# Kalman Filter

#### Michel van Biezen

SPECIAL TOPICS 1 – THE KALMAN FILTER

• Special Topics – The Kalman Filter (1 of 55) What is a Kalman Filter?
• Special Topics – The Kalman Filter (2 of 55) Flowchart of a Simple Example (Single Measured Value)
• Special Topics – The Kalman Filter (3 of 55) The Kalman Gain: A Closer Look
• Special Topics – The Kalman Filter (4 of 55) The 3 Calculations of the Kalman Filter
• Special Topics – The Kalman Filter (5 of 55) A Simple Example of the Kalman Filter
• Special Topics – The Kalman Filter (6 of 55) A Simple Example of the Kalman Filter (Continued)
• Special Topics – The Kalman Filter (7 of 55) The Multi-Dimension Model 1
• Special Topics – The Kalman Filter (8 of 55) The Multi-Dimension Model 2-The State Matrix
• Special Topics – The Kalman Filter (9 of 55) The Multi-Dimension Model 3: The State Matrix
• Special Topics – The Kalman Filter (10 of 55) 4: The Control Variable Matrix
• Special Topics – The Kalman Filter (11 of 55) 5: Find the State Matrix of a Falling Object
• Special Topics – The Kalman Filter (12 of 55) 6: Update the State Matrix
• Special Topics – The Kalman Filter (13 of 55) 7: State Matrix of Moving Object in 2-D
• Special Topics – The Kalman Filter (14 of 55) 8: What is the Control Variable Matrix?
• Special Topics – The Kalman Filter (15 of 55) 9: Converting from Previous to Current State 2-D
• Special Topics – The Kalman Filter (16 of 55) 10: Converting from Previous to Current State 3-D
• Special Topics – The Kalman Filter (17 of 55) 11: Numerical Ex. of Finding the State Matrix 1-D
• Special Topics – The Kalman Filter (18 of 55) What is a Covariance Matrix?
• Special Topics – The Kalman Filter (19 of 55) What is a Variance-Covariance Matrix?
• Special Topics – The Kalman Filter (20 of 55) Example of Covariance Matrix and Standard Deviation
• Special Topics – The Kalman Filter (21 of 55) Finding the Covariance Matrix, Numerical Ex. 1
• Special Topics – The Kalman Filter (22 of 55) Finding the Covariance Matrix, Numerical Ex. 2
• Special Topics – The Kalman Filter (23 of 55) Finding the Covariance Matrix, Numerical Example
• Special Topics – The Kalman Filter (24 of 55) Finding the State Covariance Matrix: P=?
• Special Topics – The Kalman Filter (25 of 55) Explaining the State Covariance Matrix
• Special Topics – The Kalman Filter (26 of 55) Flow Chart of 2-D Kalman Filter – Tracking Airplane
• Special Topics – The Kalman Filter (27 of 55) 1. The Predicted State – Tracking Airplane
• Special Topics – The Kalman Filter (28 of 55) 2. Initial Process Covariance – Tracking Airplane
• Special Topics – The Kalman Filter (29 of 55) 3. Predicted Process Covariance – Tracking Airplane
• Special Topics – The Kalman Filter (30 of 55) 4. Calculate the Kalman Gain – Tracking Airplane
• Special Topics – The Kalman Filter (31 of 55) 5. The New Observation – Tracking Airplane
• Special Topics – The Kalman Filter (32 of 55) 6. Calculate Current State – Tracking Airplane
• Special Topics – The Kalman Filter (33 of 55) 7. Update Process Covariance – Tracking Airplane
• Special Topics – The Kalman Filter (34 of 55) 8. Current Becomes Previous – Tracking Airplane
• Special Topics – The Kalman Filter (35 of 55) 1, 2, 3 of Second Iteration – Tracking Airplane
• Special Topics – The Kalman Filter (36 of 55) 4. Kalman Gain Second Iteration – Tracking Airplane
• Special Topics – The Kalman Filter (37 of 55) 5, 6 of Second Iteration – Tracking Airplane
• Special Topics – The Kalman Filter (38 of 55) 7, 8 of Second Iteration – Tracking Airplane
• Special Topics – The Kalman Filter (39 of 55) Part 1 of Third Iteration – Tracking Airplane
• Special Topics – The Kalman Filter (40 of 55) Part 2 of Third Iteration – Tracking Airplane
• Special Topics – The Kalman Filter (41 of 55) Graphing 1st 3 Iterations (t vs x) – Tracking Airplane
• Special Topics – The Kalman Filter (42 of 55) Graphing 1st 3 Iterations (t vs v) – Tracking Airpl***

#### MATLAB

Understanding Kalman Filters

• Understanding Kalman Filters, Part 1: Why Use Kalman Filters?
• Understanding Kalman Filters, Part 2: State Observers
• Understanding Kalman Filters, Part 3: Optimal State Estimator
• Understanding Kalman Filters, Part 4: Optimal State Estimator Algorithm
• Understanding Kalman Filters, Part 5: Nonlinear State Estimators
• Understanding Kalman Filters, Part 6: How to Use a Kalman Filter in Simulink
• Understanding Kalman Filters, Part 7: How to Use an Extended Kalman Filter in Simulink