ChevOpt: Continuous-time State Estimation by Chebyshev Polynomial Optimization
This addresses state estimation in nonlinear systems for robotics or control applications, offering a novel method with incremental improvements in accuracy.
The paper tackles continuous-time state estimation by proposing ChevOpt, a Chebyshev polynomial optimization framework that transforms nonlinear estimation into constant parameter optimization, achieving improved accuracy over extended/unscented Kalman filters and smoothers, with results close to the Cramer-Rao lower bound.
In this paper, a new framework for continuous-time maximum a posteriori estimation based on the Chebyshev polynomial optimization (ChevOpt) is proposed, which transforms the nonlinear continuous-time state estimation into a problem of constant parameter optimization. Specifically, the time-varying system state is represented by a Chebyshev polynomial and the unknown Chebyshev coefficients are optimized by minimizing the weighted sum of the prior, dynamics and measurements. The proposed ChevOpt is an optimal continuous-time estimation in the least squares sense and needs a batch processing. A recursive sliding-window version is proposed as well to meet the requirement of real-time applications. Comparing with the well-known Gaussian filters, the ChevOpt better resolves the nonlinearities in both dynamics and measurements. Numerical results of demonstrative examples show that the proposed ChevOpt achieves remarkably improved accuracy over the extended/unscented Kalman filters and extended batch/fixed-lag smoother, closes to the Cramer-Rao lower bound.