ELDORA TPARC/TCS08 Dataset

Size: px
Start display at page:

Download "ELDORA TPARC/TCS08 Dataset"

Transcription

1 ELDORA TPARC/TCS08 Dataset Wen-Chau Lee and Michael M. Bell NCAR NCAR/NPS

2 NRL-P3 ELectra DOppler RAdar 3. cm, 1.8 beam, 38.7 db Gain Antennas & Tx 40 kw Peak Power PRF in 4:5 ratio (6 m/s NV in TPARC) Scan rate up to 144 /s (87 /s in TPARC) Complex chirp w/4 (3 in TPARC) Freq. ~500 m along track resolution in TPARC Unambig. Range ~75 km (Convective) TOGA COARE (93),VORTEX 95, FASTEX (97), LAKEICE (97/98), MAP (99), IHOP (0), CRYSTAL- FACE (0), BAMEX (03), RAINEX (05), TCS- 08/TPARC (08) ELDORA Airborne Doppler Radar

3 ELDORA Data Fields

4 CAPPI Movies Bonus Dataset

5 Dataset Summary Velocity data appears very good throughout project INS Navigation corrections were stable Aft Reflectivity is low from RF16 RF1, reduced sensitivity in cloudy & clear air 165 GB dataset ready, on CODIAC soon Dorade sweep files in ~00 MB 10-minute tar files (netcdf translator available) Navigation correction factors (cfac files)

6

7 Problems in Raw Data 1. Earth surface is tilted.. Earth surface is not stationary. 3. Earth surface moves at different speeds. Testud et al 1995

8 ELDORA Navigation Corrections Accurate knowledge of the aircraft orientation and radar beam pointing angle is essential to airborne Doppler analysis Lee et al, 1994; Testud et al, 1995; Georgis et al, 000; Bosart et al, 00

9 Definitions of INS Attitude Angles Meteorological coordinates-positive clockwise Drift is the angle between track and heading (T=HD), a positive drift angle is defined as the track is more clockwise than the heading Pitch is the angle that the aircraft longitudinal axis makes with the horizontal plane, nose up is positive pitch Roll is the angle that the wings make with the horizontal plane, right wing down is positive Through these three sequential rotation, X is transformed into X a

10 Uncertainties in INS and Antenna Pointing Angles Measurement/Instrument Errors: Horizontal velocity (V H ): ± m s -1 Drift angle (α): ± 1 Aircraft vertical velocity (W): ± 0.15 m s -1 Pitch angle (β): ± 0.05 Tilt angle (θ): ± 0.05 Roll/spin angle (φ): ± 0.05 Systematic errors (e.g., mounting errors) in the order of 1 may exist

11 Spherical Trigonometry and Radial Velocity V r = usin(a z )cos(el) vcos(a z )cos(el) (w w t )sin(el) V g V a cos A z sinθ sinelsinβ = coselcosβ sinel= sinθ sinβ cosθ cosβ cosφ cosψ= cosα cosβ sinθ cosα sinβ cosθ cosφ sinα cosθ sinφ α: drift β: pitch φ: spin/rotation θ: tilt Ψ: π/-track-relative tilt A z : azimuth EL: elevation

12 Velocity Error Analysis Estimated aircraft ground speed (V Ge ): V = V cos Ψ W sin EL Ge H = ( V H V o cos λ )(cosα cos β sinθ cosα sin β cosθ cosφ sinα cosθ sinφ) W (sinθ sin β cosθ cos β sinφ) Measured aircraft ground speed by the radar (V G ): δv G : the velocity of the ground gate after removing ground speed δv G = V G = δ ( V = δw δθv V H V cos Ψ W cosθ cosφ V H H Ge sinα cosθ cosφ δβv (cosα sinθ sinα cosθ sinφ) δv = A B 1 sinφ B o sin EL) H (sinα sinθ cosα cosθ sinφ) cosφ (cosα cosθ sinα sinθ sinφ) δθ H cosα cosθ cosφ H

13 Range Error Analysis R N G G H = sin EL Rε δr tan EL δr: gate spacing R R : actual distance to the ground ε: beam width R G = H cosφ = sin EL H = sinθ sin β cosθ cos β cosφ R R ΔR R Ge = sinθ sin β e e H e cosθ e cos β cosφ e e

14 Range Error Analysis (Continue) δr G : difference between the actual distance to the ground and estimates from aircraft altitude and elevation angles of a radar beam R R δr R G Ge = = R R G G = δr R δh ( H G Ge ΔR tanθ δβ cosφ tanθδθ tanθδφ) cos φ( R R R Ge ) ΔR = H tanθ δβ cosθ Hδφ sinφ cosθ δh H tanθδθ ΔR cosφ cos φ cosθ = C D sinφ D cosφ E cos φ 1

15

16 Moving Ocean Surface If the ground is not stationary, then we match in situ wind with near aircraft dual- Doppler wind if there are scatterers near the aircraft (BLW correction) Use to refine ground speed and drift

17 Reverse Headings

18

19 TPARC/TCS08 Corrections Ground speed, Tilt error determined from reverse headings, drift from project average

20 Basic Analysis Process

21 1. *Translate the raw ELDORA field format data into DORADE sweep files. *Calculate navigation correction factors (cfac files) for each flight 3. Fine-tune navigation corrections for each leg of data 4. Edit the data to remove ground echo, noise, clutter, and radar side-lobes, as well as velocity unfolding. 5. Interpolate and/or Synthesize multiple data files to get 3-dimensional wind field and derived quantities.

22 Raw Data

23 Edited Data

24 Typhoon Hagupit

25 Typhoon Hagupit

26 Hagupit Pre-genesis

27 Multi-Doppler Synthesis V r = u sin(a)cos(e) vcos(a)cos(e) (w w t )sin(e) sin a cos e sinacosacos e sinacosesine u sinacosacos e cos a cos e cosacosesine v = sinacosesine cosacosesine sin e w w t V r sinacose V r cosacose V r sine Hildebrand et al 1996

28 Doppler Synthesis Approaches Forward Local (Sprint/Reorder & Cedric) Empirical Interpolation of V r (Distance weighted averaging), then local synthesis Forward Global (Gamache, Raymond & Carrillo*) Empirical Interpolation, then global synthesis Reverse Global (Gao et al. 1999/004, Bell) Interpolation from grid to radar space during cost function minimization

29 Forward Local synthesis Conventional using reorder/cedric Quasi-horizontal assumption Resolve horizontal velocities then integrate continuity equation vertically to obtain vertical velocities Limited to elevation angle less than 45 deg Difficult to resolve storm top when storm is close to the radar

30 Problems with Radial Velocity Interpolation and Averaging Big issue for airborne synthesis and Reorder Also a problem for ground-based platforms near the radar Solutions: Use more, small chunks Include full az/elev info Avoid it

31 3-D Variational Formulation (Gamache 1997, Reasor et al 009): Solve two or more radial velocity equations and mass continuity equation simultaneously. B B ijk K k J j I i k n ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k ijk k K k J j I i n ijk k K k J j I i n ijkl ml Tml ml ijk ml ml ijk ml ml ijk rml L l K k J j I i k m n n n n n n n n w w J z y w z x w y x w z y v z x v y x v z y v z x u y x u z w y w x w z v y v x v z u y u x u J V J v w v u V J J J J J J J F δ α φ φ φ θ φ θ λ λ λ λ λ λ ) ( ) ( ) sin sin cos sin cos cos ( } { = = = = = = = = = = = = = = = = = = r L

32 TCVAR (Bell 009) Can combine radar, dropsonde, and flight level data Low noise via cubic interpolations and spectral derivatives Tunable error specifications and filtering a q(r,z) = rv,ψ,h, q v, { }

33 Raymond & Carrillo

34 Advantages / Disadvantages Error Propagation Memory/C PU Diagnostics Multiple Data Sources Anisotropic Filtering Extra Balance Constraints Forward Local Vertical Low/Fast Established Difficult Possible Difficult Forward Global Horizontal & Vertical High/Slo w Complex Possible Difficult Possible Reverse Global (Bell) BG Error Covariance Low/Slo w Moderate Yes Yes Possible Multiple analysis techniques are a good thing!

35 Automatic Editing for Data Assimilation and New Users Still work in progress Fuzzy logic echo classification system under development Soloii scripts available now for light (80%) to heavy (99%) artifact removal In between is most difficult

36 Automatically Edited (80%)

37 Automatically Edited (99%)

38 Manually Edited Data

39 Summary Data quality is good with exception of aft reflectivity later in project. Radar data is ready, on CODIAC soon CAPPI movies will be available soon also A variety of software tools are available for viewing, editing, and processing New users welcome! Come talk to us about how you could use ELDORA data

Beam-pointing angle calibration of the Wyoming Cloud Radar on the Wyoming King Air aircraft

Beam-pointing angle calibration of the Wyoming Cloud Radar on the Wyoming King Air aircraft Beam-pointing angle calibration of the Wyoming Cloud Radar on the Wyoming King Air aircraft Samuel Haimov, Alfred Rodi University of Wyoming, Atmospheric Science Department, Laramie, WY 82071, U.S.A.,

More information

Navigational Aids 1 st Semester/2007/TF 7:30 PM -9:00 PM

Navigational Aids 1 st Semester/2007/TF 7:30 PM -9:00 PM Glossary of Navigation Terms accelerometer. A device that senses inertial reaction to measure linear or angular acceleration. In its simplest form, it consists of a case-mounted spring and mass arrangement

More information

Comparison of Wind Retrievals from a. Scanning LIDAR and a Vertically Profiling LIDAR for Wind Energy Remote Sensing Applications

Comparison of Wind Retrievals from a. Scanning LIDAR and a Vertically Profiling LIDAR for Wind Energy Remote Sensing Applications Comparison of Wind Retrievals from a Headline Scanning LIDAR and a Vertically Profiling LIDAR for Wind Energy Remote Sensing Applications PAUL T. QUELET1, JULIE K. LUNDQUIST1,2 1University of Colorado,

More information

Definition of Basic Polar Data Product

Definition of Basic Polar Data Product Definition of Basic Polar Data Product OPERA project 1d3: working document WD 02 03 Iwan Holleman and Gianmario Galli Date: September 22, 2003 1 1 Introduction During the OPERA project an additional deliverable

More information

Section Parametrized Surfaces and Surface Integrals. (I) Parametrizing Surfaces (II) Surface Area (III) Scalar Surface Integrals

Section Parametrized Surfaces and Surface Integrals. (I) Parametrizing Surfaces (II) Surface Area (III) Scalar Surface Integrals Section 16.4 Parametrized Surfaces and Surface Integrals (I) Parametrizing Surfaces (II) Surface Area (III) Scalar Surface Integrals MATH 127 (Section 16.4) Parametrized Surfaces and Surface Integrals

More information

MATHEMATICS FOR ENGINEERING TUTORIAL 5 COORDINATE SYSTEMS

MATHEMATICS FOR ENGINEERING TUTORIAL 5 COORDINATE SYSTEMS MATHEMATICS FOR ENGINEERING TUTORIAL 5 COORDINATE SYSTEMS This tutorial is essential pre-requisite material for anyone studying mechanical engineering. This tutorial uses the principle of learning by example.

More information

The Lidar-Radar Open Software Environment (LROSE) : Progress and Plans

The Lidar-Radar Open Software Environment (LROSE) : Progress and Plans The Lidar-Radar Open Software Environment (LROSE) : Progress and Plans Michael M. Bell Colorado State University Wen-Chau Lee and Mike Dixon NCAR Research supported by NSF SI2-SSI Award ACI-1661663 LROSE:

More information

Mathematics for Computer Graphics. Trigonometry

Mathematics for Computer Graphics. Trigonometry Mathematics for Computer Graphics Trigonometry Trigonometry...????? The word trigonometry is derived from the ancient Greek language and means measurement of triangles. trigonon triangle + metron measure

More information

3 - SYNTHETIC APERTURE RADAR (SAR) SUMMARY David Sandwell, SIO 239, January, 2008

3 - SYNTHETIC APERTURE RADAR (SAR) SUMMARY David Sandwell, SIO 239, January, 2008 1 3 - SYNTHETIC APERTURE RADAR (SAR) SUMMARY David Sandwell, SIO 239, January, 2008 Fraunhoffer diffraction To understand why a synthetic aperture in needed for microwave remote sensing from orbital altitude

More information

Challenges in Detecting & Tracking Moving Objects with Synthetic Aperture Radar (SAR)

Challenges in Detecting & Tracking Moving Objects with Synthetic Aperture Radar (SAR) Challenges in Detecting & Tracking Moving Objects with Synthetic Aperture Radar (SAR) Michael Minardi PhD Sensors Directorate Air Force Research Laboratory Outline Focusing Moving Targets Locating Moving

More information

EVALUATION STUDY ON WIND RETRIEVAL METHODS

EVALUATION STUDY ON WIND RETRIEVAL METHODS P8B.3 EVALUATION STUDY ON WIND RETRIEVAL METHODS FROM SINGLE DOPPLER RADAR Sang-Min Jang, Hee-Chang Lim *, Dong-In Lee, Dong-Soon Kim and Young-Sub Lee Department of Env. Atmos. Sci., Division of Mech.

More information

MTH 112: Elementary Functions

MTH 112: Elementary Functions 6.2: Right triangle trigonometry 1/16 Figure: Euclid of Alexandria was a Greek mathematician, often referred to as the Father of Geometry 6.2: Right triangle trigonometry 2/16 6.2: Right triangle trigonometry

More information

Unit 2: Trigonometry. This lesson is not covered in your workbook. It is a review of trigonometry topics from previous courses.

Unit 2: Trigonometry. This lesson is not covered in your workbook. It is a review of trigonometry topics from previous courses. Unit 2: Trigonometry This lesson is not covered in your workbook. It is a review of trigonometry topics from previous courses. Pythagorean Theorem Recall that, for any right angled triangle, the square

More information

Centre for Autonomous Systems

Centre for Autonomous Systems Robot Henrik I Centre for Autonomous Systems Kungl Tekniska Högskolan hic@kth.se 27th April 2005 Outline 1 duction 2 Kinematic and Constraints 3 Mobile Robot 4 Mobile Robot 5 Beyond Basic 6 Kinematic 7

More information

Ch. 2 Trigonometry Notes

Ch. 2 Trigonometry Notes First Name: Last Name: Block: Ch. Trigonometry Notes.0 PRE-REQUISITES: SOLVING RIGHT TRIANGLES.1 ANGLES IN STANDARD POSITION 6 Ch..1 HW: p. 83 #1,, 4, 5, 7, 9, 10, 8. - TRIGONOMETRIC FUNCTIONS OF AN ANGLE

More information

Stereo Imaging and Geolocation

Stereo Imaging and Geolocation Stereo Imaging and Geolocation Stereo imaging serves two purposes. The first is to produce three-dimensional topographic images. These can be used to produce digital elevation models DEM) and to improve

More information

Visualisation Pipeline : The Virtual Camera

Visualisation Pipeline : The Virtual Camera Visualisation Pipeline : The Virtual Camera The Graphics Pipeline 3D Pipeline The Virtual Camera The Camera is defined by using a parallelepiped as a view volume with two of the walls used as the near

More information

Aircraft Stability and Performance 2nd Year, Aerospace Engineering. Dr. M. Turner

Aircraft Stability and Performance 2nd Year, Aerospace Engineering. Dr. M. Turner Aircraft Stability and Performance 2nd Year, Aerospace Engineering Dr. M. Turner Basic Info Timetable 15.00-16.00 Monday ENG LT1 16.00-17.00 Monday ENG LT1 Typical structure of lectures Part 1 Theory Part

More information

SM 2. Date: Section: Objective: The Pythagorean Theorem: In a triangle, or

SM 2. Date: Section: Objective: The Pythagorean Theorem: In a triangle, or SM 2 Date: Section: Objective: The Pythagorean Theorem: In a triangle, or. It doesn t matter which leg is a and which leg is b. The hypotenuse is the side across from the right angle. To find the length

More information

Temporal Processing of Millimeter Wave Flight Test Data

Temporal Processing of Millimeter Wave Flight Test Data Distribution Statement C Distribution authorized to U.S. Government agencies Section and 5 their contractors. Other requests for this document shall be referred to BAE Systems. Note This information is

More information

Review of Trigonometry

Review of Trigonometry Worksheet 8 Properties of Trigonometric Functions Section Review of Trigonometry This section reviews some of the material covered in Worksheets 8, and The reader should be familiar with the trig ratios,

More information

A New Method for Correcting ScanSAR Scalloping Using Forests and inter SCAN Banding Employing Dynamic Filtering

A New Method for Correcting ScanSAR Scalloping Using Forests and inter SCAN Banding Employing Dynamic Filtering A New Method for Correcting ScanSAR Scalloping Using Forests and inter SCAN Banding Employing Dynamic Filtering Masanobu Shimada Japan Aerospace Exploration Agency (JAXA), Earth Observation Research Center

More information

GEOG 4110/5100 Advanced Remote Sensing Lecture 4

GEOG 4110/5100 Advanced Remote Sensing Lecture 4 GEOG 4110/5100 Advanced Remote Sensing Lecture 4 Geometric Distortion Relevant Reading: Richards, Sections 2.11-2.17 Review What factors influence radiometric distortion? What is striping in an image?

More information

APPLICATIONS FOR COORDINATED MOTION IN RADOME TESTING

APPLICATIONS FOR COORDINATED MOTION IN RADOME TESTING APPLICATIONS FOR COORDINATED MOTION IN RADOME TESTING Scott McBride Evan Langman Marion Baggett MI Technologies, LLC 4500 River Green Parkway, Suite 200 Duluth, GA 30096 ABSTRACT Traditional data collection

More information

High spatial resolution measurement of volume holographic gratings

High spatial resolution measurement of volume holographic gratings High spatial resolution measurement of volume holographic gratings Gregory J. Steckman, Frank Havermeyer Ondax, Inc., 8 E. Duarte Rd., Monrovia, CA, USA 9116 ABSTRACT The conventional approach for measuring

More information

Linear algebra deals with matrixes: two-dimensional arrays of values. Here s a matrix: [ x + 5y + 7z 9x + 3y + 11z

Linear algebra deals with matrixes: two-dimensional arrays of values. Here s a matrix: [ x + 5y + 7z 9x + 3y + 11z Basic Linear Algebra Linear algebra deals with matrixes: two-dimensional arrays of values. Here s a matrix: [ 1 5 ] 7 9 3 11 Often matrices are used to describe in a simpler way a series of linear equations.

More information

14 Chapter. Interference and Diffraction

14 Chapter. Interference and Diffraction 14 Chapter Interference and Diffraction 14.1 Superposition of Waves... 14-14.1.1 Interference Conditions for Light Sources... 14-4 14. Young s Double-Slit Experiment... 14-4 Example 14.1: Double-Slit Experiment...

More information

3D Computer Vision II. Reminder Projective Geometry, Transformations. Nassir Navab. October 27, 2009

3D Computer Vision II. Reminder Projective Geometry, Transformations. Nassir Navab. October 27, 2009 3D Computer Vision II Reminder Projective Geometr, Transformations Nassir Navab based on a course given at UNC b Marc Pollefes & the book Multiple View Geometr b Hartle & Zisserman October 27, 29 2D Transformations

More information

GY403 Structural Geology Laboratory. Example Orthographic Solutions to Apparent Dip, True Dip, 3-Point, and Intersecting Planes Problems

GY403 Structural Geology Laboratory. Example Orthographic Solutions to Apparent Dip, True Dip, 3-Point, and Intersecting Planes Problems GY403 Structural Geology Laboratory Example Orthographic Solutions to Apparent Dip, True Dip, 3-Point, and Intersecting Planes Problems All structural geology geometry problems can be reduced to 1 of 3

More information

PSI Precision, accuracy and validation aspects

PSI Precision, accuracy and validation aspects PSI Precision, accuracy and validation aspects Urs Wegmüller Charles Werner Gamma Remote Sensing AG, Gümligen, Switzerland, wegmuller@gamma-rs.ch Contents Aim is to obtain a deeper understanding of what

More information

Optimization-Based Calibration of a Triaxial Accelerometer-Magnetometer

Optimization-Based Calibration of a Triaxial Accelerometer-Magnetometer 2005 American Control Conference June 8-10, 2005. Portland, OR, USA ThA07.1 Optimization-Based Calibration of a Triaxial Accelerometer-Magnetometer Erin L. Renk, Walter Collins, Matthew Rizzo, Fuju Lee,

More information

PLANE TRIGONOMETRY Exam I September 13, 2007

PLANE TRIGONOMETRY Exam I September 13, 2007 Name Rec. Instr. Rec. Time PLANE TRIGONOMETRY Exam I September 13, 2007 Page 1 Page 2 Page 3 Page 4 TOTAL (10 pts.) (30 pts.) (30 pts.) (30 pts.) (100 pts.) Below you will find 10 problems, each worth

More information

The main problem of photogrammetry

The main problem of photogrammetry Structured Light Structured Light The main problem of photogrammetry to recover shape from multiple views of a scene, we need to find correspondences between the images the matching/correspondence problem

More information

Design and Development of Unmanned Tilt T-Tri Rotor Aerial Vehicle

Design and Development of Unmanned Tilt T-Tri Rotor Aerial Vehicle Design and Development of Unmanned Tilt T-Tri Rotor Aerial Vehicle K. Senthil Kumar, Mohammad Rasheed, and T.Anand Abstract Helicopter offers the capability of hover, slow forward movement, vertical take-off

More information

X-ray tomography. X-ray tomography. Applications in Science. X-Rays. Notes. Notes. Notes. Notes

X-ray tomography. X-ray tomography. Applications in Science. X-Rays. Notes. Notes. Notes. Notes X-ray tomography Important application of the Fast Fourier transform: X-ray tomography. Also referred to as CAT scan (Computerized Axial Tomography) X-ray tomography This has revolutionized medical diagnosis.

More information

SAR Image Simulation in the Time Domain for Moving Ocean Surfaces

SAR Image Simulation in the Time Domain for Moving Ocean Surfaces Sensors 2013, 13, 4450-4467; doi:10.3390/s130404450 Article OPEN ACCESS sensors ISSN 1424-8220 www.mdpi.com/journal/sensors SAR Image Simulation in the Time Domain for Moving Ocean Surfaces Takero Yoshida

More information

FAA EDR Performance Standards

FAA EDR Performance Standards FAA EDR Performance Standards Project Summary and Recommendations Presented To: Turbulence Workshop - 2 Presented by: Michael Emanuel Advanced Concepts & Technology Development, Aviation Weather Division,

More information

Optics Vac Work MT 2008

Optics Vac Work MT 2008 Optics Vac Work MT 2008 1. Explain what is meant by the Fraunhofer condition for diffraction. [4] An aperture lies in the plane z = 0 and has amplitude transmission function T(y) independent of x. It is

More information

Contours of slopes of a rippled water surface

Contours of slopes of a rippled water surface Contours of slopes of a rippled water surface Charles Cox* and Xin Zhang Scripps Institution of Oceanography, UCSD 0213, La Jolla, California 9209, USA *cscox@ucsd.edu Abstract: The appearance of a horizontal

More information

Robotics (Kinematics) Winter 1393 Bonab University

Robotics (Kinematics) Winter 1393 Bonab University Robotics () Winter 1393 Bonab University : most basic study of how mechanical systems behave Introduction Need to understand the mechanical behavior for: Design Control Both: Manipulators, Mobile Robots

More information

Wide-Field Imaging I: Non-Coplanar Visibilities

Wide-Field Imaging I: Non-Coplanar Visibilities Wide-Field Imaging I: Non-Coplanar Visibilities Rick Perley Eleventh Synthesis Imaging Workshop Socorro, June 10-17, 2008 Review: Measurement Equation From the first lecture, we have a general relation

More information

Memorandum. Clint Slatton Prof. Brian Evans Term project idea for Multidimensional Signal Processing (EE381k)

Memorandum. Clint Slatton Prof. Brian Evans Term project idea for Multidimensional Signal Processing (EE381k) Memorandum From: To: Subject: Date : Clint Slatton Prof. Brian Evans Term project idea for Multidimensional Signal Processing (EE381k) 16-Sep-98 Project title: Minimizing segmentation discontinuities in

More information

2D and 3D Transformations AUI Course Denbigh Starkey

2D and 3D Transformations AUI Course Denbigh Starkey 2D and 3D Transformations AUI Course Denbigh Starkey. Introduction 2 2. 2D transformations using Cartesian coordinates 3 2. Translation 3 2.2 Rotation 4 2.3 Scaling 6 3. Introduction to homogeneous coordinates

More information

GY403 Structural Geology Laboratory. Example Orthographic Solutions to Apparent Dip, True Dip, 3-Point, 3 Intersecting Planes Problems

GY403 Structural Geology Laboratory. Example Orthographic Solutions to Apparent Dip, True Dip, 3-Point, 3 Intersecting Planes Problems GY403 Structural Geology Laboratory Example Orthographic Solutions to Apparent Dip, True Dip, 3-Point, 3 and Intersecting Planes Problems Orthographic Example of Apparent Dip Problem Orthographic solutions

More information

Animating orientation. CS 448D: Character Animation Prof. Vladlen Koltun Stanford University

Animating orientation. CS 448D: Character Animation Prof. Vladlen Koltun Stanford University Animating orientation CS 448D: Character Animation Prof. Vladlen Koltun Stanford University Orientation in the plane θ (cos θ, sin θ) ) R θ ( x y = sin θ ( cos θ sin θ )( x y ) cos θ Refresher: Homogenous

More information

PreCalculus Unit 1: Unit Circle Trig Quiz Review (Day 9)

PreCalculus Unit 1: Unit Circle Trig Quiz Review (Day 9) PreCalculus Unit 1: Unit Circle Trig Quiz Review (Day 9) Name Date Directions: You may NOT use Right Triangle Trigonometry for any of these problems! Use your unit circle knowledge to solve these problems.

More information

CHAPTER 2 SENSOR DATA SIMULATION: A KINEMATIC APPROACH

CHAPTER 2 SENSOR DATA SIMULATION: A KINEMATIC APPROACH 27 CHAPTER 2 SENSOR DATA SIMULATION: A KINEMATIC APPROACH 2.1 INTRODUCTION The standard technique of generating sensor data for navigation is the dynamic approach. As revealed in the literature (John Blakelock

More information

Adding vectors. Let s consider some vectors to be added.

Adding vectors. Let s consider some vectors to be added. Vectors Some physical quantities have both size and direction. These physical quantities are represented with vectors. A common example of a physical quantity that is represented with a vector is a force.

More information

Motion compensation and the orbit restitution

Motion compensation and the orbit restitution InSA R Contents Introduction and objectives Pi-SAR Motion compensation and the orbit restitution InSAR algorithm DEM generation Evaluation Conclusion and future work Introduction and Objectives L-band

More information

Review Journal 7 Page 57

Review Journal 7 Page 57 Student Checklist Unit 1 - Trigonometry 1 1A Prerequisites: I can use the Pythagorean Theorem to solve a missing side of a right triangle. Note p. 2 1B Prerequisites: I can convert within the imperial

More information

An Orthogonal Curvilinear Terrain-Following Coordinate for Atmospheric Models!

An Orthogonal Curvilinear Terrain-Following Coordinate for Atmospheric Models! Solution of Partial Differential Equations on the Sphere! An Orthogonal Curvilinear Terrain-Following Coordinate for Atmospheric Models! Yiyuan Li 1, Bin Wang 1, Donghai Wang 2! 1. Institute of Atmospheric

More information

3.0 Trigonometry Review

3.0 Trigonometry Review 3.0 Trigonometry Review In trigonometry problems, all vertices (corners or angles) of the triangle are labeled with capital letters. The right angle is usually labeled C. Sides are usually labeled with

More information

A SPECTRAL ANALYSIS OF SINGLE ANTENNA INTERFEROMETRY. Craig Stringham

A SPECTRAL ANALYSIS OF SINGLE ANTENNA INTERFEROMETRY. Craig Stringham A SPECTRAL ANALYSIS OF SINGLE ANTENNA INTERFEROMETRY Craig Stringham Microwave Earth Remote Sensing Laboratory Brigham Young University 459 CB, Provo, UT 84602 March 18, 2013 ABSTRACT This paper analyzes

More information

Navigation coordinate systems

Navigation coordinate systems Lecture 3 Navigation coordinate systems Topic items: 1. Basic Coordinate Systems. 2. Plane Cartesian Coordinate Systems. 3. Polar Coordinate Systems. 4. Earth-Based Locational Reference Systems. 5. Reference

More information

EE565:Mobile Robotics Lecture 3

EE565:Mobile Robotics Lecture 3 EE565:Mobile Robotics Lecture 3 Welcome Dr. Ahmad Kamal Nasir Today s Objectives Motion Models Velocity based model (Dead-Reckoning) Odometry based model (Wheel Encoders) Sensor Models Beam model of range

More information

Computer Animation II

Computer Animation II Computer Animation II Orientation interpolation Dynamics Some slides courtesy of Leonard McMillan and Jovan Popovic Lecture 13 6.837 Fall 2002 Interpolation Review from Thursday Splines Articulated bodies

More information

Uncertainty simulator to evaluate the electrical and mechanical deviations in cylindrical near field antenna measurement systems

Uncertainty simulator to evaluate the electrical and mechanical deviations in cylindrical near field antenna measurement systems Uncertainty simulator to evaluate the electrical and mechanical deviations in cylindrical near field antenna measurement systems S. Burgos*, F. Martín, M. Sierra-Castañer, J.L. Besada Grupo de Radiación,

More information

ARPS-3dvar Program. 1. Introduction

ARPS-3dvar Program. 1. Introduction 1. Introduction The ARPS variational data assimilation program 3dvar is designed to assimilate the observation data to ARPS model. The program takes an ARPS forecast as background, and surface data, multi-level

More information

DERIVATION of the BACKSCATTERING COEFFICIENT σ o in ESA ERS SAR PRI PRODUCTS

DERIVATION of the BACKSCATTERING COEFFICIENT σ o in ESA ERS SAR PRI PRODUCTS ERS SAR CALIBRATION DERIVATION of the BACKSCATTERING COEFFICIENT σ o in ESA ERS SAR PRI PRODUCTS H. Laur 1, P. Bally 2, P. Meadows 3, J. Sanchez 4, B. Schaettler 5, E. Lopinto 6, D. Esteban 4 Document

More information

Chapter 2 Trigonometry

Chapter 2 Trigonometry Chapter 2 Trigonometry 1 Chapter 2 Trigonometry Angles in Standard Position Angles in Standard Position Any angle may be viewed as the rotation of a ray about its endpoint. The starting position of the

More information

Extraction of surface normal and index of refraction using a pair of passive infrared polarimetric sensors

Extraction of surface normal and index of refraction using a pair of passive infrared polarimetric sensors Extraction of surface normal and index of refraction using a pair of passive infrared polarimetric sensors Firooz Sadjadi Lockheed Martin Corporation Saint Paul, Minnesota firooz.sadjadi@ieee.org Farzad

More information

Coherent Auto-Calibration of APE and NsRCM under Fast Back-Projection Image Formation for Airborne SAR Imaging in Highly-Squint Angle

Coherent Auto-Calibration of APE and NsRCM under Fast Back-Projection Image Formation for Airborne SAR Imaging in Highly-Squint Angle remote sensing Article Coherent Auto-Calibration of APE and NsRCM under Fast Back-Projection Image Formation for Airborne SAR Imaging in Highly-Squint Angle Lei Yang 1,, Song Zhou 2, *, Lifan Zhao 3 and

More information

Towards Robust Airborne SLAM in Unknown Wind Environments

Towards Robust Airborne SLAM in Unknown Wind Environments Towards Robust Airborne SLAM in Unknown Wind Environments Jonghyuk Kim Department of Engineering Australian National University, Australia jonghyuk.kim@anu.edu.au Salah Sukkarieh ARC Centre for Autonomous

More information

Wave Optics. April 11, 2014 Chapter 34 1

Wave Optics. April 11, 2014 Chapter 34 1 Wave Optics April 11, 2014 Chapter 34 1 Announcements! Exam tomorrow! We/Thu: Relativity! Last week: Review of entire course, no exam! Final exam Wednesday, April 30, 8-10 PM Location: WH B115 (Wells Hall)

More information

SEA SURFACE SPEED FROM TERRASAR-X ATI DATA

SEA SURFACE SPEED FROM TERRASAR-X ATI DATA SEA SURFACE SPEED FROM TERRASAR-X ATI DATA Matteo Soccorsi (1) and Susanne Lehner (1) (1) German Aerospace Center, Remote Sensing Technology Institute, 82234 Weßling, Germany, Email: matteo.soccorsi@dlr.de

More information

Introduction to quaternions. Mathematics. Operations

Introduction to quaternions. Mathematics. Operations Introduction to quaternions Topics: Definition Mathematics Operations Euler Angles (optional) intro to quaternions 1 noel.h.hughes@gmail.com Euler's Theorem y y Angle! rotation follows right hand rule

More information

Coordinate transformations. 5554: Packet 8 1

Coordinate transformations. 5554: Packet 8 1 Coordinate transformations 5554: Packet 8 1 Overview Rigid transformations are the simplest Translation, rotation Preserve sizes and angles Affine transformation is the most general linear case Homogeneous

More information

GEOG 4110/5100 Advanced Remote Sensing Lecture 4

GEOG 4110/5100 Advanced Remote Sensing Lecture 4 GEOG 4110/5100 Advanced Remote Sensing Lecture 4 Geometric Distortion Relevant Reading: Richards, Sections 2.11-2.17 Geometric Distortion Geometric Distortion: Errors in image geometry, (location, dimensions,

More information

Lateral Ground Movement Estimation from Space borne Radar by Differential Interferometry.

Lateral Ground Movement Estimation from Space borne Radar by Differential Interferometry. Lateral Ground Movement Estimation from Space borne Radar by Differential Interferometry. Abstract S.Sircar 1, 2, C.Randell 1, D.Power 1, J.Youden 1, E.Gill 2 and P.Han 1 Remote Sensing Group C-CORE 1

More information

CSC418 / CSCD18 / CSC2504

CSC418 / CSCD18 / CSC2504 5 5.1 Surface Representations As with 2D objects, we can represent 3D objects in parametric and implicit forms. (There are also explicit forms for 3D surfaces sometimes called height fields but we will

More information

Research Article Cross Beam STAP for Nonstationary Clutter Suppression in Airborne Radar

Research Article Cross Beam STAP for Nonstationary Clutter Suppression in Airborne Radar Antennas and Propagation Volume 213, Article ID 27631, 5 pages http://dx.doi.org/1.1155/213/27631 Research Article Cross Beam STAP for Nonstationary Clutter Suppression in Airborne Radar Yongliang Wang,

More information

Distortion Correction for Conical Multiplex Holography Using Direct Object-Image Relationship

Distortion Correction for Conical Multiplex Holography Using Direct Object-Image Relationship Proc. Natl. Sci. Counc. ROC(A) Vol. 25, No. 5, 2001. pp. 300-308 Distortion Correction for Conical Multiplex Holography Using Direct Object-Image Relationship YIH-SHYANG CHENG, RAY-CHENG CHANG, AND SHIH-YU

More information

+ i a y )( cosφ + isinφ) ( ) + i( a x. cosφ a y. = a x

+ i a y )( cosφ + isinφ) ( ) + i( a x. cosφ a y. = a x Rotation Matrices and Rotated Coordinate Systems Robert Bernecky April, 2018 Rotated Coordinate Systems is a confusing topic, and there is no one standard or approach 1. The following provides a simplified

More information

TEAMS National Competition High School Version Photometry Solution Manual 25 Questions

TEAMS National Competition High School Version Photometry Solution Manual 25 Questions TEAMS National Competition High School Version Photometry Solution Manual 25 Questions Page 1 of 15 Photometry Questions 1. When an upright object is placed between the focal point of a lens and a converging

More information

Solar Panel Irradiation Exposure efficiency of solar panels with shadow

Solar Panel Irradiation Exposure efficiency of solar panels with shadow Solar Panel Irradiation Exposure efficiency of solar panels with shadow Frits F.M. de Mul MEDPHYS Software & Services 2012 www.medphys.nl email: info(at)medphys.nl Solar Panel Irradiation 1. Local Times,

More information

Chapter 2 - Basic Mathematics for 3D Computer Graphics

Chapter 2 - Basic Mathematics for 3D Computer Graphics Chapter 2 - Basic Mathematics for 3D Computer Graphics Three-Dimensional Geometric Transformations Affine Transformations and Homogeneous Coordinates Combining Transformations Translation t + t Add a vector

More information

Geometric Correction

Geometric Correction CEE 6150: Digital Image Processing Geometric Correction 1 Sources of Distortion Sensor Characteristics optical distortion aspect ratio non-linear mirror velocity detector geometry & scanning sequence Viewing

More information

Summary and additional notes for Static ti pressure measurements:

Summary and additional notes for Static ti pressure measurements: Summary and additional notes for Static ti pressure measurements: Determination of static pressure a) Wall tapping b) static tube Error in pressure is function of: Error in pressure is function of: And

More information

This was written by a designer of inertial guidance machines, & is correct. **********************************************************************

This was written by a designer of inertial guidance machines, & is correct. ********************************************************************** EXPLANATORY NOTES ON THE SIMPLE INERTIAL NAVIGATION MACHINE How does the missile know where it is at all times? It knows this because it knows where it isn't. By subtracting where it is from where it isn't

More information

Computer Vision. Coordinates. Prof. Flávio Cardeal DECOM / CEFET- MG.

Computer Vision. Coordinates. Prof. Flávio Cardeal DECOM / CEFET- MG. Computer Vision Coordinates Prof. Flávio Cardeal DECOM / CEFET- MG cardeal@decom.cefetmg.br Abstract This lecture discusses world coordinates and homogeneous coordinates, as well as provides an overview

More information

2.0 Trigonometry Review Date: Pythagorean Theorem: where c is always the.

2.0 Trigonometry Review Date: Pythagorean Theorem: where c is always the. 2.0 Trigonometry Review Date: Key Ideas: The three angles in a triangle sum to. Pythagorean Theorem: where c is always the. In trigonometry problems, all vertices (corners or angles) of the triangle are

More information

INTERFEROMETRIC ISAR IMAGING ON MARITIME TARGET APPLICATIONS: SIMULATION OF REALISTIC TARGETS AND DYNAMICS

INTERFEROMETRIC ISAR IMAGING ON MARITIME TARGET APPLICATIONS: SIMULATION OF REALISTIC TARGETS AND DYNAMICS Progress In Electromagnetics Research, Vol. 132, 571 586, 212 INTERFEROMETRIC ISAR IMAGING ON MARITIME TARGET APPLICATIONS: SIMULATION OF REALISTIC TARGETS AND DYNAMICS D. Felguera-Martín *, J. T. González-Partida,

More information

Chapter 3: Trigonometric Identities

Chapter 3: Trigonometric Identities Chapter 3: Trigonometric Identities Chapter 3 Overview Two important algebraic aspects of trigonometric functions must be considered: how functions interact with each other and how they interact with their

More information

Preview. Two-Dimensional Motion and Vectors Section 1. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion

Preview. Two-Dimensional Motion and Vectors Section 1. Section 1 Introduction to Vectors. Section 2 Vector Operations. Section 3 Projectile Motion Two-Dimensional Motion and Vectors Section 1 Preview Section 1 Introduction to Vectors Section 2 Vector Operations Section 3 Projectile Motion Section 4 Relative Motion Two-Dimensional Motion and Vectors

More information

Complete Systematic Error Model of SSR for Sensor Registration in ATC Surveillance Networks

Complete Systematic Error Model of SSR for Sensor Registration in ATC Surveillance Networks sensors Article Complete Systematic Error Model of SSR for Sensor Registration in ATC Surveillance Networks Ángel J. Jarama * ID, Jaime López-Araquistain ID, Gonzalo de Miguel ID Juan A. Besada Signals,

More information

Processing of airborne laser scanning data

Processing of airborne laser scanning data GIS-E1020 From measurements to maps Lecture 8 Processing of airborne laser scanning data Petri Rönnholm Aalto University 1 Learning objectives To realize error sources of Airborne laser scanning To understand

More information

Computational Fluid Dynamics Study for a Deep Stall Air Vehicle

Computational Fluid Dynamics Study for a Deep Stall Air Vehicle Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6410--11-9339 Computational Fluid Dynamics Study for a Deep Stall Air Vehicle Ravi Ramamurti Center for Reactive Flow and Dynamical Systems Laboratory

More information

1. ORIENTATIONS OF LINES AND PLANES IN SPACE

1. ORIENTATIONS OF LINES AND PLANES IN SPACE I Main Topics A Defini@ons of points, lines, and planes B Geologic methods for describing lines and planes C AMtude symbols for geologic maps D Reference frames 1 II Defini@ons of points, lines, and planes

More information

A simulator of sea clutter from X-band radar at low grazing angles

A simulator of sea clutter from X-band radar at low grazing angles A simulator of sea clutter from X-band radar at low grazing angles Guillaume Sicot, Nicolas Thomas Actimar 36 quai de la douane 29200 Brest - France Email: guillaume.sicot@actimar.fr Jean-Marc Le Caillec

More information

To graph the point (r, θ), simply go out r units along the initial ray, then rotate through the angle θ. The point (1, 5π 6

To graph the point (r, θ), simply go out r units along the initial ray, then rotate through the angle θ. The point (1, 5π 6 Polar Coordinates Any point in the plane can be described by the Cartesian coordinates (x, y), where x and y are measured along the corresponding axes. However, this is not the only way to represent points

More information

mmwave Radar IWR1642 People Counting Demonstration

mmwave Radar IWR1642 People Counting Demonstration mmwave Radar IWR1642 People Counting Demonstration 1 Presenters Abdulraheem Killedar Wesley He Gondalia Akash Please Note: This Webinar is being recorded and will be made available to the public. 2 mmwave

More information

Script for the Excel-based applet StereogramHeijn_v2.2.xls

Script for the Excel-based applet StereogramHeijn_v2.2.xls Script for the Excel-based applet StereogramHeijn_v2.2.xls Heijn van Gent, MSc. 25.05.2006 Aim of the applet: The aim of this applet is to plot planes and lineations in a lower Hemisphere Schmidt Net using

More information

TEAMS National Competition Middle School Version Photometry Solution Manual 25 Questions

TEAMS National Competition Middle School Version Photometry Solution Manual 25 Questions TEAMS National Competition Middle School Version Photometry Solution Manual 25 Questions Page 1 of 14 Photometry Questions 1. When an upright object is placed between the focal point of a lens and a converging

More information

10/5/09 1. d = 2. Range Sensors (time of flight) (2) Ultrasonic Sensor (time of flight, sound) (1) Ultrasonic Sensor (time of flight, sound) (2) 4.1.

10/5/09 1. d = 2. Range Sensors (time of flight) (2) Ultrasonic Sensor (time of flight, sound) (1) Ultrasonic Sensor (time of flight, sound) (2) 4.1. Range Sensors (time of flight) (1) Range Sensors (time of flight) (2) arge range distance measurement -> called range sensors Range information: key element for localization and environment modeling Ultrasonic

More information

ORIENTATIONS OF LINES AND PLANES IN SPACE

ORIENTATIONS OF LINES AND PLANES IN SPACE GG303 Lab 1 8/21/09 1 ORIENTATIONS OF LINES AND PLANES IN SPACE I Main Topics A Definitions of points, lines, and planes B Geologic methods for describing lines and planes C Attitude symbols for geologic

More information

Gernot Hoffmann. Euler Angles and Projections. Contents

Gernot Hoffmann. Euler Angles and Projections. Contents Gernot Hoffmann Euler Angles and Projections Contents Coordinate Rotations 2 Camera Angles 2 Tilted Image Angles 3 Aircraft Angles 3 Gyro Angles 4 Single Axis 3D Rotation 4 Matrix Features 4 Aligning a

More information

Computer Graphics 7: Viewing in 3-D

Computer Graphics 7: Viewing in 3-D Computer Graphics 7: Viewing in 3-D In today s lecture we are going to have a look at: Transformations in 3-D How do transformations in 3-D work? Contents 3-D homogeneous coordinates and matrix based transformations

More information

Image Collection From Orbit

Image Collection From Orbit Image Collection From Orbit Having addressed the basics of orbital motion in the previous section, we now examine the geometric and kinematic aspects of the main orbital imaging techniques. The four main

More information

PROJECTILE. 5) Define the terms Velocity as related to projectile motion: 6) Define the terms angle of projection as related to projectile motion:

PROJECTILE. 5) Define the terms Velocity as related to projectile motion: 6) Define the terms angle of projection as related to projectile motion: 1) Define Trajectory a) The path traced by particle in air b) The particle c) Vertical Distance d) Horizontal Distance PROJECTILE 2) Define Projectile a) The path traced by particle in air b) The particle

More information

Downloaded from UNIT 06 Optics

Downloaded from   UNIT 06 Optics 1 Mark UNIT 06 Optics Q1: A partially plane polarised beam of light is passed through a polaroid. Show graphically the variation of the transmitted light intensity with angle of rotation of the Polaroid.

More information