Nonlinear Filtering Method And Its Application In Navigation System

With the development of science and technology, it will put forward higher requirements of accuracy of navigation systems, and become more difficult to obtain high-precision inertial navigation system with high-precision devices for hardware technology and cost constraints. And navigation systems is demanded a high degree of autonomy, reliability and anti-jamming that a single navigation system can not meet the requirements in an increasingly complex environment. The high-precision robust filtering algorithm is provided as a main way to obtain reliable high-precision navigation system except the improvement of hardware technology.In the paper, firstly, it consider two key issues of non-linear non-Gaussian initial alignment and integrated navigation, modeling linear/non-linear system equations under different hypothesis and approximating non-Gaussian noise by three forms; secondly, three types of nonlinear filtering are investigated intensively in a unified framework of Bayesian sequential estimation theory; finally, the influence of system model error and different noises forms to navigation system state estimation are discussed by means of high-precision nonlinear filtering method. Research includes the following aspects:Under the condition of Gaussian noise, for the problem of initial alignment and integrated navigation, the influence of state estimation precision of error between (in case of small attitude error)linear system equations and (in case of small horizontal attitude error and uncertainty azimuth attitude error)non-linear system equations are compared. In other words, the estimation precision of misalignment angle and navigation state are compared under different system model, the influence of system model error is analyzed.The noise of navigation system is described in form of a random process (commonly the Gaussian white noise is used). For the initial alignment problem of statistical characteristics of noise may be unknown or vary with the surrounding environment, combining a dual-parallel structure of the noise estimator with difference filtering, and monitoring of noise covariance matrix, which can effectively prevent the problem of filter divergence. In addition, the adaptive filter selection algorithm embedded selective updating strategy, which effectively alleviated the real-time problem of the adaptive filtering algorithm. New algorithm can fast effectively estimate misalignment angle on the base of high-pricision, and estimation results are not sensitive to changes in parameters of noise.The noise of navigation system is described in form of unknown but bounded, and the initial alignment problem is discussed. Combining Set-membership theory and the linearization method as the same as extended Kalman filter, the extended set-membership filter is derived. Under this description of noise, extended set-membership filter can obtain better misalignment angle estimation when the bound of noise doesn't vary obviously but the statistical characteristics of noise varies. Set membership filter isn't sensitive to statistical characteristics of noise but the bound of noise, and has a good robust performance, and the result of misalignment angle estimation are robust to the change of the statistical characteristics of noise.The noise of navigation system and posteriori state distribution is modeled by Gaussian mixture model which can be infinitely close to the real distribution of noise and state, combining particle filter, Gaussian mixture particle filter is derived. The importance function is approximated by Gaussian mixture model updating the parameters of mixture model by UKF. The resampling is improved by expectation-maximization algorithm. New algorithm effectively relieves the degradation problem of the particle filter, the estimation accuracy of the misalignment angle and GPS/DR integrated navigation state are increasing improved.Because of the low efficiency of particle filter, the parallel particle filter is discussed. According to the characteristics of the process of recursive particle filter, the key problem of parallel realization is investigated. A design of the parallel structure of PF-UKF is realized, which can effectively improve the algorithm efficiency with equivalent estimation accuracy to original one.The simulation results of general example and the real problem of initial alignment and integrated navigation, the following conclusions can be reached:For the non-linear cases, comparing to the linear (linearized) system model, non-linear system model has a better applicability and estimation accuracy by means of high precision non-linear filter method, but the computational burden increased. When facing to the method of choice of real problems, it need to compromise between estimation performance and computational efficiency.For the non-Gaussian cases, the filter methods which describe noise with unknown but bounded and mixture model, are more robust and better applied to the less prior knowledge or the complexity environment. For the filtering problem of the noise described in form of a random process (commonly the Gaussian white noise is used), robust performance can be improved by embedding on-line adaptive estimator to estimate the statistical characteristics of noise. For a complex noise environment, there exists an inherent deficiency.For the non-linear non-Gaussian cases, according to theoretical analysis, particle filter has the obvious advantage, but the inherent degradation problem of particle filter will affect its performance. Usually the mixed algorithms of a combination of the traditional non-linear filter algorithm with particle filter have better performance. However, these mixed algorithms possess higher estimation accuracy with lower computation efficiency, and a parallel design is need to improve the computational efficiency.