高动态捷联惯导系统的并行实现研究
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摘要
针对高超声速巡航导弹的高速高机动特性,本论文研究高动态下的捷联惯导系统并行实现方法,涉及初始对准算法、并行卡尔曼滤波器设计、捷联解算算法、并行捷联解算算法设计以及FPGA实现技术等方面。其内容主要包括以下几个方面：
1.类似于组合导航中的耦合机制,在对捷联惯导系统导航计算机的功能需求以及性能需求进行分析的基础上,提出了三类导航计算机的并行体系架构,即浅并行体系架构、深并行体系架构和全并行体系架构。其中,在全并行体系架构中,所有的计算均是并行化执行的,因此就需要设计全新的捷联惯导系统初始对准和捷联解算算法,即并行初始对准算法和并行捷联解算算法等。
2.针对武器系统快反下的高晃动特性,提出了两种新的晃动基座捷联惯导系统初始对准算法,即基于动态增益调节的捷联罗经对准方法(DGA-Compass)和卡尔曼滤波对准方法(New-Kalman)。其中,在DGA-Compass对准算法中,根据滤波时间和运载体姿态变化剧烈程度动态调节对准回路的增益使系统姿态角输出随运载体的低频大幅度晃动的变化而变化,加快了对准算法的收敛速度,即缩短了系统的初始对准时间；在卡尔曼滤波对准算法中,通过在卡尔曼滤波器观测量中引入水平加速度计测量值,提高对准算法的性能。
3.针对提高卡尔曼滤波对准算法实时跟踪运载体真实姿态变化的局限性,提出了一种基于法捷耶夫算法的卡尔曼滤波器并行脉动阵列结构实现。对于任意给定的两个或多个矩阵,矩阵运算(矩阵求逆、矩阵相乘和矩阵相加)或三种运算的合运算都可通过它们对应的法捷耶夫算法实现。由脉动阵列结构的规则性、模块性等特性可知,脉动阵列结构是一种很好的实现法捷耶夫算法的并行结构。从而可将卡尔曼滤波器表示为一些列矩阵运算形式,然后基于法捷耶夫算法将其映射为并行脉冲阵列结构来实现。
4.针对高超声速巡航导弹的高速高机动运动特性,提出了一种适合高动态的捷联惯导系统捷联解算算法。其中,考虑到当前计算机的性能(高速和高吞吐量),在捷联解算算法中采用了单速结构。并且针对姿态更新中的圆锥运动和姿态更新中的划桨运动,提出了一种新的广义优化圆锥补偿算法和划桨补偿算法。其相对于现有的圆锥和划桨补偿算法,当惯性器件的输出采样速率恒定时,圆锥和划桨补偿算法的更新速率与惯性器件的输出采样个数无关,即在圆锥和划桨补偿算法的高更新速率下可采用高阶更新算法。
5.考虑到姿态更新算法是捷联解算算法的核心,也是影响系统精度的主要因素,特别是对作高速高机动运动的高超声速巡航导弹等运载体来说,定量分析了圆锥补偿算法的阶次以及更新周期对算法误差的影响大小。通过分析可知,相对于更新周期,圆锥补偿阶次对姿态误差的影响关系更为复杂。当运载体作中低动态运动时(即中低圆锥运动频率),可通过同时提高圆锥补偿的更新速率和增大圆锥补偿阶次来减小系统的姿态误差；当运载体作高动态运动时(即高圆锥运动频率),考虑到圆锥补偿的更新速率不能无限制地提高,必须仔细选择合适的圆锥补偿阶次。
6.针对捷联惯导系统减小更新周期(即提高更新速率)可提高其精度的特点,特别是对作高速高机动的高超声速巡航导弹,提出了一种并行捷联解算算法结构。根据并行算法的设计技术(即分治策略和流水线技术),对捷联解算算法进行了并行化设计,且对这种并行捷联解算算法的性能进行定量分析。通过这种并行捷联解算算法相对串行捷联解算算法的性能(即相对加速比)分析可见,这种捷联解算算法的并行化设计可显著减小算法的执行时间,从而可提高算法的更新速率。这就为工作在高动态环境下的捷联惯导系统精度的提高提供了重要基础。
7.针对捷联惯导系统的并行捷联解算算法和并行卡尔曼滤波初始对准算法的FPGA实现,分别从系统的角度进行了详细分析。其中,利用Xilinx嵌入式软核MicroBlaze控制和调度并行捷联解算算法和并行卡尔曼滤波初始对准算法中的各模块执行。通过车载试验验证了这种捷联惯导系统FPGA硬件实现的可行性。这就为在提高惯性器件输出速率的情况下,提高捷联惯导系统在高动态下的精度和实时性奠定了坚实的基础,具有非常好的现实意义和理论价值。
Considering the high-speed and high-maneuvering features of hypersonic cruise missiles, this thesis systematically investigates the parallel implementation of SINS under high dynamic conditions, which involves the initial alignment algorithm, parallel Kalman filter design, strapdown algorithm, parallel strapdown algorithm design and FPGA implementation. The main contents of this thesis are summarized as follows:
1. Similar to the matching mechanism of SINS/GPS integrated navigation systems, three parallel system architectures of navigation computer are proposed based on the analysis of SINS functional requirements and performance requirements, namely, loosely-parallel architecture, deep-parallel architecture and totally-parallel architecture. In the totally-parallel architecture, all calculations of SINS are performed on the parallel mode; it needs to design new initial alignment and strapdown algorithms of SINS, namely, parallel strapdown algorithm and parallel initial alignment algorithm.
2. Considering that the vehicle is inevitably subject to the impact of rocking disturbances by wind gust or engine idling, etc. on the initial alignment, a strapdown compass alignment method based on dynamic gain adjustment (DGA-Compass) and a new Kalman alignment method (New-Kalman) are proposed and comparatively analyzed for the effectiveness of their alignment algorithms under different disturbance conditions. In the DGA-Compass alignment algorithm, the gain parameter is dynamically adjusted based on the expected alignment time and attitude change of vehicle to make the attitude angle output of system track the low-frequency and large-amplitude rocking disturbance, so the convergence speed of compass alignment can be accelerated, that is, the alignment time is reduced; in the New-Kalman alignment algorithm, level accelerometer measurements are introduced into the observations of the Kalman filter to improve the performance of alignment algorithm.
3. Considering the limitation of Kalman filter real-time tracking the attitude change of vehicle, a parallel systolic array structure implementation of Kalman filter algorithm is proposed based on the Faddeeva algorithm. For any given two or more matrices, matrix operations (matrix inversion, matrix multiplication and matrix addition) or combined operations can be computed by their corresponding Faddeeva algorithm. From the regularity, modularity and other features of systolic array structure, it is shown that systolic array structure is a good structure to achieve the Faddeeva algorithm. Kalman filter can be expressed in the form of some matrix operations, and then can be mapped to the parallel array structure based on Faddeeva algorithm.
4. Considering the high-speed and high-maneuvering features of hypersonic cruise missiles, a new strapdown algorithm suitable for the high dynamic conditions is proposed, in which the single-speed structure is used based on the performance of current navigation computer (high speed and high throughput). And new generalized optimization coning and sculling compensation algorithms are proposed to solve the coning movement in the attitude updating algorithm and the sculling movement in the velocity updating algorithm. Different from existing algorithms, the updating rates of the coning and sculling compensations are unrelated with the number of the gyro incremental angle samples and the number of the accelerometer incremental velocity samples. When the output sampling rate of inertial sensors remains constant, this algorithm allows increasing the updating rate of the coning and sculling compensation, yet with higher-order algorithm to improve the accuracy of system.
5. Taking into account that the attitude updating algorithm is the core of strapdown algorithm, and the major factor influencing system accuracy, especially for the high-speed and high-maneuvering hypersonic cruise vehicles, the relationship between the attitude errors and the coning compensation updating rate as well as the order of the coning compensation is deduced for quantitative analysis of the new coning compensation algorithm under typical coning movement conditions. Through analysis, it is shown that relative to the update rate, the relationship between the order of coning compensation and attitude error is more complex. When a vehicle moves with "normal" dynamics (characterized by a small or moderate coning movement frequency), both the increase of the updating rate of the coning compensation and the increase of the number of gyro incremental angle samples benefit the reduction of the attitude error. When a vehicle is in a high dynamic motion described by a larger frequency, however, in consideration of the technical limitations on the updating rate of the coning compensation (e.g., due to the limited computation speed of the navigation computer), the choice of the sampling number of gyro incremental angles must be made carefully.
6. Since reducing the update cycle (namely, increasing the update rate) can improve the accuracy of SINS, especially for the high-speed and high- maneuvering hypersonic cruise vehicles, a parallel strapdown algorithm structure is proposed. According to the design techniques of parallel algorithm (i.e., divide-and-conquer strategy and pipelining), the strapdown algorithm is parallel designed, and the parallel design is quantificationally analyzed. By the comparative analysis of the performance, it is shown that this parallel strapdown algorithm on the FPGA platform can greatly decrease the execution time of algorithm to meet the real-time and high precision requirements of system on the high dynamic environment, comparative with the existing implemented on the DSP platform.
7. From the perspective of system, the FPGA implementation of parallel strapdown algorithm and parallel Kalman filter initial alignment algorithm is analyzed in detail, respectively. Among them, the Xilinx embedded IP hardware MicroBlaze is used for controlling and scheduling the execution of each module in the parallel algorithms. Through car test, it is shown that the FPGA hardware implementation of SINS is feasible. This provides a solid basis for increasing the accuracy and real-time of SINS under the high dynamic conditons, and has a very good practical and theoretical value.
1.类似于组合导航中的耦合机制,在对捷联惯导系统导航计算机的功能需求以及性能需求进行分析的基础上,提出了三类导航计算机的并行体系架构,即浅并行体系架构、深并行体系架构和全并行体系架构。其中,在全并行体系架构中,所有的计算均是并行化执行的,因此就需要设计全新的捷联惯导系统初始对准和捷联解算算法,即并行初始对准算法和并行捷联解算算法等。
2.针对武器系统快反下的高晃动特性,提出了两种新的晃动基座捷联惯导系统初始对准算法,即基于动态增益调节的捷联罗经对准方法(DGA-Compass)和卡尔曼滤波对准方法(New-Kalman)。其中,在DGA-Compass对准算法中,根据滤波时间和运载体姿态变化剧烈程度动态调节对准回路的增益使系统姿态角输出随运载体的低频大幅度晃动的变化而变化,加快了对准算法的收敛速度,即缩短了系统的初始对准时间；在卡尔曼滤波对准算法中,通过在卡尔曼滤波器观测量中引入水平加速度计测量值,提高对准算法的性能。
3.针对提高卡尔曼滤波对准算法实时跟踪运载体真实姿态变化的局限性,提出了一种基于法捷耶夫算法的卡尔曼滤波器并行脉动阵列结构实现。对于任意给定的两个或多个矩阵,矩阵运算(矩阵求逆、矩阵相乘和矩阵相加)或三种运算的合运算都可通过它们对应的法捷耶夫算法实现。由脉动阵列结构的规则性、模块性等特性可知,脉动阵列结构是一种很好的实现法捷耶夫算法的并行结构。从而可将卡尔曼滤波器表示为一些列矩阵运算形式,然后基于法捷耶夫算法将其映射为并行脉冲阵列结构来实现。
4.针对高超声速巡航导弹的高速高机动运动特性,提出了一种适合高动态的捷联惯导系统捷联解算算法。其中,考虑到当前计算机的性能(高速和高吞吐量),在捷联解算算法中采用了单速结构。并且针对姿态更新中的圆锥运动和姿态更新中的划桨运动,提出了一种新的广义优化圆锥补偿算法和划桨补偿算法。其相对于现有的圆锥和划桨补偿算法,当惯性器件的输出采样速率恒定时,圆锥和划桨补偿算法的更新速率与惯性器件的输出采样个数无关,即在圆锥和划桨补偿算法的高更新速率下可采用高阶更新算法。
5.考虑到姿态更新算法是捷联解算算法的核心,也是影响系统精度的主要因素,特别是对作高速高机动运动的高超声速巡航导弹等运载体来说,定量分析了圆锥补偿算法的阶次以及更新周期对算法误差的影响大小。通过分析可知,相对于更新周期,圆锥补偿阶次对姿态误差的影响关系更为复杂。当运载体作中低动态运动时(即中低圆锥运动频率),可通过同时提高圆锥补偿的更新速率和增大圆锥补偿阶次来减小系统的姿态误差；当运载体作高动态运动时(即高圆锥运动频率),考虑到圆锥补偿的更新速率不能无限制地提高,必须仔细选择合适的圆锥补偿阶次。
6.针对捷联惯导系统减小更新周期(即提高更新速率)可提高其精度的特点,特别是对作高速高机动的高超声速巡航导弹,提出了一种并行捷联解算算法结构。根据并行算法的设计技术(即分治策略和流水线技术),对捷联解算算法进行了并行化设计,且对这种并行捷联解算算法的性能进行定量分析。通过这种并行捷联解算算法相对串行捷联解算算法的性能(即相对加速比)分析可见,这种捷联解算算法的并行化设计可显著减小算法的执行时间,从而可提高算法的更新速率。这就为工作在高动态环境下的捷联惯导系统精度的提高提供了重要基础。
7.针对捷联惯导系统的并行捷联解算算法和并行卡尔曼滤波初始对准算法的FPGA实现,分别从系统的角度进行了详细分析。其中,利用Xilinx嵌入式软核MicroBlaze控制和调度并行捷联解算算法和并行卡尔曼滤波初始对准算法中的各模块执行。通过车载试验验证了这种捷联惯导系统FPGA硬件实现的可行性。这就为在提高惯性器件输出速率的情况下,提高捷联惯导系统在高动态下的精度和实时性奠定了坚实的基础,具有非常好的现实意义和理论价值。
Considering the high-speed and high-maneuvering features of hypersonic cruise missiles, this thesis systematically investigates the parallel implementation of SINS under high dynamic conditions, which involves the initial alignment algorithm, parallel Kalman filter design, strapdown algorithm, parallel strapdown algorithm design and FPGA implementation. The main contents of this thesis are summarized as follows:
1. Similar to the matching mechanism of SINS/GPS integrated navigation systems, three parallel system architectures of navigation computer are proposed based on the analysis of SINS functional requirements and performance requirements, namely, loosely-parallel architecture, deep-parallel architecture and totally-parallel architecture. In the totally-parallel architecture, all calculations of SINS are performed on the parallel mode; it needs to design new initial alignment and strapdown algorithms of SINS, namely, parallel strapdown algorithm and parallel initial alignment algorithm.
2. Considering that the vehicle is inevitably subject to the impact of rocking disturbances by wind gust or engine idling, etc. on the initial alignment, a strapdown compass alignment method based on dynamic gain adjustment (DGA-Compass) and a new Kalman alignment method (New-Kalman) are proposed and comparatively analyzed for the effectiveness of their alignment algorithms under different disturbance conditions. In the DGA-Compass alignment algorithm, the gain parameter is dynamically adjusted based on the expected alignment time and attitude change of vehicle to make the attitude angle output of system track the low-frequency and large-amplitude rocking disturbance, so the convergence speed of compass alignment can be accelerated, that is, the alignment time is reduced; in the New-Kalman alignment algorithm, level accelerometer measurements are introduced into the observations of the Kalman filter to improve the performance of alignment algorithm.
3. Considering the limitation of Kalman filter real-time tracking the attitude change of vehicle, a parallel systolic array structure implementation of Kalman filter algorithm is proposed based on the Faddeeva algorithm. For any given two or more matrices, matrix operations (matrix inversion, matrix multiplication and matrix addition) or combined operations can be computed by their corresponding Faddeeva algorithm. From the regularity, modularity and other features of systolic array structure, it is shown that systolic array structure is a good structure to achieve the Faddeeva algorithm. Kalman filter can be expressed in the form of some matrix operations, and then can be mapped to the parallel array structure based on Faddeeva algorithm.
4. Considering the high-speed and high-maneuvering features of hypersonic cruise missiles, a new strapdown algorithm suitable for the high dynamic conditions is proposed, in which the single-speed structure is used based on the performance of current navigation computer (high speed and high throughput). And new generalized optimization coning and sculling compensation algorithms are proposed to solve the coning movement in the attitude updating algorithm and the sculling movement in the velocity updating algorithm. Different from existing algorithms, the updating rates of the coning and sculling compensations are unrelated with the number of the gyro incremental angle samples and the number of the accelerometer incremental velocity samples. When the output sampling rate of inertial sensors remains constant, this algorithm allows increasing the updating rate of the coning and sculling compensation, yet with higher-order algorithm to improve the accuracy of system.
5. Taking into account that the attitude updating algorithm is the core of strapdown algorithm, and the major factor influencing system accuracy, especially for the high-speed and high-maneuvering hypersonic cruise vehicles, the relationship between the attitude errors and the coning compensation updating rate as well as the order of the coning compensation is deduced for quantitative analysis of the new coning compensation algorithm under typical coning movement conditions. Through analysis, it is shown that relative to the update rate, the relationship between the order of coning compensation and attitude error is more complex. When a vehicle moves with "normal" dynamics (characterized by a small or moderate coning movement frequency), both the increase of the updating rate of the coning compensation and the increase of the number of gyro incremental angle samples benefit the reduction of the attitude error. When a vehicle is in a high dynamic motion described by a larger frequency, however, in consideration of the technical limitations on the updating rate of the coning compensation (e.g., due to the limited computation speed of the navigation computer), the choice of the sampling number of gyro incremental angles must be made carefully.
6. Since reducing the update cycle (namely, increasing the update rate) can improve the accuracy of SINS, especially for the high-speed and high- maneuvering hypersonic cruise vehicles, a parallel strapdown algorithm structure is proposed. According to the design techniques of parallel algorithm (i.e., divide-and-conquer strategy and pipelining), the strapdown algorithm is parallel designed, and the parallel design is quantificationally analyzed. By the comparative analysis of the performance, it is shown that this parallel strapdown algorithm on the FPGA platform can greatly decrease the execution time of algorithm to meet the real-time and high precision requirements of system on the high dynamic environment, comparative with the existing implemented on the DSP platform.
7. From the perspective of system, the FPGA implementation of parallel strapdown algorithm and parallel Kalman filter initial alignment algorithm is analyzed in detail, respectively. Among them, the Xilinx embedded IP hardware MicroBlaze is used for controlling and scheduling the execution of each module in the parallel algorithms. Through car test, it is shown that the FPGA hardware implementation of SINS is feasible. This provides a solid basis for increasing the accuracy and real-time of SINS under the high dynamic conditons, and has a very good practical and theoretical value.
引文
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