The paper addresses the systematic error of an inertial navigation system, caused by the discrepancy between the plumb line and the normal to the reference ellipsoid surface. The methods of this discrepancy estimation, and their use for correcting the output data of inertial navigation systems are studied.

Strapdown Attitude Computation: Functional Iterative Integration versus Taylor Series Expansion There are two basic approaches to strapdown attitude computation, namely, the traditional Taylor series expansion approach and the Picard iterative method. The latter was recently implemented in a recursive form basing on the Chebyshev polynomial approximation and resulted in the so-called functional iterative integration approach. Up to now a detailed comparison of these two approaches with arbitrary number of gyroscope samples has been lacking for the reason that the first one is based on the simplified rotation vector equation while the second one uses the exact form. In this paper, the mainstream algorithms are considerably extended by the Taylor series expansion approach using the exact differential equation and recursive calculation of high-order derivatives, and the functional iterative integration approach is re-implemented on the normal polynomial. This paper applies the two approaches to solve the strapdown attitude problem, using the attitude parameter of quaternion as a demonstration. Numerical results under the classical coning motion are reported to assess all derived attitude algorithms. It is revealed that in the low and middle relative conic frequency range all algorithms have the same order of accuracy, but in the range of high relative frequency the algorithm by the functional iterative integration approach performs the best in both accuracy and robustness if the Chebyshev polynomials and a larger number of gyroscope samples are to be used. The main conclusion applies to other attitude parameters as well.

The article presents the results of an analytical study of errors of various algorithms for scalar calibration of triaxial meters of a vector physical quantity. Practical recommendations are given for implementation of the calibration algorithm. The results are confirmed by numerical modeling.

The formulas are obtained for estimating the «random walk» type noise of algorithmic compensation for the gyro bias. An example of estimating the statistical significance of the factors influencing the bias when calibrating a fiber-optic gyroscope in the operating temperature range and at different rates of their change is given. It is shown that the random error of temperature sensors can play a major role in the “random walk” noise of the algorithmic compensation for the gyro bias and exceed the gyro self noise. An example of obtaining a regression dependence of algorithmic compensation for gyro bias using a neural network with a multilayer perceptron is given. The factors influencing the choice of the time constant of the differentiating low-frequency temperature filter are considered. Experimental dependences of the random error of the bias algorithmic compensation on the value of the random error of temperature sensors are presented and the necessity of using temperature sensors with a minimum random error is shown.

Frequency response of a laser gyroscope was studies by numerical modelling of a complete system of equations describing it. The calculation results are compared to the results of experimental measurements taken on a precision dynamic test bench. The frequency response was measured for a gyroscope based on a four-mirror ring laser with a non-planar contour, operating on He-Ne active mix at the wavelength of 632.8 nm. In the gyroscope under study, the sign-variable dither was implemented on the basis of Zeeman magnetooptical effect. The relationship between the measured and designed values of the frequency response distortions has been found. The relationship between the frequency response distortions in a laser gyroscope and inequality of field intensities of the counterpropagating waves (CPW) has been numerically calculated and confirmed by experiments. Based on the research results, the parameters of a ring laser can be optimized to improve the accuracy of measurements by means of laser gyroscopes.

The article presents two methods of modeling discrete heights of a quasigeoid on a local area of the earth’s surface using a gen-eralized Fourier series. The first method is based on modeling the characteristics of the earth’s gravitational field on a plane and involves the use of a two-dimensional Fourier transform by an orthonormal system of trigonometric functions. The second method consists in the expansion of the quasigeoid heights in a Fourier series by an orthonormal system of spherical functions on a local area of the earth’s surface. The errors of approxima-tion of the obtained discrete values of the quasigeoid heights on the local territory are analyzed. It is shown that with the modern computing technology, the most accurate and technologically simple way to model the quasigeoid heights on local areas is to expand them into a Fourier series by an orthonormal system of spherical functions.

The paper describes the relevance and advantages of the geophysical support for autonomous magnetometric navigation systems (MNS). Theoretical data on the Earth’s magnetic field components are considered, and the displacement of magnetic poles in international models of the Earth’s main magnetic field is analyzed. The prospects for mapping and software support of MNS are discussed. The results obtained in the flight studies of the experimental MNS are used in the development and control of MNS databases, centralization and application of digital mapping products for geological exploration, as well as in the course of various studies concerned with earth sciences.

The article presents an algorithm for controlling the motion of an insufficiently controlled ship along a trajectory with a continuous bounded curvature, based on the feedback linearization method. The algorithm allows restricting the control signal, while the state vector of the ship motion model does not approach the singularity point of the control law. The control algorithm returns the ship to the specified trajectory-attractor at any lateral deviation of the ship from the specified trajectory.