监测水准网的滤波方法

冯延明

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监测水准网的滤波方法

冯延明

文章导航 > 武汉大学学报 ● 信息科学版 > 1987 > 12(1): 14-25

冯延明. 监测水准网的滤波方法[J]. 武汉大学学报 ● 信息科学版, 1987, 12(1): 14-25.

引用本文:

冯延明. 监测水准网的滤波方法[J]. 武汉大学学报 ● 信息科学版, 1987, 12(1): 14-25.

Feng Yanming. Filtering Method of Monitoring Levelling Networks[J]. Geomatics and Information Science of Wuhan University, 1987, 12(1): 14-25.

Citation:

Feng Yanming. Filtering Method of Monitoring Levelling Networks[J]. Geomatics and Information Science of Wuhan University, 1987, 12(1): 14-25.

监测水准网的滤波方法

冯延明

Filtering Method of Monitoring Levelling Networks

Feng Yanming

摘要: 监测水准网可采用一个线性动态系统——具有随机初始状态并带有随机动态干扰的状态方程和观测方程来描述,并运用卡尔曼滤波的方法进行状态估计。本文首先讨论了有关系统模型和滤波计算的实用公式,进一步考虑到卡尔曼滤波公式中对动态噪声与测量噪声所假定的完全的验前统计知识并不能精确得知的实际情况,提出了一种改进的卡尔曼滤波方法,即以方差分量估计原理为基础的自适应滤波方法。它还具有限制模型误差(包括初始状态误差),增强滤波稳定性的效用。文中最后通过对某复测水准网的实例计算和分析,初步证实了所提方法的可行性与有效性。
- 监测水准网 /
- 卡尔曼滤波 /
- 方差分量估计 /
- 自适应滤波
Abstract: A monitoring levelling network can be described by a linear dynamic system which consists of state equations with a random initial state vector and process noise vectors as well as observation equations: to which the Kalman filtering technique is applied for the estimate of the state vectors.As compared with the conventional dynamic adjustments,this method is more general and effective.A Kalman filter requires an exact knowledge of the process noise covariance matrix D_w and the measurement noise covarance matrix D_e.In a number of practical situations,D_w and D_e are either unknown or known only approximately.Here we consider the case in which the true values of D_w and D_e are unknown but each internal structure is known.The noise sequence {W_k} and {ε_k} are assumed to be white.Hence we give an improved approach to optimal filtering which summarizes the system and its statistical models with a few unknown parameters into a variance compoment model of the linear system.According to this model,the optimal estimates of the state vectors and the statistical parameters can be obtained simultaneously.In this paper the MINQUE formula for the variance components of two models both with and without process noise are given.The theoretical analysis shows that this approach is not only an effective adaptive filtering,but also has the functions of limiting model errors and enhancing the stability of filtering,while the Kalmam filtering is only a special case.As an example,a repeated levelling network is analysed.The results show the feasiblity and effectiveness of the approach.
- monitoring levelling networks /
- Kalman filtering /
- estimation of variance components /
- adaptive filtering

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监测水准网的滤波方法

冯延明

收稿日期: 1986-05-01
刊出日期: 1987-01-05

关键词:

摘要: 监测水准网可采用一个线性动态系统——具有随机初始状态并带有随机动态干扰的状态方程和观测方程来描述,并运用卡尔曼滤波的方法进行状态估计。本文首先讨论了有关系统模型和滤波计算的实用公式,进一步考虑到卡尔曼滤波公式中对动态噪声与测量噪声所假定的完全的验前统计知识并不能精确得知的实际情况,提出了一种改进的卡尔曼滤波方法,即以方差分量估计原理为基础的自适应滤波方法。它还具有限制模型误差(包括初始状态误差),增强滤波稳定性的效用。文中最后通过对某复测水准网的实例计算和分析,初步证实了所提方法的可行性与有效性。

English Abstract

Filtering Method of Monitoring Levelling Networks

Feng Yanming

Received Date: 1986-05-01
Publish Date: 1987-01-05

Keywords:

Abstract: A monitoring levelling network can be described by a linear dynamic system which consists of state equations with a random initial state vector and process noise vectors as well as observation equations: to which the Kalman filtering technique is applied for the estimate of the state vectors.As compared with the conventional dynamic adjustments,this method is more general and effective.A Kalman filter requires an exact knowledge of the process noise covariance matrix D_w and the measurement noise covarance matrix D_e.In a number of practical situations,D_w and D_e are either unknown or known only approximately.Here we consider the case in which the true values of D_w and D_e are unknown but each internal structure is known.The noise sequence {W_k} and {ε_k} are assumed to be white.Hence we give an improved approach to optimal filtering which summarizes the system and its statistical models with a few unknown parameters into a variance compoment model of the linear system.According to this model,the optimal estimates of the state vectors and the statistical parameters can be obtained simultaneously.In this paper the MINQUE formula for the variance components of two models both with and without process noise are given.The theoretical analysis shows that this approach is not only an effective adaptive filtering,but also has the functions of limiting model errors and enhancing the stability of filtering,while the Kalmam filtering is only a special case.As an example,a repeated levelling network is analysed.The results show the feasiblity and effectiveness of the approach.

冯延明. 监测水准网的滤波方法[J]. 武汉大学学报 ● 信息科学版, 1987, 12(1): 14-25.

引用本文:

冯延明. 监测水准网的滤波方法[J]. 武汉大学学报 ● 信息科学版, 1987, 12(1): 14-25.

Feng Yanming. Filtering Method of Monitoring Levelling Networks[J]. Geomatics and Information Science of Wuhan University, 1987, 12(1): 14-25.

Citation:

Feng Yanming. Filtering Method of Monitoring Levelling Networks[J]. Geomatics and Information Science of Wuhan University, 1987, 12(1): 14-25.