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In order to solve the problem of uncertain noise during the measurement of actual system, an extended Kalman filter fusion estimation method based on multisensor fusion algorithm with uncertain effects is proposed. Then the equivalent measurement and the corresponding error matrix are estimated by the proposed uncertain fusing algorithm. Submit the results into the system model for filter processing and the optimal estimation can be obtained by the filtering method. Finally, the algorithm is verified in the GPS/INS navigation system which shows that the fusion result with uncertainty effect is much better than then fusion result with independent noise due to the consideration of correlated noise and uncertain effects for the actual system. This is also validates the effectiveness and practicality of the proposed algorithm.

In order to improve the accuracy of vehicle positioning, multiple sensors are installed on the vehicle to overcome the defect of single sensor. For instance, global positioning system (GPS) is a satellite-based navigation system and can provide accurate three-dimensional information on the position and velocity. However, the lack of credibility and nonautonomous of GPS in some cases, often leads to blind field and cannot be effectively positioned. Inertial navigation system (INS) is a standalone system that provides linear acceleration and angular velocity at high speed, but as time goes by it significantly reduces its accuracy, position, and velocity and error rate information increased. The combination of GPS and INS can provide accuracy position and enhance the reliability of the system, and therefore has been widely applied in the integrated navigation system [

The Kalman filtering (KF) approach is one of the widely used methods for the navigation system [

In order to better describe the actual system, some scholars have studied the fusion estimation with the correlated noise [

In practice, when GPS/INS and other sensors are installed on the vehicle to navigate, the measurement noise is not only correlated, but also there exists some uncertainty effects. For instance, the common environment, like the vibration of the platform (vehicle) during the driving, will cause the measurements noise from all sensors installed on it to be intercorrelated. What is more, the not well-informed statistical characteristics of measurement noise and the transformation error of different coordinate systems causing uncertainty factors do exist in the actual system. Sometimes, the uncertainty will significantly affect the accuracy of the fusion estimation. This means that the filter method cannot be used directly for the actual system when considering the uncertainty factors during the measurement.

This paper presents an extended Kalman filter fusion estimation method based on multisensor fusion algorithm with uncertainty effect. After dealing with the measurement information of multiple sensors, the equivalent measurement is obtained, together with the corresponding error matrix. Using the extended Kalman filtering, the exact position will be obtained.

The outline of the remainder of the paper is as follows. In Section

Consider the stochastic system with multiple sensors:

Different sensors, installed on the same platform, share the same environment which makes the measurements noise

Let

Define the fusion estimator as

For any real number

Simplify the above equation, then

Define

Let

Let

Let

Considering the covariance of fusion result should be less than the covariance of any single measurement, the following is true:

Therefore, the parameters in the theory should satisfy

To illustrate the effectiveness of the algorithm, the vehicle system installed two GPS, INS, and other sensors, and the north-east-day geographic coordinates is selected as the navigation coordinate system. The system error equations and measuring equations are

Attitude error functions

Velocity error functions

Position error functions

Error functions of inertial device

^{2}is the gravitational acceleration.

Shown in Figure

Response of attitude and acceleration information of the vehicle.

Without loss of generality, the measurement noise of different sensors from the vehicle system is affected by uncertainty term.

According to formula (

Measured and estimated value of the longitude.

Measured and estimated value of the latitude.

Measured and estimated value of the latitude.

The above figures show that the estimated value of longitude and latitude is matched with the measured value very well, while the difference of the altitude is relatively large. This is due to the distance from north-south direction on the sphere changing 111 kilometers when the latitude changes one degree. That is to say, the distance will change 30.9 meters when latitude changes one second. The proportion of transfer relationship for two units for longitude is similar with latitude, while the proportion for longitudinal is not the constant; it is also related with latitude of the position, but the basic proportions will not vary too much. Therefore, when the unit of longitude and latitude is degrees, the difference between estimated and measured value is very small.

In order to illustrate uncertainty effects on the fusion error of longitude, latitude, and altitude, Figures

Longitude error with independent and uncertainty noise.

Latitude error with independent and uncertainty noise.

Altitude error with independent and uncertainty noise.

From the introduction part, it can be seen that many fusion algorithms are studied with the assumption that the measurement noises are independent with Gaussian noise distribution. In order to compare the results of this paper with the independent noise assumption, the fusion error curves with independent noise assumption are also shown in Figures

From Figures

For the actual system with multiple sensors to detect the same state vector, this paper proposed an extended Kalman filter method based on multisensor fusion algorithm with uncertainty disturbance. This method can deal with the problem of uncertainty effects of measurement noise by fusing the measurement information and filtering the system equation.

What is more, the accurate fusion results can be obtained just by one time filtering which reduces the calculation. The fusion result is verified by the GPS/INS navigation system, which shows that the algorithm proposed here considering the uncertainty influences for the system enhances the positioning accuracy for actual system.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This research is supported by the National Natural Science Foundation of China (no. 50974103) and Educational Commission of Shaanxi Province of China (2013JK0858).