A Suboptimal Estimation and Parameters Identification Algorithm for Aircraft or Other Vehicle Navigation Systems Using the Earth's Magnetic Field Information

Аuthors

Kolosovskaya T. P.

e-mail: mai703@front.ru

Abstract

The purpose of this paper is to present the solutions of the problem of nonlinear filtering algorithms synthesis and analysis for magnetic field navigation systems (NS) of an aircraft or the like for military and civil applications.

A three axis orientation magnetometer mounted on an aircraft or the like is used for sensing the earth’s magnetic field and for forming the nonlinear measurement vector with the measurement noise vector taking into account the declination maps.

The solutions of the problem of algorithms synthesis and analysis for magnetic field information signal processing were obtained by using the suboptimal extended Kalman filter (EKF) which allows to estimate the magnetic course of an aircraft, the inclination angle ( the angle a vector representing the total magnetic field makes with its trace on a horizontal plane), the module of the magnetic-field strength vector and the Poisson’s coefficients, indicating the constant and the inductive magnetization.

Computer simulation results of the adaptive filtering schemes reflect the behavior of the state vector estimates, the estimates errors, the covariance matrix, and the a posteriori hypothesis probability density with comparison for different conditions with different initial values and different Gaussian white noises vectors of the system state and of the measurements with corresponding variances, for imitation of environmental influences on the system.

The estimated magnetic course can serve as necessary information for the true course computing on board of NS, in the radar silence and radio silence modes, during a flight above surface areas with uninformative relief such as deserts and oceans, and as a method of accumulating errors correction for inertial navigation systems.

The proposed algorithms and system of course determination provide high efficiency and estimation accuracy comparing with other existing navigation algorithms and permit to abandon the performing of laborious and expensive magnetic deviation work inherent for traditional algorithms.

Many scientific researches have been performed in the class of adaptive filtering scheme of the state vector estimation together with parameter identification. The purpose of this paper is to propose new approach of the extension of EFK adaptive estimation in the classical stochastic dynamic systems with deterministic structure to the case of signal processing and parameter identification in stochastic magnetic NS using the theory of Markov processes and optimization of stochastic systems with random structure or with switching parameters.

Keywords:

extended Kalman filter, identification, navigation system, magnetic fields, Markov processes, optimization of stochastic systems with random structure

References

1. Mikhlin B.Z., Seleznev V.P., Seleznev A.V. Geomagnitnaya navigatsiya (Geomagnetic Navigation), Moscow, Mashinostroenie, 1976, 280 p.

2. Semenov N.M., Yakovlev N.I. Tsifrovye ferrozondovye magnitometry (Digital Ferroprobing Magnetometers), Leningrad, Energiya, 1978, 168 p.

3. Seidzh E.P., Melsa Dzh.L. Teoriya otsenivaniya i ee primenenie v svyazi i upravlenii (The Estimation Theory and its Application in Communication and Control), Moscow, Svyaz’, 1986, 495 p.

4. Kolosovskaya T.P. Obrabotka signalov magnitnykh polei v navigatsionnykh sistemakh (Magnetic Field Signal Processing in Navigation Systems), Moscow, VINITI RAN, no. 19, V2015, 9 p.

5. Slesarenok S.V., Shepet’ I.P., Rubinov V.I., Titov Yu.P. Trudy MAI, 2016, no. 86: http://www.mai.ru/science/trudy/published.php?ID=66381

6. Andreas R.D., Hostetler L.D., Beckman R.C. Continuous Kalman Updating of an Inertial Navigation System Using Terrain Measurements. — NAECON’78, vol. 3.

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