Color noise is a special kind of noise often occurring in localization systems, and it is more suitable than the general Gaussian white noise to model time dependence due to time delay or high-frequency sampling. This paper derives a nonlinear Gaussian filtering framework for multi-step colored noise systems using noise whitening techniques and Bayes rule. Meanwhile, the cubature rule is used to solve the Gaussian-weighted integral in the proposed Gaussian filtering framework, resulting in an analytic form of posterior state estimate. Compared with the existing nonlinear filtering algorithms, the proposed method has obvious advantages in colored noise systems because it fully takes into account the time dependence of colored noise. Finally, the effectiveness and advantages of the proposed algorithm are verified with a classical target tracking system.

Hydrogen gas sensing is critical for energy storage, industrial safety, and environmental monitoring. However, traditional sensors still face challenges in selectivity, sensitivity, and stability. This work introduces an innovative N-polar GaN/AlGaN high-electron-mobility transistor (HEMT) with a 10 nm Pd catalytic layer as a hydrogen sensor. The device achieves ppm-level H₂ detection with rapid recovery and reusability, which is comparable to or even exceeds the performance of conventional Ga-polar HEMTs. The N-polar structure enhances sensitivity through its unique polarization-induced 2DEG and intrinsic back barrier, while the Pd layer catalyzes H₂ dissociation, forming a dipole layer that can modulate the Schottky barrier height. Experimental results demonstrate superior performance at both room temperature and elevated temperatures. Specifically, at 200 °C, the sensor exhibits a response of 102% toward 200 ppm H₂, with response/recovery times of 150 s/17 s. This represents a 96% enhancement in sensitivity and a reduction of 180 s/14 s in response/recovery times compared to room-temperature conditions (23 °C). These findings highlight the potential of N-polar HEMTs for high-performance hydrogen sensing applications.