Research On The Nonlinearity Of INS/GNSS Deeply Integration

Owing to the superior performance and high reliability, the INS/GNSS deeply integration has been well recognized as one of the most promising coupling strategies. The thesis concerns about the nonlinearity of the INS/GNSS deeply integration, and investigates two fundamental problems involved in the integrated system: 1) the nonlinearity and stability of the integration, and 2) the nonlinear filtering and data fusion strategy of navigation information.The merits and demerits when the GNSS and INS work alone are briefly pointed out, which clearly show that their complementary characteristics make them ideal candidates for integrating. The working principle of the deeply integration and its superiority are further introduced in the first half of the thesis, also included in this part is the nonlinear analysis of the deeply integration, details of which include1. The nonlinearity of the integrated system is primarily introduced by the inertial navigation system(INS), where the INS describes the rigid body motion of a nonlinear dynamic system. The thesis investigates the kinetic stability of such a system, and derives the sufficient condition under the sense of Lyapunov stability. The route of the gyroscope changing from stable state to chaos is simulated to demonstrate the harm of nonlinearity;2. Compared with the loosely and tightly coupling, the major difference of the deeply integration occurs at the GNSS tracking-loop level. Aiming at this issue, the nonlinear characteristics of the tracking loop are discussed in details, and the stability condition is derived by using some graphic methods. Meanwhile, the optimal design of the bandwidth is also introduced.The above discussions aim at presenting the analytical methods that are commonly used in nonlinear problems. These methods are also valid for processing similar issues, and may have profound guiding significance for the stability design of nonlinear systems.The latter part of the thesis focuses on the nonlinear filtering techniques and data fusion strategies of navigation information, especially the newly proposed cubature Kalman filter(CKF). Some exploratory works on the theoretical basis are presented, the contributions are as follows1. The CKF is derived by combining the third-degree spherical cubature rule with the first spherical-radial rule, which is a trivial mathematical task. To simplify the derivation, a general class of CKFs using the G-orbit and invariant theory is proposed in this thesis. It can readily be shown that the conventional CKF is a special case of the proposed method;2. Actually, the third-degree spherical-radial cubature rule has some drawbacks, i.e., the rule has a complex structure and is not likely to deduce high-degree CKFs, and the third-degree cubature based filter has been found not accurate enough in many real-life applications, etc. To tackle these problems, an embedded cubature Kalman filter(ECKF) is therefore developed by using the embedded cubature rule and the property of the gamma function.3. In the framework of Kalman filtering, the CKF executes some numerically sensitive operations, such as matrix square-rooting and matrix inversion, in each update cycle. These arithmetical operations introduce large errors, which eventually lead to the loss of the positive definiteness of the error covariance matrix. It is vitally hazardous as it stops the CKF to run continuously. To address these problems, a square-root version of the ECKF(SECKF) is derived to improve the numerical stability of the ECKF. The SECKF propagates the square roots of error covariance matrices directly, thereby avoiding matrix square-rooting operations and decreasing roundoff errors as well, whereas the ECKF propagates the error covariance matrices;4. To achieve higher level estimation accuracy than the conventional CKF, a unified framework for deriving arbitrary degree of CKFs is presented in this thesis. In theory, the conventional CKF can be extended to any degree in this framework. In addition, a fifth-degree CKF(FCKF, Type I) is derived as an example to demonstrate the proposed theory. Moreover, the FCKF(Type II) is proposed based on the existing work, which is considered to be a balance between the computational load and estimation accuracy. This vividly describes the great potential and the bright prospect of high-degree CKFs;5. The differences of error of approximation among different cubature rules, including the third-degree spherical-radial cubature rule, the third-degree embedded cubature rule and the fifth-degree cubature rule, are formulated by mathematical formulae. The theoretical analysis indicates that both the embedded filters and the fifth-degree filters are more accurate than the conventional CKF. And the experimental results, presented herein, show a consistent result with the theoretical analysis;6. In general, the information form of the Kalman filter(KF) is preferred over standard covariance filters in multiple sensor fusion problems. Aiming at this issue, two types of cubature information filters(CIF) for nonlinear systems are presented in this thesis. The two approaches, which we have named the embedded cubature information filter(ECIF) and the fifth-degree cubature information filter(FCIF), are developed from the ECKF and the FCKF(Type I). The experimental results demonstrate that both the ECIF and FCIF are superior to the conventional CIF.