used to develop estimation algorithms for both linear and nonlinear problems. Much attention is given to the possibility to develop the most widespread stochastic estimators within the deterministic approach which does not involve the ideas of the probability theory. The interrelation of estimators obtained within the considered approaches with various a priori data is analyzed. The methods and algorithms developed for the constant vector are generalized as applied to the estimation of random sequences, Kalman-type algorithms being the most important of them.
The subject matter is explained using methodical examples and navigation data processing problems. They include: estimation of polynomial coefficients, positioning by reference points and satellite data, update of navigation system data using external aids and integrated processing of redundant measurements.
Highlights of the probability theory and theory of matrix calculations are given, along with the description of applied MATLAB software.

Part 2 covers the methods of filtering and smoothing of random processes applied to the navigation data processing. Two main approaches are considered: Kalman approach based on system description in time domain and in state space and Wiener approach using frequency-domain methods and transfer functions. Much attention is given to interrelation and differences between these approaches and interrelation of filtering and smoothing algorithms.
The subject matter is illustrated by the problems of integrated data processing (INS/GNSS data, gravimeter readings and satellite measurements).
Short description of the theories of dynamic systems, stochastic processes, ordinary differential equations, Laplace and Fourier transform are given along with the description of applied MATLAB software.

The book provides the senior students, post-graduates, and scientists with a working knowledge of estimation algorithms applied to navigation data processing and related fields.
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Journal "Giroskopiya i Navigatsiya" website (in Russian)
• based on fiber-optic gyros (FOG)
• based on micromechanical gyros (MMG)
• Shipborne speed and depth meters
• Magnetic compasses
• Communication complex Distancia-E
• Integrated Shipborne Communication and Broadcasting Complex P-409
• Trailing towed array device K-697E
• Equipment for shipborne self-powered telephone communication BTS
• Shipborne automatic digital telephone exchange P-443E
• Floating information assemblies for submarines
• Mobile aeromarine gravimeter Chekan-AM
• Multi-purpose bottomhole remote sensing system UZTS-90
• Micromechanical gyro MMG-2
• Micromechanical gyro MMG-EPTRON
• Multi-channel micro-acceleration measurement system SINUS
• Autonomous attitude control system for low-orbiting spacecrafts