Robust data map design using chance constrained optimization

This paper presents a chance constrained approach to extracting linear models from reference data to be used in subsequence identification or pattern matching. Due to the ordered nature of time series data, the extracted models are sequential, with feasible domains separated by transition points. In a sequence of models, a transition point is defined as the point where one model is invalid and the next model is valid. This study contributes a probabilistic description for transition points. This probabilistic framework identifies the transition points and corresponding models such that in the presence of white Gaussian noise during subsequence detection, the transitions will still be discernible. When compared to previous work in subsequence identification, the approach in this paper has several advantages. First, it provides a rigorous selection criteria for each transition point. Second, the probabilistic method described herein effectively incorporates a priori knowledge about the expected noise characteristics. Lastly, employing this criteria in reference map creation leads to the extraction of compact model reference maps that further speed up computation online. The presented algorithm is tested using vehicle pitch data obtained from a vehicle's Inertial Measurement Unit during road data collection experiments. When compared to previously published model (in)validation work, the testing shows that the extracted reference map here is much more compact and correspondingly computationally efficient for subsequence identification.