Improved Models of Imaging of Skylight Polarization Through a Fisheye Lens

Image-registration-based solar meridian detection for accurate and robust polarization navigation

Skylight polarization, inspired by the foraging behavior of insects, has been widely used for navigation for various platforms, such as robots, unmanned aerial vehicles, and others, owing to its stability and non-error-accumulation. Among the characteristics of skylight-polarized patterns, the angle of polarization (AOP) and the degree of polarization (DOP) are two of the most significant characteristics that provide abundant information regarding the position of the sun. In this study, we propose an accurate method for detecting the solar meridian for real-time bioinspired navigation through image registration. This method uses the AOP pattern to detect the solar meridian and eliminates the ambiguity between anti-solar meridian and solar meridian using the DOP pattern, resulting in an accurate heading of the observer. Simulation experiments demonstrated the superior performance of the proposed method compared to the alternative approaches. Field experiments demonstrate that the proposed method achieves real-time, robust, and accurate performance under different weather conditions with a root mean square error of 0.1° under a clear sky, 0.18° under an overcast sky with a thin layer of clouds, and 0.32° under an isolated thick cloud cover. Our findings suggest that the proposed method can be potentially used in skylight polarization for real-time and accurate navigation in GPS-denied environments.

Modeling the celestial distribution of skylight polarization patterns by incorporating the influence of both the sun and the moon through an analytical model

The orientation of many polarization-sensitive animals and the hypothetical sky-polarimetric Viking navigation both rely on the polarization pattern of skylight. For 40 years, scientists have attempted to construct various models to simulate this pattern. However, existing theoretical models have only analyzed the polarization pattern of skylight that is influenced separately by the sun or the moon and have built their modeling frameworks based on the position of one light source. This approach fails to account for the combined influence of the sun and the moon on the distribution of skylight polarization patterns at certain times. In fact, ignoring the influence of the moon during the dawn and dusk periods in clear weather conditions may lead to significant errors in the simulation results compared to the measured data. In this paper, we present an analytical model that considers various factors, including skylight intensity, horizon correction factor, atmospheric turbidity condition, and combined influence of both the sun and moon on the distribution of polarized skylight. We believe our model demonstrates enhanced agreement with measured data and will further our understanding of how animals use the celestial polarization pattern for navigation, particularly when both the sun and the moon appear in the sky. Moreover, the findings of this study may facilitate the advancement of bio-inspired navigation systems.

Impact of aerosols on the polarization patterns of full-sky background radiation

Regarding aerosol particle-laded turbid atmospheres, full-sky background radiation polarization patterns can be adversely affected, an important factor limiting their effective near-ground observation and acquisition. We established a multiple-scattering polarization computational model and measurement system and conducted the following three tasks. (a) We thoroughly analyzed the impact of aerosol scattering characteristics on polarization distributions, calculating the degree of polarization (DOP) and angle of polarization (AOP) patterns for a more comprehensive set of atmospheric aerosol compositions and aerosol optical depth (AOD) values than calculated in previous studies. (b) We assessed the uniqueness of the DOP and AOP patterns as a function of AOD. (c) By employing a new polarized radiation acquisition system for measurements, we demonstrated that our computational models are more representative of the DOP and AOP patterns under actual atmospheric conditions. We found that under a clear sky without clouds, the impact of the AOD on the DOP was detectable. With increasing AOD, the DOP decreased, and the decreasing trend became increasingly obvious. When the AOD was above 0.3, the maximum DOP did not exceed 0.5. The AOP pattern did not change notably and remained stable, except for the contraction point at the sun position under an AOD of 2.

High-similarity analytical model of skylight polarization pattern based on position variations of neutral points

The skylight polarization pattern contains rich information for navigation, meteorological monitoring, and remote sensing. In this paper, we propose a high-similarity analytical model by considering the influence of the solar altitude angle on the neutral point position variations for the distribution pattern of the polarized skylight. A novel function is built to determine the relationship between the neutral point position and solar elevation angle based on a large number of measured data. The experimental results show that the proposed analytical model achieves a higher similarity to measured data compared with existing models. Furthermore, data from several consecutive months verifies the universality, effectiveness, and accuracy of this model.

Design and calibration model of a bioinspired attitude and heading reference system based on compound eye polarization compass

Insects such as honeybees are capable of fusing the information sensed by multiple sensory organs for attitude and heading determination. In this paper, inspired by the sensory fusion mechanism of insects' polarization compass and haltere, a bioinspired polarization-based attitude and heading reference system (PAHRS) is presented. The PAHRS consists of compound eye polarization compass and inertial measurement unit (IMU). By simulating multi-view structure of the dorsal rim area in insects' compound eyes, a non-coplanar 'polarization-opponent (POL)-type' architecture is adopted for the compound eye polarization compass. The polarization compass has multi-directional observation channels, which is capable of adaptively selecting the angle of polarization and obtaining the polarization vectors. Therefore, the environmental adaptability of the polarization compass can be enhanced. In addition, the integration strategy between the compound eye polarization compass and IMU is proposed. Moreover, the sources of system errors are analyzed to improve the heading angle accuracy, based on which a new calibration model is established to compensate the installation errors of the PAHRS. Finally, experiments are carried out under both clear sky and cloudy conditions. The test results show that the error root mean square of heading angle is 0.14° in clear sky, and 0.42° in partly cloudy conditions.

Sensor Modeling and Calibration Method Based on Extinction Ratio Error for Camera-Based Polarization Navigation Sensor

The performance of camera-based polarization sensors largely depends on the estimated model parameters obtained through calibration. Limited by manufacturing processes, the low extinction ratio and inconsistency of the polarizer can reduce the measurement accuracy of the sensor. To account for the challenges, one extinction ratio coefficient was introduced into the calibration model to unify the light intensity of two orthogonal channels. Since the introduced extinction ratio coefficient is associated with degree of polarization (DOP), a new calibration method considering both azimuth of polarization (AOP) error and DOP error for the bionic camera-based polarization sensor was proposed to improve the accuracy of the calibration model parameter estimation. To evaluate the performance of the proposed camera-based polarization calibration model using the new calibration method, both indoor and outdoor calibration experiments were carried out. It was found that the new calibration method for the proposed calibration model could achieve desirable performance in terms of stability and robustness of the calculated AOP and DOP values.