Study On Extension And Application Of Adaptive Robust Filtering Theory For Controlling Influence Of Colored Noise In Kinematic Positioning

This paper mainly focuses on the theories and algorithms of adaptive robust filtering forControlling Influence of Colored Noise in kinematic positioning. The main works andcontributions are summarized as follows:1. A variety of adaptive filter algorithms for controlling the influence of the colorednoises are summarized and classified. Based on the theories and models of filters, theadvantages and disadvantages of each filter are analyzed. Comparison and analysis ofadaptive filter algorithms for controlling influence of colored noise is performanced. Thecalculation results show that the emphases of each filter in controlling the influence of thecolored noises are different. In actual application, the appropriate adaptive filter algorithmwill be chosed to control the influence of the colored noises on the kinematic filter resultaccording to the characters of the colored noises and user demand.2. Adaptive fitting of both colored noise and covariance matrices by using movingwindows are presented based on the assumption that the observation and dynamic modelnoises mainly include the colored noises with the first order self-correlation character. Theexpressions to calculate the colored noise estimators and covariance matrices of the modifiedobservations and predicted states are obtained. The feasibility and practicability of the modeland algorithm are tested by an example. It is shown that the Kalman filtering, based on theadaptive fittings of the colored noises and covariance matrices, can be effective in resistingthe influence of the colored noises on the navigation results.3. An adaptively robust filtering with classified adaptive factors was proposed, based onthe principles of the adaptively robust filtering and bi-factor robust estimation for correlatedobservations. According to the constant velocity model of Kalman filtering, the stateparameter vector was divided into two groups, namely position and velocity. The estimator ofthe adaptively robust filtering with classified adaptive factors was derived, and the calculationexpressions of the classified adaptive factors were presented. Test results show that theadaptively robust filtering with classified adaptive factors is not only robust in controlling themeasurement outliers and the kinematic state disturbing but also reasonable in balancing the contributions of the predicted position and velocity, respectively, and its filtering accuracy issuperior to the adaptively robust filter with single adaptive factor based on the discrepancy ofthe predicted position or the predicted velocity.4. An adaptively robust filter with multi adaptive factors is proposed, based on theprinciples of adaptive Kalman filter and bi-factor robust estimation for correlated observations.The estimator of the adaptive filter with multi adaptive factors is derived. An adaptive factorfor the component of the state vector is set up based on the discrepancy of the predicted statefrom the kinematic model and estimated state from the measurements. The adaptively robustfilter with multi adaptive factors is compared with the adaptively robust filter with unifiedadaptive factor. The existing problems of the adaptive filter with multi adaptive factors areanalyzed.5. In the GPS/INS integrated navigation, the adaptive factor based on the statediscrepancy cannot be applied to control the influence of the dynamic model errors on theintegrated navigation results when the number of measurements at some epochs is smallerthan the number of the state parameters. In order to solve this problem, a new adaptive factorbased on partial state discrepancy was developed and successfully applied in GPS/INSintegated navigation.6. An adaptive integrated positioning filter algorithm based on the DMI sequences, GPSand IMU is presented. The integrated estimator of position vector is derived based on theadaptively robust filter. By analyzing this algorithm, it is shown that the algorithm makes fulluse of the measurements of all the sensors installed in the MMS (Mobile Mapping System),and improves the performance of the system.7. Some notices of the GPS ephemeris algorithm in the application of the fitting orpredicting of low satellite orbit are given. And the advantages and disadvantages of geometricorbit determination are analyzed. A new adaptively robust synthetic orbit determinationalgorithm is developed based on the predicting characteristic of GPS broadcast ephemeris andthe adaptively robust filtering principle, which can effectively solve some problems orshortages of geometric orbit determination. The results show that the adaptively robustsynthetic orbit determination algorithm can not only make good use of the geometricobservation information but also reasonably adjust the contributions of the geometric observations and ephemeris predicted information to the filtering solution, and the precisionand reliability of orbit determination are insured.8. The formula of Givens transformation with weighted parameter is deduced, which isused to control the estimator range of the navigation satellite ephemeris parameters. Theresults show that Givens transformation with weighted parameter not only is steady innumerical computation and efficient in calculation but also can easily give the prior weight ofthe ephemeris parameters and expediently make the abnormal navigation satellite parametersback in the prescriptive range.9. The influence formula of the orbital plane rotation angle on the broadcast ephemerisparameters is deduced and the main factors determining the calculation value of the influencefunction are analyzed based on the least square fitting solution of the broadcast ephemerisparameters. And the effect of the orbital plane rotation angle on the ephemeris fittingalgorithm stability is analyzed. The calculation results show that not only the over limitproblem of the GEO satellite broadcast ephemeris parameters can be solved but also theprecision and reliability of the broadcast ephemeris parameter fitting algorithm can be insuredby increasing the orbital plane rotation angle.