The main purpose of this paper is design and implementation of a new linear observer for an attitude and heading reference system (AHRS), which includes three-axis accelerometers, gyroscopes, and magnetometers in the presence of sensors and modeling uncertainties. Since the increase of errors over time is the main difficulty of low-cost micro electro mechanical systems (MEMS) sensors producing instable on–off bias, scale factor (SF), nonlinearity and random walk errors, development of a high-precision observer to improve the accuracy of MEMS-based navigation systems is considered. First, the duality between controller and estimator in a linear system is presented as the base of design method. Next, Legendre polynomials together with block-pulse functions are applied for the solution of a common linear time-varying control problem. Through the duality theory, the obtained control solution results in the block-pulse functions and Legendre polynomials observer (BPLPO). According to product properties of the hybrid functions in addition to the operational matrices of integration, the optimal control problem is simplified to some algebraic equations which particularly fit with low-cost implementations. The improved performance of the MEMS AHRS owing to implementation of BPLPO has been assessed through vehicle field tests in urban area compared with the extended Kalman filter (EKF).

本文的主要目的是设计和实现用于姿态和航向参考系统 (AHRS) 的新线性观测器，其中包括三轴加速度计、陀螺仪和存在传感器和建模不确定性的磁力计。由于误差随时间增加是低成本微机电系统 (MEMS) 传感器产生不稳定开关偏置、比例因子 (SF)、非线性和随机游走误差的主要困难，因此开发高精度观测器以考虑提高基于 MEMS 的导航系统的精度。首先，将线性系统中控制器和估计器之间的对偶性作为设计方法的基础。接下来，勒让德多项式与块脉冲函数一起用于解决常见的线性时变控制问题。通过对偶理论，获得的控制解导致块脉冲函数和勒让德多项式观测器（BPLPO）。根据混合函数的乘积特性以及积分运算矩阵，将最优控制问题简化为一些特别适合低成本实现的代数方程。与扩展卡尔曼滤波器 (EKF) 相比，通过在市区进行的车辆现场测试，已经评估了由于 BPLPO 的实施而提高的 MEMS AHRS 性能。最优控制问题被简化为一些特别适合低成本实现的代数方程。与扩展卡尔曼滤波器 (EKF) 相比，通过在市区进行的车辆现场测试，已经评估了由于 BPLPO 的实施而提高的 MEMS AHRS 性能。最优控制问题被简化为一些特别适合低成本实现的代数方程。与扩展卡尔曼滤波器 (EKF) 相比，通过在市区进行的车辆现场测试，已经评估了由于 BPLPO 的实施而提高的 MEMS AHRS 性能。