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We develop a new integrated navigation system, which integrates multi-constellations GNSS precise point positioning (PPP), including GPS, GLONASS and Galileo, with low-cost micro-electro-mechanical sensor (MEMS) inertial system, for precise positioning applications. To integrate GNSS and the MEMS-based inertial system, the process and measurement models are developed. Tightly coupled mechanism is adopted, which is carried out in the GNSS raw measurements domain. Both un-differenced and between-satellite single-difference (BSSD) ionosphere-free linear combinations of pseudorange and carrier phase GNSS measurements are processed. Rigorous models are employed to correct GNSS errors and biases. The GNSS inter-system biases are considered as additional unknowns in the integrated error state vector. The developed stochastic model for inertial sensors errors and biases are defined based on first order Gaussian Markov process. Extended Kalman filter is developed to integrate GNSS and inertial measurements and estimate inertial measurements biases and errors. Two field experiments are executed, which represent different real-world scenarios in land-based navigation. The data are processed by using our developed Ryerson PPP GNSS/MEMS software. The results indicate that the proposed integrated system achieves decimeter to centimeter level positioning accuracy when the measurement updates from GNSS are available. During complete GNSS outages the developed integrated system continues to achieve decimeter level accuracy for up to 30 seconds while it achieves meter-level accuracy when a 60-second outage is introduced.

Global navigation satellite systems (GNSS) provide worldwide positioning, velocity and time synchronization. Traditionally, highly accurate GNSS positioning solution is obtained through carrier-phase observables in differential mode involving two or more receivers. However, the requirement of a base station is usually problematic for some applications. Comparable positioning accuracy, without requiring extra infrastructure, can be achieved through precise point positioning (PPP) technique [

Employing multi-GNSS systems, in contrast to GPS only, decreases the probability of partial GNSS outages due to the availability of a large number of satellites observations. However, GNSS positioning solution may not always be available due to complete GNSS outages in urban canyons. These limitations can be overcome through integrating the GNSS observations with a relatively environment-independent system, the inertial navigation system (INS). Differential GPS are traditionally used for precise positioning applications with different grade levels of inertial sensors such as a navigation grade inertial system (e.g. [

Considering the recent advances in MEMS-based accelerometers, the up to date GNSS constellations and the advances in PPP techniques, this research aims to develop a new integrated navigation system for precise positioning and navigation applications. MEMS-based accelerometers equipped with fiber optic gyros, which limit the orientation errors, are used. GNSS-based PPP including GPS, GLONASS and Galileo systems observations are used to update the system through a tightly coupled mechanism. The developed integrated system shows decimetre to centimetre level accuracy when GNSS observations are available. It is shown that the additional GNSS observations enhance the positioning accuracy in comparison with the traditional GPS kinematic positioning solution. Better positioning accuracy is obtained with BSSD ionosphere-free model, in comparison with the traditional un-differenced ionosphere-free model. In addition, the developed integrated system continues to achieve decimeter level accuracy for up to 30 seconds while it achieves meter-level accuracy when a 60-second outage is introduced.

In this study, both un-differenced and between-satellite single differenced ionosphere-free models are considered. Pseudorange and carrier phase observations of three GNSS systems are processed, namely GPS, GLONASS and Galileo. The general un-differenced ionosphere-free linear combinations of GNSS observations can be written as [

where

The IGS-MGEX precise orbital and clock products are used to mitigate the satellite orbit and clock errors [

where

function for the troposphere wet delay component

It can be seen that the receiver clock offset is cancelled out when forming our BSSD mathematical equations. Additionally, the receiver differential code and phase biases are cancelled out for the GPS system observations while these receiver biases are reduced significantly for GLONASS and Galileo observations. However, forming BSSD leads to mathematical correlations among the observations, which must be taken into account when the covariance matrix of the observations is formed. Equations (3)-(6) are used to develop the measurement models of the proposed GNSS/INS integrated system for both un-differenced and between satellites single differences modes, respectively. However, due to the nonlinearity of GNSS observation models, the GNSS mathematical model should be expanded through Tylor Expansion to be employed in updating the tight PPP/INS integration as follows

For undifferenced GNSS ionsphere-free model;

And for BSSD GNSS ionosphere-free model:

where

Inertial navigation is a method where the current position, velocity and attitude of a moving object are determined from a history of acceleration and angular velocity measurements. Acceleration and angular velocity are measured using accelerometers and gyros. Unlike GNSS systems, the INS performance is not affected in environments as urban canyons; it is independent of external electro-magnetic signals. However, the main drawback of an INS is the degradation of its performance with time. In order to control the errors to an acceptable level continues updates from, for example, GNSS are necessary.

The mathematical model of the inertial navigation system is commonly described in the framework of linear dynamic systems. The dynamic behavior of such systems can be described by using a state-space representation. For this purpose, a system of non-linear first-order differential equations can be described as [

where

The matrix

The matrix

To build the proposed GNSS/INS integrated navigation system, tightly coupled architecture is implemented adopting extended Kalman filter (EKF). GNSS pseudorange, carrier phase and Doppler measurements as well as INS-derived observations are processed to produce estimates of the state vector including position, velocity and attitude. The precise GNSS ephemerides as well as the outputs of position

tial sensors mechanization are used to predict the INS pseudorange

differenced with the INS-predicted measurements. The residuals

To implement the mechanization of the developed integrated system, the EKF is used as an estimator to merge the GNSS observations and INS records. The estimated state vector δx consists of 26 + n states describing the basic state vector including the nine navigation parameter errors, the inertial sensors errors including the bias drift and scale factor, and errors unique to the GNSS measurements, which are mainly the receiver clock offset and drift, the troposphere wet delay component, the GPS/GLONASS ISB and GPS/Galileo ISB with additional n states related to the float ambiguity parameters Bi. The complete state vector for un-differenced ionosphere-free technique can be written as.

where

meters, respectively. Both

EKF includes two parts the system model and the observation model. The system model is obtained from the INS dynamic errors augmented with the additional GNSS errors as follows.

where

δZ is the measurement vector consisting of the differences between the corrected GNSS and the predicted INS measurements. When un-differenced ionosphere-free model is used δZ can be defined as:

H is the design matrix containing geometry factors defined according to the GNSS mathematical model used. The design matrix is arranged with columns corresponding to the states unique to inertial sensors errors such as

where d are the direction cosine matrix D elements for pseudorange and phase; s is the direction cosine matrix S elements for Doppler measurements. The Element of D and S can be computed as follows

where X, Y and Z are are the satellite coordinates computed using the final IGS-MEGX orbital products and corrected for the effect of earth rotation during signal transit; φ, λ and h are the INS positioning coordinates; N is the prime vertical radius of curvature. To form the BSSD measurement model, between-satellite single difference matrix

where

where

Two real vehicular tests were conducted to evaluate the performance of the developed integrated GNSS-PPP/ MEMS-based INS system (^{®} Core i7-3517U CPU and 6 GB RAM. The computational burden of the whole process is 39.41 s including reading both INS and GNSS observations, Kalman filtering process with GNSS updating every second and results writing.

The first trajectory test area is shown in

To mimic challenging positioning conditions in urban areas, including complete blockage of the GNSS satellites, twelve simulated complete satellite outages of 60 s, 30 s and 10 s were introduced in the first trajectory.

PPP techniques | GPS (un-differenced mode) | GPS (BSSD mode) | ||||
---|---|---|---|---|---|---|

Positioning | latitude | longitude | altitude | Latitude | longitude | altitude |

RMSE (m) | 0.101 | 0.160 | 0.103 | 0.052 | 0.090 | 0.082 |

Maximum error | 0.184 | 0.303 | 0.416 | 0.121 | 0.179 | 0.306 |

PPP techniques | GNSS (un-differenced mode) | GNSS (BSSD mode) | ||||

Positioning | latitude | longitude | altitude | Latitude | longitude | altitude |

RMSE | 0.065 | 0.094 | 0.079 | 0.034 | 0.059 | 0.058 |

Maximum error | 0.108 | 0.178 | 0.245 | 0.072 | 0.106 | 0.180 |

PPP technique | Un-differenced-GPS | BSSD-GPS | ||||
---|---|---|---|---|---|---|

Outages(sec) | 60 s | 30 s | 10 s | 60 s | 30 s | 10 s |

Latitude(m) | 0.517 | 0.334 | 0.201 | 0.501 | 0.327 | 0.199 |

Longitude(m) | 0.716 | 0.429 | 0.214 | 0.699 | 0.428 | 0.210 |

Altitude(m) | 0.402 | 0.310 | 0.159 | 0.393 | 0.305 | 0.160 |

PPP technique | Un-differenced-GNSS | BSSD-GNSS | ||||

Outages(sec) | 60 s | 30 s | 10 s | 60 s | 30 s | 10 s |

Latitude(m) | 0.483 | 0.296 | 0.175 | 0.472 | 0.268 | 0.146 |

Longitude(m) | 0.681 | 0.396 | 0.186 | 0.670 | 0.363 | 0.159 |

Altitude(m) | 0.376 | 0.273 | 0.137 | 0.357 | 0.245 | 0.104 |

altitude, respectively, during the three simulated GNSS outages for both BSSD and un-differenced ionosphere- free models for the first trajectory.

The second trajectory test area is shown in

PPP techniques | GPS (un-differenced mode) | GPS (BSSD mode) | ||||
---|---|---|---|---|---|---|

Positioning | Latitude | Longitude | Altitude | Latitude | Longitude | Altitude |

RMSE (m) | 0.042 | 0.103 | 0.117 | 0.040 | 0.059 | 0.074 |

Maximum error | 0.118 | 0.232 | 0.268 | 0.123 | 0.172 | 0.255 |

PPP techniques | GNSS (un-differenced mode) | GNSS (BSSD mode) | ||||

POSITIONING | Latitude | Longitude | Altitude | Latitude | Longitude | Altitude |

RMSE | 0.029 | 0.051 | 0.062 | 0.038 | 0.030 | 0.057 |

Maximum error | 0.109 | 0.170 | 0.226 | 0.095 | 0.077 | 0.093 |

Eight simulated GNSS outages, each with duration of 60 s, 30 s and 10 s, respectively, were introduced such that they encompass all conditions of the trajectory, including straight portions and turns.

We developed new algorithms for the integration of multi-constellation GNSS PPP, including GPS, GLONASS and Galileo systems, and MEMS-based inertial system. Both un-differenced and between-satellite single difference ionosphere-free linear combinations of carrier phase and code GNSS measurements were considered. Tightly coupled mechanism was implemented and extended Kalman filter (EKF) technique was developed to merge the GNSS and inertial measurements. The performance of the newly developed models was analyzed by using two real trajectory tests. The positioning results of the integrated system showed that centimeter to

PPP technique | Un-differenced-GPS | BSSD-GPS | ||||
---|---|---|---|---|---|---|

Outages (sec) | 60 s | 30 s | 10 s | 60 s | 30 s | 10 s |

Latitude (m) | 1.123 | 0.587 | 0.261 | 1.025 | 0.550 | 0.238 |

Longitude (m) | 1.231 | 0.644 | 0.288 | 1.136 | 0.636 | 0.263 |

Altitude (m) | 0.923 | 0.483 | 0.215 | 0.843 | 0.441 | 0.197 |

PPP technique | Un-differenced-GNSS | BSSD-GNSS | ||||

Outages (sec) | 60 s | 30 s | 10 s | 60 s | 30 s | 10 s |

Latitude (m) | 1.012 | 0.528 | 0.235 | 0.935 | 0.497 | 0.215 |

Longitude (m) | 1.108 | 0.581 | 0.262 | 1.025 | 0.574 | 0.237 |

Altitude (m) | 0.832 | 0.441 | 0.194 | 0.769 | 0.398 | 0.180 |

decimeter-level accuracy was achievable when the GNSS satellite were available. The addition of GLONASS and Galileo observations enhanced the positioning accuracy in comparison with standalone GPS-based solution. Better positioning accuracy was obtained with BSSD IF model in comparison with the un-differenced IF model for both GPS- and GNSS-based models. During the GNSS outages, the integrated system showed meter-level accuracy in most cases when a 60-second outage was introduced. However, the positioning accuracy was improved to a few decimeter and decimeter-level accuracy when 30- and 10-second GPS outages were introduced. Comparable results were obtained from both BSSD and un-differenced models under GNSS outages.

Mahmoud AbdRabbou,AhmedEl-Rabbany, (2015) Integration of Multi-Constellation GNSS Precise Point Positioning and MEMS-Based Inertial Systems Using Tightly Coupled Mechanization. Positioning,06,81-95. doi: 10.4236/pos.2015.64009