Segmentation of Signals Using Piecewise Constant Linear Regression Models

The signal segmentation approach described herein assumes that the signal can be accurately modelled by a linear regression with piece-wise constant parameters. A simultaneous estimate of the change times is considered. The maximum likelihood and maximum a posteriori probability estimates are derived after marginalization of the linear regression parameters and the measurement noise variance, which are considered as nuisance parameters. A well-known problem is that the complexity of segmentation increases exponentially in the number of data. Therefore, two inequalities are derived enabling the exact estimate to be computed with quadratic complexity. A linear in time complexity recursive approximation is proposed as well, based on these inequalities. The method is evaluated on a speech signal previously analyzed in literature, showing that a comparable result is obtained directly without the usual tuning effort. It is also detailed how it successfully has been applied in a car for online segmentation of the driven path for supporting guidance systems