Segmentation of Signals Using Piecewise Constant Linear Regression Models Submitted to Ieee Transactions on Signal Processing

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 eeort. It is also detailed how it successfully has been applied in a car for online segmentation of the driven path for supporting guidance systems.