> ## Documentation Index
> Fetch the complete documentation index at: https://aegean.ai/llms.txt
> Use this file to discover all available pages before exploring further.
# Discrete Bayes Filter
> Introduction to Bayesian filtering using a discrete state space model for tracking.
This section introduces Bayesian filtering through a practical example of tracking a dog in a hallway. It demonstrates how to combine noisy sensor measurements with movement predictions to estimate position.
## Key Concepts
* **Prior and Posterior Distributions**: How beliefs are updated with new information
* **Prediction Step**: Incorporating movement uncertainty through convolution
* **Update Step**: Using Bayes' theorem to incorporate measurements
* **Multimodal Distributions**: Handling multiple hypotheses about position
This section is adapted from the excellent book [Kalman and Bayesian Filters in Python](https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python) by Roger Labbe.
Open the original interactive notebook in Google Colab to execute the code and explore the concepts.
## Notebook Preview
**Key references**: (Lukežič et al., 2016; Karl et al., 2016; Frazier, 2018; Wilson et al., 2011)
## References
* Frazier, P. (2018). *A Tutorial on Bayesian Optimization*.
* Karl, M., Soelch, M., Bayer, J., Smagt, P. (2016). *Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data*.
* Lukežič, A., Vojíř, T., Čehovin, L., Matas, J., Kristan, M. (2016). *Discriminative correlation filter with channel and Spatial Reliability*.
* Wilson, A., Knowles, D., Ghahramani, Z. (2011). *Gaussian Process Regression Networks*.
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