Kalman Filtering Application to GNSS, GPS, INS, Navigation

Application of Kalman Filtering to GPS, INS, & Navigation


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PURPOSE & SCOPE



This is a short course for engineering managers, computer scientists, and engineers. It emphasizes subtleties, problems and limitations of estimation theory as it applies to real world situations. Course emphasis is on intuitive concepts and practical applications, rather than rigorous mathematical presentation.





Emphasis on the intuitive and practical does not imply a naive treatment. For the most benefits, students should have a basic understanding of matrix theory, state-space representation of linear systems and probability theory.





This set of notes is augmented by Kalman Filtering Theory and Practice Using MATLAB®, 4th Edition (Grewal & Andrews, Wiley & Sons, 2015), and by Global Navigation Satellite Systems, Inertial Navigation, and Integration, 4th Edition (Grewal, Andrews, & Bartone, Wiley & Sons, 2020). A complete set of Course Notes is provided.



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Course Outline


Day 1
Review of Fundamentals



• What is a Kalman Filter?

• Review of Fundamentals

• Matrix Theory

• Linear Dynamic Systems

• Probability Theory

• Random Variables

• Random Vectors

• Random Processes

• Error Modeling, Noise & Power Spectral Density

• Error Propagation

• Relationship Between Discrete and Continuous Noise Covariances • Solutions—Examples



Day 2
Kalman Filtering



• Introduction—Uses and Limitations

• Nonstandard Kalman Filtering

• Discrete Linear Kalman Filter

• Continuous Kalman Filter

• Examples and Filter Tuning

• Nonlinear Kalman Filter

• Linearized and Extended Kalman Filter

• Sigma Point (Unscented Kalman Filter)

• Particle Filters

• Examples

• Kalman Filter Engineering

• Square Root Filtering, Cholesky Factors

• Computer Demo and Workshop

• Data Rejection

• Chi-squared Statistic





Day 3
Practical Considerations & Applications



• Introduction

• Divergence and Effective Cures

• Nonlinearity Considerations

• Suboptimal Filtering

• Prefiltering and Data Rejection

• Introduction to GPS

• Segment Description of GPS

• Codes, Pseudorange, Carrier Phase Measurements

• Modeling and Real Time Calibration

• Sensor Modeling and Allan Variance

• Receiver Clock, Gyro, Acc., Magnetometer, Doppler Radar, Altimeter, Compass, Odometer



Day 4
Sensor Fusion of GPS & INS Data with Examples



• GPS Errors

• Coordinate Transformations

• Measurement Models for GPS

• Fundamentals of Inertial Navigation

• Sensor Performance

• Coning, Sculling

• Continuous and Discrete Plant and Observation Models with Examples

• Application of Kalman Filtering to INS and GPS with Examples

• Feed Forward and Feed Back Configurations

• Tightly and Loosely Coupled

• Deep INS/GNSS Integration (Ultra Tight Configuration)

• Strapdown Navigation Equations for 24 States

• 8 Error State Estimation with 4 Pseudoranges, 4 Delta Pseudoranges with MATLAB®

• Tightly Coupled Examples, 4 states (4, 8, 11 states online)

• INS Sensor Parameters

• 17 State Plant Model

• Example of Vehicular Navigation

• INS for Submarines and Ships

• AHRS



Day 5
GPS & Advanced Inertial Navigation



• Integrity & Monitoring

• Ionospheric Delay Calculations, Measurement and Estimation (Computer Programs with MATLAB ®)

• The Multipath Problem

• Two Dimension Navigation Solution

• User Position & Velocity Calculations with No Errors

• Determining Satellite Positions (with MATLAB ®)

• How to Select the Satellites from DOPS

• Simulations—DOPs and covariances

• Differential GPS

• GPS Precise Positioning

• Satellite Orbit Determination

• L1/L2Bias and Ionospheric Estimation • GPS Evolution

• WAAS (SBAS)

• GEO Uplink Subsystem (GUS) Algorithms