GNSS/INS Based Estimation of Air Data and Wind Vector using Flight Maneuvers
Kerry Sun, Christopher D. Regan, Demoz Gebre Egziabher, University of Minnesota Twin Cities
Location: Big Sur
We develop a GNSS/INS based algorithm to estimate real time air data (angle-of-attack and sideslip angle) and wind vector. Accurate estimates of these parameters are essential to the efficient and safe operation of aircraft. Since many small UAV systems cannot afford high-cost sensors which directly measure these quantities due to size, weight, and power constraints, it has led to non-traditional approaches collectively known as synthetic air data systems. Our work uses observability analysis to demonstrate the feasibility of model-free synthetic air data estimation. In addition, we show that certain canonical flight maneuvers, defined by the aircraft’s orientation and airspeed, result in the high observability of the air data parameters and the wind velocity vector. Finally, we use the GNSS/INS-based algorithm to estimate these parameters, and validate it using simulation and flight test data.
We develop an augmented navigational filter based on the Extended Kalman Filter (EKF) that fuses Global Positioning System (GPS), Inertial Navigation System (INS) and airspeed measurements to estimate three dimensional wind components, angle-of-attack, and sideslip angle without the model of the aircraft. We develop two different observability analyses: nonlinear observability analysis using the Lie derivative and conditional observability analysis using the conditional number of a Gramian (explained shortly). Nonlinear observability analysis is used to show the augmented states are observable. The conditional observability analysis is used to compare different canonical flight maneuvers and to identify those that yield a high degree of observability of the wind components. We also develop a lower bound on the average time of variation of wind given an aircraft’s maneuverability.
We add three dimensional wind states to the loosely coupled GNSS/INS EKF algorithm to form an augmented navigational filter. Theoretically, the measurement model of this filter is modified to show the new system is observable using the assumption that wind is slowly varying over time.
We develop two observability analyses: nonlinear observability and conditional observability analysis. We use nonlinear observability analysis through the Lie derivative to show the augmented state is observable. Specifically, the wind states from past time are appended as additional “new measurements”, then nonlinear observability analysis is applied to show the observability matrix has full column rank.
Because nonlinear observability analysis is often complex and numerically intractable, a new observability analysis is developed to show how certain flight maneuvers can achieve a high degree of observability under the slow-varying wind assumption. This is called “conditional observability” analysis since it’s based on the condition of slow-varying wind. Furthermore, our analysis concerns flight patterns that are not typical flight trajectories such as circular or a climb/descend trajectory. Instead, we break down the flight trajectory into a frame by frame maneuver defined by the aircraft’s orientation and airspeed to see the impact on observability. Specifically, the condition number of a Linear Time Varying (LTV) observability gramian is calculated as a measure of observability using a combination of several snapshots of the aircraft. Different canonical flight patterns are examined to see how an aircraft can maneuver to achieve a high degree of observability.
Furthermore, a lower bound on the average time of variation of wind can be derived from this analysis. Knowing the lower bound of the wind model’s time constant enables users to know the fastest wind one can estimate based on a particular aircraft’s maneuverability. Finally, flight trajectories generated by canonical flight patterns are tested using both simulation and real flight data by the augmented navigational filter.
The wind augmented navigational filter was proved to have an observable state vector using the Lie derivative from nonlinear observability analysis. Furthermore, conditional observability analysis shows several important results. First, an aircraft can achieve a high degree of observability by changing its pitch and heading angle simultaneously as long as the maneuvering time is less than the average time of variation of wind. Second, varying airspeed during maneuvers can increase degree of observability in addition to changing the aircraft's orientation. Therefore, an accurate three dimensional wind vector can be estimated under those flight maneuvering criterions developed in this paper, which lead directly to accurate angle-of-attack and sideslip angle estimates. The conditional observability analysis developed here is independent of aircraft. Additional results determine what type of wind one can estimate based on a given aircraft. The significance of our work lies in the conditional observability since it is the first to investigate canonical flight patterns based on the orientation and airspeed of an aircraft to assess observability. Finally, preliminary results from simulation shows our conditional observability is correct.