UKF融合SINS/CNS/GPS的综合导航算法

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"基于UKF的SINS/CNS/GPS融合导航算法" SINS（ Strapdown Inertial Navigation System，捷联式惯性导航系统）具有提供连续导航信息的优点，不受外部环境影响。然而，由于误差漂移的问题，SINS通常需要与其他传感器如CNS（Celestial Navigation System，天基导航系统）和GPS（Global Positioning System，全球定位系统）相结合。CNS通过星敏感器提供精确的姿态信息，但易受大气环境干扰；GPS能持续获得准确的位置和速度信息，但因多路径效应或遮挡影响，可靠性不足。因此，SINS/CNS/GPS的融合能够提高导航系统的精度和可靠性。目前，线性卡尔曼滤波器被应用于SINS/CNS导航系统和SINS/GPS导航系统，如参考文献[1][2]和[3][4]所示。这些方法分别修正姿态、位置和速度，但并未将它们结合起来。Carlson提出了一种联邦卡尔曼滤波方法[5][6]，利用分布式滤波器融合姿态、位置和速度信息，成为SINS/CNS/GPS集成导航系统的基本融合方式。所有上述方法都依赖于线性误差模型。然而，线性模型无法充分处理非线性问题，特别是在SINS/CNS/GPS融合导航中，误差动态往往具有非线性特性。为了克服这一局限，Unscented Kalman Filter（UKF，无迹卡尔曼滤波器）被引入。UKF是一种适用于非线性系统的滤波算法，它通过选取少量的“关键点”（sigma点）来近似系统的概率分布，从而避免了线性化的误差，提高了估计精度。在SINS/CNS/GPS融合导航算法中，UKF可以更有效地融合来自不同传感器的数据。首先，UKF会估计每个传感器的初始状态和误差协方差，然后在每个时间步长，UKF会生成一组sigma点，这些点在状态空间中覆盖了预测分布的范围。接着，UKF通过非线性函数将sigma点转换到测量空间，再通过加权平均得到预测的系统状态。同时，UKF也会更新误差协方差，以反映系统不确定性。当新的测量数据可用时，UKF会进行测量更新，进一步优化状态估计。通过UKF的这种机制，SINS/CNS/GPS融合导航系统能够更好地处理非线性误差，增强系统对各种环境变化和传感器故障的适应性。此外，UKF还具备良好的计算效率，使得实时处理大量传感器数据成为可能。基于UKF的SINS/CNS/GPS融合导航算法是针对传统线性方法在处理非线性问题上的局限性而提出的一种改进方案，它提升了系统性能，增强了导航的精确性和稳定性。这种技术在现代航空、航海和自动驾驶等领域有着广泛的应用前景。

1 Introduction

SINS has the advantage of the giving continuous

navigation information, independent of the external

environment. However, because of the drawback of error

drift, SINS is often mixed with other sensors, such as CNS

and GPS. CNS can provide precise attitude information by

star sensor, but it is disturbed easily by atmosphere

environment. GPS can obtain the accurate position and

velocity information continuously, but it is lack of credibity

due to multipath or mask effects. Consequently, the

SINS/CNS/GPS association can improve the precision and

reliability of navigation system.

At present, the linear Kalman filter

[1][2]

is used in the

SINS/CNS navigation system

[3]

and the SINS/GPS

navigation system

[4]

. However, the above methods only

modify the attitude, position and velocity separately, not

combine them. Carlson proposed a federated Kalman filter

approach

[5][6]

to solve this problem. The approach employs

the distributed filter to fuse the attitude, position and

velocity. Now it is only the basic fusion approach of

SINS/CNS/GPS integrated navigation system. All the

methods above employ the linear error models, thus the

precisions of these approaches are less accurate than those

methods employing the nonlinear error models. Julier

proposed the UKF (Unscented Kalman Filter) method

[7-9]

solve the problem. This method employs sampling strategy

to approximate the nonlinear distribution and probability

density of nonlinear functions. The accuracy of the method

is correct up to the second order

[10]

and it can get higher

order with special sampling strategies

[11]

. Li Tao

[12]

applied

UKF to nonlinear error models for SINS/GPS integrated

navigation systems and used quaternion to denote vehicle’s

This project is supported by the National Nature Science Foundation

(60535010)

attitudes. However, this method is lack of accurate attitude

information from CNS.

This paper re-examines the above problems and

introduces a new algorithm to the SINS/CNS/GPS

nonlinear system (the SINS/CNS/GPS system with

nonlinear state models). The algorithm builds up the

SINS/CNS and the SINS/GPS nonlinear local filter and

employs UKF to filter them. The filtering results are fused

by a federated Kalman filter. The advantages of the

algorithm are as follows:

1. The rotation vector model

[13]

is introduced to denote

vehicle’s attitude and has less variables than the

quaternion. Consequently, in UKF, the rotation

vector model has less state dimensions and sigma

points than the quaternion model. Thus, the rotation

vector model can reduce the computational costs

[14]

and the sampling non-local effects

[15]

2. The algorithm incorporates UKF with federated

Kalman filter and employs more accurate nonlinear

error model.

3. The system model is divided into the linear error

and the nonlinear error model. The simplified

version of the UKF method can be utilized to

estimate the system error model, which can both

lead to less calculation and reduce algorithm

implement time, as well as improve the real time

and upgrade the precision of system.

4. A new method is introduced to avoid the singular

covariance problem in the federated Kalman filter.

The rest of this paper is organized as follows. In Section

2 we describe the UT transform, UKF and the federated

Kalman filter. In Section 3 we describe the nonlinear error

model and the whole filter process. In Section 4 we

simulate the algorithm and show the simulation results. In

Section 5 we conclude the discussion of the new algorithm.

SINS/CNS/GPS integrated navigation algorithm based on UKF

Hu Haidong, Huang Xianlin

Center for Control Theory and Guidance Technology, Haerbin Institute of Technology, Haerbin 150001, P.R.China

Abstract: In this paper a new nonlinear algorithm is proposed for SINS (Strapdown Inertial Navigation) /CNS (Celestial

Navigation System)/GPS (Global Positioning System) integrated navigation system. The algorithm employs a nonlinear

system error model which can be modified by UKF (Unscented Kalman Filter) to give predictions of local filters. And these

predictions can be fused by the federated Kalman filter. In the system error model, the rotation vector is introduced to denote

vehicle’s attitude and has less variables than the quaternion. Also, the UKF method is simplified to estimate the system error

model, which can both lead to less calculation and reduce algorithm implement time. In the information fusion section, a

modified federated Kalman filter is proposed to solve the singular covariance problem. Specifically, we apply the new

algorithm to maneuvering vehicles and simulation results show that this algorithm is more accurate than the linear integrated

navigation algorithm.

Key words: navigation system, integrated navigation, UKF, federated Kalman filter, SINS, CNS, GPS.

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