The multi-pass optimal finite impulse response (OFIR) filtering approach is developed for industrial processes with unknown initial conditions under temporary model mismatches. The forward and backward OFIR filters are derived in the batch and fast iterative forms using recursions. The doublepass OFIR (DOFIR) filter supported by the unbiased FIR (UFIR) filter and triple-pass OFIR (TOFIR) filter starting with some initial values are designed and extensively investigated using simulations and experimental data. It is shown that the DOFIR and TOFIR filters are able to essentially improve the performance close to the initial values and are more robust against temporary model mismatches than the Kalman, OFIR, and UFIR filters.

Early detection of different levels of tremors helps to obtain a more accurate diagnosis of Parkinson’s disease and to increase the therapy options for a better quality of life for patients. This work proposes a non-invasive strategy to measure the severity of tremors with the aim of diagnosing one of the first three levels of Parkinson’s disease by the Unified Parkinson’s Disease Rating Scale (UPDRS). A tremor being an involuntary motion that mainly appears in the hands; the dataset is acquired using a leap motion controller that measures 3D coordinates of each finger and the palmar region. Texture features are computed using sum and difference of histograms (SDH) to characterize the dataset, varying the window size; however, only the most fundamental elements are used in the classification stage. A machine learning classifier provides the final classification results of the tremor level. The effectiveness of our approach is obtained by a set of performance metrics, which are also used to show a comparison between different proposed designs.