Demo - Smoother - Problem - Online Estimation

Kalman Filter & Smoother Demo - Constant Velocity

Overview

This demo simulates a Kalman Filter and a Kalman Smoother applied to a constant velocity model. It tracks an object's position and velocity over time, using noisy measurements and applying the Kalman Filter to improve the state estimation. A smoother is applied in a backward pass to refine the estimates further.

How It Works

1. System Model:

   • The object moves with constant velocity.

   • The position is updated based on velocity, and noise is added to both the system's motion and the measurements.

2. Kalman Filter:

   • Prediction Step: Predict the next position and velocity based on the current state.

   • Update Step: Incorporate the noisy measurement to update the estimates of position and velocity.

   • The Kalman Gain helps balance the prediction with the measurement.

3. Kalman Smoother:

   • After filtering, a backward pass is applied to smooth the estimates over time.

   • The smoother uses the current state and past estimates to refine the trajectory.

4. Visualization:

   • True State: The real position of the object (shown in blue).

   • Noisy Measurements: Simulated noisy measurements of the position (shown in red).

   • Kalman Filter Estimate: The position estimate using the Kalman filter (shown in green).

   • Smoothed Estimate: The position estimate after applying the Kalman smoother (shown in purple).

Key Features

• Real-Time Visualization: The simulation continuously updates and visualizes the object's position, noisy measurements, and both the Kalman Filter and Smoother estimates.

• Constant Velocity Model: The object's motion assumes a constant velocity (no acceleration).

• Noise: Both measurement noise and process noise are simulated, making the filter work to improve estimates.

• Interactive Demo: Watch how the estimates evolve in real-time with the smoothing and filtering process.

Applications

✔ Navigation Systems: Kalman filters are widely used for navigation and tracking in systems like GPS, robotics, and aerospace.
✔ Signal Processing: Kalman filters are useful in denoising signals and improving measurements in uncertain environments.
✔ Control Systems: Used to estimate system states in automated control processes like robotics or vehicle control.