An adaptively robust filter with multi adaptive factors is proposed, based on the principles of adaptive Kalman filter and bifactor robust estimation for correlated observations. The estimator of the adaptive filter with multi adaptive factors is derived. The corresponding adaptive factors for the components of the position vector and velocity vector are set up based on the discrepancy of the predicted state from the kinematic model and the estimated state from the measurements. The adaptively robust filter with multi adaptive factors is more flexible in controlling the disturbing effects of the state components compared to the adaptively robust filters with unified adaptive factor and classified adaptive factors. The existing problems of the adaptive filter with multi adaptive factors are analyzed. An actual GPS dada set of an aircraft is calculated and analyzed with four schemes. It is shown by the actual calculation that the results of the adaptive filter with multi adaptive factors are slightly superior to those of the adaptive filter with unified adaptive factor. However, the new adaptively robust filter cannot be applied when the number of measurements at some epochs is smaller than the number of state parameters. It is proposed that the adaptively robust filter with multi adaptive factors and that with unified adaptive factor could be integrated in practical applications.
The IMU(inertial measurement unit) error equations in the earth fixed coordinates are introduced firstly. A fading Kalman filtering is simply introduced and its shortcomings are analyzed, then an adaptive filtering is applied in IMU/GPS integrated navigation system, in which the adaptive factor is replaced by the fading factor. A practical example is given. The results prove that the adaptive filter combined with the fading factor is valid and reliable when applied in IMU/GPS integrated navigation system.
An adaptive integrated Kalman filtering based on the adjustment outputs of local navigation sensors and the outputs of a dynamic or kinematic state model is presented, which avoids the correlations of the local Kalman filtering outputs affected by the same disturbances of the dynamic state model. It has the advantage of rigor in theory and simple in calculation as well as adaptive in the various local navigation outputs. An integrated navigation estimator that is similar to the federated Kalman filtering is given as an initial estimate of a state based on the information sharing principle, but without any dynamic model information. An adaptive integrated fusion of the local navigation outputs and the dynamic model information is followed, in which the weights of the local navigation outputs and the dynamic model outputs are determined based on their differences from the integrated navigation results. The processing algorithms, logic, and associated computer burden are similar to those of federated filter. A simulated example is given to show the effectiveness of the new adaptive integrated navigation algorithm.
With the development of global navigation satellite system (GNSS) precise point positioning (PPP) technology, higher positioning accuracy is required in some applications. An important error source in PPP is the residual higher-order (i.e. second- and third-order) ionospheric error after the first-order ionospheric error has been removed by dual-frequency observation combinations. Generally, higher-order ionospheric errors are negligible; but at high ionospheric activities, higher-order ionospheric errors can reach a few centimeters, which must be considered in high-precision positioning. In this study, a quad-constellation PPP approach with higher-order ionospheric corrections is proposed. The temporal variations of the higher-order ionospheric errors for GPS, GLONASS, BDS and Galileo are analyzed and their effects on quad-constellation PPP are evaluated. The GNSS observations collected at different solar activities are used to analyze the effect of the higher-order ionospheric errors and the results indicate that their magnitudes can reach almost 2 cm for their first frequency signals at high solar activity. The occurrence of geomagnetic storms further increases the higher-order ionospheric errors by a few millimeters. Multi-GNSS datasets collected at low, middle and high latitude stations at different ionospheric activities are processed and the results indicate that the higher-order ionospheric delay can affect the 3D position solutions of the quad-constellation PPP at a maximum of 6 mm.
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