  The iterated posterior linearization filter (IPLF) is an algorithm for
Bayesian state estimation that performs the measurement update using iterative
statistical regression. The main result behind IPLF is that the posterior
approximation is more accurate when the statistical regression of measurement
function is done in the posterior instead of the prior as is done in
non-iterative Kalman filter extensions. In IPLF, each iteration in principle
gives a better posterior estimate to obtain a better statistical regression and
more accurate posterior estimate in the next iteration. However, IPLF may
diverge. IPLF's fixed- points are not described as solutions to an optimization
problem, which makes it challenging to improve its convergence properties. In
this letter, we introduce a double-loop version of IPLF, where the inner loop
computes the posterior mean using an optimization algorithm. Simulation results
are presented to show that the proposed algorithm has better convergence than
IPLF and its accuracy is similar to or better than other state-of-the-art
algorithms.
