Nonlinear techniques for Mode C climb/descent rate estimation in ATC systems

Secondary surveillance radars (SSRs) currently form the main data source for target tracking in air traffic control systems. Altitude and climb/descent rate estimation is then based on Mode C altitude reports obtained from transponder replies from the aircraft. Accurate climb/descent rates are essential for the performance of short-term conflict alert (STCA) systems where prediction times of up to 2 min may be required. This is however difficult to accomplish because of the 100 ft quantization of the Mode C reports which limits the applicability of standard Kalman filtering techniques. To overcome these problems two new nonlinear filters have been derived. They perform recursive state estimation when only coarsely quantized measurements are available. The first method follows from a solution to the Fokker-Planck equation, and is therefore optimal. A linear trend model with uniform prior probability density function (pdf) forms the model assumptions. Together with properties of the quantizer this allows an exact and recursive updating of the pdf using only the corners of a convex polygon. The second method is obtained by modifications of the extended Kalman filter (EKF), and is therefore more widely applicable, at the price of being suboptimal