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This paper extends the multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, multilevel Monte Carlo is applied to a certain variant of the particle filter, the ensemble transform particle filter (EPTF). A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles.
Due to their electrically polarized air-filled internal pores, optimized ferroelectrets exhibit a remarkable piezoelectric response, making them suitable for energy harvesting. Expanded polytetrafluoroethylene (ePTFE) ferroelectret films are laminated with two fluorinated-ethylene-propylene (FEP) copolymer films and internally polarized by corona discharge. Poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS)-coated spandex fabric is employed for the electrodes to assemble an all-organic ferroelectret nanogenerator (FENG). The outer electret-plus-electrode double layers form active device layers with deformable electric dipoles that strongly contribute to the overall piezoelectric response in the proposed concept of wearable nanogenerators. Thus, the FENG with spandex electrodes generates a short-circuit current which is twice as high as that with aluminum electrodes. The stacking sequence spandex/FEP/ePTFE/FEP/ePTFE/FEP/spandex with an average pore size of 3 mu m in the ePTFE films yields the best overall performance, which is also demonstrated by the displacement-versus-electric-field loop results. The all-organic FENGs are stable up to 90 degrees C and still perform well 9 months after being polarized. An optimized FENG makes three light emitting diodes (LEDs) blink twice with the energy generated during a single footstep. The new all-organic FENG can thus continuously power wearable electronic devices and is easily integrated, for example, with clothing, other textiles, or shoe insoles.