Biomimetic polarization navigation is a growing field in navigation that aims to replicate the superior abilities of natural organisms to perceive and gather information about spatial motion information, the environmental and targets. Natural organisms possess compound eye structure can perceive polarized visual information over a wide field of view, with rapid response and high accuracy. Additionally, their internal neurons sensitive to polarization (POL-sensitive neurons) can sense the sky's polarization status in real time with strong polarization contrast. Marine organisms, such as mantis shrimp and salmonids, utilize underwater polarization information to carry out feeding, homing, localization, navigation and communication [[1], [2], [3]]. In that case, it is crucial to establish the underwater polarization pattern and eliminate interference in the intricate aquatic environment, which is the key to extending polarization orientation from the atmosphere to underwater environments [[4], [5]].

Sunlight is scattered by the atmosphere to form polarized skylight. In the aquatic environment, optical reactions such as refraction at the air-water interface and scattering by water molecules generate polarization distribution patterns with a certain degree of regularity. The spatial and temporal distribution of underwater polarization patterns is variable [6,7]. However, it consistently remains constant at the majority of ocean depths where sunlight can penetrate. The polarization patterns remain observable at a depth of 200 m [8], mostly characterized by partially linear polarization [9]. This demonstrates the predictability of the underwater polarization patterns. Underwater polarization characteristics research is primarily conducted through measurement and numerical simulation, as it is constrained by the limitations of detection equipment and ambient conditions.

The degree of polarization (DoP) and angle of polarization (AoP) are related to the position of the sun. The angle of polarization patterns is less affected by disturbances, making it a reliable source of underwater polarization information [10]. Bhandari et al. [11] studied the distribution of polarized radiation with depth at the ideal sea surface and determined that the scattering of light in water is the leading cause of the polarization phenomenon. Its properties are unstable in the deep sea and easily distorted by surface waves [12,13]. Additionally, the underwater polarization pattern is similar to the light field in Snell's window [14]. The Snell's window is a conical shape that occurs underwater, with an upward-looking aperture angle of about 97.5°. It is the main research scope of the underwater polarized navigation vision. Atmospheric measurements yield underwater polarization angles similar to underwater measurements [15], skylight scattering particles are different. Furthermore, the single Rayleigh scattering model is not able to accurately describe the distribution of light radiative polarization when the solar zenith angle is large [16]. In 2023, Beihang University proposed the ellipse Hough transform (EHT) algorithm based on Hannay's model to provide a better description of the polarization pattern in the real atmosphere [17].

In 1989, Kattawar et al. [18] conducted a numerical simulation to analyze the polarization characteristics of underwater transmitted light, employing the principles of Rayleigh scattering theory. In 2001, Cronin et al. [19] investigated a study on the polarized light field in natural seawater and collected linearly polarized spectra by all-weather collection. Sabbah et al. [20] employed Muller's matrix and Stokes' vector to model the distribution of polarization underwater, considering the refraction occurs at the water-air interface. On this basis, Zhou et al. [21] simulated the polarization distribution of underwater modes', taking into account wind speed and surface waves. You et al. [22] used the matrix operator and Monte Carlo radiative transfer model to predict the polarized light field. Xu et al. [23] investigated a three-dimensional Monte Carlo vector radiative transfer method to simulate polarized light propagation modes in the coupled atmosphere-ocean system and verified its accuracy. Foster et al. [24] combined a vector radiative transfer model with a Monte Carlo method to determine the transfer function of polarized light on the ocean surface in 2016. In 2018, Powel et al. [25] achieved the first instance of underwater navigation by utilizing a bionic polarization-sensitive detector instrument. This device measured polarized light underwater at multiple locations, depths, and periods, thereby providing a new solution for the underwater polarization navigation challenge. In 2021, Zhang et al. [26] designed a biomimetic point source polarization sensor for underwater orientation. He established a new sensor model based on the underwater light intensity attenuation coefficient and optical coupling coefficient. These developments pave the way for new possibilities in long-distance navigation.

Underwater polarization theory above has achieved relatively complete development at present. however, it is challenging to obtain accurate orientation in the face of complex underwater scenes. Underwater polarization pattern is affected by both atmospheric conditions and the state of the water surface. The composition of the water body also has a significant influence on the polarization pattern [27,28]. The underwater particle composition interferes with the linear and circular polarization significantly [29]. Research on the impact of underwater interference factors, such as light intensity, turbidity, and cloud cover, on underwater polarization is still in its primary stages. In 2011, Lerner et al. [30] analyzed the polarized light in both clear and murky aquatic environments. In 2020, Chu et al. [31] used a combination of Monte Carlo numerical simulation and Mie scattering theory to describe the polarization distribution in turbid underwater conditions utilizing a single Rayleigh scattering model for water molecules only. In 2021, Cheng et al. [32] investigated a simulation study about the influences of factors (wavelength, water turbidity, water composition and water quality) on underwater polarization patterns. The study also verified the feasibility of underwater polarization navigation in various conditions. In 2023, Gu et al. [33] proposed an air-water model to calculate the polarization pattern of sky light under varying wave conditions. The method simulated the underwater polarization distribution pattern under the influence of wave refraction and improve the environmental adaptability of underwater polarization navigation under fluctuating water surface conditions.

This paper proposes a novel bionic neurons enhancement approach and optimize the performance of polarization compass in the context of degradation caused by weakly polarized and noisy patterns underwater. The proposed method is bio-inspired and highly robust, and it forms an integrated system for noise reduction. The main contributions are as follows: (1) the method develops an algorithm to improve the perception of underwater polarization information in weakly polarized patterns. It also establishes a model of photoreceptor cell and layer monopole cell mechanism in the visual system of syrphid fly. This model allows for improved orientation accuracy in the weakly polarized mode, even in low illumination and thin cloud cover conditions; (2) the non-local sparse coding denoising part is supplemented to inhibit and compensate for the noise of polarized images in turbid water bodies. This effectively reduces the polarization orientation error in the underwater scenes in the presence of noise.

The remainder of this paper is organized as follows: section 2 is the theoretical model and problem formulation; Section 3 is the biomimetic enhancement of the optimal orientation method; Section 4 is the design of the underwater experiment demonstration and analysis of the experimental results; section 5 is the summary of the conclusion.