基于MARG传感器的AHRS关键技术研究
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摘要
基于各向异性磁阻（AMR）的三轴磁强计以及基于微机电系统（MEMS）的三轴加速度计和三轴陀螺仪具有小体积、低成本、低功耗等突出优点。这三种传感器的组合，即MARG传感器，提供了一种可用于测量载体姿态以及导航定位的便捷可靠的手段。采用MARG传感器的航向与姿态参考系统（AHRS）性能优越且用途广泛，其相关理论与技术的研究具有重要的学术价值和现实意义。
本文针对基于MARG传感器的AHRS研发及应用中的若干关键问题展开研究，主要进行了以下工作。
首先，针对三轴磁强计和三轴加速度计的误差校正与补偿问题，深入研究和探讨了三轴矢量场传感器的校正方法，特别是在无外部设备辅助条件下的校正方法。对已有文献和研究报道中广泛采用的基于椭球拟合的校正方法进行了详细分析，指出了该方法的固有缺陷，即无法有效辨识和补偿传感器间的非对准误差，并揭示了这一缺陷对AHRS的影响。进而，提出了三轴矢量场传感器校正的“点积不变法”，从根本上改善了校正效果，并且能与椭球拟合法相互配合而实现无需外部基准的三轴矢量场传感器自动校正。
其次，针对三轴MEMS陀螺仪的标定问题，尤其是在缺少转台等精密设备的条件下标定陀螺仪的问题，提出了“叉积标定法”。该方法利用三轴矢量场传感器经校正后的测量值为参考，无需外部设备辅助即可实现三轴MEMS陀螺仪的标定，且标定精度能接近传统的转台标定法的水平。叉积标定法与点积不变法和椭球拟合法联合使用，可以实现MARG传感器在使用环境下的全自动误差校正与补偿，对基于MARG传感器的AHRS的实际应用具有重大意义。
再者，针对基于MARG传感器的AHRS中的姿态融合滤波问题，通过对各种滤波算法的比较，选择以乘性姿态误差矢量为基础，介绍和分析了由其衍生出的乘性扩展卡尔曼滤波（MEKF）、乘性无迹卡尔曼滤波（MUKF）和广义互补滤波（GCF）三种算法，详细讨论了三者具体设计实现中的关键问题。进而在各种软硬件环境下对这三种姿态融合滤波算法进行了数值模拟实验，检验和对比了三者的性能表现，证明了GCF是一种计算量小且性能稳定可靠的姿态融合滤波解决方案。
最后，针对基于重力与地磁场双矢量的姿态解算问题，引入CORDIC（坐标旋转数字计算机）算法，并在其基础上设计了双矢量CORDIC（DV-CORDIC）姿态解算方法，以提高计算效率。深入分析了CORDIC和DV-CORDIC的误差来源及上限，并分别讨论和推导了二者计算角度的不确定度，继而通过数值模拟验证了所提出的不确定度表达式的合理性。同时，模拟结果也显示了32位DV-CORDIC算法的精度可以达到单精度浮点运算的水平，但其速度相对后者具有明显的优势。
Tri-axial anisotropic magneto-resistive (AMR) magnetometers, as well as tri-axialmicro electro-mechanical system (MEMS) accelerometers and gyros, have theoutstanding advantages of small size, low cost, low power consumption, etc. Thecombination of the above three types of sensors, which is called MARG sensor,provides an efficient and reliable solution for attitude determination and navigation. Theattitude and heading reference systems (AHRS) based on MARG sensors have highperformance and versatility. Therefore, the research on its theory and technology hasacademic and practical significance.
The research presented in this dissertation is focused on several critical problemsin the development and application of the AHRS based on MARG sensor. The majorcontributions are listed below.
Firstly, aiming at the calibration and compensation for the errors of tri-axialmagnetometers and accelerometers, the calibration methods for tri-axial vector fieldsensors, especially the calibration techniques without external equipments, are studiedand discussed in depth. The ellipsoid fitting method, which was commonly used in theexisting literature, is analyzed in detail. It is pointed out that the inherent defect of theellipsoid fitting method is that it cannot identify and compensate the mutualmisalignment, or inter-triad misalignment, between different sensors. The impact of thisdefect on the AHRS is also revealed. And then the dot product invariance method fortri-axial vector field sensors calibration is introduced, which brings in essentialenhancement for the calibration results. The dot product invariance method can also beused with the ellipsoid fitting method, in order to form a self-calibration scheme fortri-axial vector field sensors without the aim of external equipment.
Secondly, the cross product calibration method is presented for the calibration oftri-axial MEMS gyros, especially the calibration without a rate table or other precisiondevices. The cross product calibration method uses the measurement of calibratedtri-axial vector field sensors as the reference, instead of external equipment, to carry outthe calibration of tri-axial MEMS gyros. And its precision is very close to that of thetradition method using a rate table. Moreover, the combination of the cross productcalibration method, the dot product invariance method, and the ellipsoid fitting methodcan accomplish the fully automatic in-use calibration for MARG sensor, and thus it hasgreat significance for the applications of MARG sensor.
Thirdly, the attitude fusion and filtering problem of MARG-based AHRS isdiscussed. After the comparison of different filtering methods, the multiplicative attitudeerror vector is chosen as the basis of attitude fusion and filtering. Then themultiplicative extended Kalman filters (MEKF), the multiplicative unscented Kalmanfilters (MUKF), as well as the generalized complementary filters (GCF), are presentedand analyzed. The critical points in the design and implementations of the above threealgorithms are discussed. Furthermore, numerical simulations of the above threealgorithms are performed in different software and hardware environments, to evaluateand compare their performance. The GCF is proved to be an efficient, stable, andreliable solution for attitude fusion and filtering.
Last but not least, for the attitude determination using the gravity and thegeomagnetic vectors, the CORDIC (coordinate rotation digital computer) algorithm isadopted. The dual-vector CORDIC (DV-CORDIC) algorithm is presented, which canimprove the computational efficiency. The error sources and the upper bound of errorsfor CORDIC and DV-CORDIC are analyzed in depth, and the expressions of the angleuncertainties are also given and verified by numerial simulations. Simulation resultsalso prove that the precision of32-bit DV-CORDIC algorithm can achieve the level ofsingle precision floating point arithmetic, but the former has an obvious advantage incomputation speed over the latter.
本文针对基于MARG传感器的AHRS研发及应用中的若干关键问题展开研究，主要进行了以下工作。
首先，针对三轴磁强计和三轴加速度计的误差校正与补偿问题，深入研究和探讨了三轴矢量场传感器的校正方法，特别是在无外部设备辅助条件下的校正方法。对已有文献和研究报道中广泛采用的基于椭球拟合的校正方法进行了详细分析，指出了该方法的固有缺陷，即无法有效辨识和补偿传感器间的非对准误差，并揭示了这一缺陷对AHRS的影响。进而，提出了三轴矢量场传感器校正的“点积不变法”，从根本上改善了校正效果，并且能与椭球拟合法相互配合而实现无需外部基准的三轴矢量场传感器自动校正。
其次，针对三轴MEMS陀螺仪的标定问题，尤其是在缺少转台等精密设备的条件下标定陀螺仪的问题，提出了“叉积标定法”。该方法利用三轴矢量场传感器经校正后的测量值为参考，无需外部设备辅助即可实现三轴MEMS陀螺仪的标定，且标定精度能接近传统的转台标定法的水平。叉积标定法与点积不变法和椭球拟合法联合使用，可以实现MARG传感器在使用环境下的全自动误差校正与补偿，对基于MARG传感器的AHRS的实际应用具有重大意义。
再者，针对基于MARG传感器的AHRS中的姿态融合滤波问题，通过对各种滤波算法的比较，选择以乘性姿态误差矢量为基础，介绍和分析了由其衍生出的乘性扩展卡尔曼滤波（MEKF）、乘性无迹卡尔曼滤波（MUKF）和广义互补滤波（GCF）三种算法，详细讨论了三者具体设计实现中的关键问题。进而在各种软硬件环境下对这三种姿态融合滤波算法进行了数值模拟实验，检验和对比了三者的性能表现，证明了GCF是一种计算量小且性能稳定可靠的姿态融合滤波解决方案。
最后，针对基于重力与地磁场双矢量的姿态解算问题，引入CORDIC（坐标旋转数字计算机）算法，并在其基础上设计了双矢量CORDIC（DV-CORDIC）姿态解算方法，以提高计算效率。深入分析了CORDIC和DV-CORDIC的误差来源及上限，并分别讨论和推导了二者计算角度的不确定度，继而通过数值模拟验证了所提出的不确定度表达式的合理性。同时，模拟结果也显示了32位DV-CORDIC算法的精度可以达到单精度浮点运算的水平，但其速度相对后者具有明显的优势。
Tri-axial anisotropic magneto-resistive (AMR) magnetometers, as well as tri-axialmicro electro-mechanical system (MEMS) accelerometers and gyros, have theoutstanding advantages of small size, low cost, low power consumption, etc. Thecombination of the above three types of sensors, which is called MARG sensor,provides an efficient and reliable solution for attitude determination and navigation. Theattitude and heading reference systems (AHRS) based on MARG sensors have highperformance and versatility. Therefore, the research on its theory and technology hasacademic and practical significance.
The research presented in this dissertation is focused on several critical problemsin the development and application of the AHRS based on MARG sensor. The majorcontributions are listed below.
Firstly, aiming at the calibration and compensation for the errors of tri-axialmagnetometers and accelerometers, the calibration methods for tri-axial vector fieldsensors, especially the calibration techniques without external equipments, are studiedand discussed in depth. The ellipsoid fitting method, which was commonly used in theexisting literature, is analyzed in detail. It is pointed out that the inherent defect of theellipsoid fitting method is that it cannot identify and compensate the mutualmisalignment, or inter-triad misalignment, between different sensors. The impact of thisdefect on the AHRS is also revealed. And then the dot product invariance method fortri-axial vector field sensors calibration is introduced, which brings in essentialenhancement for the calibration results. The dot product invariance method can also beused with the ellipsoid fitting method, in order to form a self-calibration scheme fortri-axial vector field sensors without the aim of external equipment.
Secondly, the cross product calibration method is presented for the calibration oftri-axial MEMS gyros, especially the calibration without a rate table or other precisiondevices. The cross product calibration method uses the measurement of calibratedtri-axial vector field sensors as the reference, instead of external equipment, to carry outthe calibration of tri-axial MEMS gyros. And its precision is very close to that of thetradition method using a rate table. Moreover, the combination of the cross productcalibration method, the dot product invariance method, and the ellipsoid fitting methodcan accomplish the fully automatic in-use calibration for MARG sensor, and thus it hasgreat significance for the applications of MARG sensor.
Thirdly, the attitude fusion and filtering problem of MARG-based AHRS isdiscussed. After the comparison of different filtering methods, the multiplicative attitudeerror vector is chosen as the basis of attitude fusion and filtering. Then themultiplicative extended Kalman filters (MEKF), the multiplicative unscented Kalmanfilters (MUKF), as well as the generalized complementary filters (GCF), are presentedand analyzed. The critical points in the design and implementations of the above threealgorithms are discussed. Furthermore, numerical simulations of the above threealgorithms are performed in different software and hardware environments, to evaluateand compare their performance. The GCF is proved to be an efficient, stable, andreliable solution for attitude fusion and filtering.
Last but not least, for the attitude determination using the gravity and thegeomagnetic vectors, the CORDIC (coordinate rotation digital computer) algorithm isadopted. The dual-vector CORDIC (DV-CORDIC) algorithm is presented, which canimprove the computational efficiency. The error sources and the upper bound of errorsfor CORDIC and DV-CORDIC are analyzed in depth, and the expressions of the angleuncertainties are also given and verified by numerial simulations. Simulation resultsalso prove that the precision of32-bit DV-CORDIC algorithm can achieve the level ofsingle precision floating point arithmetic, but the former has an obvious advantage incomputation speed over the latter.
引文
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