高动态环境捷联惯导算法研究
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摘要
本课题从提高捷联惯导系统姿态与速度输出精度的实际需求出发,分析了高动态环境下算法误差的产生机理,针对载体机动对姿态、速度计算的影响,设计了高性能的捷联算法。并对其中的关键技术展开深入的研究。论文的主要工作有:
首先分析了高动态环境下姿态算法的误差源,包括:陀螺的频带宽度限制、陀螺安装误差、陀螺采样不同步、陀螺的量化误差和陀螺标度因数误差。给出了它们与陀螺测量角速度误差的关系式。从惯导系统的误差传播方程入手,推导出上述陀螺器件误差引入的姿态误差整流分量表达式。全面而系统得阐述了高动态环境下姿态误差的产生机理。
论述了经典圆锥运动不同表述方式的一致性。由经典圆锥运动引申出伪圆锥运动。以机抖激光陀螺捷联惯导系统为例,研究了机械抖动偏频引入伪圆锥运动,推导出伪圆锥误差的表达式。分析了伪圆锥误差的起因、影响因素,研究了圆锥补偿算法在伪圆锥运动中的适用性。从姿态计算误差最小化的角度,提出了机械抖动频率的设计准则,并设计数字滤波器去除抖动信号噪声。分析结果表明:圆锥补偿算法的使用增加了伪圆锥运动造成的伪圆锥误差。合理设置抖动频率,结合低通数字滤波方案可以有效避免伪圆锥运动对于姿态计算的影响。
证明了在典型圆锥运动中优化的姿态算法在载体其它机动环境中具有普遍适用性。提出了评价姿态算法的精度准则,并推导出采用四阶龙格库塔积分的四元数算法在典型圆锥环境中的算法误差。设计了角速度为输入的圆锥补偿算法,应用于陀螺输出为角速度的捷联惯导系统,有效地提高了姿态精度。设计了陀螺滤波信号作为输入的圆锥补偿算法,应用于机抖激光陀螺捷联惯导系统,避免了滤波信号畸变对姿态计算的影响,保证了系统的姿态输出精度。
证明了在典型划船运动下优化算法在载体其它机动环境中具有普遍适用性。根据线性微分方程的叠加定理,在两时间尺度上对捷联惯导系统方程进行分析,重新编排了捷联速度算法。应用一种新的划船补偿算法应对比力转换过程中比力矢量的改变。分析结果表明:该算法与传统四子样速度算法精度近似,且具有数字离散形式,更适合在导航计算机上使用。
最后以螺旋理论作为数学工具设计螺旋补偿算法。算法用惯性传感器输出值的叉乘项构造螺旋补偿项,并设置典型螺旋环境,优化了螺旋补偿项中的待定系数。对算法进行编排,给出了由螺旋矢量计算导航参数的具体步骤。证明了螺旋补偿算法与传统算法在导航微分方程上的一致性,并对两种算法的误差源进行了分析比较。仿真与分析看出:采用相同子样数,螺旋补偿算法的计算精度高于传统算法。
For the requirement of improving the attitude and velocity accuracy for strapdown inertial navigation system (SINS), this dissertation analyses the causes of algorithm error under high dynamic environments. The efficient SINS algorithms are designed and the key techniques of SINS algorithms are studied deeply, so that the SINS can deal with the infection of vehicle maneuvers. The main works are as follows:
Firstly the causes of attitude algorithm error under highly dynamic environments are analyzed. Those are sample-bandwidth limitation, installation error, synchronous samples, quantization error and scale-factor error. The error of gyro measured angle velocity is given. According to the basic error equation for SINS, the expressions for DC portion of attitude error caused by gyro errors are deduced. The causes of attitude error under high dynamic environment are expatiated completely and systemically.
The consistency of different representations for classical coning motion is discussed here. Referred to the classical coning motion, the pseudo coning motion is presented. Setting the example of dithered Laser gyro, the pseudo coning motion induced by dithered machine is studied. The expression of pseudo coning error is obtained, and the causes and influence factors of pseudo coning error are given. The applicability of conventional coning algorithms is studied under pseudo coning motion. In order to minimize the attitude error, the guide line for dithered machine design is provided. The digital filter is designed to demodulate gyro signal. The analysis and simulation show: using coning algorithm will increase the pseudo coning error made by pseudo coning motion. Setting the dithered frequency reasonably, using low-pass digital filter can avoid the effect of pseudo coning motion.
The coning algorithms optimized under classical coning motion are applicable under other testing environments. The accuracy rule is provided to evaluate the attitude algorithms. The error expression for quaternion algorithm using Runge-Kutta integration is presented. The improved coning algorithm using angle velocity as input is designed to improve the accuracy for attitude compute. The modified coning algorithm using filter signal as input is designed to avoid the infection of filter-signal aberrance. The modified algorithm can improve the attitude accuracy for dithered laser gyro SINS.
The sculling algorithms optimized under classical sculling motion are applicable under other testing environment. Based on the superposition theorem of linear differential equation, the SINS equation is analyzed. The strapdown algorithm is rearranged after predigesting the states equations in two-time scales. A new sculling compensation algorithm is designed to deal with the specific force variation during velocity updating interval. The simulation results show that the new algorithm and the conventional four-sample algorithm have the similar accuracy. The new algorithm expressed in digital discrete format is more suitable for SINS computer than conventional ones.
In the end, the screw compensation algorithm based on screw theory is designed. The algorithm uses the cross products of the outputs from inertial sensors to compute the screw compensation term. Set the classical screw environment to optimize the undecided coefficients. The algorithm arrangement and the procedure using the screw vector to compute navigation parameters are listed. The differential equation consistency between screw compensation algorithm and conventional algorithm is verified. The causes of computation error for the two algorithms are analyzed. The analysis and simulations show that the screw compensation algorithm performs better than conventional algorithms with the same samples per update interval.
首先分析了高动态环境下姿态算法的误差源,包括:陀螺的频带宽度限制、陀螺安装误差、陀螺采样不同步、陀螺的量化误差和陀螺标度因数误差。给出了它们与陀螺测量角速度误差的关系式。从惯导系统的误差传播方程入手,推导出上述陀螺器件误差引入的姿态误差整流分量表达式。全面而系统得阐述了高动态环境下姿态误差的产生机理。
论述了经典圆锥运动不同表述方式的一致性。由经典圆锥运动引申出伪圆锥运动。以机抖激光陀螺捷联惯导系统为例,研究了机械抖动偏频引入伪圆锥运动,推导出伪圆锥误差的表达式。分析了伪圆锥误差的起因、影响因素,研究了圆锥补偿算法在伪圆锥运动中的适用性。从姿态计算误差最小化的角度,提出了机械抖动频率的设计准则,并设计数字滤波器去除抖动信号噪声。分析结果表明:圆锥补偿算法的使用增加了伪圆锥运动造成的伪圆锥误差。合理设置抖动频率,结合低通数字滤波方案可以有效避免伪圆锥运动对于姿态计算的影响。
证明了在典型圆锥运动中优化的姿态算法在载体其它机动环境中具有普遍适用性。提出了评价姿态算法的精度准则,并推导出采用四阶龙格库塔积分的四元数算法在典型圆锥环境中的算法误差。设计了角速度为输入的圆锥补偿算法,应用于陀螺输出为角速度的捷联惯导系统,有效地提高了姿态精度。设计了陀螺滤波信号作为输入的圆锥补偿算法,应用于机抖激光陀螺捷联惯导系统,避免了滤波信号畸变对姿态计算的影响,保证了系统的姿态输出精度。
证明了在典型划船运动下优化算法在载体其它机动环境中具有普遍适用性。根据线性微分方程的叠加定理,在两时间尺度上对捷联惯导系统方程进行分析,重新编排了捷联速度算法。应用一种新的划船补偿算法应对比力转换过程中比力矢量的改变。分析结果表明:该算法与传统四子样速度算法精度近似,且具有数字离散形式,更适合在导航计算机上使用。
最后以螺旋理论作为数学工具设计螺旋补偿算法。算法用惯性传感器输出值的叉乘项构造螺旋补偿项,并设置典型螺旋环境,优化了螺旋补偿项中的待定系数。对算法进行编排,给出了由螺旋矢量计算导航参数的具体步骤。证明了螺旋补偿算法与传统算法在导航微分方程上的一致性,并对两种算法的误差源进行了分析比较。仿真与分析看出:采用相同子样数,螺旋补偿算法的计算精度高于传统算法。
For the requirement of improving the attitude and velocity accuracy for strapdown inertial navigation system (SINS), this dissertation analyses the causes of algorithm error under high dynamic environments. The efficient SINS algorithms are designed and the key techniques of SINS algorithms are studied deeply, so that the SINS can deal with the infection of vehicle maneuvers. The main works are as follows:
Firstly the causes of attitude algorithm error under highly dynamic environments are analyzed. Those are sample-bandwidth limitation, installation error, synchronous samples, quantization error and scale-factor error. The error of gyro measured angle velocity is given. According to the basic error equation for SINS, the expressions for DC portion of attitude error caused by gyro errors are deduced. The causes of attitude error under high dynamic environment are expatiated completely and systemically.
The consistency of different representations for classical coning motion is discussed here. Referred to the classical coning motion, the pseudo coning motion is presented. Setting the example of dithered Laser gyro, the pseudo coning motion induced by dithered machine is studied. The expression of pseudo coning error is obtained, and the causes and influence factors of pseudo coning error are given. The applicability of conventional coning algorithms is studied under pseudo coning motion. In order to minimize the attitude error, the guide line for dithered machine design is provided. The digital filter is designed to demodulate gyro signal. The analysis and simulation show: using coning algorithm will increase the pseudo coning error made by pseudo coning motion. Setting the dithered frequency reasonably, using low-pass digital filter can avoid the effect of pseudo coning motion.
The coning algorithms optimized under classical coning motion are applicable under other testing environments. The accuracy rule is provided to evaluate the attitude algorithms. The error expression for quaternion algorithm using Runge-Kutta integration is presented. The improved coning algorithm using angle velocity as input is designed to improve the accuracy for attitude compute. The modified coning algorithm using filter signal as input is designed to avoid the infection of filter-signal aberrance. The modified algorithm can improve the attitude accuracy for dithered laser gyro SINS.
The sculling algorithms optimized under classical sculling motion are applicable under other testing environment. Based on the superposition theorem of linear differential equation, the SINS equation is analyzed. The strapdown algorithm is rearranged after predigesting the states equations in two-time scales. A new sculling compensation algorithm is designed to deal with the specific force variation during velocity updating interval. The simulation results show that the new algorithm and the conventional four-sample algorithm have the similar accuracy. The new algorithm expressed in digital discrete format is more suitable for SINS computer than conventional ones.
In the end, the screw compensation algorithm based on screw theory is designed. The algorithm uses the cross products of the outputs from inertial sensors to compute the screw compensation term. Set the classical screw environment to optimize the undecided coefficients. The algorithm arrangement and the procedure using the screw vector to compute navigation parameters are listed. The differential equation consistency between screw compensation algorithm and conventional algorithm is verified. The causes of computation error for the two algorithms are analyzed. The analysis and simulations show that the screw compensation algorithm performs better than conventional algorithms with the same samples per update interval.
引文
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