scholarly journals An Efficient Nonlinear Filter for Spacecraft Attitude Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bing Liu ◽  
Zhen Chen ◽  
Xiangdong Liu ◽  
Fan Yang
Keyword(s):  
Estimation Error ◽  
Attitude Estimation ◽  
Local Error ◽  
Computationally Efficient ◽  
Critical Problem ◽  
Estimation Strategy ◽  
The Matrix ◽  
Constant Coefficients ◽  
Error System ◽  
Normalization Constraint

Increasing the computational efficiency of attitude estimation is a critical problem related to modern spacecraft, especially for those with limited computing resources. In this paper, a computationally efficient nonlinear attitude estimation strategy based on the vector observations is proposed. The Rodrigues parameter is chosen as the local error attitude parameter, to maintain the normalization constraint for the quaternion in the global estimator. The proposed attitude estimator is performed in four stages. First, the local attitude estimation error system is described by a polytopic linear model. Then the local error attitude estimator is designed with constant coefficients based on the robustH2filtering algorithm. Subsequently, the attitude predictions and the local error attitude estimations are calculated by a gyro based model and the local error attitude estimator. Finally, the attitude estimations are updated by the predicted attitude with the local error attitude estimations. Since the local error attitude estimator is with constant coefficients, it does not need to calculate the matrix inversion for the filter gain matrix or update the Jacobian matrixes online to obtain the local error attitude estimations. As a result, the computational complexity of the proposed attitude estimator reduces significantly. Simulation results demonstrate the efficiency of the proposed attitude estimation strategy.

scholarly journals Partial Component Consensus of Discrete-Time Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Wenjun Hu ◽  
Gang Zhang ◽  
Zhongjun Ma ◽  
Binbin Wu
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
Matrix Theory ◽  
Pinning Control ◽  
Directed Network ◽  
Strong Function ◽  
Partial Stability ◽  
Partial Component ◽  
The Matrix ◽  
Error System

The multiagent system has the advantages of simple structure, strong function, and cost saving, which has received wide attention from different fields. Consensus is the most basic problem in multiagent systems. In this paper, firstly, the problem of partial component consensus in the first-order linear discrete-time multiagent systems with the directed network topology is discussed. Via designing an appropriate pinning control protocol, the corresponding error system is analyzed by using the matrix theory and the partial stability theory. Secondly, a sufficient condition is given to realize partial component consensus in multiagent systems. Finally, the numerical simulations are given to illustrate the theoretical results.

scholarly journals Evaluation of Matrix Square Root Operations for UKF within a UAV GPS/INS Sensor Fusion Application

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Matthew Rhudy ◽  
Yu Gu ◽  
Jason Gross ◽  
Marcello R. Napolitano
Keyword(s):  
Sensor Fusion ◽  
Unscented Kalman Filter ◽  
Attitude Estimation ◽  
Square Root ◽  
Fusion Algorithm ◽  
Matrix Square Root ◽  
Global Positioning ◽  
The Matrix ◽  
Aerial Vehicle ◽  
Diagonalization Method

Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.

DESIGN OF STATE ESTIMATOR FOR SWITCHED HOPFIELD NEURAL NETWORKS WITH TIME-DELAY

2011 ◽  
Vol 20 (04) ◽  
pp. 657-666
Author(s):  
CHOON KI AHN
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Estimation Error ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
State Estimator ◽  
Error System ◽  
Delay Dependent ◽  
Dependent State

In this paper, the delay-dependent state estimation problem for switched Hopfield neural networks with time-delay is investigated. Based on the Lyapunov–Krasovskii stability theory, a new delay-dependent state estimator for switched Hopfield neural networks is established to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The gain matrix of the proposed estimator is characterized in terms of the solution to a linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

The algebra of differential forms on a full matric bialgebra

1993 ◽  
Vol 114 (1) ◽  
pp. 111-130 ◽  
Author(s):  
A. Sudbery
Keyword(s):  
Vector Space ◽  
Commutative Algebra ◽  
Differential Algebra ◽  
Differential Forms ◽  
Sufficient Conditions ◽  
Classical Case ◽  
Algebra Of Functions ◽  
The Matrix ◽  
Constant Coefficients ◽  
Necessary And Sufficient

AbstractWe construct a non-commutative analogue of the algebra of differential forms on the space of endomorphisms of a vector space, given a non-commutative algebra of functions and differential forms on the vector space. The construction yields a differential bialgebra which is a skew product of an algebra of functions and an algebra of differential forms with constant coefficients. We give necessary and sufficient conditions for such an algebra to exist, show that it is uniquely determined by the differential algebra on the vector space, and show that it is a non-commutative superpolynomial algebra in the matrix elements and their differentials (i.e. that it has the same dimensions of homogeneous components as in the classical case).

Stationary waiting-time distributions in the GI/PH/1 queue

1981 ◽  
Vol 18 (4) ◽  
pp. 901-912 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Waiting Time ◽  
Embedded Markov Chain ◽  
Asymptotic Results ◽  
Waiting Time Distributions ◽  
Structured Systems ◽  
Queue Discipline ◽  
The Matrix ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Stationary Waiting Time

It is known that the stable GI/PH/1 queue has an embedded Markov chain whose invariant probability vector is matrix-geometric with a rate matrix R. In terms of the matrix R, the stationary waiting-time distributions at arrivals, at an arbitrary time point and until the customer's departure may be evaluated by solving finite, highly structured systems of linear differential equations with constant coefficients. Asymptotic results, useful in truncating the computations, are also obtained. The queue discipline is first-come, first-served.

scholarly journals On a New Formula for Fibonacci’s Family m-step Numbers and Some Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 805 ◽  
Author(s):  
Monther Rashed Alfuraidan ◽  
Ibrahim Nabeel Joudah
Keyword(s):  
Number Theory ◽  
Time Complexity ◽  
Matrix Multiplication ◽  
Square Roots ◽  
Computational Number Theory ◽  
The Matrix ◽  
Theory Application ◽  
Constant Coefficients ◽  
New Formula

In this work, we obtain a new formula for Fibonacci’s family m-step sequences. We use our formula to find the nth term with less time complexity than the matrix multiplication method. Then, we extend our results for all linear homogeneous recurrence m-step relations with constant coefficients by using the last few terms of its corresponding Fibonacci’s family m-step sequence. As a computational number theory application, we develop a method to estimate the square roots.

Kirchhoff image propagation

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 126-134 ◽  
Author(s):  
Frank Adler
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Computation Time ◽  
Velocity Model ◽  
Image Point ◽  
Computationally Efficient ◽  
Initial Image ◽  
Migration Velocity Analysis ◽  
The Matrix ◽  
First Order Approximation

Seismic imaging processes are, in general, formulated under the assumption of a correct macrovelocity model. However, seismic subsurface images are very sensitive to the accuracy of the macrovelocity model. This paper investigates how the output of Kirchhoff inversion/migration changes for perturbations of a given 3‐D laterally inhomogeneous macrovelocity model. The displacement of a reflector image point from a perturbation of the given velocity model is determined in a first‐order approximation by the corresponding traveltime and slowness perturbations as well as the matrix. of the Beylkin determinant. The required traveltime derivatives can be calculated with ray perturbation theory. Using this result, a new, computationally efficient Kirchhoff inversion/migration technique is developed to predict in parallel a series of subsurface images for perturbations of a given macrovelocity model during a single inversion/migration process applied to the unmigrated seismic data. These images are constructed by superposition of the seismic data at predicted image point locations which lie on surfaces that expand from the initial image point as a function of the velocity perturbation. Because of the analogy to Huygens wavefronts in wave propagation, the technique is called Kirchhoff image propagation. A 2‐D implementation of Kirchhoff image propagation requires about 1.2 times the computation time of a single migration to calculate a set of propagated images. The propagated images provide good approximations to remigrated images and are applied to migration velocity analysis.

On a Numerical Method for Solution of the Mathieu-Hill Type Equations

1980 ◽  
Vol 102 (3) ◽  
pp. 619-626 ◽  
Author(s):  
A. Midha ◽  
M. L. Badlani
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Initial Conditions ◽  
Linear Equations ◽  
Solution Process ◽  
Constraint Equations ◽  
Step Functions ◽  
The Matrix ◽  
Constant Coefficients ◽  
Simultaneous Linear Equations

This paper presents a computer-programmable numerical method for the solution of a class of linear, second order differential equations with periodic coefficients of the Mathieu-Hill type. The method is applicable only when the initial conditions are prescribed and the solution is not requiried to be periodic. The solution is facilitated by representing the coefficient functions as a sum of step functions over corresponding sub-intervals of the fundamental interval. During each sub-interval, the solution form is assumed to be that of the differential equations with “constant” coefficients. Constraint equations are derived from imposing the conditions of “compatibility” of response at the end nodes of the intermediate sub-intervals. This set of simultaneous linear equations is expressed in matrix form. The matrix of coefficients may be represented as a triangular one. This form greatly simplifies the solution process for simultaneous equations. The method is illustrated by its application to some specific problems.

scholarly journals Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

2016 ◽  
Vol 14 (1) ◽  
pp. 934-945
Author(s):  
Cenker Biçer ◽  
Levent Özbek ◽  
Hasan Erbay
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Stochastic Systems ◽  
Estimation Error ◽  
The State ◽  
Forgetting Factor ◽  
The Matrix ◽  
Stochastic Framework ◽  
Theoretical Results

AbstractIn this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.

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