Celestial compass sensor mimics the insect eye for navigation under cloudy and occluded skies

Accurate and reliable compass systems are crucial for navigation, especially over long distances. Idiothetic orientation, relying on internal sensors like inertial measurement units (IMUs), accumulates error over time. Allothethic methods like magnetometers suffer from interference, and GPS relies on satellite infrastructure. A celestial compass, inspired by insect navigation, offers a solution that is independent, lightweight, inexpensive, and energy-efficient. Insects utilize the polarization and intensity patterns of skylight to determine the sun's position, even under partially obscured skies. This pattern is characterized by intensity peaks at the sun's location, and strong polarization in the opposite direction (90° from the sun). The angle of polarization (AoP) is always perpendicular to the arc between the sun and any given point. Previous celestial compass sensors primarily focus on accurately extracting the AoP, often employing complex algorithms (eigenvectors, DFT, or finding the straightest line of AoPs). This paper explores a bio-inspired alternative which offers a potentially more efficient and robust solution by leveraging the geometrical arrangement of light receptors in insect eyes, thereby shifting the computational complexity from algebraic methods to geometrical solutions.

Existing celestial compass sensors often rely on sophisticated algorithms to process AoP measurements from multiple points in the sky to locate the sun. These methods often involve computationally expensive calculations such as computing eigenvectors, discrete Fourier transforms (DFTs), or identifying the straightest line of AoPs passing through the zenith. In contrast, insect eyes provide a simpler, more biologically plausible solution. Many insects use the dorsal rim area (DRA) of their compound eyes, which contains ommatidia sensitive to polarized light, to extract directional information from the sky. The fan-like arrangement of these ommatidia acts as a 'matched filter,' effectively translating the spatial polarization pattern of the sky into a directional signal. Lambrinos et al. developed an early sensor mimicking this DRA structure, using pairs of photodiodes behind orthogonal polarization filters. However, their approach resulted in 180° ambiguity in solar azimuth determination. Smith's observations suggested that the fan-like DRA arrangement could resolve this ambiguity, and this formed the basis for the current study.

This research presents a hardware prototype of a celestial compass sensor mimicking the insect eye's DRA. The sensor consists of an array of eight polarization axis analysers (PAAs), each tilted at 45° to mimic the insect's fan-like arrangement. Each PAA has four UV-sensitive photodiodes behind linear polarizers at 0°, 45°, 90°, and 135°. The model uses only two photodiodes (0° and 90°) to process light, mirroring the insect eye. Light intensity (*I*) is calculated as the average of these two signals. Polarization information (*p*) is the intensity-normalized difference between the two signals, ranging from -1 to 1. Celestial integration (*c*) is the difference between *I* and *p*. A circular-mean model integrates the *c* values from each PAA (represented as vectors) to estimate the solar azimuth. This model is compared to alternative models that utilize only *I*, *p*, or use more complex algorithms (eigenvectors and four-zeros models). Extensive datasets were collected under various sky conditions (clear, cloudy, occluded) using a robot equipped with the sensor and a camera. The robot's orientation was tracked using an IMU. The global reference error (deviation from true solar azimuth) and local reference error (deviation from starting direction) were calculated to evaluate sensor performance.

The celestial compass sensor, based on the insect-eye design and the circular-mean model integrating intensity and polarization information, demonstrated superior performance compared to alternative compass models under a variety of sky conditions. In almost all conditions, the celestial integration (*c*) provided better solar azimuth estimations than intensity (*I*) or polarization (*p*) alone. An exception was observed when the sun was completely hidden; the polarization compass performed slightly better. Increasing the number of PAAs improved the accuracy of the polarization and celestial compasses under occlusions, but not significantly for the intensity compass. Analysis revealed robust performance across different solar elevations (above 10°), locations (with varying atmospheric conditions), and varying levels of cloud cover (up to broken cloud cover). Performance deteriorated significantly with thick, uniform cloud cover. Under occluded skies (canopy cover or buildings), the celestial integration model consistently outperformed the intensity and polarization-only compasses, effectively utilizing whichever signal provided the most usable information. The study showed that even a small number of PAAs (eight) provided accurate predictions of both solar azimuth and orientation change. Compared to the eigenvector and four-zeros models, the proposed model showed significantly superior performance in most conditions, with considerably lower RMSE values for both global and local errors.

The findings demonstrate the effectiveness of the bio-inspired design and the circular-mean model. The superior performance, particularly under challenging conditions, validates the advantages of integrating both intensity and polarization information, mimicking the insect's approach. The simplicity and robustness of the model offer significant advantages over more computationally complex alternatives. The close alignment between the model's processing stages and known neural pathways in insects (e.g., Drosophila) strengthens the biological relevance and potential for further development based on existing biological understanding. Future studies could explore improved noise reduction using Kalman filters or recurrent neural networks, potentially mimicking biological noise reduction mechanisms. Incorporation of color opponency (mimicking insect visual systems) and improved sensor miniaturization (using stretchable electronics or nanowire technology) could further enhance performance and applicability.

This study successfully created and validated a bio-inspired celestial compass sensor. The sensor's performance, particularly its robustness under diverse sky conditions, highlights the benefits of integrating intensity and polarization data. The circular-mean model offers a computationally efficient and biologically plausible approach to celestial navigation, surpassing the performance of other existing models. Future research should focus on miniaturizing the sensor and incorporating advanced signal processing techniques to further enhance its capabilities for various applications, including autonomous navigation systems.

The study primarily focused on daytime navigation. While the sensor demonstrated some response in twilight conditions, a systematic test of its nocturnal performance remains to be done. The current sensor design is relatively bulky compared to some camera-based systems; further miniaturization efforts are needed for widespread practical applications. The accuracy of the true solar azimuth determination in sky images might have introduced some error, particularly at high solar elevations.