The infrared angle estimation at the fine scale is a nonlinear
process that is commonly dealt with the extended Kalman filter
(EKF) [13], the unscented Kalman filter (UKF) [14] and particle filter
(PF) [15]. In the EKF, the state distribution is approximated by a
Gaussian random variable (GRV), which is then propagated analytically
through the first-order linearization of the nonlinear system.
This can introduce larger errors in the true posterior mean and
covariance of the transformed GRV, which may lead to suboptimal
performance and sometimes result in divergence of the filter.
The UKF uses a deterministic sampling approach based on the
unscented transformation. The state distribution is also approximated
by a GRV, but is represented by using a minimal set of carefully
chosen sampling points. These sampling points can capture
the true mean and covariance of the GRV completely. When propagated
through the true nonlinear system, they can estimate the
posterior mean and covariance accurately to the 3rd order for
any nonlinearity. PF method is a set of online posterior density
estimation algorithm that estimates the posterior density of the
state-space by implementing the Bayesian recursion equations
directly. It’s not restricted by state transition and the measurement
model, and has a higher estimated accuracy. However, PF has
heavy calculation and is troubled by the problem of particle degradation.
Taken together, the UKF can achieve 3rd-order accuracy
with proper computational complexity, while the EKF only
achieves first-order accuracy and the PF has a greater computational
complexity than the UKF. Therefore the UKF algorithm is
adopted to achieve angle estimation at the fine scale in this paper.