A Symmetry-Based Unscented Particle Filter for State Estimation of a Ballistic Vehicle

Abstract

The problem of state estimation for vehicles when an initial fix is highly uncertain and/or the number of sensors is not sufficient (and changes with time) is very relevant for both aircraft and spacecraft navigation. This work proposes a Locally Linearized Particle Filter based on a quaternion-adapted Unscented Kalman Filter to estimate the state of a vehicle with minimal sensors and uncertain initial conditions, exploiting geometrical symmetries. The algorithm is applied to a ballistic vehicle navigating towards a laser-illuminated target using on-board sensors, including a triad of accelerometers and gyroscopes, a barometric altimeter and a laser receiver. A symmetry around the vertical axis is identified; based on it, the algorithm becomes capable of solving the navigation problem, even with highly uncertain initial conditions and without enough sensor information; this second condition is particularly severe when the laser receiver is not yet obtaining data. The proposed navigation algorithm offers promising results in simulation, rapidly converging to an accurate estimate of the real trajectory when the laser receiver becomes active.