SINS/Doppler/Odometer导航系统：一种有效的Sage-Husa卡尔曼滤波器

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"这篇研究论文关注的是提升SINS( Strapdown Inertial Navigation System, 惯性导航系统)/Doppler(多普勒雷达)/Odometer(里程计)集成导航系统的定位精度和稳定性。文章通过分析系统特性与性能，建立了系统模型，并推导出离散状态和测量方程。传统卡尔曼滤波器在此类系统中的应用通常不够稳定，容易发散，因此对使用传统卡尔曼滤波器导致的集成导航系统发散原因进行了深入分析。接下来，文章设计了一种基于UD分解的Sage-Husa卡尔曼滤波器，并根据分析结果进行了一些改进。最后，通过多个仿真实验验证了改进算法的效果，结果显示，基于UD分解的改进型Sage-Husa卡尔曼滤波器能够确保SINS/Doppler/Platform Compass集成导航系统的精度和稳定性。" 本文的核心知识点包括： 1. **惯性导航系统（SINS）**：SINS是一种无需外部信息、隐蔽性强、抗干扰能力高的自主导航技术，它利用惯性传感器（如陀螺仪和加速度计）来确定物体的运动状态。 2. **多普勒雷达（Doppler）**：多普勒效应在导航中的应用，可以提供物体的速度信息，增强了定位的准确性。 3. **里程计（Odometer）**：里程计主要用于测量设备的移动距离，常作为辅助传感器，与惯性导航系统结合以提高位置估计的精确度。 4. **卡尔曼滤波器**：卡尔曼滤波是一种统计滤波方法，用于融合来自不同传感器的数据，以获得最优的估计。在SINS/Doppler/Odometer集成导航系统中，卡尔曼滤波用于融合三者的测量信息，减少误差并提高定位精度。 5. **Sage-Husa卡尔曼滤波器**：相较于传统的卡尔曼滤波器，Sage-Husa滤波器是一种适应性强、鲁棒性好的改进型滤波器，尤其适用于存在大噪声或非线性情况下的系统。 6. **UD分解**：在Sage-Husa滤波器中，UD分解是一种矩阵分解技术，用于处理非对称协方差矩阵，提高滤波的稳定性和计算效率。 7. **系统模型与方程**：建立系统模型是实现滤波算法的基础，包括离散状态方程和测量方程，它们描述了系统动态行为和传感器的观测过程。 8. **仿真实验**：通过仿真实验，论文验证了改进后的Sage-Husa滤波器在实际应用中的性能，证明了其在精度和稳定性上的优势。这些知识点共同构成了一个针对集成导航系统优化的解决方案，旨在通过改进的滤波技术提升系统的整体表现。



Abstract—This article aims at im proving positioning

precision and stability of the SINS/Doppler/Platform Compass

integrated navigation system. Firstly, based on considering of

the characteristic and performance of the integrated system, the

system model is established. And the discrete state and

measurement equations are achieved. Secondly, traditional

Kalman filter for this system is usuall y unstable, and easy to

divergent. So reasons for divergence of integrated navigation

with traditional Kalm an filter is analyzed. Thirdly, Sage-Husa

Kalman filter based on UD decomposition is designed. And

some improvements have been made according to the analysis

results. Finally, several simulation experiments were made to

test the effect of the improved algorithms. The simulation

results indicate that improved Sage-Husa Kalman filter based

on UD decomposition can guarantee the precision and stability

of the SINS/Doppler/Platform Compass integrated navigation

system.

I. INTRODUCTION

Strapdown inertial navigation system(SINS) has many

advantages. Such as independence of external information,

good concealment, strong radio resistance, all-weather work,

etc. However,it’s positioning error is accumulated over time.

So it cannot be used for long time and long distance navigation.

In order to improve precision and stability of the navigation

system, SINS is integrated with Doppler and platform

compass. And Kalman filtering technology is currently the

most widely used algorithm in integrated navigation system.

In order to obtain the optimal estimation,traditional

Kalman filter heavily relays on accurate error model and on

that the calculation error is as small as possible. However, the

running environment of navigation system is time-variant

system which is more complex. So it is difficult to obtain the

error model of the navigation system. On the other hand,

rounding error and interception error of the computer can

cause the error co-variance loss of positive definiteness. These

factors are likely lead Kalman filter to divergent and even fail,

which affects the accuracy of integrated navigation system.

Based on analysis of reasons for divergence of integrated

navigation with traditional Kalman filter, Sage-Husa adaptive

Kalman filter algorithm is introduced. According to

This work was sponsored by China’s National Science Foundation

(No.61304259), Youth Backbone Teacher Training Project in Henan

University of Technology, Major Scientific Research Project in Henan

Province (No.122102210044).

Jianjuan Liu is with School of Electrical Engineering, Henan University

of Technology, Zhengzhou, 450001 China (corresponding author:

86-18623718257; fax: 86-371-6775-8827; e-mail: ljjhaut@gmail.com).

Hongmei Chen is with School of Electrical Engineering, Henan

University of Technology, Zhengzhou, 450001 China (e-mail:

chenhongmei_seu@163.com).

Nanbo Liu is with School of Electrical Engineering, Henan University of

Technology, Zhengzhou, 450001 China (e-mail: lnb@haut.edu.cn).

characteristic of the SINS/Doppler/Platform Compass

navigation system, this algorithm is improved. And the

improved algorithm is called improved Sage-Husa adaptive

Kalman filter based on UD Decomposition. Finally, the

effective Sage-Husa Kalman filter is used in the

SINS/Doppler/ Platform Compass navigation system. The

simulation results indicate that the effective Sage-Husa

Kalman filter is better than traditional Kalman filter when

model parameter error or noise characteristic error exist.

II. SINS/DOPPLER/P

LATFORM COMPASS INTEGRATED

NAVIGATION SYSTEM FILTER MODEL

The strapdown inertial navigation system is to provide

local reference attitude for other devices. So other navigation

equipment can be used as the external information. The speed

information comes from Doppler log is selected as the external

information. Due to speed information has no obvious effect to

the heading angle, the error of heading angle between

strapdown navigation system and platform compass is also

selected as the observation quantity. State equation and

measurement equation of this linear discrete system are as

followings.

kkkk

kkkkkk

VXHZ

WXX









 ,11

(1)

Where,

bzbybxbybxUNENE

LVVX ][







are the east and north error of velocity respectively.



are the east, north and sky error of the attitude angle

respectively.





are the latitude and longitude error

respectively.



、



are the east and north zero bias of the

accelerometer respectively.



are the east, north and

sky drift of gyroscope respectively.

UNE

VVZ ][







are the east and north error of speed between

strapdown navigation system and Doppler log.



is the

heading angle error between strapdown navigation and

platform compass .

are system noise and observation

noise respectively. And they are uncorrelated white noise.

III. ANALYSIS OF RESONS FOR DIVERGENCE OF

INTEGRATED NAVIGATION WITH TRDTITIONAL

KALMAN FILTER

In the process of using Kalman filter, actual error of state

estimation is many times larger than theoretically predicted

error, and it increases with the data increasing despite of

decreasing of the error covariance matrix

.This

phenomenon is called divergence. Divergence will affect the

Effective Sage-Husa Kalman Filter for SINS/Doppler/Platform

Compass Integrated Navigation System*

Jianjuan Liu, Hongmei Chen, Nanbo Liu

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