The document discusses the Kalman Filter and its applications in navigation and positioning, including an overview of its mathematical process and relevant equations. It specifically details its use in train position tracking, outlining the approach for accurate predictions despite measurement noise. Additionally, it highlights various other applications of the Kalman Filter in fields such as autopilots, weather forecasting, and computer vision.

1. Click to edit Master title style
IEM3010 – Navigation and Positioning
Kalman Filter and it’s application in
Navigation and Positioning
Presenter Harish Kumar Singh
(IVEM177319)
Communicative Electronics
Thomas Johann Seebeck Department of
Electronics

2. Topics
1. Kalman Filter
2. Flow Chart
3. Important Equations
4. Multi-Dimension Example
5. Equations and Matrixes
6. Train Position Tracking using Kalman Filter
6.1 Motion Equations
6.2 Kalman Filter Calculation
6.3 Position Analysis
6.4 Velocity Analysis
5. Additional Applications of Kalman Filter
4/24/2018 Navigation and Positioning (IEM3010)

3. Kalman Filter
It’s a iterative mathematical process that use a
set of equations and consecutive data inputs
to quickly estimate the true value, position,
velocity etc of the object being measured,
when the measured value contain unpredicted
or random error,uncertainty or variation.
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4. Flow Chart
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5. Important Equations
Emea ↓ =>KG↑=>Eestt moves faster to actual value
Emea ↑ =>KG↓=>Eestt moves slower to actual value
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6. Multi-Dimension Example
X: State matrix
u : control variable matrix
w: predicted state noise matrix
Q: process noise covariance
matrix
K: Kalman gain
H,C,I: Identity matrix
Y: measurement of the state
Z: measurement noise
P: Process covariance matrix
(represent error in the
estimation)
R: Sensor noise covariance
matrix (measurement error)
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7. Equations and Matrixes
• The Kinematic Equations
• Variance - Standard Deviation –
Covariance
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8. Equation and Matrix
• State Covariance
•
• Kalman Gain
•
•
• New Observation
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9. Equation and Matrix
• Current State
•
•
• Previous covariance matrix
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10. Train Position Tracking using
Kalman Filter
Problem Statement: Predict the position and
velocity of a moving train 2 seconds ahead.
Approach: Measuring (sample) the position of the train every dt
= 0.1 seconds. But, because of imperfect apparatuses, weather etc., the
instantaneous velocity, derived from 2 consecutive position
measurements is inaccurate. So, we use Kalman filter as we need an
accurate and smooth estimate for the velocity in order to predict train's
position in the future. We assume that the measurement noise is normally
distributed, with mean 0 and standard deviation SIGMA.
Simulation:
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11. Motion Equations
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12. Kalman Filter Calculation
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13. Position Analysis
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14. Velocity Analysis
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15. Velocity Analysis
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16. Additional Applications of
Kalman Filter
• Autopilot
• Battery state of charge (SoC) estimation
• Brain-computer interface
• Tracking of charged particles in particle
detectors
• Tracking of objects in computer vision
• Inertial guidance system
• Orbit Determination
• Radar tracker
• Seismology
• Speech enhancement
• Weather forecasting
4/24/2018 Navigation and Positioning (IEM3010)

17. Thank You!
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