Related papers: Strapdown Attitude Computation: Functional Iterati…
The defects of the traditional strapdown inertial navigation algorithms become well acknowledged and the corresponding enhanced algorithms have been quite recently proposed trying to mitigate both theoretical and algorithmic defects. In…
Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and…
Inertial-based navigation refers to the navigation methods or systems that have inertial information or sensors as the core part and integrate a spectrum of other kinds of sensors for enhanced performance. Through a series of papers, the…
The acquisition of attitude, velocity, and position is an essential task in the field of inertial navigation, achieved by integrating the measurements from inertial sensors. Recently, the ultra-precision inertial navigation computation has…
Inertial navigation computation is to acquire the attitude, velocity and position information of a moving body by integrating inertial measurements from gyroscopes and accelerometers. Over half a century has witnessed great efforts in…
Attitude computation is of vital importance for a variety of applications. Based on the functional iteration of the Rodrigues vector integration equation, the RodFIter method can be advantageously applied to analytically reconstruct the…
Rigid motion computation or estimation is a cornerstone in numerous fields. Attitude computation can be achieved by integrating the angular velocity measured by gyroscopes, the accuracy of which is crucially important for the dead-reckoning…
The article is devoted to the construction of expansions of iterated Stratonovich stochastic integrals of fifth, sixth, seventh and eighth multiplicities based on the method of generalized multiple Fourier series converging in the sense of…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
RodFIter is a promising method of attitude reconstruction from inertial measurements based on the functional iterative integration of Rodrigues vector. The Rodrigues vector is used to encode the attitude in place of the popular rotation…
The article is devoted to comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential equations in the framework of the method of…
The article is devoted to the expansions of iterated Stratonovich stochastic integrals on the basis of the method of generalized multiple Fourier series that converge in the sense of norm in Hilbert space $L_2([t, T]^k),$ $k\in\mathbb{N}.$…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
The task of strapdown inertial navigation system (SINS) initial alignment is to calculate the attitude transformation matrix from body frame to navigation frame. In this paper, such attitude transformation matrix is divided into two parts…
This paper proposes to use a newly-derived transformed inertial navigation system (INS) mechanization to fuse INS with other complementary navigation systems. Through formulating the attitude, velocity and position as one group state of…
The article is devoted to the development of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in the mean. We adapt this method for iterated…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
The matrix exponential is a fundamental operator in scientific computing and system simulation, with applications ranging from control theory and quantum mechanics to modern generative machine learning. While Pad\'e approximants combined…
For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the…