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This notebook introduces the Kalman filter through one-dimensional examples. Starting from simple cases, it builds intuition about how the filter combines predictions with noisy measurements to estimate hidden state.

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Key Concepts

  • Gaussian Distributions: The Kalman filter’s representation of uncertainty
  • Prediction and Update: The two-step recursive estimation process
  • Kalman Gain: Optimal weighting between prediction and measurement
  • Tracking Examples: Position estimation from noisy sensor data
This notebook is adapted from the excellent book Kalman and Bayesian Filters in Python by Roger Labbe.

Run the Tutorial

Open the original interactive notebook in Google Colab to execute the code and explore the concepts.

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Notebook Preview

Key references: (Wilson et al., 2011; Raissi et al., 2017; Frazier, 2018; Lukežič et al., 2016)

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References

  • Frazier, P. (2018). A Tutorial on Bayesian Optimization.
  • Lukežič, A., Vojíř, T., Čehovin, L., Matas, J., Kristan, M. (2016). Discriminative correlation filter with channel and Spatial Reliability.
  • Raissi, M., Perdikaris, P., Karniadakis, G. (2017). Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations.
  • Wilson, A., Knowles, D., Ghahramani, Z. (2011). Gaussian Process Regression Networks.
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