Upper-bounding bias errors in satellite navigation

A satellite navigation system for a safety critical application is required to provide an integrity alert of any malfunction; the probability that a navigation positioning error exceeds a given alert limit without an integrity alert is required to be smaller than a given integrity risk. So far, a little number of applications provide integrity alerts, because signal propagation from a satellite to a receiver depends on diversified phenomena and makes probabilistic upper-bound of possible threats difficult. To widen application fields of satellite navigation, two methods to upper-bound wide classes of bias errors are shown in this paper. The worst bias error in a maximum likelihood estimate caused by an interference signal within a given small power is derived. A novel inequality condition with a clock bias error and magnification coefficients that upper-bounds a horizontal position error is presented. Robustness of the inequality condition is numerically shown based on actual configurations of satellites.Comment: To appear in IEEE Workshop on Statistical Signal Processing, Gold Coast, Australia, 201

Cycle Flux Algebra for Ion and Water Flux through the KcsA Channel Single-File Pore Links Microscopic Trajectories and Macroscopic Observables

In narrow pore ion channels, ions and water molecules diffuse in a single-file manner and cannot pass each other. Under such constraints, ion and water fluxes are coupled, leading to experimentally observable phenomena such as the streaming potential. Analysis of this coupled flux would provide unprecedented insights into the mechanism of permeation. In this study, ion and water permeation through the KcsA potassium channel was the focus, for which an eight-state discrete-state Markov model has been proposed based on the crystal structure, exhibiting four ion-binding sites. Random transitions on the model lead to the generation of the net flux. Here we introduced the concept of cycle flux to derive exact solutions of experimental observables from the permeation model. There are multiple cyclic paths on the model, and random transitions complete the cycles. The rate of cycle completion is called the cycle flux. The net flux is generated by a combination of cyclic paths with their own cycle flux. T.L. Hill developed a graphical method of exact solutions for the cycle flux. This method was extended to calculate one-way cycle fluxes of the KcsA channel. By assigning the stoichiometric numbers for ion and water transfer to each cycle, we established a method to calculate the water-ion coupling ratio (CRw-i) through cycle flux algebra. These calculations predicted that CRw-i would increase at low potassium concentrations. One envisions an intuitive picture of permeation as random transitions among cyclic paths, and the relative contributions of the cycle fluxes afford experimental observables