The Kalman Filter by Hand: Noisy Measurements, Predict & Update Steps, Kalman Gain, Constant-Velocity Tracking, Sensor Fusion & Tuning
Build the famous estimation filter one cell at a time. You will average noisy readings recursively, add process and measurement noise, run predict and update steps with the Kalman gain, track a moving object with a constant-velocity model written out cell by cell, fuse two sensors by their variances, handle missing readings and tune the filter by error, all with toy data and every cell checked as you go.
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About this course
This course builds a Kalman filter one cell at a time on toy data from a fictional sensor lab. You start with the running average as a recursive update, weight two sensors by inverse variance and then run a full one-dimensional filter: predict the state and its variance, compute the Kalman gain and update both. You find the steady gain for different process noise, measure lag after a level jump, track a cart with a constant-velocity model whose 2×2 covariance is written out as four cells, fuse two sensors, gate outliers and skip missing readings, and finally compare five estimators by RMSE in a chart.
Lessons
- Noisy Measurements: True Value vs Readings and the Running Average as a Recursive Update Pro
- Variances and Weighting: Inverse-Variance Weights, Combining Two Readings and the Uncertainty After Combining Pro
- The 1-D Filter: Predict, the Kalman Gain K = P/(P+R) and Update in a Step Table Pro
- Process Noise: Q vs R, How the Gain Settles, and Lag vs Noise in a Chart Pro
- Constant-Velocity Model: Position and Velocity States and the 2×2 Covariance as Four Cells Pro
- Sensor Fusion: Two Sensors with Different Noise, Sequential Updates and the Fused Estimate Pro
- Missing and Outlier Readings: Skipping the Update and a Gating Rule on the Innovation Pro
- Tuning & Comparison: RMSE for Several Q/R Pairs vs a Moving Average and an Alpha–Beta Filter Pro