scholarly journals A Novel Coarse Alignment Method for SINS Using Special Orthogonal Group Optimal Estimation

Sensors ◽  
2020 ◽  
Vol 20 (20) ◽  
pp. 5740
Author(s):  
Fujun Pei ◽  
Yang Su ◽  
Desen Zhu ◽  
Shunan Yin
Keyword(s):  
Lie Algebra ◽  
Orthogonal Group ◽  
Inertial Navigation System ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Alignment Method ◽  
Special Orthogonal Group ◽  
Alignment Problem ◽  
Vector Observation ◽  
Definition Of

Aimed at the alignment problem of strapdown inertial navigation system (SINS) on the swing base, a novel coarse alignment method using special orthogonal group optimal estimation is proposed. There are two main contributions in this paper. First, based on the Lie group differential equation, the rotation matrix is updated directly by using error Lie algebra, which avoids the non-convexity of traditional methods and the need for non-collinear vector observation. Second is that a novel optimal estimation method is developed by using the exact error Lie algebra, which is calculated based on the physical definition of Lie algebra, as the innovation term to compensate the initial special orthogonal group in the estimation process. The asymptotic convergence of the proposed optimal estimation method is proved by Lyapunov's second law. The simulation and experimental results demonstrate that the proposed method exhibits better performance than existing methods in alignment accuracy and time, which can achieve the self-alignment of SINS on the swing base.

Coarse alignment of marine strapdown inertial navigation system using the location of fitted parametric circle of gravity movement

2021 ◽  
pp. 1-20
Author(s):  
Hossein Rahimi ◽  
Amir Ali Nikkhah
Keyword(s):  
Navigation System ◽  
Inertial Navigation System ◽  
Reference Frames ◽  
Estimation Method ◽  
Inertial Navigation ◽  
Strapdown Inertial Navigation System ◽  
Direct Extraction ◽  
Trajectory Simulation ◽  
Definition Of ◽  
Strapdown Inertial Navigation

Abstract This paper presents a novel estimation method for coarse alignment of a marine strapdown inertial navigation system (SINS) under mooring conditions. The properties of gravitational motion are used to improve the accuracy of coarse alignment. The parametric motion of gravitational apparent is a circle that is on the surface of a sphere. The location of this parametric circle is dependent on the definition of the reference frames and the initial angles of SINS. In the method proposed here the initial direct cosine matrix is calculated only from the location of the gravity motion parametric circle. The novelty of this paper is to provide a new method for estimating the gravity motion trajectory in inertial frame, as well as direct extraction of the initial direct cosine matrix from this estimated trajectory. Simulation and testing show that the proposed method is suitable for coarse alignment in mooring conditions.

A Study on Neural Learning on Manifold Foliations: The Case of the Lie Group SU(3)

2008 ◽  
Vol 20 (4) ◽  
pp. 1091-1117 ◽  
Author(s):  
Simone Fiori
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Orthogonal Group ◽  
Special Orthogonal Group ◽  
Neural Learning ◽  
Gradient Based ◽  
Special Case

Learning on differential manifolds may involve the optimization of a function of many parameters. In this letter, we deal with Riemannian-gradient-based optimization on a Lie group, namely, the group of unitary unimodular matrices SU(3). In this special case, subalgebras of the associated Lie algebra su(3) may be individuated by computing pair-wise Gell-Mann matrices commutators. Subalgebras generate subgroups of a Lie group, as well as manifold foliation. We show that the Riemannian gradient may be projected over tangent structures to foliation, giving rise to foliation gradients. Exponentiations of foliation gradients may be computed in closed forms, which closely resemble Rodriguez forms for the special orthogonal group SO(3). We thus compare optimization by Riemannian gradient and foliation gradients.

scholarly journals Industrial Plume Properties Retrieved by Optimal Estimation Using Combined Hyperspectral and Sentinel-2 Data

2021 ◽  
Vol 13 (10) ◽  
pp. 1865
Author(s):  
Gabriel Calassou ◽  
Pierre-Yves Foucher ◽  
Jean-François Léon
Keyword(s):  
Matched Filter ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Model Parameters ◽  
Surface Reflectance ◽  
Sequential Method ◽  
Modal Radius ◽  
Sentinel 2

Stack emissions from the industrial sector are a subject of concern for air quality. However, the characterization of the stack emission plume properties from in situ observations remains a challenging task. This paper focuses on the characterization of the aerosol properties of a steel plant stack plume through the use of hyperspectral (HS) airborne remote sensing imagery. We propose a new method, based on the combination of HS airborne acquisition and surface reflectance imagery derived from the Sentinel-2 Multi-Spectral Instrument (MSI). The proposed method detects the plume footprint and estimates the surface reflectance under the plume, the aerosol optical thickness (AOT), and the modal radius of the plume. Hyperspectral surface reflectances are estimated using the coupled non-negative matrix factorization (CNMF) method combining HS and MSI data. The CNMF reduces the error associated with estimating the surface reflectance below the plume, particularly for heterogeneous classes. The AOT and modal radius are retrieved using an optimal estimation method (OEM), based on the forward model and allowing for uncertainties in the observations and in the model parameters. The a priori state vector is provided by a sequential method using the root mean square error (RMSE) metric, which outperforms the previously used cluster tuned matched filter (CTMF). The OEM degrees of freedom are then analysed, in order to refine the mask plume and to enhance the quality of the retrieval. The retrieved mean radii of aerosol particles in the plume is 0.125 μμm, with an uncertainty of 0.05 μμm. These results are close to the ultra-fine mode (modal radius around 0.1 μμm) observed from in situ measurements within metallurgical plant plumes from previous studies. The retrieved AOT values vary between 0.07 (near the source point) and 0.01, with uncertainties of 0.005 for the darkest surfaces and above 0.010 for the brightest surfaces.

An Improved Initial Alignment Method of Strap-Down Inertial Navigation System on a Swaying Base

2013 ◽  
Vol 415 ◽  
pp. 143-148
Author(s):  
Li Hua Zhu ◽  
Xiang Hong Cheng
Keyword(s):  
Navigation System ◽  
Inertial Navigation System ◽  
Alignment Algorithm ◽  
Alignment Method ◽  
Initial Alignment ◽  
Vehicle Simulation ◽  
Robust Property ◽  
Simulation Results ◽  
Lever Arm Effect ◽  
The Impact

The design of an improved alignment method of SINS on a swaying base is presented in this paper. FIR filter is taken to decrease the impact caused by the lever arm effect. And the system also encompasses the online estimation of gyroscopes’ drift with Kalman filter in order to do the compensation, and the inertial freezing alignment algorithm which helps to resolve the attitude matrix with respect to its fast and robust property to provide the mathematical platform for the vehicle. Simulation results show that the proposed method is efficient for the initial alignment of the swaying base navigation system.

Estimation of Failure Probability and its Applications in Reliability Data Analysis

2010 ◽  
Vol 118-120 ◽  
pp. 601-605
Author(s):  
Han Ming
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Bayesian Estimation ◽  
Failure Probability ◽  
Evaluation Method ◽  
Estimation Method ◽  
New Method ◽  
Reliability Parameter ◽  
Hierarchical Bayesian Estimation ◽  
Definition Of

Evaluation method of reliability parameter estimation needs to be improved effectively with the advance of science and technology. This paper develops a new method of parameter estimation, which is named E-Bayesian estimation method. In the case one hyper-parameter, the definition of E-Bayesian estimation of the failure probability is provided, moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation, and the property of E-Bayesian estimation of the failure probability are also provided. Finally, calculation on practical problems shows that the provided method is feasible and easy to perform.

scholarly journals On the limit to resolution and information on basal properties obtainable from surface data on ice streams

2008 ◽  
Vol 2 (2) ◽  
pp. 167-178 ◽  
Author(s):  
G. H. Gudmundsson ◽  
M. Raymond
Keyword(s):  
Flow Line ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Surface Flow ◽  
Ice Thickness ◽  
Ice Streams ◽  
Statistical Estimates ◽  
Surface Data ◽  
Highly Sensitive ◽  
Surface Measurements

Abstract. An optimal estimation method for simultaneously determining both basal slipperiness and basal topography from variations in surface flow velocity and topography along a flow line on ice streams and ice sheets is presented. We use Bayesian inference to update prior statistical estimates for basal topography and slipperiness using surface measurements along a flow line. Our main focus here is on how errors and spacing of surface data affect estimates of basal quantities and on possibly aliasing/mixing between basal slipperiness and basal topography. We find that the effects of spatial variations in basal topography and basal slipperiness on surface data can be accurately separated from each other, and mixing in retrieval does not pose a serious problem. For realistic surface data errors and density, small-amplitude perturbations in basal slipperiness can only be resolved for wavelengths larger than about 50 times the mean ice thickness. Bedrock topography is well resolved down to horizontal scale equal to about one ice thickness. Estimates of basal slipperiness are not significantly improved by accurate prior estimates of basal topography. However, retrieval of basal slipperiness is found to be highly sensitive to unmodelled errors in basal topography.

scholarly journals Isometries of the special orthogonal group

2013 ◽  
Vol 439 (1) ◽  
pp. 174-188 ◽  
Author(s):  
Toshikazu Abe ◽  
Shigeki Akiyama ◽  
Osamu Hatori
Keyword(s):  
Orthogonal Group ◽  
Special Orthogonal Group

scholarly journals First application of the optimal estimation method to retrieve temperature from pure rotational raman scatter lidar measurements

2018 ◽  
Vol 176 ◽  
pp. 01011
Author(s):  
S. Mahagammulla Gamage ◽  
A. Haefele ◽  
R.J. Sica
Keyword(s):  
Estimation Method ◽  
Optimal Estimation ◽  
Forward Model ◽  
Temperature Calibration ◽  
Lidar Measurements ◽  
Raman Scatter ◽  
Calibration Coefficients

We present the application of the Optimal Estimation Method (OEM) to retrieve atmospheric temperatures from pure rotational Raman (PRR) backscatter lidar measurements. A forward model (FM) is developed to retrieve temperature and tested using synthetic measurements. The OEM offers many advantages for this analysis, including eliminating the need to determine temperature calibration coefficients.

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