Interactive Multiple Model Sensor Analysis for Unmanned Aircraft Systems (UAS) Detect and Avoid (DAA)
Adriano Canolla, Michael B. Jamoom and Boris Pervan, Illinois Institute of Technology
This research describes new methods to apply safety standards in Detect and Avoid (DAA) functions for Unmanned Aircraft Systems (UAS) using target tracking and encounter models. With the expanding range of applications for UAS operations, the United States Congress mandated the Federal Aviation Administration (FAA), through the FAA Modernization and Reform Act of 2012, to develop necessary requirements for integration of UAS into the National Airspace System.
One of the challenges for the FAA to meet this mandate is to ensure that safety targets are met. While a manned aircraft's pilot relies on human vision to see and avoid non-cooperative intruders (those not employing a transponder or Automatic Dependent Surveillance-Broadcast, ADS-B) an Unmanned Aircraft System requires a DAA system to provide self-separation between the own unmanned aircraft and any intruder aircraft.
Previous work used predefined linear encounter trajectories (either with constant velocity or linear acceleration) for the sensor uncertainty analysis, focusing on potential borderline cases as a test for the methodology. In this work, an established encounter model generates the intruder trajectories. This better accounts for the likelihood of different types of encounters, to include potential worst-case maneuvering (non-linear) intruder trajectories. In addition, to improve the intruder dynamics estimation we use multiple models to track maneuvering intruders. Our preliminary effort in this area focused on the effect of the estimation errors on the only one hazard state, horizontal closest point of approach (CPA). This paper serves as a continuation effort to evaluate the Multiple Model Adaptive Estimation (MMAE) tracking concept applied to UAS DAA performance evaluation against realistic, maneuvering intruder encounters, as well as analyzing the effects of estimation errors on all hazard states.
In the field of target tracking, state estimation of maneuvering targets, such as intruder aircraft, from sensor measurements usually accounts for different target behavior. This is formulated as a hybrid state estimation problem in which the target’s dynamics are modeled by multiple motion regimes (or modes) that cover different possible system patterns, such as maneuvering and non-maneuvering trajectories. The performance of a tracking system is determined by the fidelity of the hybrid state estimation algorithm employed as well as the sensor measurement error.
The Interactive Multiple Model (IMM) algorithm is an MMAE method for combining state hypotheses from multiple filter models to estimate the states of targets with changing dynamics. The IMM has been shown to be an efficient algorithm (robust but not computationally expensive) for the estimation of hybrid systems. It has been successfully implemented in maneuvering target tracking for air traffic control systems. At each update, the IMM runs multiple filters and then combines their outputs into an overall state estimate, weighting the results from each filter. In an IMM filter, the goal is to apply the maximum likelihood model at each time update. The weights are based on the best available knowledge of target behavior. The different modes used for the filter can be approximated for an intruder aircraft as certain predefined standard maneuvers, such as coordinated turns and constant ascent rates, which are widely used on radar tracking application and ATC.
The simulation sequence starts with the generation and extraction of the initial intruder conditions and control variables from an encounter model. These are only scalars (velocity, linear acceleration, turn rate, and the vertical velocity) so we need to provide an initial intruder position and direction in relation to our own aircraft. We initialize the position of the intruder aircraft on the surface of an "encounter cylinder" centered on the own aircraft, at a random heading angle. We apply sampling rejection for the initial position conjugated with the initial control variables from the encounter model. If the intruder is not in an inward trajectory from the surface, we repeat the initialization. The intruder trajectory is built using point-mass kinematics to update the aircraft states. The trajectory is then inserted into the IMM estimation algorithm, using encounter model outputs as inputs for the true intruder trajectory. Finally, we get the simulation outputs for analysis.
The IMM algorithm has estimation errors that are not directly related with its calculated covariances. The total error in the relative intruder position and velocity, Hazard States and trajectory prediction will be a sum of different error sources. Some will depend on the quality of the implementation of the algorithm, others on the inherently noisy measurements from the DAA system. We can divide the main contributors of the error into four parts:
• Mode transition adaptation: estimation error caused by lack of knowledge of mode switches during tracking, i.e. the mode adaptation might not be rapid enough.
• Mode transition prediction: Since our analysis covers maneuver changes along the simulation and we cannot predict future intruder intent, we have an additional source of error which consists of the prediction error of the Hazard States from the actual Hazard States, which is only known after the simulation has ended.
• Modeling error: This error exists when a maneuver, by its nature, does not follow the assumptions of the standard dynamic models used in the IMM.
• Sensor noise: Random noise on the sensor measurements.
Thus even an IMM implementation with perfect measurements would still have uncertainty in trajectory estimation due to the approximate motion models used.
The hazards associated with an intruder aircraft are defined using “Hazard State” parameters; these include the horizontal distance to the closest point of approach (CPA) between the own aircraft and intruder, the time to horizontal closest point of approach, and the current vertical separation between the own aircraft and intruder. The Well Clear Threshold (a separation standard that includes thresholds on time to closest point of approach, a horizontal miss distance and a vertical miss distance) is broken down into thresholds on each of these hazard states. In our previous work, we focused on CPA estimation error only, for a perfect sensor. This work will advance that analysis by addressing all three hazard states, adding sensor noise and also a new method for the Hazard States estimation.
In order to minimize prediction errors on the Hazard States, we introduce a new method instead of using the RTCA DAA MOPS calculations (which are based on a linear trajectory). We don’t know future aircraft intent and maneuver changes, but using knowledge of the latest maneuver can significantly reduce our estimation error relative to the MOPS algorithm; also the estimate gets even better after the IMM recognizes the maneuver and adapts to the new predictions. We use the Kalman prediction step to estimate CPA, which will be the IMM Prediction.
Then, there will be four main different CPA definitions that we will evaluate in this work:
-MOPS: using the formula as defined by the MOPS.
-IMM-MOPS: using the formula as defined by the MOPS and the best trajectory estimation produced by the IMM algorithm.
-IMM-Predicted: the estimated closest point of approach calculated at each timestep, using the IMM prediction (the new method).
-True: only known after the simulation has ended (influenced by future mode switches), used here only for analysis purposes.
A new method based on the Kalman prediction phase inside the Interactive Multiple Model (IMM) algorithm is presented to estimate time to closest point of approach, horizontal miss distance, and vertical separation. An analysis of the sensor error on the algorithm estimation and the sensor field of regard requirement from the Air-to-Air Radar Minimum Operational Performance Standards (MOPS) is performed. The efficiency of the trajectory estimation has direct implication on the estimation of the intruder trajectory in relation to the own aircraft. In addition, we minimize mode transition prediction errors by introducing a new method for estimation of true CPA based on the Kalman prediction update, the IMM prediction. The methods described in this research can aid a certification authority in determining if a DAA system is sufficient for safely integration of UAS into the National Airspace System.