非线性SPKF滤波算法研究及其在组合导航中的应用
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摘要
捷联惯性导航系统(Strap-down Inertial Navigation System, SINS)和全球定位系统(Global Positioning System, GPS)所构成的组合导航系统本质上是非线性的,且具有模型不确定性。目前,应用于SINS/GPS组合导航系统的非线性滤波方法主要是扩展卡尔曼滤波器(Extended Kalman Filter, EKF)。然而,EKF存在一阶线性化精度偏低及需要计算非线性函数雅克比矩阵的缺点,造成了其在组合导航实际工程应用中估计精度不佳;且EKF不具有克服系统模型不确定的鲁棒性。近年来,随着对非线性滤波技术的需求不断加深,非线性滤波理论也取得了显著进步,尤其是以Sigma点卡尔曼滤波(Sigma Point Kalman Filter, SPKF)为代表的新兴非线性滤波方法的发展成熟,使得非线性滤波理论取得了长足的发展。
SPKF具有实现简单、滤波精度高、收敛性好等优点,正逐渐成为当前及未来非线性滤波技术的研究热点和发展方向。本文以SINS/GPS组合导航系统为应用背景,针对SPKF所存在的理论局限性,主要在以下几方面进行了理论创新:
1)根据线性最小方差估计准则,详细推导了非线性最优滤波递推公式。
2)传统SPKF在噪声先验统计未知或时变情况下滤波精度下降甚至发散,针对此问题,基于极大后验估计原理,设计了一种带噪声统计估计器的自适应SPKF算法。
3)类似于EKF,传统SPKF不具有克服系统模型不确定的鲁棒性,为此提出了一种带次优渐消因子的强跟踪SPKF算法。
同时,将上述非线性SPKF滤波理论创新成果应用于SINS/GPS组合系统导航定位中,主要从以下几方面进行了研究:
1)建立了以姿态、速度及位置等误差为基础的SINS/GPS组合导航系统非线性模型,并比较了EKF和SPKF的滤波性能,仿真结果验证了SPKF比EKF具有更好的定位精度。
2)针对惯性器件随机噪声统计在恶略工作环境下具有时变性的特点,将自适应UKF算法应用于SINS/GPS组合系统中,仿真结果表明了自适应SPKF在滤波前不要求精确已知惯性器件随机噪声的先验统计,且具有应对惯性器件随机噪声统计变化的自适应能力。
3)通常情况下,惯性器件随机常值漂移会被视为状态变量的一部分而采用滤波器进行估计,且其易受运行环境影响中不确定因素的影响而发生突变。为此,将强跟踪SPKF应用于SINS/GPS组合系统的仿真分析表明:强跟踪SPKF对突变的惯性器件随机常值漂移具有很强跟踪能力,验证了其具有克服组合导航系统模型不确定的鲁棒性。
SINS/GPS integrated navigation system is essentially non-linear, and has model uncertainty. At present, the non-linear filtering method applied for SINS/GPS integrated navigation system is mainly extended Kalman filter (EKF). However, EKF has some shortcomings including low precision resulted from the first-order linear and calculating Jacobian matrix of non-linear function, so its estimation accuracy is poor in the integrated navigation, and EKF does not have robustness to overcome the system model uncertainty. In recent years, with the deepening demand for non-linear filtering technique, non-linear filtering theory has made remarkable progress. Especially the emerging non-linear filtering methods, such as Sigma-point Kalman filter (SPKF) and particle filter (PF) developed, making non-linear filtering theory has made considerable development.
SPKF with easy implementation, high precision and good convergence, etc., is becoming the research focus and development direction of the current and future non-linear filtering technique. This paper applies SINS/GPS integrated navigation system for the application background, and for the theory limitations existing in SPKF, the theory innovation is mainly made from the following aspects:
1) According to the linear minimum variance estimation criteria, the recurrence formula of the non-linear optimal filter is derived in detail.
2) For this problem that filtering accuracy of the traditional SPKF reduces or even diverges when noisy priori statistics is unknown or time-varying, based on maximum a posteriori estimation principle, a kind of adaptive SPKF algorithm with noise statistics estimator is designed.
3) Similar to the EKF, the traditional SPKF does not have the robustness to overcome the system model uncertainty. For this, a strong track SPKF algorithmwith suboptimal fading factor is presented.
Meanwhile, the above-mentioned non-linear filtering theory innovations about SPKF is used in SINS/GPS integrated system navigation, and the following aspects were mainly studied:
1) This papr establishes the non-linear model of SINS/GPS integrated navigation system based on the errors of posture, speed and location, and compares the filtering performance of EKF and SPKF. Simulation results validate the SPKF has better positioning accuracy than EKF.
2) For time-varying characteristics of inertial device random noise statistics on the working environment with a slightly evil, the adaptive UKF algorithm is applied to SINS/GPS integrated system. Simulation results show that the adaptive SPKF does not require to precisely know the priori statistics of inertia device random noise before the filter, and has a adaptive capacity to response to changes in inertial random noise statistics.
3) Under normal circumstances, inertial device regular random drift will be seen as part of the state variable to been estimated in fitering, and is prone to mutation caused by the uncertain factors of operation environmental. For this, the strong tracking SPKF is applied to SINS/GPS integrated system, and simulation analysis shows that strong track SPKF has a strong ability to track inertial device regular random drift when it has a mutation, and possesses a robustness to overcome model uncertainty of the integrated navigation system.
SPKF具有实现简单、滤波精度高、收敛性好等优点,正逐渐成为当前及未来非线性滤波技术的研究热点和发展方向。本文以SINS/GPS组合导航系统为应用背景,针对SPKF所存在的理论局限性,主要在以下几方面进行了理论创新:
1)根据线性最小方差估计准则,详细推导了非线性最优滤波递推公式。
2)传统SPKF在噪声先验统计未知或时变情况下滤波精度下降甚至发散,针对此问题,基于极大后验估计原理,设计了一种带噪声统计估计器的自适应SPKF算法。
3)类似于EKF,传统SPKF不具有克服系统模型不确定的鲁棒性,为此提出了一种带次优渐消因子的强跟踪SPKF算法。
同时,将上述非线性SPKF滤波理论创新成果应用于SINS/GPS组合系统导航定位中,主要从以下几方面进行了研究:
1)建立了以姿态、速度及位置等误差为基础的SINS/GPS组合导航系统非线性模型,并比较了EKF和SPKF的滤波性能,仿真结果验证了SPKF比EKF具有更好的定位精度。
2)针对惯性器件随机噪声统计在恶略工作环境下具有时变性的特点,将自适应UKF算法应用于SINS/GPS组合系统中,仿真结果表明了自适应SPKF在滤波前不要求精确已知惯性器件随机噪声的先验统计,且具有应对惯性器件随机噪声统计变化的自适应能力。
3)通常情况下,惯性器件随机常值漂移会被视为状态变量的一部分而采用滤波器进行估计,且其易受运行环境影响中不确定因素的影响而发生突变。为此,将强跟踪SPKF应用于SINS/GPS组合系统的仿真分析表明:强跟踪SPKF对突变的惯性器件随机常值漂移具有很强跟踪能力,验证了其具有克服组合导航系统模型不确定的鲁棒性。
SINS/GPS integrated navigation system is essentially non-linear, and has model uncertainty. At present, the non-linear filtering method applied for SINS/GPS integrated navigation system is mainly extended Kalman filter (EKF). However, EKF has some shortcomings including low precision resulted from the first-order linear and calculating Jacobian matrix of non-linear function, so its estimation accuracy is poor in the integrated navigation, and EKF does not have robustness to overcome the system model uncertainty. In recent years, with the deepening demand for non-linear filtering technique, non-linear filtering theory has made remarkable progress. Especially the emerging non-linear filtering methods, such as Sigma-point Kalman filter (SPKF) and particle filter (PF) developed, making non-linear filtering theory has made considerable development.
SPKF with easy implementation, high precision and good convergence, etc., is becoming the research focus and development direction of the current and future non-linear filtering technique. This paper applies SINS/GPS integrated navigation system for the application background, and for the theory limitations existing in SPKF, the theory innovation is mainly made from the following aspects:
1) According to the linear minimum variance estimation criteria, the recurrence formula of the non-linear optimal filter is derived in detail.
2) For this problem that filtering accuracy of the traditional SPKF reduces or even diverges when noisy priori statistics is unknown or time-varying, based on maximum a posteriori estimation principle, a kind of adaptive SPKF algorithm with noise statistics estimator is designed.
3) Similar to the EKF, the traditional SPKF does not have the robustness to overcome the system model uncertainty. For this, a strong track SPKF algorithmwith suboptimal fading factor is presented.
Meanwhile, the above-mentioned non-linear filtering theory innovations about SPKF is used in SINS/GPS integrated system navigation, and the following aspects were mainly studied:
1) This papr establishes the non-linear model of SINS/GPS integrated navigation system based on the errors of posture, speed and location, and compares the filtering performance of EKF and SPKF. Simulation results validate the SPKF has better positioning accuracy than EKF.
2) For time-varying characteristics of inertial device random noise statistics on the working environment with a slightly evil, the adaptive UKF algorithm is applied to SINS/GPS integrated system. Simulation results show that the adaptive SPKF does not require to precisely know the priori statistics of inertia device random noise before the filter, and has a adaptive capacity to response to changes in inertial random noise statistics.
3) Under normal circumstances, inertial device regular random drift will be seen as part of the state variable to been estimated in fitering, and is prone to mutation caused by the uncertain factors of operation environmental. For this, the strong tracking SPKF is applied to SINS/GPS integrated system, and simulation analysis shows that strong track SPKF has a strong ability to track inertial device regular random drift when it has a mutation, and possesses a robustness to overcome model uncertainty of the integrated navigation system.
引文
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