Steven Langel

GPS spoofing detection using RAIM with INS coupling

In this work, we develop, implement, and test a monitor to detect GPS spoofing attacks using residual-based Receiver Autonomous Integrity Monitoring (RAIM) with inertial navigation sensors. Signal spoofing is a critical threat to all navigation applications that utilize GNSS, and is especially hazardous in aviation applications. This work develops a new method to directly detect spoofing using a GPS/INS integrated navigation system that incorporates fault detection concepts based on RAIM. The method is also capable of providing an upper bound on the proposed monitors integrity risk.

Tightly coupled GPS/INS integration for differential carrier phase navigation systems using decentralized estimation

Much research has been conducted in the area of tightly coupled GPS/INS, and this work has resulted in a vast array of navigation algorithms. A common theme of these methods is that they operate on low rate GPS ranging measurements of code and carrier phase together with high rate raw inertial measurements, such as specific force and inertial angular velocity. For stand-alone (i.e., non-differential) GPS navigation applications, high data rate INS outputs can be properly accommodated with todays computer processors. For relative (i.e., differential) GPS navigation applications, the optimal analogous solution would be for the mobile user to have access to the reference stations raw inertial measurements along with its own. However, due to communication bandwidth limitations, it is generally not possible to broadcast high data rate inertial navigation data. In response, an alternative tightly-coupled, differential GPS/INS navigation system is developed here using a decentralized Kalman filtering approach, which can operate at manageable broadcast data rates.

Overbounding position errors in the presence of carrier phase multipath error model uncertainty

In this paper, a methodology is developed to overbound the error in position estimation for carrier phase navigation systems subject to multipath error mis-modeling. In high accuracy and high integrity applications, carrier phase positioning systems with cycle resolution usually rely on time-filtering, in many cases using Kalman filters. Naturally, for a computed integrity risk to be meaningful, it must be guaranteed that the predicted state estimation error covariance always bounds the true covariance. The Kalman filter ensures state error covariance bounding provided that the measurement errors and system dynamics are accurately modeled. However, uncertainties in the dynamic model of the multipath error states always exist. In response, the focus of this work is to quantify and bound position estimate errors subject to uncertainties associated with the time correlation of multipath error.

Bounding Integrity Risk for Sequential State Estimators with Stochastic Modeling Uncertainty

A new method is introduced to upper bound integrity risk for sequential state estimators when the autocorrelation functions of measurement noise and disturbance inputs are subject to bounded uncertainties. Integrity risk is defined as the probability of the state estimate error exceeding predefined bounds of acceptability. In the first part of the paper, a new expression is derived that relates the measurement noise and disturbance input autocorrelation functions to the state estimate error vector. Using this relation, an efficient algorithm is developed in the second part of the paper to upper bound the estimation integrity risk when each input autocorrelation function is known to lie between upper and lower bounding functions. Numerical simulations for a one-dimensional position and velocity estimation problem are conducted to demonstrate the practical feasibility and effectiveness of this new bounding method.

Bounding the integer bootstrapped GNSS baseline’s tail probability in the presence of stochastic uncertainty

Differential carrier phase applications that utilize cycle resolution need the probability density function of the baseline estimate to quantify its region of concentration. For the integer bootstrap estimator, the density function has an analytical definition that enables probability calculations given perfect statistical knowledge of measurement and process noise. This paper derives a method to upper bound the tail probability of the integer bootstrapped GNSS baseline when the measurement and process noise correlation functions are unknown, but can be upper and lower bounded. The tail probability is shown to be a non-convex function of a vector of conditional variances, whose feasible region is a convex polytope. We show how to solve the non-convex optimization problem globally by discretizing the polytope into small hyper-rectangular elements, and demonstrate the method for a static baseline estimation problem.

Bounding integrity risk subject to structured time correlation modeling uncertainty

Sequential state estimation of linear dynamical systems with time correlation uncertainty in the measurement and process noise is considered. The presence of random noise introduces a state estimate error that is defined in terms of a probability distribution. For high integrity navigation applications, the probability of the estimate error vector residing outside a specified boundary must be explicitly quantified. This probability, or integrity risk, can only be computed accurately when the measurement and process noise distributions are precisely known. Unfortunately, precise knowledge of the input noise distributions is rarely available; the use of inexact models can lead to optimistic integrity risks and potentially life-threatening situations can ensue. This paper focuses on developing a methodology to compute upper bounds on integrity risk subject to a bounded uncertainty structure on the input noise autocorrelation functions.

Optimal antenna topologies for spatial gradient detection in differential GNSS

This paper describes new methods to determine optimal reference antenna topologies for detection of spatial gradients in differential Global Navigation Satellite Systems (GNSS). Such gradients can be caused by ionospheric fronts and orbit ephemeris faults, and if undetected, represent major threats to aircraft navigation integrity. Differential carrier phase measurements between ground antennas are highly sensitive to spatial gradients. Therefore, monitors using spatially separated ground antennas have recently attracted great interest. However, they cannot detect gradients of all sizes and directions due to the presence of integer ambiguities. These ambiguities cannot be resolved because the gradient magnitude is unknown a priori. Furthermore, the performance of such monitors is highly dependent on the spatial distribution of reference antennas. In this work, we introduce new methods to find optimized antenna topologies for spatial gradient detection.

Bounding Integrity Risk for Sequential State Estimators in the Presence of Stochastic Modeling Uncertainty

A new method is introduced to upper bound integrity risk for sequential state estimators when the autocorrelation functions of measurement noise and disturbance inputs are subject to bounded uncertainties. Integrity risk is defined as the probability of the state estimate error exceeding predefined bounds of acceptability. In the first part of the paper, a new expression is derived that relates the measurement noise and disturbance input autocorrelation functions to the state estimate error vector. Using this relation, an efficient algorithm is developed in the second part of the paper to upper bound the estimation integrity risk when each input autocorrelation function is known to lie between upper and lower bounding functions. Numerical simulations for a one-dimensional position and velocity estimation problem are conducted to demonstrate the practical feasibility and effectiveness of this new bounding method.