Hyperspectral remote sensing imagery contains rich spectral image information, which shows a strong ability to distinguish targets on the ground. Anomaly target detection does not require prior information about the target; this characteristic makes it more convenient to detect the target because prior information is hard to acquire. Therefore, anomaly target detection is widely used in hyperspectral imagery applications. Many anomaly target detection algorithms are proposed by researchers. We propose two models to improve the traditional Kernel Reed-Xiaoli (RX) and Orthogonal RX method. First, Gram–Schmidt Orthogonalization and Householder Transformation are respectively used to construct a data-related basis to approximate the kernel function, and a model based on definite orthogonal features is created. Second, parameters for the models are adjusted to evaluate the efficiency of the algorithms. Finally, experiments conducted with both simulated and real hyperspectral data sets are applied to verify whether the proposed algorithms are effective for hyperspectral anomaly detection. Quantitative evaluation shows that the proposed algorithms are superior to other state-of-the-art algorithms.