TIS-B: calculation of navigation accuracy category for position and velocity parameters

Traffic information service-broadcast (TIS-B) is a surveillance service that derives traffic information from one or more ground surveillance sources and broadcasts to automatic dependant surveillance-broadcast (ADS-B) equipped aircraft or surface vehicles, with the intention of supporting aircraft separation assurance (ASA) applications. ASA Minimum Aviation System Performance Standards (MASPS) require that the navigation accuracy category for position (NAC_P) and velocity (NAC_V) be reported so that ASA applications may determine whether the reported position and velocity have an acceptable level of accuracy for the intended use. This paper develops two methods to compute NAC_P and NAC_V. The two methods are denoted exact and bounded, and their performance is investigated in computing the 95% containment threshold for a broad range of values of elliptical eccentricity. The algorithms for the two methods can be easily implemented regardless of the eccentricity of the underlying uncertainty. The proposed algorithm computes NAC_P and NAC_V parameters for position and rate estimates that are derived from Kalman filter based estimators. These estimators provide a covariance matrix that is a measure of the uncertainty associated with the estimates. It is first shown that the covariance matrix computed by Kalman-based estimators can be partitioned into horizontal position and rate terms. Eigenvalues can be computed for the partitioned covariance matrix to provide the squares of the major and minor axes of the representative uncertainty ellipses regardless of their orientation with respect to the reference frame. Conversion factors from the elliptical to circular bounds were computed for relative accuracy that accounts for random error only. A follow-on paper addresses absolute accuracy that in addition to random error accounts for uncorrected bias errors that may occur after an aircraft maneuver due to a position lag in the estimated positions.