Biologically inspired polarization navigation is a promising approach due to its autonomous nature, high precision, and robustness. Many researchers have built point source-based and camera-based polarization navigation prototypes in recent years. Camera-based prototypes can benefit from their high spatial resolution but incur a heavy computation load. The pattern recognition algorithm in most polarization imaging algorithms involves several nonlinear calculations that impose a significant computation burden. In this paper, the polarization imaging and pattern recognition algorithms are optimized through reduction to several linear calculations by exploiting the orthogonality of the Stokes parameters without affecting precision according to the features of the solar meridian and the patterns of the polarized skylight. The algorithm contains a pattern recognition algorithm with a Hough transform as well as orientation measurement algorithms. The algorithm was loaded and run on a digital signal processing system to test its computational complexity. The test showed that the running time decreased to several tens of milliseconds from several thousand milliseconds. Through simulations and experiments, it was found that the algorithm can measure orientation without reducing precision. It can hence satisfy the practical demands of low computational load and high precision for use in embedded systems.