Research On Cubature Kalman Filter And Its Application For Navigation

With the development of modern science and technology, the requirement of navigationaccuracy is forward to higher, and nonlinear filtering algorithm can provide a strongfoundation to improve the navigation accuracy, which gets a lot of attention and research.Cubature Kalman Filter(CKF) is a kind of superior nonlinear filtering algorithm rising inrecent years, which has simple structure, high estimation accuracy, good numerical stability,and overcomes some problems existed in other nonlinear filtering algorithms, thus it isbecoming popular research in nonlinear filtering algorithm. In this paper, CKF algorithm isstudied, the main work is as follows.1) According to the nonlinear system with correlative noises appeared in multiple sourceinformation confusion technology, two nonlinear Gaussian filterings with correlative noisesare proposed: nonlinear Gaussian filtering with correlative noises based on modeltransformation and nonlinear Gaussian filtering with correlative noises based on one-stepprediction recursion, then the equivalence between them is proved by updating innovationtheorem. At last the third Spherical-Radial Cubature rule is used to approximate Gaussianintegral, and two equivalent CKF algorithm with correlative noises is obtained.2) When conventional deterministic sampling filtering algorithms process highdimension nonlinear system, the sampling points increase, and the calculation amoutincreases correspondingly. According to this problem, it is proved that the posterior mean andvariance of the state is multiple Gaussian integral of its component vector, and the integralformula is obtained. Then the third Spherical-Radial Cubature rule is used to approximatemultiple Gaussian integral, the reduced dimension CKF algorithm is proposed, which reducesthe samping points, so as to the calculation amount. At last, further discussion is carried out,and it is pointed that it will be more meaningful if this idea is extended to GHF.3) The running mechanism of Strong Tracking Filtering (STF) is discussed, it is pointedthat owing to inaccurate approximation of the covariance of measurement one-step prediction,STF produces fading factor with high probability, leads to excessive regulation for filteringgain, and eventually makes the state estimation lack smoothness, while sofenting factor isintroduced by experience to realease this problem. According to this disadvantage, animproved STF is proposed, which can advoid this problem. Then a unified nonlinear systemstrong tracking filtering recursive formula is proposed, and different nonlinear system STFalgorithem can be derived by different approximation strategy to the Gaussian integral, then the third Spherical-Radial Cubature rule is used to approximate the Gaussian integral, andStrong Tracking CKF algorithm is derived, meanwhile, according to a class of specialnonlinear system, multiple fading factors CKF algorithm with better performance is proposed,which can generate multiple fading factors, and fades the data channel with different rates, soas to achieve better estimation result.4) Reduced dimension CKF is ultilized to SINS alignment with large azimuth misalignmentangle to reduced the calculation amout, and multiple fading factors CKF is ultilized to SINSalignment with large azimuth misalignment angle with inaccuraten oise statistics to improveestimation accuracy, at last, multiple fading factors CKF is ultilized to SINS/GPS ingegratednavigation with inertial instrument sudden change to improve navigation accuracy.