Steady-state circular errors for basic tracking filters

Deterministic steady-state errors for circular manoeuvres are discussed for two basic tracking filters: a two-state continuous-time filter and the discrete-time update α-β filter. Radial and angular errors are expressed in terms of target acceleration and filter bandwidth, and it is shown that the radial error dominates. The α-β filter bandwidth is given and a useful approximation is obtained. The tracking index can then be interpreted in terms of bandwidth and a rule-of-thumb for an upper bound of the index can be formulated. The paper contributes relationships for basic filter performance during circular manoeuvring that should be useful in a design process. Some design aspects are discussed. The results are obtained by using transfer functions.