James P. Chryssanthacopoulos

Accounting for State Uncertainty in Collision Avoidance

An important consideration in the development of aircraft collision avoidance systems is how to account for state uncertainty due to sensor limitations and noise. However, many collision avoidance systems simply use point estimates of the state instead of leveraging the full posterior state distribution. Recently, there has been work on applying decision-theoretic methods to collision avoidance, but the importance of accommodating state uncertainty has not yet been well studied. This paper presents a computationally efficient framework for accounting for state uncertainty based on dynamic programming. Examination of characteristic encounters and Monte Carlo simulations demonstrates that properly handling state uncertainty rather than simply using point estimates can significantly enhance safety and improve robustness to sensor error.

A decision-theoretic approach to developing robust collision avoidance logic

All large transport aircraft are required to be equipped with a collision avoidance system that instructs pilots how to maneuver to avoid collision with other aircraft. The uncertainty in the behavior of the intruding aircraft makes developing a robust collision avoidance logic challenging. This paper presents an automated approach for optimizing collision avoidance logic based on probabilistic models of aircraft behavior and a performance metric that balances the competing objectives of maximizing safety and minimizing alert rate. The approach involves framing the problem of collision avoidance as a Markov decision process that is solved using dynamic programming. Although this paper focuses on airborne collision avoidance for manned aircraft, the methods may be applied to collision avoidance for other categories of vehicles, both manned and unmanned.

Collision avoidance system optimization with probabilistic pilot response models

All large transport aircraft are required to be equipped with a collision avoidance system that instructs pilots how to maneuver to avoid collision with other aircraft. Uncertainty in the compliance of pilots to advisories makes designing collision avoidance logic challenging. Prior work has investigated formulating the problem as a Markov decision process and solving for the optimal collision avoidance strategy using dynamic programming. The logic was optimized to a pilot response model in which the pilot responds deterministically to all alerts. Deviation from this model during flight can degrade safety. This paper extends the methodology to include probabilistic pilot response models that capture the variability in pilot behavior in order to enhance robustness.

Improved Monte Carlo Sampling for Conict Probability Estimation

Probabilistic alerting systems for airborne collision avoidance often depend upon accurate estimates of the probability of con ict. Analytical, numerical approximation, and Monte Carlo methods have been applied to con ict probability estimation. The advantage of a Monte Carlo approach is the greater exibility a orded in modeling the stochastic behavior of aircraft encounters, but typically many samples are required to provide an adequate con ict probability estimate. One approach to improve accuracy with fewer samples is to use importance sampling, where trajectories are sampled according to a proposal distribution that is di erent from the one speci ed by the model. This paper suggests several di erent sample proposal distributions and demonstrates how they result in signi cantly improved estimates.

Vertical State Estimation for Aircraft Collision Avoidance with Quantized Measurements

A IR traffic control separation services rely on aircraft transponders to provide altitude information. The vast majority of general aviation aircraft today carries mode C transponders, which came into civilian use during the 1950s. Mode C transponders report their barometric altitude with 100 ft quantization. Large aircraft typically carrymode S transponders, which report altitudes with 25 ft quantization. Although 100 ft quantization is generally satisfactory for basic separation services, it makes last-minute collision avoidance difficult because of the need to accurately estimate the vertical rate of the aircraft to predict the future trajectories of the aircraft. During the development of the Traffic Alert and Collision Avoidance System (TCAS) [1], the system nowmandatedworldwide on large aircraft, it was recognized that 100 ft quantization made rate estimation significantly more difficult. Although vertical rate could be tracked easily from 25 ft reports using a simple linear filter, 100 ft reports required the introduction of a complex nonlinear filter designed specifically for mode C tracking [2]. Even with the special nonlinear filter, simulation studies show that collision risk withmode C intruders is significantly greater than with an intruder with 25 ft quantization [3]. In the U.S. airspace, over 70% of the TCAS resolution advisories involve mode C aircraft. This note studies the safety and operational impact of improving collision avoidance involving intruders with 100 ft encoding. The trackers embedded in TCAS were designed to produce single point estimates of the vertical rate, but recent analysis has shown that collision avoidance performance can be greatly improved if state uncertainty is taken into account [4]. Adapting TCAS to accommodate covariance information is far from straightforward, but recent research has investigated a decision-theoretic approach that naturally accommodates state uncertainty as a probability distribution [5]. This new approach is being used to develop the next generation of TCAS [6]. Different state estimation techniques have been developed for quantized measurements. The Kalman filter can be used by treating the quantization as Gaussian noise and using the Sheppard correction [7]. Curry et al. show how to update state estimates using knowledge that the observation is quantized [8]. This approach requires numerical approximation. Sviestins andWigren developed a method from the Fokker–Planck equation under the assumption of constant rate [9]. A particle filter can accommodate quantization but with additional computational cost and certification challenges [10]. This note compares the tracking performance of the TCAS nonlinear filter against several different filters. The Kalman filter and the modified Kalman filter are integrated into the next-generation TCAS logic, and the performance is evaluated on both operational radar data and a high-fidelity airspace encounter model [11]. Experiments reveal that adding a couple checks can further improve performance of the modified Kalman filter.

Collision Avoidance Using Partially Controlled Markov Decision Processes

Optimal collision avoidance in stochastic environments requires accounting for the likelihood and costs of future sequences of outcomes in response to different sequences of actions. Prior work has investigated formulating the problem as a Markov decision process, discretizing the state space, and solving for the optimal strategy using dynamic programming. Experiments have shown that such an approach can be very effective, but scaling to higher-dimensional problems can be challenging due to the exponential growth of the discrete state space. This paper presents an approach that can greatly reduce the complexity of computing the optimal strategy in problems where only some of the dimensions of the problem are controllable. The approach is applied to aircraft collision avoidance where the system must recommend maneuvers to an imperfect pilot.

Robustness of optimized collision avoidance logic to modeling errors

Collision avoidance systems, whether for manned or unmanned aircraft, must reliably prevent collision while minimizing alerts. Deciding what action to execute at a particular instant may be framed as a multiple-objective optimization problem has exploredm ethods of efficiently computing the that can be solved offline by computers. Prior work optimal collision avoidance logic from a probabilistic model of aircraft behavior and a cost function. One potential concern with using a probabilistic model to construct the logic is that the model may not adequately represent the real world. Inaccuracies in the model could lead to vulnerabilities in the system when deployed. This paper evaluates the robustness of collision avoidance optimization to modeling errors.

Analysis of open-loop and closed-loop planning for aircraft collision avoidance

Open-loop planning has been a popular approach for developing aircraft collision avoidance systems. Open-loop planning computes a future plan to follow without anticipation of how future observations can affect the future course of action. Closed-loop planning, in contrast, takes into account the ability to react to future information. This paper explores trade-offs that exist between the two strategies as they apply to aircraft collision avoidance. It demonstrates some of the performance gains that can be realized by adopting a closed-loop planning strategy.

Collision avoidance for general aviation

• Approach based on Markov decision process used to optimize collision avoidance logic for GA • Compared current TCAS and Descend/Climb responsive coordination with GA optimized logic — Optimized logic safer than TCAS and D/C against non-GA and GA intruder aircraft — Performance against GA intruders also resulted in lower Pr(NMAC) • Probability of alert and reversal with optimized logic on GA aircraft lower than with TCAS — Probability of TCAS-equipped intruder reversing was slightly higher — High cost of reversing (0.4) desirable from operational standpoint

Decomposition methods for optimized collision avoidance with multiple threats

Aircraft collision avoidance systems assist in the resolution of collision threats from nearby aircraft by issuing avoidance maneuvers to pilots. Encounters where multiple aircraft pose a threat, though rare, can be difficult to resolve because a maneuver that might resolve a conflict with one aircraft might induce conflicts with others. Recent efforts to develop robust collision avoidance systems for single-threat encounters have involved modeling the problem as a Markov decision process and applying dynamic programming to solve for the optimal avoidance strategy. Because this methodology does not scale well to multiple threats, this paper evaluates a variety of decomposition methods that leverage the optimal avoidance strategy for single-threat encounters.