# Quantitative Analysis to the Impacts of IMU Quality in GPS/INS Deep Integration

^{*}

## Abstract

**:**

## 1. Introduction

**Figure 1.**Two architectures of GPS/INS deeply coupled integration. (

**a**) Scalar-based architechture; (

**b**) Vector-based architechture.

#### 1.1. Previous Work

#### 1.2. Objectives

## 2. Methodology

#### 2.1. Error Dynamic Solutions of INS

_{M}, R

_{N}are radii of curvature in the meridian and prime vertical, h is ellipsoidal height and L is geodetic latitude.

- (a)
- It only needs to consider the stationary conditions (i.e., static and uniform rectilinear motion) as the main object of this paper is the maneuver-independent velocity error;
- (b)
- The minor terms (e.g., terms contain the reciprocal of the earth radius parameters) are ignored as they have little effect on the navigation errors;
- (c)
- The impact of position error can be ignored after simplification (as the left equations group in Equation (2)) because the position errors do not affect the velocity errors and attitude errors in the analysis;
- (d)
- Assume that the sensor selection of each axial is the same and it can be considered that the sensor errors characteristics in n-frame are the same with that in the b-frame, because the rotation matrix from b-frame to n-frame is an identity and orthogonal matrix.

#### 2.2. Detailed Modeling of the Error Sources in IMU

**b**

_{a},

**b**

_{g}are residual biases of the accelerometers and gyros, respectively, after the GPS update.

**w**

_{a},

**w**

_{g}are the noise of the accelerometer and gyros, respectively, which are usually modeled by Gaussian white-noise. The bias generally consists of two parts, a constant part that can be modeled as random constant (i.e.,

**b**

_{a_c}and

**b**

_{g_c}in Equation (7)) and a various part that can be modeled as first-order Gauss-Markov process (i.e., GM

_{a}and GM

_{g}in Equation (7)).

**T**is the correlation time and

**w**

_{GM}is the driving noise of the Gauss-Markov process [26].

## 3. Quantitative Analysis of INS Velocity Errors

#### 3.1. Quantitative Analysis Results in the Short Term

- (a)
- The parameters are obtained based on real GPS/INS data processing and the inertial sensors specifications; and the GPS measurements are single point positioning results;
- (b)
- The bias constants are the statistics of the standard deviation of the bias estimation right after the GPS update;
- (c)
- The initial errors are the statistics of the navigation errors right after the GPS update;
- (d)
- The other parameters are set according to the real data process parameters.

Characteristics | Inertial Measurement Unit IMU | ||
---|---|---|---|

MTi-G | SPAN-FSAS | ||

Grade | MEMS | Tactical Frade | |

Gyro | Mean squared value of bias drift (σ) | 100 deg/h | 0.1 deg/h |

Correlation time (T) | 600 s | 10,800 s | |

Gyro white-noise (ARW) | 3 deg/h | 0.15 deg/h | |

Accel | Mean squared value of bias drift (σ) | 2000 mGal | 100 mGal |

Correlation time (T) | 600 s | 10,800 s | |

Accel. white-noise (VRW) | 0.12 m/s/h | 0.03 m/s/h | |

Gyro bias Constant (
b) *_{g*_c} | 15 deg/h | 0.1 deg/h | |

Accel. bias Constant (
b) *_{a*_c} | 800 mGal | 50 mGal | |

Initial velocity error $\delta {v}_{N}(0)$ ** | 0.04 m/s | 0.025 m/s | |

Initial attitude error ${\text{\varphi}}_{E}(0)$ ** | 0.3 deg | 0.015 deg |

**Figure 3.**The quantitative velocity errors caused by micro-electro-mechanical system (MEMS) INS error sources.

#### 3.2. Real Tests Validation of the INS Velocity Errors

**Figure 6.**The maneuver-independent velocity errors of the real tests data from different grades of IMUs comparing to theoretical analysis results.

## 4. Quantitative Error Analysis in GPS Tracking Loop

**Figure 8.**Carrier phase tracking errors caused by the maneuver-independent velocity error sources of MEMS IMU.

**Figure 9.**Carrier phase tracking errors caused by the maneuver-independent velocity error sources of tactical grade IMU.

**Figure 10.**Total carrier phase tracking errors caused by the maneuver-independent velocity errors of different grades of IMUs.

- (1)
- The quantitative analysis given in this paper is based on a set of assumptions such as the IMU parameters, design parameters of the INS aiding loop, etc., which are essential to make the analysis feasible. We have chosen the most typical cases.
- (2)
- The 2nd order tracking loop was used as example. However the 3rd order loop won’t perform much different since the initial velocity error, which can be regarded as Doppler step input to the loop, is the dominant factor.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Niu, X.; Ban, Y.; Zhang, Q.; Zhang, T.; Zhang, H.; Liu, J.
Quantitative Analysis to the Impacts of IMU Quality in GPS/INS Deep Integration. *Micromachines* **2015**, *6*, 1082-1099.
https://doi.org/10.3390/mi6081082

**AMA Style**

Niu X, Ban Y, Zhang Q, Zhang T, Zhang H, Liu J.
Quantitative Analysis to the Impacts of IMU Quality in GPS/INS Deep Integration. *Micromachines*. 2015; 6(8):1082-1099.
https://doi.org/10.3390/mi6081082

**Chicago/Turabian Style**

Niu, Xiaoji, Yalong Ban, Quan Zhang, Tisheng Zhang, Hongping Zhang, and Jingnan Liu.
2015. "Quantitative Analysis to the Impacts of IMU Quality in GPS/INS Deep Integration" *Micromachines* 6, no. 8: 1082-1099.
https://doi.org/10.3390/mi6081082