This project implements a discrete-time Kalman Filter in MATLAB to estimate the trajectory of a moving object from noisy measurements.
The simulation:
- generates a real trajectory,
- adds Gaussian measurement noise,
- applies a Kalman Filter,
- reconstructs the original trajectory.
The filter estimates both:
- position,
- velocity,
even though only the position is directly measured.
The system is modeled using a discrete state-space representation:
x(k+1) = A x(k) + w(k)
y(k) = H x(k) + v(k)
Where:
| Variable | Description |
|---|---|
x(k) |
State vector [position velocity]ᵀ |
A |
State transition matrix |
H |
Observation matrix |
w(k) |
Process noise |
v(k) |
Measurement noise |
State transition matrix:
A = [1 dt
0 1]
Observation matrix:
H = [1 0]
The filter operates in two stages:
x_pred = A x_hat
x_hat = x_pred + K(measurement - Hx_pred)
The Kalman Gain K automatically balances:
- model prediction,
- sensor confidence.
| Parameter | Value |
|---|---|
Time Step dt |
1 |
Process Noise q |
0.1 |
Measurement Noise R |
0.1 |
Simulation Steps N |
50 |
The simulation compares:
- true trajectory,
- noisy measurements,
- filtered trajectory.
The Kalman Filter successfully reduces noise and reconstructs the original motion.
Kalman Filters are widely used in:
- aerospace guidance,
- robotics,
- GPS navigation,
- autonomous vehicles,
- radar tracking,
- sensor fusion,
- embedded systems.
- MATLAB
- State-Space Modeling
- Stochastic Estimation
- Control Systems
Fils Elie Boungoueres M.Sc. Complex Systems Engineering — AM2AS University of Bordeaux
Fields:
- Control Systems
- Embedded Systems
- Aerospace Dynamics
- Signal Processing