Inertial sensors based on micro-electro-mechanical systems (MEMS) technology, such as accelerometers and angular rate sensors, are cost-effective solutions used in inertial navigation systems in a broad spectrum of applications that estimate position, velocity and orientation of a system with respect to an inertial reference frame. Although they present several advantages in terms of cost and form factor, they are prone to various disturbances such as noise, biases, and random walk that degrade their orientation estimation. The task of an orientation filter is to compute an optimal solution for the attitude state, consisting of roll, pitch and yaw, through the fusion of angular rate, accelerometer, and magnetometer measurements, regardless of the underlying environmental constraints. The aim of this paper is threefold: first, it serves researchers and practitioners in the signal processing community seeking the most appropriate attitude estimators that fulfills their needs, shedding light on the drawbacks and the advantages of a wide variety of designs. Second, it serves as a survey and tutorial for existing estimator designs in the literature, assessing their design aspects and components, and dissecting their hidden details for the benefit of researchers. Third, a comprehensive list of algorithms is discussed for a fully functional inertial navigation system, starting from the navigation equations and ending with the filter equations, keeping in mind their suitability for power-limited embedded processors. The source code of all algorithms is published, with the aim of it being an out-of-box solution for researchers in the field. The reader will take away the following concepts from this article: understand the key concepts of an inertial navigation system; be able to implement and test a complete stand alone solution; be able to evaluate and understand different algorithms; understand the trade-offs between different filter architectures and techniques; and understand efficient embedded processing techniques, trends and opportunities.

基于微机电系统（MEMS）技术的惯性传感器（例如加速度计和角速率传感器）是惯性导航系统中使用的经济有效的解决方案，可广泛应用于估算系统位置，速度和方向的惯性导航系统中。相对于惯性参考系。尽管它们在成本和形状因数方面均具有多种优势，但它们容易受到各种干扰（例如噪声，偏差和随机游走）的干扰，从而降低了其方向估计的准确性。定向滤波器的任务是通过角速度，加速度计和磁力计测量值的融合来计算姿态状态的最佳解决方案，该姿态状态包括侧倾，俯仰和偏航，而不受潜在的环境约束。本文的目的是三方面的：首先，它为信号处理领域的研究人员和从业人员提供服务，以寻求最合适的姿态估计器来满足他们的需求，并阐明各种设计的弊端和优势。其次，它用作文献中现有估算器设计的调查和教程，评估其设计方面和组成部分，并剖析其隐藏的细节，以使研究人员受益。第三，从导航方程式开始，以滤波器方程式结束，讨论了功能齐全的惯性导航系统的算法的完整列表，并牢记它们对功率受限的嵌入式处理器的适用性。所有算法的源代码均已发布，目的是为该领域的研究人员提供即用型解决方案。读者将从本文中删除以下概念：了解惯性导航系统的关键概念；了解惯性导航系统的主要概念。能够实施和测试完整的独立解决方案；能够评估和理解不同的算法；了解不同滤波器架构和技术之间的权衡；并了解有效的嵌入式处理技术，趋势和机会。