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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

This study developed a smartphone application that provides wireless communication, NRTIP client, and RTK processing features, and which can simplify the Network RTK-GPS system while reducing the required cost. A determination method for an error model in Network RTK measurements was proposed, considering both random and autocorrelation errors, to accurately calculate the coordinates measured by the application using state estimation filters. The performance evaluation of the developed application showed that it could perform high-precision real-time positioning, within several centimeters of error range at a frequency of 20 Hz. A Kalman Filter was applied to the coordinates measured from the application, to evaluate the appropriateness of the determination method for an error model, as proposed in this study. The results were more accurate, compared with those of the existing error model, which only considered the random error.

In cooperation with Dortmund University in Germany, the Federal Agency for Cartography and Geodesy (BKG) introduced HTTP-based Differential GPS (DGPS) data streaming technology and developed Networked Transport of RTCM via Internet Protocol (NTRIP) as the format of DGPS data [

Representative NRTK services include the EUREF-IP service of the EU [

The composition of the NRTK system was simplified, and the cost required to organize the system was reduced, by including the NTRIP client feature for correction message reception, NRTK processing feature, and applied features for using the NRTK positioning results in a smartphone application. A suitable method for determining the error model for the NRTK positioning results is also presented, to estimate highly reliable positioning values with a suitable filter in the application program, utilizing the NRTK positioning results.

This study designed the NRTK application using the advantages of the smartphone, including fast data processing speed, diverse wired/wireless communication features, and an installation environment for the universal user of the development application. Most of the processing for NRTK positioning could thus be conducted in the smartphone. This structure was applied for the following reasons. First, the system composition cost can be reduced, as the smartphone provides the RTK processing function, which until now was performed by the GPS receiver. Second, a smartphone performs all the functions that have been provided by a computer device, such as a PDA and a cell phone, simplifying the composition of the NRTK positioning system.

Considering the cost required for the system composition and equipment simplification, the design result in

The NRTK application was developed in a smartphone equipped with the Android OS.

The application uses carrier-phase (L1 and L2) and pseudorange data as primary GPS observables and also uses correction messages enclosing correction information of all GPS observables for precise positioning. The supported formats of correction messages are RTCM v2.3, RTCM v3.0, and CMR.

The most important of the functions of the NRTK application is the high accuracy and frequency positioning function. The normal accuracy levels for the RTK-GPS positioning method are 1 cm ± 1 ppm horizontally, and 2 cm ± 2 ppm vertically [

The NRTK positioning method is used in a wide range of areas, including geodetic survey [

The 3D absolute coordinate measured using the RTK-GPS positioning method is very accurate, with an error as large as several centimeters. The error statistically represents the characteristic of the random error. However, Schwieger [

The correlogram analysis, which has the autocorrelation coefficient marked on the time domain, helps determine whether the NRTK measurements include the autocorrelation error. If the _{1},_{2},_{3}, …, _{k}_{N}_{k}_{k}_{−1} is _{i}

In _{δ}_{Δ}, then the statistical error model of the NRTK measurements is expressed in

The parameters that must be determined, to apply the error model in _{δ}_{Δ} and _{δ}_{Δ} and

If the variances of the sample mean by sample size (

The static measurement results were filtered, to evaluate the effectiveness of the error model for the NRTK application that is calculated considering the random and autocorrelation errors. The test results were classified into two cases:

In this study, an NRTK application for smartphones was developed, and its performance evaluated via tests. A method for determining the error model of the measured coordinates was proposed, to use the NRTK measurements with higher accuracy, using dynamic state estimation filters. The study results are summarized as follows:

The advantages of smartphones were used to develop a NRTK application with wireless communication, NTRIP client, and RTK processing functions. The composition of the NRTK measurement system was thus simplified, while the NRTK measurement system was put together without using an expensive GPS receiver with RTK processing functions.

The evaluation of the positioning accuracy of the NRTK application showed that the RMSEs of the north, east, and ellipsoid height coordinates were very precise (0.0069 m, 0.0068 m, and 0.0269 m, respectively), when the NRTK positioning was conducted at a high frequency (20 Hz).

The latency for correction message transfer, which significantly affected the accuracy of the NRTK measurements, was 0.71 ± 0.32 s. This confirmed that 3G smartphones are very suitable for NRTK positioning.

A method for determining the error model of NRTK application positioning results was presented. This method aimed to use the NRTK application positioning results more accurately, via state estimation filters. An error model was developed (by considering both the random error and autocorrelation error), and was applied to the Kalman Filter. The positioning results were more accurate, compared with those from an error model that only considered random errors.

Design of the NRTK application for smartphones when use the general GPS receiver without the RTK function. (

Design plan of the NRTK application for smartphones when use the expensive GPS receiver supporting the RTK function. (

Application development results (main user interfaces and operation screens). (

Test points for evaluating the performance of the NRTK application.

A sample of test results (at

A Sample of test results (at Point 1) of performance evaluation. (

Correlograms for the elements of the 3D coordinates measured via the NRTK positioning method. (

Variances of the sample mean were calculated from the observation values and estimated using the least square method. (

Filtering results of NRTK positioning for the 3D coordinates. (

Main functions of the application and considerations by functions.

NTRIP client (SOCKET communication) |
NTRIP broadcaster connection and user authentication NRTK corrective message reception User position data transmission |
The time required to transfer the correction message must be short |

NRTK positioning |
Enter the GPS observation value Enter the NRTK correction message Check NRTK positioning |
Real-time positioning must be possible at 20 Hz or higher GPS observation values and correction messages in diverse formats must be recognized |

GPS receiver control and Data reception (Bluetooth communication) |
Receive GPS observation value GPS receiver control (positioning frequency and interface format) |
A control function suitable for the communication protocol of the GPS receiver is required |

Utility |
Save and retrieve position data Set out and other functions |
Scalability for meeting the diverse requirements of the user is required |

Application development environment.

OS | Android 2.2 (Froyo) |

SDK | Android API Level 8 & JDK 1.7 |

Integrated Development Environment | Eclipse |

Programming Language | Java |

Statistical indicators of the positioning accuracy of the NRTK application calculated from the test results at twelve fixed points displayed in

RMSE | 0.69 cm | 0.68 cm | 2.69 cm |

Average deviation | 0.56 cm | 0.55 cm | 2.12 cm |

Maximum deviation | 2.86 cm | 2.77 cm | 15.12 cm |

Ratio of accurate measurements | 99.12% |
98.91% |
89.66% |

Error model applied to the NRTK application positioning results.

_{δ} |
_{Δ} |
|||
---|---|---|---|---|

Coordinate Component | North | 0.60 cm |
0.53 cm |
0.004587 s^{−1}^{−1}) |

East | 0.53 cm |
0.36 cm |
0.008014 s^{−1}^{−1}) | |

Height | 1.62 cm |
1.15 cm |
0.005921 s^{−1}^{−1}) |

Statistical indicators of the filtering effects for use of random and autocorrelation error model in NRTK application.

| ||||||
---|---|---|---|---|---|---|

RMSE | 0.65 cm | 0.47 cm | 0.44 cm | 0.32 cm | 1.41 cm | 1.06 cm |

Average deviation | 0.58 cm | 0.31 cm | 0.55 cm | 0.24 cm | 1.87 cm | 1.02 cm |

Maximum deviation | 2.91 cm | 2.03 cm | 1.89 cm | 1.34 cm | 6.73 cm | 4.74 cm |

Ratio of accurate measurements | 99.21% | 99.97% | 99.35% | 100.00% | 91.74% | 97.66% |