Study Of Nonlinear Gaussian Filters And Its Application To CNS/SAR/SINS Integrated Navigation

The long-flight-time vehicles such as unmanned aerial vehicle, military transport plane and intercontinental missile generally utilize integrated navigation system to obtain positioning and orientation information, since precision of inertial navigation descends along with the lapse of time. The integrated navigation in military vehicles must be accurate and independent of external information. Celestial navigation system(CNS) has the characteristics of high precision and independence. Synthetic aperture radar(SAR) is a new form of radar with advantages of long-range propagation, complex information processing capability and high precision. Moreover, it can work well under hot and cold climate, adverse weather conditions all-around-the-clock. So combining CNS and SAR with SINS(strap-down inertial navigation system) will be a promising integrated navigation system. This system is essentially nonlinear, and when the misalignment angles are large enough, the error equation and measurement equation present strong nonlinearity. This paper takes integrated navigation system of high-altitude and long-flight-time vehicles as study background and focuses on the research of nonlinear filter.First, the state equation and measurement equation of CNS/SAR/SINS are built by deriving from nonlinear error models deriving of SINS and navigation principle analysis of CNS and SAR. Then, the UKF, CKF and GHQF are introduced and compared utilizing the Taylor expansion of function. The Taylor expansion analyses demonstrate that the GHQF can approximate posterior mean of nonlinear system at any order expansions, while the UKF and CKF produce truncation error since the fourth order term. So the GHQF is more accurate than the UKF and CKF, and the GHQF is invariably numerical stable for different dimensions. However, due to the point number of GHQF increases exponentially with the system dimension, it suffers from the curse of large computational load. The sparse grid method based on Smolyak’s formula has been used to solve this problem, but this method equally distributes quadrature points and the utilization efficiency of points is low.In order to solve the curse of dimensionality problem in numerical integration for certain practical applications where the computational power is limited, a novel extension of the SGHQF is proposed in this paper to further decrease the quadrature points. In view of the nonlinear system and the requirement of resolving observable degree synchronously with filtering process, the differential geometry and the singular value decomposition(SVD) method are utilized conjunctively. To reduce risk from state parameters with poor observable degree, an adaptive filtering algorithm based on the observable degree analysis of state parameters is proposed. The new algorithm is applied to CNS/SAR/SINS integrated navigation system and the simulation results show that the adaptive filtering algorithm has higher precision compared to classic methods. Based on adaptive algorithm, an improved GHQF named AASGHQF is proposed in which a mechanism for controlling accuracy level of each dimension is embed utilizing the state parameters’ observable degree and anisotropic importance vector, and this mechanism can distribute the quadrature points nonuniformly and reasonably. The AASGHQF can find important dimensions adaptively according to parameters’ observable degree and place more points in more important dimensions. The AASGHQF is computationally more efficient in contrast to conventional equally distribution method. The AASGHQF is applied to CNS/SAR/SINS nonlinear integrated navigation system and compared with the CKF and SGHQF. Simulation results demonstrate that the AASGHQF is outstanding both in estimation precision and computational efficient.On the other hand, the navigation sensors are unavoidably contaminated by various outliers in practical system, result in the performance of filtering estimation being affected severely or even divergent. The conventional H￥ and maximum likelihood(M) estimator break down while occurring randomly outliers which are induced by the thick tails of a noise distribution. By analyzing the limitation and deficiency of conventional robust filters, a novel robust filter named RAASGHQF is proposed based on projection statistics(PS) detection method, M estimator, and the AASGHQF nonlinear framework. The RAASGHQF can suppress both contaminated gaussian noise and multiple outliers without linear or statistically linear approximation by using nonlinear optimization theory to solve the GM indicator function. The RAASGHQF is applied to CNS/SAR/SINS nonlinear integrated navigation system and compared with the CKF, HUKF and AASGHQF. Simulation results demonstrate that the novel RAASGHQF outperforms other three filters in terms of robustness and estimation accuracy, and it converges fast at each time step of the filtering process.