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, close to the Cramer-Rao lower bound.

中文翻译：

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ChevOpt：切比雪夫多项式优化的连续时间状态估计

本文提出了一种基于切比雪夫多项式优化（ChevOpt）的连续时间最大值后验估计新框架，将非线性连续时间状态估计转化为常数参数优化问题。具体来说，时变系统状态由切比雪夫多项式表示，未知切比雪夫系数通过最小化先验、动力学和测量的加权和来优化。所提出的 ChevOpt 是最小二乘意义上的最佳连续时间估计，需要批处理。还提出了递归滑动窗口版本以满足实时应用的要求。与著名的高斯滤波器相比，ChevOpt 更好地解决了动力学和测量中的非线性问题。