The document discusses mathematical tools for Bayesian tracking, specifically focusing on the Kalman filter and particle filters. It provides an overview of how the Kalman filter uses a time update to predict the state and a measurement update to correct it based on new measurements. It also discusses how particle filters represent the state as a set of weighted particles without requiring linearization, making them more robust though with increased computational costs compared to the Kalman filter.

1. Monocular Model-Based 3D Tracking of Rigid Objects: A Survey2008. 12. 11.백운혁Chapter 2. Mathematical Tools (Bayesian Tracking)

2. 2.6 Kalman FilteringThe kalman filter is the best possible (optimal) estimator for a large class of problems and a very effective and useful estimator for an even larger class

3. 2.6.1. Kalman FilteringTime Update(“Predict”)Measurement Update(“Correct”)

4. Discrete kalman filter time update equationsproject the state and covariance estimates forward from time step to step .2.6.1. Kalman FilteringMeasurements are derived from the internal stateNew state is modeled as a linear combination of both the previous state and som noiseuncertaintystate transitionactual stateestimate statenoiseposteriori estimate error covariancepriori estimate error covariance

5. Discrete kalman filter measurement update equationsthe next step is to actually measure the process to obtain ,and then to generate an a posteriori state estimate.2.6.1. Kalman Filteringthe actual measurementgain or blending factormeasurement matrixpredicted measurement

6. 2.6.1. Kalman FilteringTime Update (“Predict”)(1) Compute the kalman gain(1) Project the state ahead(2) Update estimate with measurement(2) Project the error covariance ahead(3) Update the error covarianceInitializeMeasurement Update (“Correct”)Initial estimates for and

7. 2.6.1. Kalman Filtering2D Position-Velocity (PV Model)

8. 2.6.1. Kalman Filtering2D Position-Velocity (PV Model)

9. 2.6.1. Extended Kalman Filtering

10. 2.6 Particle Filters

11. 2.6.2. Particle Filtersgeneral representation by a set of weighted hypotheses, or particlesdo not require the linearization of the relation between the state and the measurementsgives increased robustnessbut few papers on particle based 3D pose estimation

12. 2.6.2. Particle Filters

13. 2.6.2. Particle Filters

14. 2.6.2. Particle Filters

15. Thanks for your attention