This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group \mathbb{SO}\left(3\right) with the tracking error of the normalized Euclidean distance meeting predefined transient and steady-state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low-cost inertial measurement units. Unit-quaternion representation of the proposed filters are presented. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form. Keywods: Attitude estimates, transient, steady-state error, nonlinear filter, special orthogonal group, SO(3), stochastic system, stochastic differential equations, Ito, Stratonovich, asymptotic stability, Wong-Zakai, inertial measurment unit, IMU, prescribed performance function, Euler Angles, roll, bitch, yaw, color noise, white noise, Nonlinear attitude filter, Nonlinear attitude observer, Orientation, nonlinear stochastic attitude filter on SO(3), unit-quaternion based nonlinear stochastic attitude filter, discrete stochastic attitude filter.

中文翻译：

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特殊正交群 SO(3) 上非线性随机估计量的系统收敛

本文介绍了在特殊正交群 \mathbb{SO}\left(3\right) 上开发的两种新型非线性随机姿态估计器，其跟踪误差归一化欧几里得距离满足预定义的瞬态和稳态特性。跟踪误差被限制在一个预定的大集合内初始开始，从而保证瞬态性能服从动态减少边界，并从几乎任何初始条件平滑渐近地下降到概率原点。建议的估计器使用从低成本惯性测量单元获得的测量值产生具有显着收敛特性的准确姿态估计。提出了所提出的滤波器的单位四元数表示。为实现目的，以连续形式提出的估计器由其离散版本补充。仿真结果说明了所提出的估计器对不确定测量和大初始化误差的有效性和鲁棒性，无论是连续形式还是离散形式。关键字：姿态估计、瞬态、稳态误差、非线性滤波器、特殊正交群、SO(3)、随机系统、随机微分方程、Ito、Stratonovich、渐近稳定性、Wong-Zakai、惯性测量单元、IMU、规定性能函数，欧拉角，滚转，母狗，偏航，颜色噪声，白噪声，非线性姿态滤波器，非线性姿态观测器，方向，SO(3) 上的非线性随机姿态滤波器，基于单位四元数的非线性随机姿态滤波器，