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.