Linear/Extended Kalman and Particle Filters

GitHub Repository

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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