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Theory of estimation and navigation

Important results in the theory of inertial navigation, obtained at DAMC, found direct application in the industry of navigating systems.

A transparent interpretation of an inertial navigating system (INS) as material point (the effective sensitive mass of an accelereometer) under gravitation and a measured external forces was suggested (E.A.Devjanin, N.A.Parusnikov), and the concepts of model, instrument and ideal trihedrons were introduced.

The general equations of inertial navigation imbedding all the known special cases were derived. This allowed to understand the properties of such systems and to point out new possible schemes. Mathematical equivalence of the equations of a non-disturbed gyro-pendulum navigating systems and systems of inertial navigation was established. This result allowed to unite independent directions of research into a uniform theory of such systems (E.A.Devjanin).

The instability of three-componental INS over a wide range of velocities was proven and an estimate of the degree of this instability was obtained using the Lyapunov functions (E.A.Devjanin, N.A.Parusnikov).

A theory of INS using the Hamiltonian mechanics formalism was suggested. This allowed to use the energy considerations to calculate the achievable borders of tubes, limiting trajectories of relative movement of the proof mass model (N.A.Parusnikov).

A general theory of navigating systems containing accelerometers as sensitive elements only for the case motion in a central gravitational filed was introduced. The equations defining a vertical, the distance to the gravity center and the angular velocity of the body were obtained and solved (E.A.Devjanin).

Using the observability theory, algorithms of alignment of INS on a motionless or mobile base were constructed, and the role of maneuver in the case of a mobile base was specified (N.A.Parusnikov).

Modern navigating systems, as a rule, include a number of navigating devices operating on different physical principles. Thus a basic role is in the diverse data processing, allowing to provide an accuracy essentially surpassing that of each separate device.

The information approach was used to construct a theory of corrected navigating systems using such concepts as observability, reduction, regularization, conditioning (N.A.Parusnikov). The INS observability was analyzed for the basic kinds of aiding information, such as position, velocity, bearings (N.A.Parusnikov, V.M.Morozov, V.I.Kalenova, A.G.Shakotko). The problem of INS correction in height depending on velocity (N.A.Parusnikov) was solved.

Within the offered formalization of aided navigation equivalence of the control and estimation approaches was shown. Algorithms resolving one kind of correction to another were constructed. The additional feedback was shown to be unable to deliver better results than pure estimation (N.A.Parusnikov).

Methods of state space identification of linear dynamic systems as "grey boxes", i.e. with partial information on parameters of a system were offered. The developed identification algorithms were used in a number of applied problems (L.J.Blazhenova-Miculich).

A number of studies in the specified direction is connected with topographic positioning. This problem differs to navigation in that postprocessing is allowed. Suboptimum topographic positioning algorithms (in various modifications) of helicopters, ground transport, meteorological trassers, defectoscopes in gas and oil pipelines were investigated. In particular, processing of data of an INS located on a car moving with periodic stops has shown possible to raise accuracy in comparison with the INS accuracy by three orders (A.A.Golovan, A.Ju.Goritsky, N.B.Vavilov, N.A.Parusnikov, V.V.Tikhomirov).

Since 1995 DAMC and the Laboratory of control and navigation works on data processing for airborne gravimetry directed by N.A.Parusnikov. The ultimate goal is to construct gravitaty field maps for investigation of minerals. Comprehensible accuracy of airborne gravimetry is of the order of one milligal, i.e. 10^{-6} g.

Joint studies of the Moscow State University, MIEA, Institute of physics of the Earth of the Russian Academy of Science, "Aero geophysics" and "Gravimetric technologies" companies has allowed to create airborne gravimetry systems consisting of an INS with a leveled platform, a block of accelerometers and a set of GPS receivers.

Difficulty of processing of airborne gravity data lies in that is an ill-conditioned inverse problem of mechanics (determining forces by motion) when the pay signal is exceeded by the noise by many orders. DAMC and the laboratory developed a unique gravimetry data processing system "Gravia". The leading roles here was played by Yu.V.Bolotin and A.A.Golovan. At different stages this research involved V.V.Tikhomirov, N.B.Vavilova, S.A.Trubnikov, P.A.Kruchinin, M.Yu.Popelensky. This system was used in data processing with three types of airborne gravimeters in different areas: the Vologda region, the Ladoga lake, the Kaluga region, Moravia (Czech Republic), desert Victoria (Australia), the Arkhangelsk area, gulf of Ob. The accuracy of obtained gravity maps was one of the best in the world. Of course, a significant part in that was due to high quality of Russia made gravimeters, especially the gravimeter MAG-1 (GT1A) developed by the company "Gravimetric Technologies", with which DAMC and the laboratory closely cooperate.

The opportunities provided by aiding airborne gravimetry with gravity gradiometers (N.B.Vavilova, I.A.Papusha) were investigated. A great role in gravimetry and topographic positioning is played by GPS data processing. One of the problems here is the cycle slips caused by the phase lock loss by a receiver. A new approach to GPS data processing has allowed to improve accuracy of velocity and accelerations determination (A.A.Golovan, N.B.Vavilova).

Opportunities of the minimal modules method as means to deal with failures were investigated for various problems of navigation and airborne gravimetry (N.A.Parusnikov, A.Ju.Nevidomsky).

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