To provide stable and accurate position information of control points in a complex coastal environment, an adaptive iterated extended Kalman filter (AIEKF) for fixed-point positioning integrating global navigation satellite system, inertial navigation system, and ultra wide band (UWB) is proposed. In this method, the switched global navigation satellite system (GNSS) and UWB measurement are used as the measurement of the proposed filter. For the data fusion filter, the expectation-maximization (EM) based IEKF is used as the forward filter, then, the Rauch-Tung-Striebel smoother for IEKF filter’s result smoothing. Tests illustrate that the proposed AIEKF is able to provide an accurate estimation.

During the construction phase of the construction project, various measurements must be carried out, such as the measurement of known length, the measurement of known angle, the measurement of the plane position of building detail points, etc. The premise of these measurements is that the control points of the construction site must be accurately measured [

To further improve position information accuracy, many works have been done, which mainly include two aspects: data fusion model and data fusion filtering algorithm [

To continuously improve the localization accuracy, an adaptive iterated EKF (AIEKF) for fixed-point positioning integrating GNSS, INS and ultra wide band (UWB) is proposed. In our method, the switched GNSS and UWB measurement is used as the measurement of the proposed filter. For data fusion, the expectation-maximization (EM) based IEKF is used as the forward filter; Then, the Rauch-Tung-Striebel smoother is used for the IEKF filter’s results smoothing. Tests illustrate the effectiveness of the proposed AIEKF.

The contribution of this paper mainly includes the following two parts:

An improved localization model is proposed to fuse the INS-based and the switched GNSS-based and UWB-based distance tightly. In this model, when the GNSS data is available, the INS-based and GNSS-based distances are used by the data fusion filter, which is able to provide the fixed-point position. When the GNSS is unavailable, the INS-based and UWB-based distances are employed to fuse the fixed-point position, which is used to compensate for the outage of the GNSS.

An AIEKF algorithm is designed with a forward filter of expectation-maximization (EM) based IEKF and a backward smoother of R-T-S. To this method, the IEKF method is used to reduce the truncation error caused by nonlinear systems. Meanwhile, the EM method is employed by the IEKF to estimate the noise statistics. Moreover, the threshold is used to improve the adaptability of the algorithm. Finally, the R-T-S smoothing method is used to smooth the output of the IEKF filter, which can improve the localization accuracy.

This section introduces the positioning scheme integrating GNSS/INS/UWB (G-I-U) firstly. Secondly, the state equation and measurement equation based on the integrated scheme will be designed.

The structure of the G-I-U-integrated positioning scheme is shown in

In this subsection, the state equation and measurement equation for the proposed improved filter will be designed. The stated equation of the proposed improved filter which will be introduced in the next section is listed as

To the measurement equation, when the GNSS data is available, the measurement equation can be derived as follows:

Based on the models

For more accurate noise statistics, we improve the Algorithm 1, and the improved IEKF is listed in the Algorithm 1 based on the models

This section verifies the proposed improved AIEKF performance. First, the experimental configuration is introduced. Second, the localization error is compared.

In this work, one test has been done in the University of Jinan, China. In the test, we employ the GPS to provide the GNSS’s solution, meanwhile, the UWB is used to provide the UWB’s solution. The structure of experimental platform is shown in

In this subsection, the localization error of the proposed method will be compared with the EKF and the traditional IEKF to verify the performance.

Moreover, to further prove the accuracy of our improved AIEKF, the absolute position errors in E and N directions of the EKF, the traditional IEKF, and the proposed improved AIEKF are shown in

Method | RMSE (m) | |||
---|---|---|---|---|

East | Improvement | North | Improvement | |

EKF | 0.0299 | - | 0.0392 | - |

IEKF | 0.0286 | 4.35% | 0.0546 | −39.29% |

The proposed improved AIEKF | 0.0194 | 35.12% | 0.0240 | 38.78% |

In this subsection, we will investigate the number of iterations of the proposed algorithm. The number of iterations of the proposed improved AIEKF is shown in

In this work, an improved localization scheme is proposed to fuse the INS-based and the switched GNSS-based and UWB-based distance tightly. Moreover, an AIEKF algorithm is designed with a forward filter of expectation-maximization (EM) based IEKF and a backward smoother of R-T-S.