This paper presents detailed derivations and further explanations of the state transformation extended Kalman filter (ST-EKF) from the common frame error definition perspective. Both the system error and measurement models of strapdown inertial navigation system (SINS)/Odometer (OD) tightly-coupled navigation are derived based on the ST-EKF. Both theoretical analysis and test results indicate the effectiveness of the proposed velocity error definition on mitigating the covariance-inconsistency problem that is caused by the specific force calculation error in the EKF state transition matrix. The excellent covariance-consistency of the ST-EKF makes it not necessary to remove gyro and accelerometer bias errors from the initial alignment Kalman filter states. This phenomenon can ensure the subsequent integrated navigation performance. Single-position ground SINS alignment experiments by using a navigation grade inertial measurement unit (IMU) showed that the estimated yaw angle from the conventional 15-state EKF slowly diverged over time. Furthermore, this phenomenon became more distinct when the initial yaw angle error was larger. In contrast, the estimated yaw angle from the proposed 15-state ST-EKF was significantly more stable and less degraded by large initial yaw angle errors. Long- distance land-vehicle SINS/OD integrated navigation tests also exhibited the ST-EKF's higher positioning and heading accuracy than the EKF.

Animals, such as Savannah sparrows and North American monarch butterflies, are able to obtain compass information from skylight polarization patterns to help them navigate effectively and robustly. Inspired by excellent navigation ability of animals, this paper proposes a novel image-based polarized light compass, which has the advantages of having a small size and being light weight. Firstly, the polarized light compass, which is composed of a Charge Coupled Device (CCD) camera, a pixelated polarizer array and a wide-angle lens, is introduced. Secondly, the measurement method of a skylight polarization pattern and the orientation method based on a single scattering Rayleigh model are presented. Thirdly, the error model of the sensor, mainly including the response error of CCD pixels and the installation error of the pixelated polarizer, is established. A calibration method based on iterative least squares estimation is proposed. In the outdoor environment, the skylight polarization pattern can be measured in real time by our sensor. The orientation accuracy of the sensor increases with the decrease of the solar elevation angle, and the standard deviation of orientation error is $0.{15}^{\circ }$ at sunset. Results of outdoor experiments show that the proposed polarization navigation sensor can be used for outdoor autonomous navigation.

Skylight polarization provides a significant navigation cue for certain polarization-sensitive animals. However, the precision of the angle of polarization (AOP) of skylight for vehicle orientation is not clear. An evaluation of AOP must be performed before it is utilized. This paper reports an evaluation of AOP of skylight by measuring the skylight polarization patterns of clear and cloudy skies using a full-sky imaging polarimetry system. AOP measurements of skylight are compared with the pattern calculated by the single-scattering Rayleigh model and these differences are quantified. The relationship between the degree of polarization (DOP) and the deviation of AOP of skylight is thoroughly studied. Based on these, a solar meridian extracted method is presented. The results of experiments reveal that the DOP is a key parameter to indicate the accuracy of AOP measurements, and all the output solar meridian orientations extracted by our method in both clear and cloudy skies can achieve a high accuracy for vehicle orientation.

Gyroscopes based on micro-electromechanical system (MEMS) technology suffer in high-dynamic applications due to obvious g-sensitivity errors. These errors can induce large biases in the gyroscope, which can directly affect the accuracy of attitude estimation in the integration of the inertial navigation system (INS) and the Global Positioning System (GPS). The observability determines the existence of solutions for compensating them. In this paper, we investigate the observability of the INS/GPS system with consideration of the g-sensitivity errors. In terms of two types of g-sensitivity coefficients matrix, we add them as estimated states to the Kalman filter and analyze the observability of three or nine elements of the coefficient matrix respectively. A global observable condition of the system is presented and validated. Experimental results indicate that all the estimated states, which include position, velocity, attitude, gyro and accelerometer bias, and g-sensitivity coefficients, could be made observable by maneuvering based on the conditions. Compared with the integration system without compensation for the g-sensitivity errors, the attitude accuracy is raised obviously.

In this paper we present a bionic multi-sensor anavigation and control system for unmanned ground vehicles to complete the homing task. The system consists of the pixelated polarized sensor, a Micro Inertial Measurement Unit (MIMU), and a monocular camera. To compensate for the installation error, we provide a joint calibration method for multiple sensors. Utilizing the measurements of pixelated polarized vision sensor, we firstly propose an adaptive integrated method with the Visual-Inertial System. The integrated algorithm can not only solve the ambiguity problem of polarized orientation and reduce the cumulative error of the system, but also increase the navigation output rate and enhance the robustness of the system. We present a homevector-based strategy for the goal-directed navigation and control of the unmanned ground vehicles. When the external data link is interrupted, the unmanned vehicles can return to the starting point autonomously, which benefits for improving the survivability of the system. Finally, we design various experiments to verify the algorithm proposed in this paper. The experimental results of the calibration demonstrate that the RMSE of the orientation after calibration is only 0.014°. In the navigation and homing experiment, the RMSE of the position error is 0.64m, and the minimum homing error is only 0.49m (1.09% of the travelled distance). Finally, we discuss interesting insights gained with respect to future work in multi-sensor integration and robot control strategies.