In this project, is avaialable a practical Demonstration of Linear/Extended Kalman and Particle Filters in actions in order to solve first a regression and then a classification problem.

## Third Order Autoregressive Time Series with constant parameters

In this section, a Linear Kalman filter is implemented in order to estimate the coefficients (1.2, -0.4 and 0.1) of a synthetic third order Autoregressive (AR) Process.

Overall 1.137, -0.367 and 0.0562 have been the final estimated parameters using the Linear Kalman Filter.

## Autoregressive Time Series with slowly changing parameters

In the following video, is shown how a Particle Filter Algorithm with Resampling can be used in order to reliably estimate the Autoregressive Time Series coefficients values (in this case X=1.4 and Y=-0.7).

An analogous representation, showing how the algorithm converges towards the actual coefficient values, is shown below.

## Binary classification using Extended Kalman Filter and Logistic Regression

In this example, has been used some syntetic data in which the class conditional likelihoods are Gaussian distributed with distinct means (-5 and 5) and a common covariance matrix. An Extended Kalman Filter using Logistic Regression has then been implemented in order to reliably estimate a classification boundary for this classification problem.

In order to make this classification task more challenging, different class distributions values have been tried (eg. -3, 3)

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