Kalman Filters in AI & Artificial Intelligence

The Kalman Filter starts with the Predict step. It uses the robot's internal model of motion (e.g., 'If I turn the wheels at this speed, I should be here in 10ms') to estimate the new state. This prediction is not perfect—motors slip and physics is complex—so the Uncertainty (the width of our Gaussian bell curve) grows larger during this step. We are 'Guessing' our new position based on our previous actions.

Once a sensor reading arrives (e.g., from a GPS or LiDAR), we perform the Update step. We compare the Measurement to our Prediction. If they match, our uncertainty shrinks. If they disagree, the filter calculates the Kalman Gain—a weight that decides whether to trust the prediction or the measurement more. This results in an Optimal Estimate that is mathematically more accurate than either the sensor or the prediction alone.

The standard Kalman Filter assumes that systems move in straight lines (linear). But the real world is Non-Linear—robots turn, accelerate, and rotate. To handle this, we use the Extended Kalman Filter (EKF). It uses a mathematical trick called Linearization (calculating the derivative or 'Jacobian') at every step to approximate the curved motion as a series of tiny straight lines. This is the foundation of modern navigation systems in everything from smartphones to self-driving cars.

How does a robot know where it is when its sensors are noisy and imperfect? The Kalman Filter is the mathematical 'Predictor' that combines noisy data into a single, accurate estimate.

A Kalman Filter works in two steps: 'Predict' (where we should be based on our motion) and 'Update' (where we are based on a new sensor reading).

The filter uses 'Gaussian Distributions' (bell curves) to represent uncertainty. The peak is the estimate, and the width is our doubt.

Checkpoint: What are the two main steps of the Kalman Filter loop?

• →Read and Write
• →Predict and Update

We use 'Extended Kalman Filters' (EKF) for non-linear systems, like a robot turning. This is the math that keeps self-driving cars in their lanes and rockets on their trajectories.

By mastering Kalman Filters, you learn to see through the 'Noise' of the physical world, creating stable and reliable autonomous systems.

Checkpoint: What does a 'Bell Curve' (Gaussian) represent in a Kalman Filter?

• →The speed of the robot
• →The probability of the robot being in a specific location, including its uncertainty

Kalman Filters mastered! You've learned to estimate. Ready to handle multiple possibilities with Particle Filters?

Compute a Real Kalman Gain. Finish computing the Kalman gain that balances trust between the model's prediction and a new sensor measurement.