GPS精密单点定位算法及故障诊断研究
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摘要
精密单点定位技术是GPS领域的一个研究热点。本文主要研究GPS精密单点定位理论和算法,其主要贡献如下：
1.采用Kalman滤波处理静态GPS数据和动态GPS数据。针对载体不同运动状态,给出不同的状态方程和观测方程,并利用多组数据进行了验证。考虑运动载体多接收机之间的距离为固定常数,提出距离约束的动态精密单点定位,提高其精度和可靠性。
2.使用方差分量估计调整伪距与载波相位观测值的权比。在精密单点定位中,伪距与载波相位观测值的权比一般为固定常数,这与实际测量情况不符,另外这也不利于提高模糊度的收敛速度。采用简化Helmert方差分量估计实时地调整两类观测值的权比,提高模糊度收敛速度和定位精度。
3.讨论了基于CORS对流层延迟信息的精密单点定位。若观测时间内发生下雨、下雪等天气变化,采用一般对流层延迟模型将无法得到高精度的天顶延迟量。根据CORS网的对流层延迟信息,可内插得到测站的对流层延迟时间序列,并将该序列替代由模型估计的对流层延迟,如此,可以提高定位精度。
4.讨论了单差模糊度固定方法在动态精密单点定位中的应用。模糊度一般作为状态参数进行估计,显然增大了计算矩阵的维数,并且不利于滤波收敛。采用单差无电离层组合模糊度固定方法首先固定模糊度,一方面减少状态参数的维数,另一方面可以提高初始阶段的收敛速度和定位精度。GPS数据的噪声一般都不为高斯白噪声,在模糊度固定的基础上,本文讨论了有色噪声最小二乘估计,如此可削弱有色噪声的影响。动力学模型误差的协方差矩阵一般靠经验取值任何经验值都有可能出现偏差,从而影响动力学模型对定位结果的贡献。本文采用自适应因子调整预测值的协方差矩阵与观测量噪声的协方差矩阵的比例,使动力学模型更加有效。
5.针对GPS数据处理中的非正态分布噪声与非线性函数线性化的问题,采用粒子滤波降低由这两方面造成的精度损失。粒子滤波的粒子数选取与状态参数的维数有很大关系,降低状态参数维数可以减少粒子个数。本文将单差模糊度固定方法与粒子滤波相结合应用于精密单点定位中,不但可以减少粒子滤波的粒子个数,而且能够提高动态精密单点定位的精度。针对粒子滤波容易出现粒子退化的问题,采用Kalman滤波进行重点采样,提高随机样本的精度,进而提高粒子滤波的解算精度。为了进一步提高粒子的精度,在重点采样的基础上,采用粒子群优化智能算法优化重点采样得到的粒子。另外,计算效率是粒子滤波的一个难点,本文采用均值漂移算法提高粒子滤波的计算效率。
6.对于单频精密单点定位,尝试采用顾及电离层延迟先验信息的估计方法。一般情况下,采用已知的电离层模型,如采用格网电离层模型等仅能消除电离层延迟的60%左右,剩余残差对于精密定位的影响仍然较大。本文在电离层模型估计的基础上,根据观测信息重新估计电离层延迟影响,从而提高电离层延迟的估计精度。
7.精密单点定位的故障诊断是提高精密单点定位精度的重要环节。但由于精密单点定位中不存在冗余观测,抗差估计方法难以实现。本文采用交互多模型方法诊断精密单点定位的观测故障。为了提高诊断的效率,提出了基于相邻历元模型概率比的方法。进而又提出使用粒子滤波处理含有观测异常的数据。神经网络具有强大的逼近能力与模式识别能力,本文构造二级神经网络进行诊断故障,提高故障诊断的效率。
Precise point positioning (PPP) is an important subject in GPS. The paper focuses on the theories and algorithms of PPP. The main works are shown as follows: 1. Kalman filtering is used to process the static data and the dynamic data. To the different state, the different dynamic models are given in Kalman filtering, and examined by several data in the different state. The reliability and accuracy of dynamic PPP will be improved if the immobile distances of GPS receivers in the aircraft as contraints are considered. 2. The variance component estimation is used to adjust the proportion of weights between phase observations and pseudorange observations. In PPP, the proportion of weights for two kinds of observations is a constant during the computation, so it is not consistent with the fact, it will slow down the convergence speed of ambiguities. Simplified Helmert variance component estimation is employed to adjust efficiently the proportion in the real time in order to improve the accuracy of PPP and the convergence speed of ambiguities. 3. The information of troposphere delay in CORS is used in PPP. When it rains or snows, the common model of troposphere will get the higher delay. The sequence of troposphere delay in the position of the receiver will be interpolated by the information of troposphere delay of CORS, and is used to replace the adjustment estimated by troposphere model. So the accuracy of positioning will be improved. 4. The algorithms to fix the ambiguities are applied to dynamic PPP. When ambiguities are estimated as the state parameters, it obviously enlarges the dimensions of the matrix, and is disadvantageous to the convergence of ambiguities. Firstly fixing single difference ionosphere ambiguities can not only reduce the dimensions of the parameters, but also improve the convergence speed and the accuracy of position in the initial time. For noises of GPS data always are not Gaussian noises, the least square is used to weaken the influence of colored noises on the base of ambiguities fixed. Because the covariance matrix of the state noise is given by experience which always has bias, it can affect the contribution to the positioning result. The adaptive factor is used to modulate the proportion between the covariance matrix of predicted state vector and the covariance matrix of observational noise in order to make full use of dynamic model.
5. To the linearization of nonlinear functions and non-Guasssian noise of GPS data, particle filter is employed to reduce the loss of accuracy. The number of particles in particle filter relates with dimensions of the state vector. If dimensions of the state vector are reduced, the number of particle can decrease. Particle filter based on fixing single difference ambiguities can not only reduce the number of particles, but also improve the positioning accuracy in the paper. Important sampling with Kalman filtering can optimize particles for degeneracy of the particle occurs in particle filter. To get higher accuracy of the particle, particle swarm optimization on the base of important sampling with Kalman filtering can heighten accuracy of particles. Mean shift algorithm is used to improve the efficiency of particle filter which is a shortcoming for particle filter.
6. The prior information of ionosphere is considered in Kalman filtering for single frequency PPP. The residual of ionosphere delay has strong influence on the result of positioning as grid ionosphere model only can eliminate 60% delay. Ionosphere delay is estimated again as parameter to further improve accuracy of ionosphere delay on the base of ionosphere model predicting delay with observations.
7. Detection and diagnosis of failures in PPP is the important segment. It is difficult that robust estimation can come true for there are redundant observations in PPP. In the paper, interacting multiple models based on the ratio of the probability of failure models is proposed to improve efficiency of diagnosis. And particle filter is used deal with observations with outliers. Two neural networks are designed to diagnose failure to get higher efficiency of correction as neural network has strong approach ability and pattern recognition ability.
1.采用Kalman滤波处理静态GPS数据和动态GPS数据。针对载体不同运动状态,给出不同的状态方程和观测方程,并利用多组数据进行了验证。考虑运动载体多接收机之间的距离为固定常数,提出距离约束的动态精密单点定位,提高其精度和可靠性。
2.使用方差分量估计调整伪距与载波相位观测值的权比。在精密单点定位中,伪距与载波相位观测值的权比一般为固定常数,这与实际测量情况不符,另外这也不利于提高模糊度的收敛速度。采用简化Helmert方差分量估计实时地调整两类观测值的权比,提高模糊度收敛速度和定位精度。
3.讨论了基于CORS对流层延迟信息的精密单点定位。若观测时间内发生下雨、下雪等天气变化,采用一般对流层延迟模型将无法得到高精度的天顶延迟量。根据CORS网的对流层延迟信息,可内插得到测站的对流层延迟时间序列,并将该序列替代由模型估计的对流层延迟,如此,可以提高定位精度。
4.讨论了单差模糊度固定方法在动态精密单点定位中的应用。模糊度一般作为状态参数进行估计,显然增大了计算矩阵的维数,并且不利于滤波收敛。采用单差无电离层组合模糊度固定方法首先固定模糊度,一方面减少状态参数的维数,另一方面可以提高初始阶段的收敛速度和定位精度。GPS数据的噪声一般都不为高斯白噪声,在模糊度固定的基础上,本文讨论了有色噪声最小二乘估计,如此可削弱有色噪声的影响。动力学模型误差的协方差矩阵一般靠经验取值任何经验值都有可能出现偏差,从而影响动力学模型对定位结果的贡献。本文采用自适应因子调整预测值的协方差矩阵与观测量噪声的协方差矩阵的比例,使动力学模型更加有效。
5.针对GPS数据处理中的非正态分布噪声与非线性函数线性化的问题,采用粒子滤波降低由这两方面造成的精度损失。粒子滤波的粒子数选取与状态参数的维数有很大关系,降低状态参数维数可以减少粒子个数。本文将单差模糊度固定方法与粒子滤波相结合应用于精密单点定位中,不但可以减少粒子滤波的粒子个数,而且能够提高动态精密单点定位的精度。针对粒子滤波容易出现粒子退化的问题,采用Kalman滤波进行重点采样,提高随机样本的精度,进而提高粒子滤波的解算精度。为了进一步提高粒子的精度,在重点采样的基础上,采用粒子群优化智能算法优化重点采样得到的粒子。另外,计算效率是粒子滤波的一个难点,本文采用均值漂移算法提高粒子滤波的计算效率。
6.对于单频精密单点定位,尝试采用顾及电离层延迟先验信息的估计方法。一般情况下,采用已知的电离层模型,如采用格网电离层模型等仅能消除电离层延迟的60%左右,剩余残差对于精密定位的影响仍然较大。本文在电离层模型估计的基础上,根据观测信息重新估计电离层延迟影响,从而提高电离层延迟的估计精度。
7.精密单点定位的故障诊断是提高精密单点定位精度的重要环节。但由于精密单点定位中不存在冗余观测,抗差估计方法难以实现。本文采用交互多模型方法诊断精密单点定位的观测故障。为了提高诊断的效率,提出了基于相邻历元模型概率比的方法。进而又提出使用粒子滤波处理含有观测异常的数据。神经网络具有强大的逼近能力与模式识别能力,本文构造二级神经网络进行诊断故障,提高故障诊断的效率。
Precise point positioning (PPP) is an important subject in GPS. The paper focuses on the theories and algorithms of PPP. The main works are shown as follows: 1. Kalman filtering is used to process the static data and the dynamic data. To the different state, the different dynamic models are given in Kalman filtering, and examined by several data in the different state. The reliability and accuracy of dynamic PPP will be improved if the immobile distances of GPS receivers in the aircraft as contraints are considered. 2. The variance component estimation is used to adjust the proportion of weights between phase observations and pseudorange observations. In PPP, the proportion of weights for two kinds of observations is a constant during the computation, so it is not consistent with the fact, it will slow down the convergence speed of ambiguities. Simplified Helmert variance component estimation is employed to adjust efficiently the proportion in the real time in order to improve the accuracy of PPP and the convergence speed of ambiguities. 3. The information of troposphere delay in CORS is used in PPP. When it rains or snows, the common model of troposphere will get the higher delay. The sequence of troposphere delay in the position of the receiver will be interpolated by the information of troposphere delay of CORS, and is used to replace the adjustment estimated by troposphere model. So the accuracy of positioning will be improved. 4. The algorithms to fix the ambiguities are applied to dynamic PPP. When ambiguities are estimated as the state parameters, it obviously enlarges the dimensions of the matrix, and is disadvantageous to the convergence of ambiguities. Firstly fixing single difference ionosphere ambiguities can not only reduce the dimensions of the parameters, but also improve the convergence speed and the accuracy of position in the initial time. For noises of GPS data always are not Gaussian noises, the least square is used to weaken the influence of colored noises on the base of ambiguities fixed. Because the covariance matrix of the state noise is given by experience which always has bias, it can affect the contribution to the positioning result. The adaptive factor is used to modulate the proportion between the covariance matrix of predicted state vector and the covariance matrix of observational noise in order to make full use of dynamic model.
5. To the linearization of nonlinear functions and non-Guasssian noise of GPS data, particle filter is employed to reduce the loss of accuracy. The number of particles in particle filter relates with dimensions of the state vector. If dimensions of the state vector are reduced, the number of particle can decrease. Particle filter based on fixing single difference ambiguities can not only reduce the number of particles, but also improve the positioning accuracy in the paper. Important sampling with Kalman filtering can optimize particles for degeneracy of the particle occurs in particle filter. To get higher accuracy of the particle, particle swarm optimization on the base of important sampling with Kalman filtering can heighten accuracy of particles. Mean shift algorithm is used to improve the efficiency of particle filter which is a shortcoming for particle filter.
6. The prior information of ionosphere is considered in Kalman filtering for single frequency PPP. The residual of ionosphere delay has strong influence on the result of positioning as grid ionosphere model only can eliminate 60% delay. Ionosphere delay is estimated again as parameter to further improve accuracy of ionosphere delay on the base of ionosphere model predicting delay with observations.
7. Detection and diagnosis of failures in PPP is the important segment. It is difficult that robust estimation can come true for there are redundant observations in PPP. In the paper, interacting multiple models based on the ratio of the probability of failure models is proposed to improve efficiency of diagnosis. And particle filter is used deal with observations with outliers. Two neural networks are designed to diagnose failure to get higher efficiency of correction as neural network has strong approach ability and pattern recognition ability.
引文
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