Cubature Particle filter applied in a tightly-coupled GPS/INS navigation system

Size: px
Start display at page:

Download "Cubature Particle filter applied in a tightly-coupled GPS/INS navigation system"

Transcription

1 Cubature Particle filter applied in a tightly-coupled GPS/INS navigation system Yingwei Zhao & David Becker Physical and Satellite Geodesy Institute of Geodesy TU Darmstadt 1 Yingwei Zhao & David Becker InterGeo 08/10/13

2 Main Contents I. The Cubature Particle Filter (CPF) II. Gaussian Particle Filter (GPF) Cubature Kalman Filter (CKF) GPS/INS tightly-coupled navigation system Nonlinear IMU model GPS/INS measurement model III. Navigation results Experiment Comparison IV. Conclusion & Future work Conclusion Future work 2 Yingwei Zhao & David Becker InterGeo 08/10/13

3 The Cubature Particle Filter The Gaussian Particle Filter Use the Gaussian distribution to approximate the importance density function in the Particle Filter No particles degeneration No need in resampling the particles Reduce the computational burden The Cubature Kalman Filter The heart is the spherical-radial cubature rules Use 2n equal weighted cubature points A third-order approximation to the nonlinear system The Cubature Particle Filter Use the state estimated by the CKF to form the importance density function 3 Yingwei Zhao & David Becker InterGeo 08/10/13

4 The Cubature Kalman Filter Time update T P S S k 1 k 1 k 1 k 1 k 1 k 1 S x k 1 k 1 k 1 k 1 k 1 k 1 * f(, u k 1) k k k k m 1 * x k k 1 i, k 1 k 1 m i1 m 1 * * T T P x x Q k k 1 i, k k 1 i, k k 1 k k 1 k k 1 m i1 Measurement update k 1 T P S S k k 1 k k 1 k k 1 S x k k 1 k k 1 k k 1 Z h(, u ) k k k k k m 1 z Z k k 1 i, k 1 k 1 m i1 m 1 T T P Z Z z z R zz, k k 1 i, k k 1 i, k k 1 k k 1 k k 1 m i1 m 1 T T P Z x z xz, k k 1 i, k k 1 i, k k 1 k k 1 k k 1 m i1 1 Kk P P xz, k k 1 zz, k k 1 x x K ( ) k k k k 1 k zk zkk 1 T P P K k k k k 1 kp K zz, k k 1 k k 4 Yingwei Zhao & David Becker InterGeo 08/10/13

5 The Cubature Particle Filter The particles will be generated using the CKF a posteriori estimates as X ki, N( x, P ) k k k k The weights can be calculated as ( X ) ki, p( z X ) N( X x, P ) k k, i k, i k k 1 k k 1 N( X x, P ) ki, k k k k ( X ) The states and covariance can be estimated as N k ( k, i ) k, i i1 x X X ki, N k k, i k, i k k, i k i1 P ( X )[ X x ][ X x ] ( X ) N i1 T ki, ( X ) ki, 5 Yingwei Zhao & David Becker InterGeo 08/10/13

6 The Cubature Particle Filter Initialization ( x, P ) k k-1 k k-1 ( zr, ) Cubature Kalman Filter.. X N( x, P ), 1/ N k, i kk kk k, i Calculate the importance weights Get the new estimates x k, P k 6 Yingwei Zhao & David Becker InterGeo 08/10/13

7 GPS/INS tightly-coupled navigation system System structure IMU angular velocity acceleration Mechanization + - P,V,A Ephemeris GPS P,V,A Pseudorange, Pseudorange rate IMU Errors Filter Pseudorange Doppler Yingwei Zhao & David Becker InterGeo 08/10/13

8 GPS/INS tightly-coupled navigation system State vector x [,,, v, v, v, l, b, h,,,,,,, ct, ct] The difference between the true value and estimated value,, v, v, v l, b, h,, :the attitude error :the velocity error x y z :the position error (longitude, latitude and height) :the gyro drift x y z x, y, z c t c t :the acceleration bias x y z x y z x y z :the receiver clock offset expressed in meters : the receiver clock drift expressed in meters 8 Yingwei Zhao & David Becker InterGeo 08/10/13

9 GPS/INS tightly-coupled navigation system Transition function n n n n n b ( I Cn ) in Cnin Cbib v [ I Cn ] Cb f Cb f (2 ie en ) v (2 ie en) v g n n vn hvn L 2 M h ( M h) n n n ve sec L LvE tan Lsec L hve sec L b 2 N h N h ( N h) n h vu n n n b n b n n n n n n n 9 Yingwei Zhao & David Becker InterGeo 08/10/13

10 GPS/INS tightly-coupled navigation system An approximation to the attitude error The attitude error is treated as the rotational angle between the true and estimated navigation frames The direction cosine matrix can be used Different from the psi-angle expression z z δγ x O δα x δβ y ỹ n C n cos cos sin sin sin cos sin sin sin cos sin cos cos sin cos cos sin sin cos cos sin sin sin sin cos sin cos cos cos 10 Yingwei Zhao & David Becker InterGeo 08/10/13

11 GPS/INS tightly-coupled navigation system Measurement update Pseudo-range and Pseudo-range rate Difference between the observation and the estimated value Position is transferred from ECEF to LBH Pseudo-range r ( x x) ( y y) ( z z) j s, j s, j s, j Difference c t e x e y e z r j1 j2 j3 Pseudo-range rate Difference r e ( x x) e ( y y) e ( z z) j j1 s, j j1 s, j j1 s, j g x g y g z e x e y e z c t j j1 j2 j3 j1 j2 j3 r 11 Yingwei Zhao & David Becker InterGeo 08/10/13

12 Experiment MEMS IMU Gyroscope Acceleration Bias 0.1 /s 0.1 mg Noise 2 / h 36 g / Hz RLG IMU Gyroscope Acceleration Bias /h 25 μg Noise / h 8 g / Hz 12 Yingwei Zhao & David Becker InterGeo 08/10/13

13 Experiment 13 Yingwei Zhao & David Becker InterGeo 08/10/13

14 Yaw(deg) Pitch(deg) Roll(deg) Comparison among different particle s number--attitude UTCtime(s) 500 x UTCtime(s) x UTCtime(s) x Yingwei Zhao & David Becker InterGeo 08/10/13

15 Comparison among different particle s number--attitude Roll(deg) Pitch(deg) Yaw(deg) Max Mean RMS Max Mean RMS Max Mean RMS Yingwei Zhao & David Becker InterGeo 08/10/13

16 Yaw(deg) Pitch(deg) Roll(deg) Comparison among different filtering methods--attitude EKF5.14 UTCtime(s) CKF x 10 4 CPF UTCtime(s) x UTCtime(s) x Yingwei Zhao & David Becker InterGeo 08/10/13

17 Comparison among different filtering methods--attitude Roll(deg) Pitch(deg) Yaw(deg) Max Mean RMS Max Mean RMS Max Mean RMS EKF CKF CPF Yingwei Zhao & David Becker InterGeo 08/10/13

18 Height(m) Northing(m) Easting(m) Coasting Performance EKF 5.14 UTCtime(s) CKF x 10 4 CPF UTCtime(s) x UTCtime(s) x Yingwei Zhao & David Becker InterGeo 08/10/13

19 Coasting-Maximum Position difference Easting(m) Northing(m) Height(m) CT 1 CT 2 CT 3 CT 1 CT 2 CT 3 CT 1 CT 2 CT 3 EKF CKF CPF Yingwei Zhao & David Becker InterGeo 08/10/13

20 Conclusion & Future work Conclusion The CPF performs better than the EKF The CPF shows similar performance with the CKF using Gaussian distribution The CKF can ease the curse of dimensionality, but can t eliminate it High computation burden Future work Rao-Blackwellized Cubature Particle Filter Gaussian-sum Cubature Particle Filter 20 Yingwei Zhao & David Becker InterGeo 08/10/13

21 Thank you very much for the attention!! 21 Yingwei Zhao & David Becker InterGeo 08/10/13

22 22 Yingwei Zhao & David Becker InterGeo 08/10/13

23 Comparison between the UKF and the CKF Difference CKF: 2n Cubature points UKF: 2n+1 Sigma points CKF: all the weights are positive, no possibility in negative definite UKF: has the possibility in negative definite CKF: more suitable for higher-order system UKF: more suitable for lower-order system CKF: proved in theory UKF: based on the assumption CKF: only has one parameter to tune UKF: has three parameters to tune Similarity A third order approximation to the nonlinear system The CKF can be treated as a special case of the UKF Gaussian filter (0,0) (0,0) O O y (0,0) A (0,0) A (0,0) CKF Cubature points distribution y (0,0) A (0,0) (0,0) A (0,0) UKF Sigma points distribution A A A x x A A 23 Yingwei Zhao & David Becker InterGeo 08/10/13

24 The function of the CKF in the CPF a priori likelihood Bootstrap Particle Filter 24 Yingwei Zhao & David Becker InterGeo 08/10/13

25 The function of the CKF in the CPF likelihood a priori a posteriori Measurement update Cubature Particle Filter 25 Yingwei Zhao & David Becker InterGeo 08/10/13

26 Longitude The reason of the jumps in the beginning stage in the attitude RLG IMU MEMS IMU Latitude 26 Yingwei Zhao & David Becker InterGeo 08/10/13

27 The observability of the attitude error a E =0 a E 0 S maneuvering Turning δα 1.2e-7 1.2e-7 1.7e-7 1.3e-7 δβ 1.2e-7 1.2e-7 1.7e-7 1.3e-7 δγ 1.4e-3 9.3e-4 8.5e-4 2.8e-5 27 Yingwei Zhao & David Becker InterGeo 08/10/13

Tampere University of Technology Tampere Finland

Tampere University of Technology Tampere Finland IGNSS 2013 Surfer s Paradise, Queensland, Australia 16-18.7.2013 Estimation of initial state and model parameters for autonomous GNSS orbit prediction Juha Ala-Luhtala, Mari Seppänen, Simo Ali-Löytty,

More information

EE 570: Location and Navigation

EE 570: Location and Navigation EE 570: Location and Navigation Aided INS Aly El-Osery Kevin Wedeward Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA In Collaboration with Stephen Bruder Electrical and Computer

More information

Lecture 2: From Linear Regression to Kalman Filter and Beyond

Lecture 2: From Linear Regression to Kalman Filter and Beyond Lecture 2: From Linear Regression to Kalman Filter and Beyond January 18, 2017 Contents 1 Batch and Recursive Estimation 2 Towards Bayesian Filtering 3 Kalman Filter and Bayesian Filtering and Smoothing

More information

Fundamentals of attitude Estimation

Fundamentals of attitude Estimation Fundamentals of attitude Estimation Prepared by A.Kaviyarasu Assistant Professor Department of Aerospace Engineering Madras Institute Of Technology Chromepet, Chennai Basically an IMU can used for two

More information

Czech Technical University in Prague. Faculty of Electrical Engineering Department of control Engineering. Diploma Thesis

Czech Technical University in Prague. Faculty of Electrical Engineering Department of control Engineering. Diploma Thesis Czech Technical University in Prague Faculty of Electrical Engineering Department of control Engineering Diploma Thesis Performance comparison of Extended and Unscented Kalman Filter implementation in

More information

Lecture 7: Optimal Smoothing

Lecture 7: Optimal Smoothing Department of Biomedical Engineering and Computational Science Aalto University March 17, 2011 Contents 1 What is Optimal Smoothing? 2 Bayesian Optimal Smoothing Equations 3 Rauch-Tung-Striebel Smoother

More information

Lecture. Aided INS EE 570: Location and Navigation. 1 Overview. 1.1 ECEF as and Example. 1.2 Inertial Measurements

Lecture. Aided INS EE 570: Location and Navigation. 1 Overview. 1.1 ECEF as and Example. 1.2 Inertial Measurements Lecture Aided EE 570: Location and Navigation Lecture Notes Update on April 13, 2016 Aly El-Osery and Kevin Wedeward, Electrical Engineering Dept., New Mexico Tech In collaoration with Stephen Bruder,

More information

STATISTICAL ORBIT DETERMINATION

STATISTICAL ORBIT DETERMINATION STATISTICAL ORBIT DETERMINATION Satellite Tracking Example of SNC and DMC ASEN 5070 LECTURE 6 4.08.011 1 We will develop a simple state noise compensation (SNC) algorithm. This algorithm adds process noise

More information

Dead Reckoning navigation (DR navigation)

Dead Reckoning navigation (DR navigation) Dead Reckoning navigation (DR navigation) Prepared by A.Kaviyarasu Assistant Professor Department of Aerospace Engineering Madras Institute Of Technology Chromepet, Chennai A Navigation which uses a Inertial

More information

Rao-Blackwellized Particle Filtering for 6-DOF Estimation of Attitude and Position via GPS and Inertial Sensors

Rao-Blackwellized Particle Filtering for 6-DOF Estimation of Attitude and Position via GPS and Inertial Sensors Rao-Blackwellized Particle Filtering for 6-DOF Estimation of Attitude and Position via GPS and Inertial Sensors GRASP Laboratory University of Pennsylvania June 6, 06 Outline Motivation Motivation 3 Problem

More information

FIBER OPTIC GYRO-BASED ATTITUDE DETERMINATION FOR HIGH- PERFORMANCE TARGET TRACKING

FIBER OPTIC GYRO-BASED ATTITUDE DETERMINATION FOR HIGH- PERFORMANCE TARGET TRACKING FIBER OPTIC GYRO-BASED ATTITUDE DETERMINATION FOR HIGH- PERFORMANCE TARGET TRACKING Elias F. Solorzano University of Toronto (Space Flight Laboratory) Toronto, ON (Canada) August 10 th, 2016 30 th AIAA/USU

More information

GPS Geodesy - LAB 7. Neglecting the propagation, multipath, and receiver errors, eq.(1) becomes:

GPS Geodesy - LAB 7. Neglecting the propagation, multipath, and receiver errors, eq.(1) becomes: GPS Geodesy - LAB 7 GPS pseudorange position solution The pseudorange measurements j R i can be modeled as: j R i = j ρ i + c( j δ δ i + ΔI + ΔT + MP + ε (1 t = time of epoch j R i = pseudorange measurement

More information

Application of state observers in attitude estimation using low-cost sensors

Application of state observers in attitude estimation using low-cost sensors Application of state observers in attitude estimation using low-cost sensors Martin Řezáč Czech Technical University in Prague, Czech Republic March 26, 212 Introduction motivation for inertial estimation

More information

FUSION OF GPS, INS AND ODOMETRIC DATA FOR AUTOMOTIVE NAVIGATION

FUSION OF GPS, INS AND ODOMETRIC DATA FOR AUTOMOTIVE NAVIGATION 1th European Signal Processing Conference (EUSIPCO 27), Poznan, Poland, September 3-7, 27, copyright by EURASIP FUSION OF GPS, INS AND ODOMETRIC DATA FOR AUTOMOTIVE NAVIGATION M. Spangenberg, V. Calmettes

More information

SIMPLIFIED ORBIT DETERMINATION ALGORITHM FOR LOW EARTH ORBIT SATELLITES USING SPACEBORNE GPS NAVIGATION SENSOR

SIMPLIFIED ORBIT DETERMINATION ALGORITHM FOR LOW EARTH ORBIT SATELLITES USING SPACEBORNE GPS NAVIGATION SENSOR ARTIFICIAL SATELLITES, Vol. 49, No. 2 2014 DOI: 10.2478/arsa-2014-0007 SIMPLIFIED ORBIT DETERMINATION ALGORITHM FOR LOW EARTH ORBIT SATELLITES USING SPACEBORNE GPS NAVIGATION SENSOR ABSTRACT Sandip Tukaram

More information

Tampere University of Technology. Ala-Luhtala, Juha; Seppänen, Mari; Ali-Löytty, Simo; Piché, Robert; Nurminen, Henri

Tampere University of Technology. Ala-Luhtala, Juha; Seppänen, Mari; Ali-Löytty, Simo; Piché, Robert; Nurminen, Henri Tampere University of Technology Author(s) Title Ala-Luhtala, Juha; Seppänen, Mari; Ali-Löytty, Simo; Piché, Robert; Nurminen, Henri Estimation of initial state and model parameters for autonomous GNSS

More information

Automated Tuning of the Nonlinear Complementary Filter for an Attitude Heading Reference Observer

Automated Tuning of the Nonlinear Complementary Filter for an Attitude Heading Reference Observer Automated Tuning of the Nonlinear Complementary Filter for an Attitude Heading Reference Observer Oscar De Silva, George K.I. Mann and Raymond G. Gosine Faculty of Engineering and Applied Sciences, Memorial

More information

Fuzzy Adaptive Kalman Filtering for INS/GPS Data Fusion

Fuzzy Adaptive Kalman Filtering for INS/GPS Data Fusion A99936769 AMA-99-4307 Fuzzy Adaptive Kalman Filtering for INS/GPS Data Fusion J.Z. Sasiadek* and Q. Wang** Dept. of Mechanical & Aerospace Engineering Carleton University 1125 Colonel By Drive, Ottawa,

More information

Fundamentals of High Accuracy Inertial Navigation Averil B. Chatfield Table of Contents

Fundamentals of High Accuracy Inertial Navigation Averil B. Chatfield Table of Contents Navtech Part #2440 Preface Fundamentals of High Accuracy Inertial Navigation Averil B. Chatfield Table of Contents Chapter 1. Introduction...... 1 I. Forces Producing Motion.... 1 A. Gravitation......

More information

Adaptive Unscented Kalman Filter with Multiple Fading Factors for Pico Satellite Attitude Estimation

Adaptive Unscented Kalman Filter with Multiple Fading Factors for Pico Satellite Attitude Estimation Adaptive Unscented Kalman Filter with Multiple Fading Factors for Pico Satellite Attitude Estimation Halil Ersin Söken and Chingiz Hajiyev Aeronautics and Astronautics Faculty Istanbul Technical University

More information

Principles of the Global Positioning System Lecture 14

Principles of the Global Positioning System Lecture 14 12.540 Principles of the Global Positioning System Lecture 14 Prof. Thomas Herring http://geoweb.mit.edu/~tah/12.540 Propagation Medium Propagation: Signal propagation from satellite to receiver Light-time

More information

Design of Adaptive Filtering Algorithm for Relative Navigation

Design of Adaptive Filtering Algorithm for Relative Navigation Design of Adaptive Filtering Algorithm for Relative Navigation Je Young Lee, Hee Sung Kim, Kwang Ho Choi, Joonhoo Lim, Sung Jin Kang, Sebum Chun, and Hyung Keun Lee Abstract Recently, relative navigation

More information

An Adaptive Initial Alignment Algorithm Based on Variance Component Estimation for a Strapdown Inertial Navigation System for AUV

An Adaptive Initial Alignment Algorithm Based on Variance Component Estimation for a Strapdown Inertial Navigation System for AUV S S symmetry Article An Adaptive Initial Alignment Algorithm Based on Variance Component Estimation for a Strapdown Inertial Navigation System for AUV Qianhui Dong 1,, Yibing Li 1, Qian Sun 1, * and Ya

More information

Particle Filters. Outline

Particle Filters. Outline Particle Filters M. Sami Fadali Professor of EE University of Nevada Outline Monte Carlo integration. Particle filter. Importance sampling. Degeneracy Resampling Example. 1 2 Monte Carlo Integration Numerical

More information

Full-dimension Attitude Determination Based on Two-antenna GPS/SINS Integrated Navigation System

Full-dimension Attitude Determination Based on Two-antenna GPS/SINS Integrated Navigation System Full-dimension Attitude Determination Based on Two-antenna GPS/SINS Integrated Navigation System Lifan Zhang Institute of Integrated Automation School of Electronic and Information Engineering Xi an Jiaotong

More information

CDGPS-Based Relative Navigation for Multiple Spacecraft. Megan Leigh Mitchell

CDGPS-Based Relative Navigation for Multiple Spacecraft. Megan Leigh Mitchell CDGPS-Based Relative Navigation for Multiple Spacecraft by Megan Leigh Mitchell Bachelor of Science Aerospace Engineering University of Texas at Austin, 2000 Submitted to the Department of Aeronautics

More information

1 Kalman Filter Introduction

1 Kalman Filter Introduction 1 Kalman Filter Introduction You should first read Chapter 1 of Stochastic models, estimation, and control: Volume 1 by Peter S. Maybec (available here). 1.1 Explanation of Equations (1-3) and (1-4) Equation

More information

Design and Flight Performance of the Orion. Pre-Launch Navigation System

Design and Flight Performance of the Orion. Pre-Launch Navigation System Design and Flight Performance of the Orion Pre-Launch Navigation System Renato Zanetti 1, Greg Holt 2, Robert Gay 3, and Christopher D Souza 4 NASA Johnson Space Center, Houston, Texas 77058. Jastesh Sud

More information

EESC Geodesy with the Global Positioning System. Class 4: The pseudorange and phase observables

EESC Geodesy with the Global Positioning System. Class 4: The pseudorange and phase observables EESC 9945 Geodesy with the Global Positioning System Class 4: The pseudorange and phase observables In previous classes we had presented the equation for the pseudorange as the true range biased by the

More information

ENGR352 Problem Set 02

ENGR352 Problem Set 02 engr352/engr352p02 September 13, 2018) ENGR352 Problem Set 02 Transfer function of an estimator 1. Using Eq. (1.1.4-27) from the text, find the correct value of r ss (the result given in the text is incorrect).

More information

EE565:Mobile Robotics Lecture 6

EE565:Mobile Robotics Lecture 6 EE565:Mobile Robotics Lecture 6 Welcome Dr. Ahmad Kamal Nasir Announcement Mid-Term Examination # 1 (25%) Understand basic wheel robot kinematics, common mobile robot sensors and actuators knowledge. Understand

More information

Autonomous Mobile Robot Design

Autonomous Mobile Robot Design Autonomous Mobile Robot Design Topic: Extended Kalman Filter Dr. Kostas Alexis (CSE) These slides relied on the lectures from C. Stachniss, J. Sturm and the book Probabilistic Robotics from Thurn et al.

More information

Nonlinear State Estimation! Particle, Sigma-Points Filters!

Nonlinear State Estimation! Particle, Sigma-Points Filters! Nonlinear State Estimation! Particle, Sigma-Points Filters! Robert Stengel! Optimal Control and Estimation, MAE 546! Princeton University, 2017!! Particle filter!! Sigma-Points Unscented Kalman ) filter!!

More information

State Estimation for Autopilot Control of Small Unmanned Aerial Vehicles in Windy Conditions

State Estimation for Autopilot Control of Small Unmanned Aerial Vehicles in Windy Conditions University of Colorado, Boulder CU Scholar Aerospace Engineering Sciences Graduate Theses & Dissertations Aerospace Engineering Sciences Summer 7-23-2014 State Estimation for Autopilot Control of Small

More information

Nonlinear Estimation Techniques for Impact Point Prediction of Ballistic Targets

Nonlinear Estimation Techniques for Impact Point Prediction of Ballistic Targets Nonlinear Estimation Techniques for Impact Point Prediction of Ballistic Targets J. Clayton Kerce a, George C. Brown a, and David F. Hardiman b a Georgia Tech Research Institute, Georgia Institute of Technology,

More information

CS491/691: Introduction to Aerial Robotics

CS491/691: Introduction to Aerial Robotics CS491/691: Introduction to Aerial Robotics Topic: Midterm Preparation Dr. Kostas Alexis (CSE) Areas of Focus Coordinate system transformations (CST) MAV Dynamics (MAVD) Navigation Sensors (NS) State Estimation

More information

Integrated Navigation System Using Sigma-Point Kalman Filter and Particle Filter

Integrated Navigation System Using Sigma-Point Kalman Filter and Particle Filter Integrated Navigation System Using Sigma-Point Kalman Filter and Particle Filter Dr. Milos Sota and Dr. Milan Sopata and Dr. Stefan Berezny Academy of Armed Forces, Demanova 393, 311 Liptovsy Miulas, Slova

More information

A Low-Cost GPS Aided Inertial Navigation System for Vehicular Applications

A Low-Cost GPS Aided Inertial Navigation System for Vehicular Applications A Low-Cost GPS Aided Inertial Navigation System for Vehicular Applications ISAAC SKOG Master of Science Thesis Stockholm, Sweden 2005-03-09 IR-SB-EX-0506 1 Abstract In this report an approach for integration

More information

VN-100 Velocity Compensation

VN-100 Velocity Compensation VN-100 Velocity Compensation Velocity / Airspeed Aiding for AHRS Applications Application Note Abstract This application note describes how the VN-100 can be used in non-stationary applications which require

More information

Investigation of the Attitude Error Vector Reference Frame in the INS EKF

Investigation of the Attitude Error Vector Reference Frame in the INS EKF Investigation of the Attitude Error Vector Reference Frame in the INS EKF Stephen Steffes, Jan Philipp Steinbach, and Stephan Theil Abstract The Extended Kalman Filter is used extensively for inertial

More information

Improving Adaptive Kalman Estimation in GPS/INS Integration

Improving Adaptive Kalman Estimation in GPS/INS Integration THE JOURNAL OF NAVIGATION (27), 6, 517 529. f The Royal Institute of Navigation doi:1.117/s373463374316 Printed in the United Kingdom Improving Adaptive Kalman Estimation in GPS/INS Integration Weidong

More information

Refinements to the General Methodology Behind Strapdown Airborne Gravimetry

Refinements to the General Methodology Behind Strapdown Airborne Gravimetry Refinements to the General Methodology Behind Strapdown Airborne Gravimetry AE 8900 MS Special Problems Report Space Systems Design Lab (SSDL) Guggenheim School of Aerospace Engineering Georgia Institute

More information

L06. LINEAR KALMAN FILTERS. NA568 Mobile Robotics: Methods & Algorithms

L06. LINEAR KALMAN FILTERS. NA568 Mobile Robotics: Methods & Algorithms L06. LINEAR KALMAN FILTERS NA568 Mobile Robotics: Methods & Algorithms 2 PS2 is out! Landmark-based Localization: EKF, UKF, PF Today s Lecture Minimum Mean Square Error (MMSE) Linear Kalman Filter Gaussian

More information

State-Estimator Design for the KTH Research Concept Vehicle

State-Estimator Design for the KTH Research Concept Vehicle DEGREE PROJECT IN VEHICLE ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2016 State-Estimator Design for the KTH Research Concept Vehicle FAN GAO KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING

More information

Lecture 6: Bayesian Inference in SDE Models

Lecture 6: Bayesian Inference in SDE Models Lecture 6: Bayesian Inference in SDE Models Bayesian Filtering and Smoothing Point of View Simo Särkkä Aalto University Simo Särkkä (Aalto) Lecture 6: Bayesian Inference in SDEs 1 / 45 Contents 1 SDEs

More information

UAVBook Supplement Full State Direct and Indirect EKF

UAVBook Supplement Full State Direct and Indirect EKF UAVBook Supplement Full State Direct and Indirect EKF Randal W. Beard March 14, 217 This supplement will explore alternatives to the state estimation scheme presented in the book. In particular, we will

More information

State Estimation of Linear and Nonlinear Dynamic Systems

State Estimation of Linear and Nonlinear Dynamic Systems State Estimation of Linear and Nonlinear Dynamic Systems Part III: Nonlinear Systems: Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) James B. Rawlings and Fernando V. Lima Department of

More information

Quaternion based Extended Kalman Filter

Quaternion based Extended Kalman Filter Quaternion based Extended Kalman Filter, Sergio Montenegro About this lecture General introduction to rotations and quaternions. Introduction to Kalman Filter for Attitude Estimation How to implement and

More information

with Application to Autonomous Vehicles

with Application to Autonomous Vehicles Nonlinear with Application to Autonomous Vehicles (Ph.D. Candidate) C. Silvestre (Supervisor) P. Oliveira (Co-supervisor) Institute for s and Robotics Instituto Superior Técnico Portugal January 2010 Presentation

More information

Static alignment of inertial navigation systems using an adaptive multiple fading factors Kalman filter

Static alignment of inertial navigation systems using an adaptive multiple fading factors Kalman filter Systems Science & Control Engineering An Open Access Journal ISSN: (Print) 2164-2583 (Online) Journal homepage: http://www.tandfonline.com/loi/tssc20 Static alignment of inertial navigation systems using

More information

Low-Cost Integrated Navigation System

Low-Cost Integrated Navigation System Institute of Flight System Dynamics Technische Universität München Prof. Dr.-Ing. Florian Holzapfel Eecuted at Robotics and Automation Lab Centre for Intelligent Information Processing Systems University

More information

Locating and supervising relief forces in buildings without the use of infrastructure

Locating and supervising relief forces in buildings without the use of infrastructure Locating and supervising relief forces in buildings without the use of infrastructure Tracking of position with low-cost inertial sensors Martin Trächtler 17.10.2014 18th Leibniz Conference of advanced

More information

Attitude determination method using single-antenna GPS, Gyro and Magnetometer

Attitude determination method using single-antenna GPS, Gyro and Magnetometer 212 Asia-Pacific International Symposium on Aerospace echnology Nov. 13-1, Jeju, Korea Attitude determination method using single-antenna GPS, Gyro and Magnetometer eekwon No 1, Am Cho 2, Youngmin an 3,

More information

Multi-sensor data fusion based on Information Theory. Application to GNSS positionning and integrity monitoring

Multi-sensor data fusion based on Information Theory. Application to GNSS positionning and integrity monitoring Multi-sensor data fusion based on Information Theory. Application to GNSS positionning and integrity monitoring Nourdine Aït Tmazirte, Maan E. El Najjar, Cherif Smaili and Denis Pomorski LAGIS UMR 89 CNRS/Université-Lille

More information

Sigma-Point Kalman Filters for Integrated Navigation

Sigma-Point Kalman Filters for Integrated Navigation Sigma-Point Kalman Filters for Integrated Navigation Rudolph van der Merwe and Eric A. Wan Adaptive Systems Lab, OGI School of Science & Engineering, Oregon Health & Science University BIOGRAPHY Rudolph

More information

GPS/INS Tightly coupled position and attitude determination with low-cost sensors Master Thesis

GPS/INS Tightly coupled position and attitude determination with low-cost sensors Master Thesis GPS/INS Tightly coupled position and attitude determination with low-cost sensors Master Thesis Michele Iafrancesco Institute for Communications and Navigation Prof. Dr. Christoph Günther Supervised by

More information

Lecture 13 Visual Inertial Fusion

Lecture 13 Visual Inertial Fusion Lecture 13 Visual Inertial Fusion Davide Scaramuzza Outline Introduction IMU model and Camera-IMU system Different paradigms Filtering Maximum a posteriori estimation Fix-lag smoothing 2 What is an IMU?

More information

TSRT14: Sensor Fusion Lecture 8

TSRT14: Sensor Fusion Lecture 8 TSRT14: Sensor Fusion Lecture 8 Particle filter theory Marginalized particle filter Gustaf Hendeby gustaf.hendeby@liu.se TSRT14 Lecture 8 Gustaf Hendeby Spring 2018 1 / 25 Le 8: particle filter theory,

More information

OPTIMAL TIME TRANSFER

OPTIMAL TIME TRANSFER OPTIMAL TIME TRANSFER James R. Wright and James Woodburn Analytical Graphics, Inc. 220 Valley Creek Blvd, Exton, PA 19341, USA Abstract We have designed an optimal time transfer algorithm using GPS carrier-phase

More information

The Research of Tight MINS/GPS Integrated navigation System Based Upon Date Fusion

The Research of Tight MINS/GPS Integrated navigation System Based Upon Date Fusion International Conference on Computer and Information echnology Application (ICCIA 016) he Research of ight MINS/GPS Integrated navigation System Based Upon Date Fusion ao YAN1,a, Kai LIU1,b and ua CE1,c

More information

Principles of the Global Positioning System Lecture 18" Mathematical models in GPS" Mathematical models used in GPS"

Principles of the Global Positioning System Lecture 18 Mathematical models in GPS Mathematical models used in GPS 12.540 Principles of the Global Positioning System Lecture 18" Prof. Thomas Herring" Room 54-820A; 253-5941" tah@mit.edu" http://geoweb.mit.edu/~tah/12.540 " Mathematical models in GPS" Review assignment

More information

Autonomous Orbit Determination via Kalman Filtering of Gravity Gradients

Autonomous Orbit Determination via Kalman Filtering of Gravity Gradients TAES-15387-R1 1 Autonomous Orbit Determination via Kalman Filtering of Gravity Gradients Xiucong Sun, Pei Chen, Christophe Macabiau, and Chao Han Abstract Spaceborne gravity gradients are proposed in this

More information

Pseudo-Measurements as Aiding to INS during GPS. Outages

Pseudo-Measurements as Aiding to INS during GPS. Outages Pseudo-Measurements as Aiding to INS during GPS Outages Itzik Klein 1, Sagi Filin 2, Tomer Toledo 3 Faculty of Civil Engineering Technion Israel Institute of Technology, Haifa 32000, Israel Published in

More information

Chapter 4 State Estimation

Chapter 4 State Estimation Chapter 4 State Estimation Navigation of an unmanned vehicle, always depends on a good estimation of the vehicle states. Especially if no external sensors or marers are available, more or less complex

More information

Particle Filter Data Fusion Enhancements for MEMS-IMU/GPS

Particle Filter Data Fusion Enhancements for MEMS-IMU/GPS ntelligent nformation Management,,, 47-4 doi:.436/iim..75 Published Online July (http://www.scirp.org/journal/iim) Particle Filter Data Fusion Enhancements for MEMS-MU/PS Abstract Yafei Ren, Xizhen Ke

More information

Kalman filtering and friends: Inference in time series models. Herke van Hoof slides mostly by Michael Rubinstein

Kalman filtering and friends: Inference in time series models. Herke van Hoof slides mostly by Michael Rubinstein Kalman filtering and friends: Inference in time series models Herke van Hoof slides mostly by Michael Rubinstein Problem overview Goal Estimate most probable state at time k using measurement up to time

More information

Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions*

Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions* Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions* Nuno Filipe Michail Kontitsis 2 Panagiotis Tsiotras 3 Abstract Based on the highly successful Quaternion Multiplicative Extended

More information

Nonlinear Observers for Integrated INS/GNSS Navigation Implementation Aspects

Nonlinear Observers for Integrated INS/GNSS Navigation Implementation Aspects Nonlinear Observers for Integrated INS/GNSS Navigation Implementation Aspects Torleiv H. Bryne, Jakob M. Hansen, Robert H. Rogne, Nadezda Sokolova, Thor I. Fossen and Tor A. Johansen POC: T.H. Bryne (torleiv.h.bryne@itk.ntnu.no)

More information

Local Positioning with Parallelepiped Moving Grid

Local Positioning with Parallelepiped Moving Grid Local Positioning with Parallelepiped Moving Grid, WPNC06 16.3.2006, niilo.sirola@tut.fi p. 1/?? TA M P E R E U N I V E R S I T Y O F T E C H N O L O G Y M a t h e m a t i c s Local Positioning with Parallelepiped

More information

A Close Examination of Multiple Model Adaptive Estimation Vs Extended Kalman Filter for Precision Attitude Determination

A Close Examination of Multiple Model Adaptive Estimation Vs Extended Kalman Filter for Precision Attitude Determination A Close Examination of Multiple Model Adaptive Estimation Vs Extended Kalman Filter for Precision Attitude Determination Quang M. Lam LexerdTek Corporation Clifton, VA 4 John L. Crassidis University at

More information

AE2160 Introduction to Experimental Methods in Aerospace

AE2160 Introduction to Experimental Methods in Aerospace AE160 Introduction to Experimental Methods in Aerospace Uncertainty Analysis C.V. Di Leo (Adapted from slides by J.M. Seitzman, J.J. Rimoli) 1 Accuracy and Precision Accuracy is defined as the difference

More information

Joint GPS and Vision Estimation Using an Adaptive Filter

Joint GPS and Vision Estimation Using an Adaptive Filter 1 Joint GPS and Vision Estimation Using an Adaptive Filter Shubhendra Vikram Singh Chauhan and Grace Xingxin Gao, University of Illinois at Urbana-Champaign Shubhendra Vikram Singh Chauhan received his

More information

Simultaneous Localization and Mapping (SLAM) Corso di Robotica Prof. Davide Brugali Università degli Studi di Bergamo

Simultaneous Localization and Mapping (SLAM) Corso di Robotica Prof. Davide Brugali Università degli Studi di Bergamo Simultaneous Localization and Mapping (SLAM) Corso di Robotica Prof. Davide Brugali Università degli Studi di Bergamo Introduction SLAM asks the following question: Is it possible for an autonomous vehicle

More information

Tracking an Accelerated Target with a Nonlinear Constant Heading Model

Tracking an Accelerated Target with a Nonlinear Constant Heading Model Tracking an Accelerated Target with a Nonlinear Constant Heading Model Rong Yang, Gee Wah Ng DSO National Laboratories 20 Science Park Drive Singapore 118230 yrong@dsoorgsg ngeewah@dsoorgsg Abstract This

More information

Sensor Aided Inertial Navigation Systems

Sensor Aided Inertial Navigation Systems Arvind Ramanandan Department of Electrical Engineering University of California, Riverside Riverside, CA 92507 April, 28th 2011 Acknowledgements: 1 Prof. Jay A. Farrell 2 Anning Chen 3 Anh Vu 4 Prof. Matthew

More information

A Stochastic Observability Test for Discrete-Time Kalman Filters

A Stochastic Observability Test for Discrete-Time Kalman Filters A Stochastic Observability Test for Discrete-Time Kalman Filters Vibhor L. Bageshwar 1, Demoz Gebre-Egziabher 2, William L. Garrard 3, and Tryphon T. Georgiou 4 University of Minnesota Minneapolis, MN

More information

Spacecraft attitude and system identication via marginal modied unscented Kalman lter utilizing the sun and calibrated three-axis-magnetometer sensors

Spacecraft attitude and system identication via marginal modied unscented Kalman lter utilizing the sun and calibrated three-axis-magnetometer sensors Scientia Iranica B (2014) 21(4), 1451{1460 Sharif University of Technology Scientia Iranica Transactions B: Mechanical Engineering www.scientiairanica.com Research Note Spacecraft attitude and system identication

More information

A Sensor Driven Trade Study for Autonomous Navigation Capabilities

A Sensor Driven Trade Study for Autonomous Navigation Capabilities A Sensor Driven Trade Study for Autonomous Navigation Capabilities Sebastián Muñoz and E. Glenn Lightsey The University of Texas at Austin, Austin, TX, 78712 Traditionally, most interplanetary exploration

More information

Orbit Representation

Orbit Representation 7.1 Fundamentals 223 For this purpose, code-pseudorange and carrier observations are made of all visible satellites at all monitor stations. The data are corrected for ionospheric and tropospheric delays,

More information

Satellite Attitude Determination with Attitude Sensors and Gyros using Steady-state Kalman Filter

Satellite Attitude Determination with Attitude Sensors and Gyros using Steady-state Kalman Filter Satellite Attitude Determination with Attitude Sensors and Gyros using Steady-state Kalman Filter Vaibhav V. Unhelkar, Hari B. Hablani Student, email: v.unhelkar@iitb.ac.in. Professor, email: hbhablani@aero.iitb.ac.in

More information

Two dimensional rate gyro bias estimation for precise pitch and roll attitude determination utilizing a dual arc accelerometer array

Two dimensional rate gyro bias estimation for precise pitch and roll attitude determination utilizing a dual arc accelerometer array Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections -- Two dimensional rate gyro bias estimation for precise pitch and roll attitude determination utilizing a dual

More information

Extension of Farrenkopf Steady-State Solutions with Estimated Angular Rate

Extension of Farrenkopf Steady-State Solutions with Estimated Angular Rate Extension of Farrenopf Steady-State Solutions with Estimated Angular Rate Andrew D. Dianetti and John L. Crassidis University at Buffalo, State University of New Yor, Amherst, NY 46-44 Steady-state solutions

More information

On Underweighting Nonlinear Measurements

On Underweighting Nonlinear Measurements On Underweighting Nonlinear Measurements Renato Zanetti The Charles Stark Draper Laboratory, Houston, Texas 7758 Kyle J. DeMars and Robert H. Bishop The University of Texas at Austin, Austin, Texas 78712

More information

Invariant Extended Kalman Filter: Theory and application to a velocity-aided estimation problem

Invariant Extended Kalman Filter: Theory and application to a velocity-aided estimation problem Invariant Extene Kalman Filter: Theory an application to a velocity-aie estimation problem S. Bonnabel (Mines ParisTech) Joint work with P. Martin (Mines ParisTech) E. Salaun (Georgia Institute of Technology)

More information

n j u = (3) b u Then we select m j u as a cross product between n j u and û j to create an orthonormal basis: m j u = n j u û j (4)

n j u = (3) b u Then we select m j u as a cross product between n j u and û j to create an orthonormal basis: m j u = n j u û j (4) 4 A Position error covariance for sface feate points For each sface feate point j, we first compute the normal û j by usin 9 of the neihborin points to fit a plane In order to create a 3D error ellipsoid

More information

Influence Analysis of Star Sensors Sampling Frequency on Attitude Determination Accuracy

Influence Analysis of Star Sensors Sampling Frequency on Attitude Determination Accuracy Sensors & ransducers Vol. Special Issue June pp. -8 Sensors & ransducers by IFSA http://www.sensorsportal.com Influence Analysis of Star Sensors Sampling Frequency on Attitude Determination Accuracy Yuanyuan

More information

Verification of a Dual-State Extended Kalman Filter with Lidar-Enabled Autonomous Hazard- Detection for Planetary Landers

Verification of a Dual-State Extended Kalman Filter with Lidar-Enabled Autonomous Hazard- Detection for Planetary Landers Marquette University e-publications@marquette Master's Theses (29 -) Dissertations, Theses, and Professional Projects Verification of a Dual-State Extended Kalman Filter with Lidar-Enabled Autonomous Hazard-

More information

UAV Navigation: Airborne Inertial SLAM

UAV Navigation: Airborne Inertial SLAM Introduction UAV Navigation: Airborne Inertial SLAM Jonghyuk Kim Faculty of Engineering and Information Technology Australian National University, Australia Salah Sukkarieh ARC Centre of Excellence in

More information

Gaussian Mixture Filter in Hybrid Navigation

Gaussian Mixture Filter in Hybrid Navigation Digest of TISE Seminar 2007, editor Pertti Koivisto, pages 1-5. Gaussian Mixture Filter in Hybrid Navigation Simo Ali-Löytty Institute of Mathematics Tampere University of Technology simo.ali-loytty@tut.fi

More information

Adaptive cubature Kalman filter based on the variance-covariance components estimation

Adaptive cubature Kalman filter based on the variance-covariance components estimation Zhang et al. The Journal of Global Positioning Systems (2017) 15:1 DOI 10.116/s41445-017-0006-z The Journal of Global Positioning Systems ORIGINAL ARTICLE Adaptive cubature Kalman filter based on the variance-covariance

More information

Impact of GPS box-wing models on LEO orbit determination

Impact of GPS box-wing models on LEO orbit determination Impact of GPS box-wing models on LEO orbit determination Heike Peter (1), Tim Springer (1),(2), Michiel Otten (1),(2) (1) PosiTim UG Sentinel-1 GPS-IIF (2) ESA/ESOC Sentinel-2 Credits:ESA gps.gov IGS Workshop

More information

State Estimation for UAVs Using Sensor Fusion

State Estimation for UAVs Using Sensor Fusion State Estimation for UAVs Using Sensor Fusion Zsófia Bodó, Béla Lantos Budapest University of Technology and Economics, Department of Control Engineering and Information Technology, MTA-BME Control Engineering

More information

Norm-Constrained Kalman Filtering

Norm-Constrained Kalman Filtering Norm-Constrained Kalman Filtering Renato Zanetti The University of Texas at Austin, Austin, Texas, 78712 Manoranjan Majji Texas A&M University, College Station, Texas 77843 Robert H. Bishop The University

More information

DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Aircraft Velocity Determination

DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Aircraft Velocity Determination DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Aircraft Velocity Determination Capt. J. Hebert and J. Keith 76th Test Squadron (CIGTF) Holloman AFB, NM S. Ryan, M. Szarmes, G. Lachapelle

More information

Measurement Observers for Pose Estimation on SE(3)

Measurement Observers for Pose Estimation on SE(3) Measurement Observers for Pose Estimation on SE(3) By Geoffrey Stacey u4308250 Supervised by Prof. Robert Mahony 24 September 2010 A thesis submitted in part fulfilment of the degree of Bachelor of Engineering

More information

An Adaptive Filter for a Small Attitude and Heading Reference System Using Low Cost Sensors

An Adaptive Filter for a Small Attitude and Heading Reference System Using Low Cost Sensors An Adaptive Filter for a Small Attitude and eading Reference System Using Low Cost Sensors Tongyue Gao *, Chuntao Shen, Zhenbang Gong, Jinjun Rao, and Jun Luo Department of Precision Mechanical Engineering

More information

Autonomous Mobile Robot Design

Autonomous Mobile Robot Design Autonomous Mobile Robot Design Topic: Inertial Measurement Unit Dr. Kostas Alexis (CSE) Where am I? What is my environment? Robots use multiple sensors to understand where they are and how their environment

More information

Bayes Filter Reminder. Kalman Filter Localization. Properties of Gaussians. Gaussians. Prediction. Correction. σ 2. Univariate. 1 2πσ e.

Bayes Filter Reminder. Kalman Filter Localization. Properties of Gaussians. Gaussians. Prediction. Correction. σ 2. Univariate. 1 2πσ e. Kalman Filter Localization Bayes Filter Reminder Prediction Correction Gaussians p(x) ~ N(µ,σ 2 ) : Properties of Gaussians Univariate p(x) = 1 1 2πσ e 2 (x µ) 2 σ 2 µ Univariate -σ σ Multivariate µ Multivariate

More information

Sigma-Point Kalman Filters for Nonlinear Estimation and Sensor-Fusion - Applications to Integrated Navigation - Rudolph van der Merwe and Eric A.

Sigma-Point Kalman Filters for Nonlinear Estimation and Sensor-Fusion - Applications to Integrated Navigation - Rudolph van der Merwe and Eric A. Sigma-Point Kalman Filters for Nonlinear Estimation and Sensor-Fusion - Applications to Integrated Navigation - Rudolph van der Merwe and Eric A. Wan OGI School of Science & Engineering, Oregon Health

More information