It is well known that ionospheric anomalies that may occur during severe ionospheric storms could pose integrity threats to Ground-based Augmentation System (GBAS) users [1]. To determine the potential impact of the worst-case ionosphere anomalies on the Local Area Augmentation System (LAAS), a GBAS developed by the U.S. Federal Aviation Administration (FAA), an ionospheric threat model first should be defined. The ionospheric threat was modeled as a spatially linear and semi-infinite wave front. The slope (or gradient) of the front, its width, and its speed with respect to the ground are the parameters in the LAAS ionospheric threat model. Along with the spatial gradient, the speed of the wave front is a key parameter for GBAS integrity analysis.
This study aims to develop an automated velocity estimation algorithm for anomalous ionospheric fronts. Ionospheric threat model should be derived for all regions where GBAS will become operational, and for ongoing development of the LAAS, it is necessary to validate and update the threat model over the life cycle of the system by continuously monitoring ionospheric behavior [2]. Since the current threat model was derived from the Conterminous U.S. (CONUS) ionospheric storm archive observed only during the last solar peak in the early 2000s, and the next maximum solar cycle is predicted to occur in around 2013, ionospheric data should be analyzed continuously going forward. However, in earlier work 0, large portion of ionospheric storm data analysis was done manually, including the estimation of ionospheric front propagation velocity. It is necessary to develop an automated velocity estimation algorithm of ionospheric front so as to enables us to process the vast amount of data in near real time.
In prior studies, an automated algorithm using the three-station-based trigonometric method has been previously developed to estimate the ionosphere wave front speed and its direction [3]. However, this algorithm was proved to be sensitive to measurement errors and also has limitations due to the underlying assumptions of the simplified threat model (the front is assumed to always be a straight line and to move with constant speed with relative to the ground) [1]. The two-station-based method, which has been developed to overcome the weakness of the three-station-based method, remains to operate manually. In this paper, a robust algorithm which combines a three-station-based method and a two-station-based method is developed to estimate ionospheric front-velocity along with some additional techniques such as pattern-recognition and idea of linear programming, which are introduced for automation.
The automated ionospheric front velocity estimation algorithm is comprised of the following steps. Two reference stations between which extremely large ionospheric gradients are observed are inputs to this algorithm. The first step searches for additional stations whose distances from the two stations are less than a predefined threshold. In the second step, we implement a k-means algorithm (a well-known pattern-recognition technique [4][5]) to identify stations that exhibit similar ionospheric delay patterns. Two types of input parameters to the k-means algorithm are used. One is a real vector whose components consist of coefficients obtained from a polynomial curve fit to delay data, and the other is the total number of groups, k, into which delay patterns are grouped. A real vector with thirty one components (i.e. 30th??order is used) and a k of three are chosen as the optimal values through empirical analysis. One of the three groups, in which delay patterns are not similar to the both of reference stations, is excluded from the following steps. Third, the orientation of the front is determined via the three-station-based method. The position of the first three stations swept by the front and the travel time of the front are used as inputs to the three-station-based algorithm. The fourth step is to determine the forward propagation direction of the front from the peak delay times. The peak delay times, at which ionospheric delays of each station reach the local maximum or minimum value within the arcs, makes it possible to deduce the order in which stations were affected by the front and the travel time of the front from one station to others. Additionally, the idea of a linear programming method, in which a feasible region is defined by a set of linear constraints [6], is applied to remove any stations that could not be impacted by the front under the assumption of unvarying propagation direction. Fifth, a range of front speeds is estimated by constructing all feasible pairs of stations and computing the speed between the pairs for the given orientation using the two-station-based method. Sixth, it is necessary to remove the speed of Ionosphere Pierce Point (IPP) motion from the range of speeds so that the speed estimates relative to the ground can be estimated. Finally, we take the mean value of the resulting range of speeds as the speed estimate of the ionosphere front.
This study presents the automated algorithm for the ionospheric front velocity estimation and validates the performance of this algorithm by obtaining the results from the CONUS storm data processing and comparing these results to those manually estimated previously. All speed estimates from the automated algorithm fall within ??30% error bars of the manually computed speeds. We processed data on ionospheric storm days using this algorithm and showed that the current threat space could be populated with newly-generated threat points.
It is well known that ionospheric anomalies that may occur during severe ionospheric storms could pose integrity threats to Ground-based Augmentation System (GBAS) users [1]. To determine the potential impact of the worst-case ionosphere anomalies on the Local Area Augmentation System (LAAS), a GBAS developed by the U.S. Federal Aviation Administration (FAA), an ionospheric threat model first should be defined. The ionospheric threat was modeled as a spatially linear and semi-infinite wave front. The slope (or gradient) of the front, its width, and its speed with respect to the ground are the parameters in the LAAS ionospheric threat model. Along with the spatial gradient, the speed of the wave front is a key parameter for GBAS integrity analysis.
This study aims to develop an automated velocity estimation algorithm for anomalous ionospheric fronts. Ionospheric threat model should be derived for all regions where GBAS will become operational, and for ongoing development of the LAAS, it is necessary to validate and update the threat model over the life cycle of the system by continuously monitoring ionospheric behavior [2]. Since the current threat model was derived from the Conterminous U.S. (CONUS) ionospheric storm archive observed only during the last solar peak in the early 2000s, and the next maximum solar cycle is predicted to occur in around 2013, ionospheric data should be analyzed continuously going forward. However, in earlier work 0, large portion of ionospheric storm data analysis was done manually, including the estimation of ionospheric front propagation velocity. It is necessary to develop an automated velocity estimation algorithm of ionospheric front so as to enables us to process the vast amount of data in near real time.
In prior studies, an automated algorithm using the three-station-based trigonometric method has been previously developed to estimate the ionosphere wave front speed and its direction [3]. However, this algorithm was proved to be sensitive to measurement errors and also has limitations due to the underlying assumptions of the simplified threat model (the front is assumed to always be a straight line and to move with constant speed with relative to the ground) [1]. The two-station-based method, which has been developed to overcome the weakness of the three-station-based method, remains to operate manually. In this paper, a robust algorithm which combines a three-station-based method and a two-station-based method is developed to estimate ionospheric front-velocity along with some additional techniques such as pattern-recognition and idea of linear programming, which are introduced for automation.
The automated ionospheric front velocity estimation algorithm is comprised of the following steps. Two reference stations between which extremely large ionospheric gradients are observed are inputs to this algorithm. The first step searches for additional stations whose distances from the two stations are less than a predefined threshold. In the second step, we implement a k-means algorithm (a well-known pattern-recognition technique [4][5]) to identify stations that exhibit similar ionospheric delay patterns. Two types of input parameters to the k-means algorithm are used. One is a real vector whose components consist of coefficients obtained from a polynomial curve fit to delay data, and the other is the total number of groups, k, into which delay patterns are grouped. A real vector with thirty one components (i.e. 30th??order is used) and a k of three are chosen as the optimal values through empirical analysis. One of the three groups, in which delay patterns are not similar to the both of reference stations, is excluded from the following steps. Third, the orientation of the front is determined via the three-station-based method. The position of the first three stations swept by the front and the travel time of the front are used as inputs to the three-station-based algorithm. The fourth step is to determine the forward propagation direction of the front from the peak delay times. The peak delay times, at which ionospheric delays of each station reach the local maximum or minimum value within the arcs, makes it possible to deduce the order in which stations were affected by the front and the travel time of the front from one station to others. Additionally, the idea of a linear programming method, in which a feasible region is defined by a set of linear constraints [6], is applied to remove any stations that could not be impacted by the front under the assumption of unvarying propagation direction. Fifth, a range of front speeds is estimated by constructing all feasible pairs of stations and computing the speed between the pairs for the given orientation using the two-station-based method. Sixth, it is necessary to remove the speed of Ionosphere Pierce Point (IPP) motion from the range of speeds so that the speed estimates relative to the ground can be estimated. Finally, we take the mean value of the resulting range of speeds as the speed estimate of the ionosphere front.
This study presents the automated algorithm for the ionospheric front velocity estimation and validates the performance of this algorithm by obtaining the results from the CONUS storm data processing and comparing these results to those manually estimated previously. All speed estimates from the automated algorithm fall within ??30% error bars of the manually computed speeds. We processed data on ionospheric storm days using this algorithm and showed that the current threat space could be populated with newly-generated threat points.
