论文标题
Chevopt：Chebyshev多项式优化的连续时间估计
ChevOpt: Continuous-time State Estimation by Chebyshev Polynomial Optimization
论文作者
论文摘要
在本文中，提出了一个基于Chebyshev多项式优化（CHEVOPT）的后时间最大估计的新框架，这将非线性连续时状态估计转换为恒定参数优化的问题。具体而言，随时间变化的系统状态由Chebyshev多项式表示，未知的Chebyshev系数通过最大程度地降低了先验，动力学和测量的加权总和来优化。在最小二乘中，提出的CHEVOPT是最佳的连续时间估计，需要进行批处理处理。还提出了递归滑动窗口版本，以满足实时应用程序的要求。与众所周知的高斯过滤器相比，Chevopt可以更好地解决动力学和测量中的非线性。示例示例的数值结果表明，所提出的Chevopt在扩展/无情的卡尔曼过滤器和扩展的批处理/固定lag更平滑的情况下，取得了明显提高的精度，闭上了Cramer-Rao的下限。
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.
