This paper computationally explores the optical response of various designs of one-dimensional photonic crystal optical filters comprised of alternating layers of dense zirconia and zirconia aerogel. COMSOL Multiphysics software is used to assess the optical characteristics of the filters. The performance of the filters within a thermophotovoltaic (TPV) system with a blackbody emitter and GaSb PV cell is investigated using two different methods including an ideal case wherein the emitter and PV cell are infinite parallel planes and the Monte Carlo ray-tracing method (MCM) with finite areas of its components. Results show that the optimized filter structure is comprised of two stacks of 5 bilayers with different peak positions stacked to form a single structure. When the optimized filter is used in the ideal TPV configuration, a spectral efficiency of 46%, a system efficiency of 33%, and a power density of 8.5 W/cm2 are achieved at the emitter temperature of 1800 K. According to the MCM code, a TPV system comprised of the optimized filter, an emitter, and a PV cell with equal areas of 2 x 2 cm and a 1 mm gap achieves a spectral efficiency of 45%, a system efficiency of 25% and a power density of 7.8 W/cm2 at the emitter temperature of 1800 K. Moreover, MCM results reveal that when the emitter temperature and gap length are 1800 K and 1 mm, respectively, a maximum system efficiency of 27% is realized at an optimal ratio of 0.75 between the PV cell area and the emitter area.