Assessment of Aided-INS Performance

2011 ◽  
Vol 65 (1) ◽  
pp. 169-185 ◽  
Author(s):  
Itzik Klein ◽  
Sagi Filin ◽  
Tomer Toledo ◽  
Ilan Rusnak
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Navigation Systems ◽  
Inertial Navigation Systems ◽  
Closed Form Solutions ◽  
Land Vehicles ◽  
Error Covariance ◽  
Model Dependency ◽  
Error State ◽  
Insight Into

Aided Inertial Navigation Systems (INS) systems are commonly implemented in land vehicles for a variety of applications. Several methods have been reported in the literature for evaluating aided INS performance. Yet, the INS error-state-model dependency on time and trajectory implies that no closed-form solutions exist for such evaluation. In this paper, we derive analytical solutions to evaluate the fusion performance. We show that the derived analytical solutions manage to predict the error covariance behavior of the full aided INS error model. These solutions bring insight into the effect of the various parameters involved in the fusion of the INS and an aiding sensor.

Analysis of transient amplification for a torsional system passing through resonance

2014 ◽  
Vol 229 (13) ◽  
pp. 2341-2354 ◽  
Author(s):  
Laihang Li ◽  
Rajendra Singh
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Classical Problem ◽  
Peak Frequency ◽  
Empirical Formulas ◽  
Closed Form Solutions ◽  
Analytical Approximations ◽  
Numerical Predictions ◽  
Prior Literature ◽  
Run Up

The classical problem of vibration amplification of a linear torsional oscillator excited by an instantaneous sinusoidal torque is re-examined with focus on the development of new analytical solutions of the transient envelopes. First, a new analytical method in the instantaneous frequency (or speed) domain is proposed to directly find the closed-form solutions of transient displacement, velocity, and acceleration envelopes for passage through resonance during the run-up or run-down process. The proposed closed-form solutions are then successfully verified by comparing them with numerical predictions and limited analytical solutions as available in prior literature. Second, improved analytical approximations of maximum amplification and corresponding peak frequency are found, which are also verified by comparing them with prior analytical or empirical formulas. In addition, applicability of the proposed analytical solution is clarified, and their error bounds are identified. Finally, the utility of analytical solutions and approximations is demonstrated by application to the start-up process of a multi-degree-of-freedom vehicle driveline system.

Analytical and Graphical Solutions to the Forward Position Problem of Two Robots Manipulating a Spatial Linkage Payload

1997 ◽  
Vol 119 (3) ◽  
pp. 349-358
Author(s):  
G. R. Pennock ◽  
K. G. Mattson
Keyword(s):  
Closed Form ◽  
Orthogonal Transformation ◽  
Solution Technique ◽  
Closed Form Solutions ◽  
Transformation Matrices ◽  
Kinematic Geometry ◽  
Order Polynomial ◽  
Position Problem ◽  
Four Bar Linkage ◽  
Insight Into

This paper presents a solution to the forward position problem of two PUMA-type robots manipulating a spatial four-bar linkage payload. To simplify the kinematic analysis, the Bennett linkage, which is a special geometry spatial four-bar, will be regarded as the payload. The orientation of a specified payload link is described by a sixth-order polynomial and a specified joint displacement in the wrist subassembly of one of the robots is described by a second-order polynomial. A solution technique, based on orthogonal transformation matrices with dual number elements, is used to obtain closed-form solutions for the remaining unknown joint displacements in the wrist subassembly of each robot. An important result is that, for a given set of robot input angles, twenty-four assembly configurations of the robot-payload system are possible. Repeated roots of the polynomials are shown to correspond to the stationary configurations of the system. The paper emphasizes that an understanding of the kinematic geometry of the system is essential to verify the number of possible solutions to the forward position problem. Graphical methods are also presented to provide insight into the assembly and stationary configurations. A numerical example of the two robots manipulating the Bennett linkage is included to demonstrate the importance of the polynomial and closed-form solutions.

Attitude Estimation By Divided Difference Filter-Based Sensor Fusion

2006 ◽  
Vol 60 (1) ◽  
pp. 119-128 ◽  
Author(s):  
Setoodeh Peyman ◽  
Khayatian Alireza ◽  
Farjah Ebrahim
Keyword(s):  
Nonlinear Filtering ◽  
Divided Difference ◽  
Sampling Period ◽  
Navigation Systems ◽  
Inertial Navigation Systems ◽  
Fusion Algorithm ◽  
State Estimate ◽  
Error Covariance ◽  
Difference Filter ◽  
Divided Difference Filter

Strapdown inertial navigation systems (INS) often employ aiding sensors to increase accuracy. Nonlinear filtering algorithms are then needed to fuse the collected data from these aiding sensors with measurements of strapdown rate gyros. Aiding sensors usually have slower dynamics compared to gyros and therefore collect data at lower rates. Thus the system will be unobservable between aiding sensors' sampling instants, and the error covariance, which shows the uncertainty in the estimation, grows during the sampling period. This paper presents a divided difference filter (DDF)-based data fusion algorithm, which utilizes the complementary noise profile of rate gyros and gravimetric inclinometers to extend their limits and achieve more accurate attitude estimates. It is confirmed experimentally that DDF achieves better covariance estimates compared to the extended Kalman filter (EKF) because the uncertainty in the state estimate is taken care of in the DDF polynomial approximation formulation.

scholarly journals Analytical Solutions for Flow of a Dusty Fluid Between Two Porous Flat Plates

1994 ◽  
Vol 116 (2) ◽  
pp. 354-356 ◽  
Author(s):  
Ali J. Chamkha
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Skin Friction ◽  
Analytical Solutions ◽  
Velocity Profiles ◽  
Flat Plates ◽  
Friction Coefficients ◽  
Dusty Fluid ◽  
Closed Form Solutions

Equations governing flow of a dusty fluid between two porous flat plates with suction and injection are developed and closed-form solutions for the velocity profiles, displacement thicknesses, and skin friction coefficients for both phases are obtained. Graphical results of the exact solutions are presented and discussed.

scholarly journals A novel-iterative simulation method for performance analysis of non-coherent FSK/ASK systems over Rice/Rayleigh channels using the wolfram language

2016 ◽  
Vol 13 (2) ◽  
pp. 157-174 ◽  
Author(s):  
Vladimir Mladenovic ◽  
Danijela Milosevic
Keyword(s):  
Closed Form ◽  
Communication Systems ◽  
Rayleigh Fading ◽  
Simulation Method ◽  
Rician Fading ◽  
New Approach ◽  
Closed Form Solutions ◽  
Numerical Tools ◽  
The Impact ◽  
Insight Into

In this paper, a new approach in solving and analysing the performances of the digital telecommunication non-coherent FSK/ASK system in the presence of noise is derived, by using a computer algebra system. So far, most previous solutions cannot be obtained in closed form, which can be a problem for detailed analysis of complex communication systems. In this case, there is no insight into the influence of certain parameters on the performance of the system. The analysis, modelling and design can be time-consuming. One of the main reasons is that these solutions are obtained by utilising traditional numerical tools in the shape of closed-form expressions. Our results were obtained in closed-form solutions. They are resolved by the introduction of an iteration-based simulation method. The Wolfram language is used for describing applied symbolic tools, and SchematicSolver application package has been used for designing. In a new way, the probability density function and the impact of the newly introduced parameter of iteration are performed when errors are calculated. Analyses of the new method are applied to several scenarios: without fading, in the presence of Rayleigh fading, Rician fading, and in cases when the signals are correlated and uncorrelated.

scholarly journals Closed-form quaternion representations for rigid body rotation: application to error assessment in orientation algorithms of strapdown inertial navigation systems

2020 ◽  
Author(s):  
Yuriy Plaksiy ◽  
Dmitriy Breslavsky ◽  
Irina Homozkova ◽  
Konstantin Naumenko
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Closed Form ◽  
Inertial Navigation ◽  
Navigation Systems ◽  
Body Rotation ◽  
Inertial Navigation Systems ◽  
Rigid Body Rotation ◽  
Reference Models ◽  
Strapdown Inertial Navigation

AbstractClosed-form analytical representations of the rigid body orientation quaternion, angular velocity vector and the external moment vector satisfying kinematic equations and equations of motion are derived. In order to analyze errors of orientation algorithms for strapdown inertial navigation systems, reference models for specific rigid body rotation cases are formulated. Based on solutions, analytical expressions for ideal signals of angular velocity sensors in the form of quasi-coordinates are derived. For several sets of parameters, numerical implementations of the reference models are performed and trajectories in the configuration space of orientation parameters are presented. Numerical analysis of the drift error for the third-order orientation algorithm is performed. The results show that the value of the accumulated drift error using the derived two-frequency models exceeds the value of the accumulated drift error in the conventional case of a regular precession.

The Forward Position Problem of Two Puma-Type Robots Manipulating a Bennett Linkage Payload

1996 ◽  
Author(s):  
Gordon R. Pennock ◽  
Keith G. Mattson
Keyword(s):  
Closed Form ◽  
Orthogonal Transformation ◽  
Solution Technique ◽  
Closed Form Solutions ◽  
Transformation Matrices ◽  
Kinematic Geometry ◽  
Order Polynomial ◽  
Position Solution ◽  
Position Problem ◽  
Insight Into

Abstract This paper presents a solution to the forward position problem of two PUMA-type robots manipulating a Bennett linkage payload. The orientation of a specified payload link is described by a sixth-order polynomial and a specified angular joint displacement in the wrist subassembly of one of the robots is described by a second-order polynomial. A solution technique, based on orthogonal transformation matrices with dual number elements, is used to obtain closed-form solutions for the remaining unknown angular joint displacements in the wrist subassembly of each robot. The paper shows that, for a given set of robot input angles, twenty-four assembly configurations of the robot-payload system are possible. The polynomials provide insight into these configurations, and also reveal stationary configurations of the system. The paper emphasizes that insight into the kinematic geometry of the system is essential in developing the forward position solution. Graphical methods are presented which provide insight into the geometry, and a check of the analytical approach. For illustrative purposes, a numerical example of the two robots manipulating a Bennett linkage is included in this paper to demonstrate the importance of the polynomials and the closed-form solutions.

Generalized Reference Basis Model Updating in Structural Dynamics

1997 ◽  
Author(s):  
Rachel Kenigsbuch ◽  
Yoram Halevi
Keyword(s):  
Experimental Data ◽  
Closed Form ◽  
Prior Knowledge ◽  
Structural Dynamics ◽  
Optimization Problem ◽  
Model Updating ◽  
Optimization Criterion ◽  
Constrained Optimization Problem ◽  
Closed Form Solutions ◽  
Insight Into

Abstract The paper considers the problem of updating an analytical model from experimental data. The approach that is taken is the reference basis, where some of the parameters are considered to be completely accurate while the others are updated by solving a constrained optimization problem. The main results of this paper are closed form solutions to these problems with general weighting matrices in the optimization criterion. These are generalizations of several model reference updating problems that were solved and reported in the literature. The importance of this generalization is the ability to incorporate prior knowledge regarding the accuracy of the model in specified areas into the method. Another aspect of this work is the investigation of geometrical interpretation of the results which provides insight into the mechanism of the updating process. The advantages of the new updating schemes are demonstrated by means of examples.

scholarly journals Analytical and Semi-Analytical Solutions for the Self and Mutual Inductances of Concentric Coplanar Ordinary and Bitter Disk Coils

2021 ◽  
Author(s):  
Slobodan Babic
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Simple Form ◽  
Elliptic Integral ◽  
Mutual Inductance ◽  
The Self ◽  
Computational Time ◽  
Closed Form Solutions

In this paper, closed and semi-closed form solutions are presented for the self - and mutual inductance of ordinary and Better disk coils which lie concentrically in a plane. The solutions are given as the combination of the elliptic integral of the first kind and a simple integral or only as the second elliptic integral of the second kind. All formulas or obtained in remarkably simple form and give extremely accurate results with significantly neglectable computational time. All cases either regular or singular (disks in contact or overlap) are covered. The formulas for the mutual inductances can be directly used to calculating the self-inductance of the ordinary disk coil or the Bitter disk coil, respectively. Many presented examples show the excellent numerical agreement with previous publish methods.

The Lure of the Mean Axes

2006 ◽  
Vol 74 (3) ◽  
pp. 497-504 ◽  
Author(s):  
Leonard Meirovitch ◽  
Ilhan Tuzcu
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Space Structures ◽  
Aerodynamic Forces ◽  
State Equations ◽  
Flexible Bodies ◽  
Closed Form Solutions ◽  
The Mean

A variety of aerospace structures, such as missiles, spacecraft, aircraft, and helicopters, can be modeled as unrestrained flexible bodies. The state equations of motion of such systems tend to be quite involved. Because some of these formulations were carried out decades ago when computers were inadequate, the emphasis was on analytical solutions. This, in turn, prompted some investigators to simplify the formulations beyond all reasons, a practice continuing to this date. In particular, the concept of mean axes has often been used without regard to the negative implications. The allure of the mean axes lies in the fact that in some cases they can help decouple the system inertially. Whereas in the case of some space structures this may mean complete decoupling, in the case of missiles, aircraft, and helicopters the systems remain coupled through the aerodynamic forces. In fact, in the latter case the use of mean axes only complicates matters. With the development of powerful computers and software capable of producing numerical solutions to very complex problems, such as MATLAB and MATHEMATICA, there is no compelling reason to insist on closed-form solutions, particularly when undue simplifications can lead to erroneous results.

Sign in / Sign up

Export Citation Format

Share Document