Fixed-Gain Augmented-State Tracking-Filters

The complex frequency response is a complete description of a tracking filter's behavior at steady state. For example: 1) The flatness order at zero frequency determines the kinematic state dimension, thus the polynomial degree of trackable target trajectories; 2) The magnitude and phase error at a given non-zero frequency determine the radial and angular (bias) errors for a target on a circular orbit of a given angular velocity; and 3) The integral of squared magnitude determines the (random) measurement-noise attenuation. A procedure for the design of fixed-gain tracking filters, using an augmented-state observer with signal and interference subspaces, is proposed as a way of satisfying these frequency-response requirements. The signal subspace incorporates an integrating Newtonian model and a second-order maneuver model that is matched to a sustained constant-g turn; the deterministic interference model attenuates high frequencies for smoother track estimates. The selected models provide a simple means of shaping the steady-state response of tracking-filters of elevated order, when noise statistics are unknown and non-Gaussian. Pole placement is used to tune the transient response as an alternative to process noise.