GNSS/INS组合导航误差补偿与自适应滤波理论的拓展
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摘要
本文对GNSS/INS组合导航误差补偿与自适应滤波理论进行了系统而深入的研究。内容涵盖GNSS/INS组合导航基本原理、INS惯性元件随机误差分析和建模、GNSS/INS组合导航姿态角对准、GNSS/INS组合导航函数模型和随机模型误差补偿、GNSS/INS组合导航自适应滤波算法以及GNSS失锁时INS导航算法研究等。主要工作和创新点概括如下：
1.总结了GNSS/INS组合导航数据处理的基本原理,介绍了INS导航、GNSS导航的基本原理以及GNSS/INS组合导航的滤波模型,分析了INS误差闭环校正和开环校正的优缺点。
2.对INS随机误差进行了系统的分析和处理；分析和比较了陀螺信号中几种性质不同的随机误差在功率谱密度和Allan方差上不同的特性和表现形式；对三种陀螺实测信号中的随机误差进行了分析,给出这些陀螺信号中存在的主要噪声类型及其相应的系数；通过对分解后高频系数进行检验,给出了一种自动判别小波多分辨分析尺度的方法；建立了三种陀螺随机误差的ARMA模型,确定了相应的ARMA模型阶数和模型参数。
3.在INS力学编排基础上从误差分析角度提出一种基于累积误差极小值的精对准方法,有效缩短了初始对准时间；实测算例表明这种方法不受初始对准时间的约束,在较短时间内可以获得较高的对准精度。
4.针对车载系统,提出一种顾及姿态角更新的低成本车载GNSS/INS组合导航算法,推导了利用GNSS测速确定航向角的原理,并且对低成本车载INS系统的俯仰角和翻滚角进行了分析；利用实测算例确定了不同速度下的航向角精度,并且验证了新算法的有效性。
5.给出了三种确定INS白噪声谱密度的方法：直接估计法、基于小波变换的谱密度估计法和Allan方差法。利用实测数据对这三种方法进行了比较和分析,结果表明直接估计法和基于小波变换的谱密度估计所估计的噪声谱密度不仅仅是白噪声,还包含其它各种噪声在内的高频噪声,而Allan方差能够很好地分辨出信号中主要干扰噪声,但是一旦白噪声不占主导,就很容易淹没在别的高频噪声中；GNSS/INS组合导航结果也表明基于Allan方差所确定的白噪声谱密度能够更好地反映惯性元件中的白噪声统计特性。
6.INS信号自相关和偏相关系数表明AR模型尤其是ARMA模型能够更好地反映信号的低频噪声；分别基于AR模型和基于ARMA模型,推导了GNSS/INS组合导航动力学模型方程和随机误差模型。实测算例表明,基于AR模型和ARMA模型的Kalman滤波精度都要高于根据经验设定参数的标准Kalman滤波,其中ARMA模型能够更好地反映低频信号的特性。
7.推导了基于载波相位平滑伪距的实时GNSS/INS组合导航的公式,并且进行了误差分析。利用实测算例对算法进行验证,结果表明如果GPS周跳较少或者不发生周跳,基于载波相位平滑伪距技术的GPS/INS组合导航的精度较伪距紧组合导航有较大的提高,但是当GPS周跳较多时,精度提高不显著。
8.提出伪距差分求解速度的方法,给出了相邻历元和历元间伪距差分测速的公式,并且对其精度进行了分析。利用实测算例对伪距差分测速的精度进行了比较和分析,指出在外界环境恶劣的情况下伪距差分可以保证较高的可靠性。
9.在GNSS/INS松组合和紧组合导航中,为避免单一自适应因子对可靠参数的作用,基于预测残差和选权滤波构造出分类自适应因子,该自适应滤波能够将位置、速度、姿态角误差、陀螺仪和加速度计误差分别赋予不同的自适应因子,避免精度损耗。实测算例表明相比于标准Kalman滤波和单因子自适应滤波,分类因子自适应滤波精度有所提高。
10.针对紧组合导航中观测值存在粗差的问题,提出通过部分状态不符值来构造自适应因子的方法,给出部分状态不符值构造自适应因子的过程,并与单因子自适应滤波和分类因子自适应滤波进行了分析和比较。实测算例结果表明,当观测无异常时,三种自适应因子都能够较好地抑制动态模型误差的影响；但是当观测存在异常时,由预测残差构造的自适应因子不能分辨模型误差和观测误差,而由部分状态不符值构造的自适应因子能够抵制观测异常的影响,滤波结果优于由预测残差构造的自适应因子滤波结果。
11.从参数可观测性角度提出一种两步自适应Kalman滤波算法,推导了两步自适应抗差滤波的公式和具体步骤,并且进行了分析和比较；实测算例结果表明,相比于标准Kalman滤波,两步自适应抗差滤波的导航精度受组合周期的长短、INS惯性元件误差的大小影响较小,并且能够控制动态扰动异常和观测异常的影响。
12.针对由GNSS观测条件不佳或观测不足引起的误差,在一般自适应滤波的基础之上,对其进行扩展,自适应地调节状态预测向量的协方差阵,使其既能控制动态模型误差又能抑制由GNSS观测条件不佳引起的误差的影响。实际计算结果表明,相比于一般自适应滤波,扩展自适应滤波能够很好地控制这两种误差的影响。
13.在GNSS信号失锁时,提出一种速度先验信息和Odometer观测信息辅助车载INS导航的方法,并且对位置修正法进行了改进。实测计算结果表明,与INS单独导航相比较,新算法可以大幅度提高载体位置和速度精度。
14.给出了一种对INS单独导航累积误差建立模型的方法,并且用实测算例对所建立的模型进行验证,结果表明通过所建立的模型对INS累积误差进行修正,可以大幅度地削弱INS误差。
This dissertation mainly focuses on the theories and algorithms of positioning and attitude determination in GNSS/INS integrated navigation which includes the principles of GNSS/INS integrated navigation, the random errors analysis and modeling of INS, the initial alignment and kinematic attitude alignment, error compensation of function model and random model, the adaptive filtering algorithms in GNSS/INS integrated navigation and INS navigation algorithms during GNSS outages. The main works and contributions are summarized as follows:
1. The principles of GNSS/INS integrated navigation are summarized including the principles of INS navigation and GNSS navigation, the filtering models of GNSS/INS integrated navigation and the differences and advantages of open loop and close loop for error modification.
2. The INS random errors are analyzed and processed systematically. Several kinds of random errors are analyzed and compared by power spectral density and Allan variance. And the random errors of three kinds of gyros are analyzed and the main characteristics and the corresponding coefficients are achieved. A method of determining the scale of wavelet multiresolution analysis automatically is presented and used to de-noise the high frequency noise. And ARMA models are used to fit the low frequency noise and the order and parameters are determined for the three kinds of gyros.
3. In the refined initial alignment, a new method of SINS initial alignment based on the minimum of cumulated error is presented for the situation of short time. Real experiments are carried out to show that the new method can get good results when the initial static time is very short.
4. A new algorithm considering attitude update in GNSS/INS integrated navigation for land vehicle is presented. Then the principle of yaw angle determined by GNSS velocity is introduced and the pitch and roll angles of low-cost INS in land vehicle are analyzed. By the actual data calculation, the precision of yaw angle determined by GNSS velocity is comfirmed and it is shown that the new algorithm can improve the navigation accuracy greatly compared with the Kalman filtering based on position and velocity.
5. Three methods of direct estimation, estimation based on wavelet transform and Allan variance estimation are given to determine the power spectral density of white noise in INS random errors. By the calculations, it is shown that direct estimation and estimation based on wavelet transform can not recognize the white noise and other noises while Allan variance estimation can do. However, Allan variance estimation can not estimate the power spectral density when white noise buries in other noises. GNSS/INS integrated navigation results also show Allan variance can reflect the charactoristic of the white noise in INS random errors.
6. Autocorrelation and parcorrelation parameters of INS errors show that AR model espectially ARMA model can reflect the low frequency errors better than GM model. Based on AR(3) model and ARMA(3,3) model, the dynamic model function and process noise random model are deduced. Real experiment results show compared with GM model, AR model or ARMA model can improve navigation precision, espectially ARMA model.
7. In GNSS/INS real-time tight integration, the phase smoothing code method is introduced into the GNSS/INS tight integration. By the calculation, it is shown that when cycle slip occurs few times during a period, the method of phase smoothing code can improve the precision of GPS/INS integration greatly. But if cycle slip occurs many times during a period, the precision of GPS/INS integration is improved slightly.
8. A new method of velocity determination by derived pseudoranges is presented. The formulas of derived pseudoranges are given and the precision of the velocity is analyzed. By two actual experiments, the accuracy of velocity determination by derived pseudoranges is compared and analyzed. It is also shown that in urban areas velocity determination by derived pseudoranges can ensure the reliability.
9. In loose integration and tight integration, in order to avoid degrading the accuracy of reliable parameters by single adaptive factor, classified adaptive factors based on predicted residuals and selecting the parameter weights filtering. The new adaptive factors give position, velocity, attitude, gyro and accelerators errors parameters different weights for their charactorics. Compared with standard Kalman filtering and the adaptive filtering with single factor, the new algorithm can improve the navigation precision.
10. A new factor based on partial state discrepancy is developed. The formula of the new adaptive factor is deduced. And the differences of the three factors including single adaptive factor and classified adaptive factors based on predicted residuals are compared and analyzed. By the calculation, it is shown that all adaptive factors constructed by the predicted residuals and partial state discrepancy can resist the influence of the dynamic model errors when no outliers exist in measurements, and the precision of their navigation are almost equal. But if outliers exist in measurements, the adaptive factor based on the predicted residuals can not identify the state model errors and the observation errors while the adaptive factor based on partial state discrepancy can resist the influence of the outliers, so the latter navigation precision is prior to the former navigation precision.
11. A two-step adaptive robust Kalman filtering based on the observability of the parameters is presented. First the process of the tight integration is given and then the formulas and the approches of the new method are deduced and analyzed. Finally an actual calculation is given. It is shown that campared with tight integration, the two-step adaptive robust Kalman filtering can control the disturbances of the state and the outliers of the observation. And the navigation precision does not decrease while the integration period becomes longer and the INS errors become bigger. The INS errors can be rightly estimated and the precision of attitude angles is improved.
12. In tight coupled GNSS/INS integration by using Kalman filtering, the main error includes not only the dynamic model error (INS error), but also the errors caused by the poor geometry of GNSS satellites or short of GNSS satellites. An extended adaptive Kalman filtering algorithm is presented based on the adaptive filter. The new algorithm can not only resist the influence of the dynamic model errors but also control the influence of the errors caused by the poor geometry of GNSS satellites by adjusting the coefficient matrix of the predicted states. An actual computation example shows that the new algorithm can degrade the influence of the two kinds of errors and improve the precision of navigation.
13. When GNSS occurs outages in land vehicle navigation, the Odometer observations are added to the measurement equation to improve the system observability and navigation accuracy based on velocity constrains. And a new method is implemented on the position modification. By calculation, it is shown that compared with INS navigation, the precision of position and velocity are improved further.
14. When GNSS outages occur, INS errors will accumulate quickly. Then error model modification is given. By the actual calculation, error model modification can compensate INS errors more effectively and improve the precision of INS navigation alone obviously.
1.总结了GNSS/INS组合导航数据处理的基本原理,介绍了INS导航、GNSS导航的基本原理以及GNSS/INS组合导航的滤波模型,分析了INS误差闭环校正和开环校正的优缺点。
2.对INS随机误差进行了系统的分析和处理；分析和比较了陀螺信号中几种性质不同的随机误差在功率谱密度和Allan方差上不同的特性和表现形式；对三种陀螺实测信号中的随机误差进行了分析,给出这些陀螺信号中存在的主要噪声类型及其相应的系数；通过对分解后高频系数进行检验,给出了一种自动判别小波多分辨分析尺度的方法；建立了三种陀螺随机误差的ARMA模型,确定了相应的ARMA模型阶数和模型参数。
3.在INS力学编排基础上从误差分析角度提出一种基于累积误差极小值的精对准方法,有效缩短了初始对准时间；实测算例表明这种方法不受初始对准时间的约束,在较短时间内可以获得较高的对准精度。
4.针对车载系统,提出一种顾及姿态角更新的低成本车载GNSS/INS组合导航算法,推导了利用GNSS测速确定航向角的原理,并且对低成本车载INS系统的俯仰角和翻滚角进行了分析；利用实测算例确定了不同速度下的航向角精度,并且验证了新算法的有效性。
5.给出了三种确定INS白噪声谱密度的方法：直接估计法、基于小波变换的谱密度估计法和Allan方差法。利用实测数据对这三种方法进行了比较和分析,结果表明直接估计法和基于小波变换的谱密度估计所估计的噪声谱密度不仅仅是白噪声,还包含其它各种噪声在内的高频噪声,而Allan方差能够很好地分辨出信号中主要干扰噪声,但是一旦白噪声不占主导,就很容易淹没在别的高频噪声中；GNSS/INS组合导航结果也表明基于Allan方差所确定的白噪声谱密度能够更好地反映惯性元件中的白噪声统计特性。
6.INS信号自相关和偏相关系数表明AR模型尤其是ARMA模型能够更好地反映信号的低频噪声；分别基于AR模型和基于ARMA模型,推导了GNSS/INS组合导航动力学模型方程和随机误差模型。实测算例表明,基于AR模型和ARMA模型的Kalman滤波精度都要高于根据经验设定参数的标准Kalman滤波,其中ARMA模型能够更好地反映低频信号的特性。
7.推导了基于载波相位平滑伪距的实时GNSS/INS组合导航的公式,并且进行了误差分析。利用实测算例对算法进行验证,结果表明如果GPS周跳较少或者不发生周跳,基于载波相位平滑伪距技术的GPS/INS组合导航的精度较伪距紧组合导航有较大的提高,但是当GPS周跳较多时,精度提高不显著。
8.提出伪距差分求解速度的方法,给出了相邻历元和历元间伪距差分测速的公式,并且对其精度进行了分析。利用实测算例对伪距差分测速的精度进行了比较和分析,指出在外界环境恶劣的情况下伪距差分可以保证较高的可靠性。
9.在GNSS/INS松组合和紧组合导航中,为避免单一自适应因子对可靠参数的作用,基于预测残差和选权滤波构造出分类自适应因子,该自适应滤波能够将位置、速度、姿态角误差、陀螺仪和加速度计误差分别赋予不同的自适应因子,避免精度损耗。实测算例表明相比于标准Kalman滤波和单因子自适应滤波,分类因子自适应滤波精度有所提高。
10.针对紧组合导航中观测值存在粗差的问题,提出通过部分状态不符值来构造自适应因子的方法,给出部分状态不符值构造自适应因子的过程,并与单因子自适应滤波和分类因子自适应滤波进行了分析和比较。实测算例结果表明,当观测无异常时,三种自适应因子都能够较好地抑制动态模型误差的影响；但是当观测存在异常时,由预测残差构造的自适应因子不能分辨模型误差和观测误差,而由部分状态不符值构造的自适应因子能够抵制观测异常的影响,滤波结果优于由预测残差构造的自适应因子滤波结果。
11.从参数可观测性角度提出一种两步自适应Kalman滤波算法,推导了两步自适应抗差滤波的公式和具体步骤,并且进行了分析和比较；实测算例结果表明,相比于标准Kalman滤波,两步自适应抗差滤波的导航精度受组合周期的长短、INS惯性元件误差的大小影响较小,并且能够控制动态扰动异常和观测异常的影响。
12.针对由GNSS观测条件不佳或观测不足引起的误差,在一般自适应滤波的基础之上,对其进行扩展,自适应地调节状态预测向量的协方差阵,使其既能控制动态模型误差又能抑制由GNSS观测条件不佳引起的误差的影响。实际计算结果表明,相比于一般自适应滤波,扩展自适应滤波能够很好地控制这两种误差的影响。
13.在GNSS信号失锁时,提出一种速度先验信息和Odometer观测信息辅助车载INS导航的方法,并且对位置修正法进行了改进。实测计算结果表明,与INS单独导航相比较,新算法可以大幅度提高载体位置和速度精度。
14.给出了一种对INS单独导航累积误差建立模型的方法,并且用实测算例对所建立的模型进行验证,结果表明通过所建立的模型对INS累积误差进行修正,可以大幅度地削弱INS误差。
This dissertation mainly focuses on the theories and algorithms of positioning and attitude determination in GNSS/INS integrated navigation which includes the principles of GNSS/INS integrated navigation, the random errors analysis and modeling of INS, the initial alignment and kinematic attitude alignment, error compensation of function model and random model, the adaptive filtering algorithms in GNSS/INS integrated navigation and INS navigation algorithms during GNSS outages. The main works and contributions are summarized as follows:
1. The principles of GNSS/INS integrated navigation are summarized including the principles of INS navigation and GNSS navigation, the filtering models of GNSS/INS integrated navigation and the differences and advantages of open loop and close loop for error modification.
2. The INS random errors are analyzed and processed systematically. Several kinds of random errors are analyzed and compared by power spectral density and Allan variance. And the random errors of three kinds of gyros are analyzed and the main characteristics and the corresponding coefficients are achieved. A method of determining the scale of wavelet multiresolution analysis automatically is presented and used to de-noise the high frequency noise. And ARMA models are used to fit the low frequency noise and the order and parameters are determined for the three kinds of gyros.
3. In the refined initial alignment, a new method of SINS initial alignment based on the minimum of cumulated error is presented for the situation of short time. Real experiments are carried out to show that the new method can get good results when the initial static time is very short.
4. A new algorithm considering attitude update in GNSS/INS integrated navigation for land vehicle is presented. Then the principle of yaw angle determined by GNSS velocity is introduced and the pitch and roll angles of low-cost INS in land vehicle are analyzed. By the actual data calculation, the precision of yaw angle determined by GNSS velocity is comfirmed and it is shown that the new algorithm can improve the navigation accuracy greatly compared with the Kalman filtering based on position and velocity.
5. Three methods of direct estimation, estimation based on wavelet transform and Allan variance estimation are given to determine the power spectral density of white noise in INS random errors. By the calculations, it is shown that direct estimation and estimation based on wavelet transform can not recognize the white noise and other noises while Allan variance estimation can do. However, Allan variance estimation can not estimate the power spectral density when white noise buries in other noises. GNSS/INS integrated navigation results also show Allan variance can reflect the charactoristic of the white noise in INS random errors.
6. Autocorrelation and parcorrelation parameters of INS errors show that AR model espectially ARMA model can reflect the low frequency errors better than GM model. Based on AR(3) model and ARMA(3,3) model, the dynamic model function and process noise random model are deduced. Real experiment results show compared with GM model, AR model or ARMA model can improve navigation precision, espectially ARMA model.
7. In GNSS/INS real-time tight integration, the phase smoothing code method is introduced into the GNSS/INS tight integration. By the calculation, it is shown that when cycle slip occurs few times during a period, the method of phase smoothing code can improve the precision of GPS/INS integration greatly. But if cycle slip occurs many times during a period, the precision of GPS/INS integration is improved slightly.
8. A new method of velocity determination by derived pseudoranges is presented. The formulas of derived pseudoranges are given and the precision of the velocity is analyzed. By two actual experiments, the accuracy of velocity determination by derived pseudoranges is compared and analyzed. It is also shown that in urban areas velocity determination by derived pseudoranges can ensure the reliability.
9. In loose integration and tight integration, in order to avoid degrading the accuracy of reliable parameters by single adaptive factor, classified adaptive factors based on predicted residuals and selecting the parameter weights filtering. The new adaptive factors give position, velocity, attitude, gyro and accelerators errors parameters different weights for their charactorics. Compared with standard Kalman filtering and the adaptive filtering with single factor, the new algorithm can improve the navigation precision.
10. A new factor based on partial state discrepancy is developed. The formula of the new adaptive factor is deduced. And the differences of the three factors including single adaptive factor and classified adaptive factors based on predicted residuals are compared and analyzed. By the calculation, it is shown that all adaptive factors constructed by the predicted residuals and partial state discrepancy can resist the influence of the dynamic model errors when no outliers exist in measurements, and the precision of their navigation are almost equal. But if outliers exist in measurements, the adaptive factor based on the predicted residuals can not identify the state model errors and the observation errors while the adaptive factor based on partial state discrepancy can resist the influence of the outliers, so the latter navigation precision is prior to the former navigation precision.
11. A two-step adaptive robust Kalman filtering based on the observability of the parameters is presented. First the process of the tight integration is given and then the formulas and the approches of the new method are deduced and analyzed. Finally an actual calculation is given. It is shown that campared with tight integration, the two-step adaptive robust Kalman filtering can control the disturbances of the state and the outliers of the observation. And the navigation precision does not decrease while the integration period becomes longer and the INS errors become bigger. The INS errors can be rightly estimated and the precision of attitude angles is improved.
12. In tight coupled GNSS/INS integration by using Kalman filtering, the main error includes not only the dynamic model error (INS error), but also the errors caused by the poor geometry of GNSS satellites or short of GNSS satellites. An extended adaptive Kalman filtering algorithm is presented based on the adaptive filter. The new algorithm can not only resist the influence of the dynamic model errors but also control the influence of the errors caused by the poor geometry of GNSS satellites by adjusting the coefficient matrix of the predicted states. An actual computation example shows that the new algorithm can degrade the influence of the two kinds of errors and improve the precision of navigation.
13. When GNSS occurs outages in land vehicle navigation, the Odometer observations are added to the measurement equation to improve the system observability and navigation accuracy based on velocity constrains. And a new method is implemented on the position modification. By calculation, it is shown that compared with INS navigation, the precision of position and velocity are improved further.
14. When GNSS outages occur, INS errors will accumulate quickly. Then error model modification is given. By the actual calculation, error model modification can compensate INS errors more effectively and improve the precision of INS navigation alone obviously.
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