光纤捷联惯导及其卫星深组合导航算法研究
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摘要
捷联惯性导航系统可全天候自主地实时定位，全球导航卫星系统虽然依赖卫星信号实现定位，但是其精度不随时间发散，所以利用二者优势互补的SINS/GNSS组合导航系统在性能上有很大的提升，尤其是在SINS/GNSS深组合导航系统中，不仅提高了系统的定位精度，长时间工作能力，也使系统在弱信号和高动态的环境下依然能够保持较高精度的工作。本文针对SINS/GPS深组合导航系统中的深组合系统闭环算法和组合导航数据融合算法进行了以下讨论和研究。
分析了光纤捷联惯导系统的导航方程，并且根据SINS/GPS深组合导航系统的特点，选取地球系导航方程作为系统中实际应用的导航方程。分析了角速度敏感元件即光纤陀螺对SINS导航精度的影响，并对相应结果做了仿真验证。
详细分析了SINS/GPS深组合系统的组成和结构，对各种不同结构的深组合方式进行了对比，并在此基础上给出了各种深组合结构的数学模型，总结了深组合系统的定义，给出了将联邦式系统列为深组合系统的理由。
分析了SINS/GPS组合导航系统的可观测性。因为深组合导航系统中的观测模型十分复杂，为了避免在可观测性分析中引入该复杂模型，论证了在观测矩阵非零列构成的矩阵列满秩时系统的可观测性与观测矩阵对应位置为单位阵时相同，如此，就可以将系统的状态矩阵脱离出观测矩阵而进行单独分析。
研究了SINS辅助GPS接收机在高动态条件下的弱信号捕获的问题。为了有效捕获弱GPS信号，采用了40ms的相干积分。而为了去除导航数据位对长相干时间的影响，采用了循环去除和翻转的方法。为了捕获动态信号，利用SINS短期输出相对精度高的特点，在同一个相干积分时间内采用多个多普勒估计值共同剥除载波，有效降低了因载体动态造成的捕获信号能量损失，缩小了相干积分内平均多普勒误差与搜索范围中心频率的距离，提高了高动态条件下对弱信号的捕获效率。
研究了SINS/GPS深组合系统中惯性器件噪声统计特性未知的条件下的导航算法。在此情况下，首先利用极大似然准则，构造含有系统噪声统计特性的对数似然函数，进而利用最大期望算法，将噪声估计问题转化为对数似然函数数学期望极大化问题，得到带次优递推噪声估计器的自适应SPKF算法。使导航算法在其为载体提供导航信息的同时，不断的在线估计惯性器件的误差方差，进而对系统进行修正和更新。
研究了SINS/GPS深组合系统中状态存在突变的情况下的导航算法，利用矩阵对算法的滤波记忆长度进行限制，并且对矩阵进行自适应的调整，得到带自适应渐消矩阵的扩维UKF算法，有效抑制可能发生的系统状态突变对系统带来的不利影响。根据正交性设计自适应渐消矩阵，并根据SINS/GPS组合导航的特点简化计算，再利用渐消矩阵修正算法中的相应变量，使SINS/GPS组合导航能够抵抗系统状态的突变，并且该算法也能在系统噪声统计特性不确定的情况下提高导航精度。
Strapdown inertial navigation system(SINS) which is self-contained can implementreal-time positioning in all weathers while the accuracy of the global navigation satellitesystem(GNSS) is independent of time although it have to rely on satellite signals to achievepositioning. Therefore, by integrating these two systems, the performance can be greatlyimproved. Specifically, the ultra-tight SINS/GPS integration can not only improve positioningaccuracy in the long run but also maintain high precision in situations of weak signals or highdynamic. This dissertation focuses on the closed loop algorithm and data fusion algorithm inultra-tight SINS/GPS integration system conducted the following discussions and researches.
Firstly, the dissertation analyzes the navigation equations of fiber optical SINS. Thenavigation equations in the earth centered frame are selected based on the features of theultra-tight SINS/GPS integration system. The influences of fiber optical gyroscope on theaccuracy of SINS are also analyzed. Related simulation results are given in detail.
Secondly, the dissertation elaborately explores the composition and structure of theultra-tight SINS/GPS integration system and compares systems in different deep integrations.Based on that, the mathematical models of different deep integrations are illustrated.Definition of deep integration system is concluded, and the reasons of Federal system areincluded in deep integration are provided.
Thirdly, the observability of the SINS/GPS integrated navigation system has beenstudied. Due to the complexity of observability model in deep integration system, it ispreferred that the model is not involved in observability analysis. The dissertationdemonstrates the effects of observability matrix on observation matrix. Therefore, the systemobservability when the corresponding position of observation matrix is unit matrix areanalyzed and the system abservability when transform the observation matrix to the unitmatrix are analyzed, separately.
Fourthly, the weak signal acquisition issue when SINS aids GPS receiver in highdynamic situations is studied. In order to efficiently capture GPS signal, the40ms coherentintegration is adopted. In order to break through the navigation data to the long coherent time,loop remove and flip method are adopted. The data synchronous issues in SINS/GPS deepintegrated system are studied by providing the same frenquency data to receiver channels, andforcing the outputs of each channel and the represent system state are strictly the same in time.Moreover, In order to finish the relative of signals, stripped the C/A code in receiver by adopting changed C/A code phrase in the internal of each channels.
Fifthly, the navigation algorithm for ultra-tight SINS/GPS integrated system withunknown inertial sensors noise statistical properties is researched. First of all, the logarithmiclikelihood function containing systematic noise statistical properties is designed based on themaximum Likelihood criteria. Then by applying maximum expectations algorithm, the noiseestimation issue is turned into problem of maximizing the expectation of logarithmiclikelihood function. This leads to the adaptive sigma-points Kalman filter(SPKF) algorithm,which provides navigation information and estimates inertial sensor error variance on-line atthe same time. This further corrects and updates the integrated navigation system.
Lastly, the dissertation studies the situation when sudden changes exist in ultra-tightSINS/GPS integrated system. Based on the restrain of matrix on the memory length offiltering algorithm and adjusting matrix adaptively, the augmented UKF with adaptive fadingmatrix can be obtained. This algorithm can effectively inhibit the adverse effects of systemstates mutation. The adaptive fading matrix is designed according to the orthogonality. Thecalculation is simplified based on the features of SINS/GPS integrated navigation system. Thefading matrix is applied to correct the corresponding variables, which makes the SINS/GPSintegrated navigation system immune to system states mutation. This algorithm can alsoimprove navigation accuracy when systematic noises statistical characteristics are uncertain.
分析了光纤捷联惯导系统的导航方程，并且根据SINS/GPS深组合导航系统的特点，选取地球系导航方程作为系统中实际应用的导航方程。分析了角速度敏感元件即光纤陀螺对SINS导航精度的影响，并对相应结果做了仿真验证。
详细分析了SINS/GPS深组合系统的组成和结构，对各种不同结构的深组合方式进行了对比，并在此基础上给出了各种深组合结构的数学模型，总结了深组合系统的定义，给出了将联邦式系统列为深组合系统的理由。
分析了SINS/GPS组合导航系统的可观测性。因为深组合导航系统中的观测模型十分复杂，为了避免在可观测性分析中引入该复杂模型，论证了在观测矩阵非零列构成的矩阵列满秩时系统的可观测性与观测矩阵对应位置为单位阵时相同，如此，就可以将系统的状态矩阵脱离出观测矩阵而进行单独分析。
研究了SINS辅助GPS接收机在高动态条件下的弱信号捕获的问题。为了有效捕获弱GPS信号，采用了40ms的相干积分。而为了去除导航数据位对长相干时间的影响，采用了循环去除和翻转的方法。为了捕获动态信号，利用SINS短期输出相对精度高的特点，在同一个相干积分时间内采用多个多普勒估计值共同剥除载波，有效降低了因载体动态造成的捕获信号能量损失，缩小了相干积分内平均多普勒误差与搜索范围中心频率的距离，提高了高动态条件下对弱信号的捕获效率。
研究了SINS/GPS深组合系统中惯性器件噪声统计特性未知的条件下的导航算法。在此情况下，首先利用极大似然准则，构造含有系统噪声统计特性的对数似然函数，进而利用最大期望算法，将噪声估计问题转化为对数似然函数数学期望极大化问题，得到带次优递推噪声估计器的自适应SPKF算法。使导航算法在其为载体提供导航信息的同时，不断的在线估计惯性器件的误差方差，进而对系统进行修正和更新。
研究了SINS/GPS深组合系统中状态存在突变的情况下的导航算法，利用矩阵对算法的滤波记忆长度进行限制，并且对矩阵进行自适应的调整，得到带自适应渐消矩阵的扩维UKF算法，有效抑制可能发生的系统状态突变对系统带来的不利影响。根据正交性设计自适应渐消矩阵，并根据SINS/GPS组合导航的特点简化计算，再利用渐消矩阵修正算法中的相应变量，使SINS/GPS组合导航能够抵抗系统状态的突变，并且该算法也能在系统噪声统计特性不确定的情况下提高导航精度。
Strapdown inertial navigation system(SINS) which is self-contained can implementreal-time positioning in all weathers while the accuracy of the global navigation satellitesystem(GNSS) is independent of time although it have to rely on satellite signals to achievepositioning. Therefore, by integrating these two systems, the performance can be greatlyimproved. Specifically, the ultra-tight SINS/GPS integration can not only improve positioningaccuracy in the long run but also maintain high precision in situations of weak signals or highdynamic. This dissertation focuses on the closed loop algorithm and data fusion algorithm inultra-tight SINS/GPS integration system conducted the following discussions and researches.
Firstly, the dissertation analyzes the navigation equations of fiber optical SINS. Thenavigation equations in the earth centered frame are selected based on the features of theultra-tight SINS/GPS integration system. The influences of fiber optical gyroscope on theaccuracy of SINS are also analyzed. Related simulation results are given in detail.
Secondly, the dissertation elaborately explores the composition and structure of theultra-tight SINS/GPS integration system and compares systems in different deep integrations.Based on that, the mathematical models of different deep integrations are illustrated.Definition of deep integration system is concluded, and the reasons of Federal system areincluded in deep integration are provided.
Thirdly, the observability of the SINS/GPS integrated navigation system has beenstudied. Due to the complexity of observability model in deep integration system, it ispreferred that the model is not involved in observability analysis. The dissertationdemonstrates the effects of observability matrix on observation matrix. Therefore, the systemobservability when the corresponding position of observation matrix is unit matrix areanalyzed and the system abservability when transform the observation matrix to the unitmatrix are analyzed, separately.
Fourthly, the weak signal acquisition issue when SINS aids GPS receiver in highdynamic situations is studied. In order to efficiently capture GPS signal, the40ms coherentintegration is adopted. In order to break through the navigation data to the long coherent time,loop remove and flip method are adopted. The data synchronous issues in SINS/GPS deepintegrated system are studied by providing the same frenquency data to receiver channels, andforcing the outputs of each channel and the represent system state are strictly the same in time.Moreover, In order to finish the relative of signals, stripped the C/A code in receiver by adopting changed C/A code phrase in the internal of each channels.
Fifthly, the navigation algorithm for ultra-tight SINS/GPS integrated system withunknown inertial sensors noise statistical properties is researched. First of all, the logarithmiclikelihood function containing systematic noise statistical properties is designed based on themaximum Likelihood criteria. Then by applying maximum expectations algorithm, the noiseestimation issue is turned into problem of maximizing the expectation of logarithmiclikelihood function. This leads to the adaptive sigma-points Kalman filter(SPKF) algorithm,which provides navigation information and estimates inertial sensor error variance on-line atthe same time. This further corrects and updates the integrated navigation system.
Lastly, the dissertation studies the situation when sudden changes exist in ultra-tightSINS/GPS integrated system. Based on the restrain of matrix on the memory length offiltering algorithm and adjusting matrix adaptively, the augmented UKF with adaptive fadingmatrix can be obtained. This algorithm can effectively inhibit the adverse effects of systemstates mutation. The adaptive fading matrix is designed according to the orthogonality. Thecalculation is simplified based on the features of SINS/GPS integrated navigation system. Thefading matrix is applied to correct the corresponding variables, which makes the SINS/GPSintegrated navigation system immune to system states mutation. This algorithm can alsoimprove navigation accuracy when systematic noises statistical characteristics are uncertain.
引文
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