# An Improved Adaptive Kalman Filter for a Single Frequency GNSS/MEMS-IMU/Odometer Integrated Navigation Module

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Conventional Robust Adaptive Extended Kalman Filter

## 3. The Proposed Improved Robust Adaptive Kalman Filter

#### 3.1. System Overview

#### 3.2. Improvement Algorithm

#### 3.2.1. Scaling Factor Based on GNSS Solution State

#### 3.2.2. Adaptive Factor Based on the Mahalanobis Distance

#### 3.2.3. One-Step Prediction Kalman Filter Model

## 4. Experimental Route and Hardware Platform

## 5. Results

#### 5.1. Operands Analysis and Comparison

#### 5.2. Performance Verification

#### 5.3. Comparison with Other Filtering Algorithms

#### 5.4. Real-Time Power Consumption Verification and Comparision

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The algorithm flow chart of improved robust adaptive Kalman filter algorithm applied to GNSS/INS/odometer integrated navigation module.

**Figure 2.**Real-time performance verification experiment trajectory and scenes of vehicle navigation.

**Figure 4.**The operand number of the operation type in the extended Kalman filter and the one-step prediction Kalman filter.

**Figure 5.**The positioning errors of the extended Kalman filter and the one-step prediction Kalman filter in North, East, and Down directions: (

**a**) curve overlap; (

**b**) curve separation.

**Figure 6.**The real-time horizontal position error, velocity error, and heading error of the conventional robust adaptive Kalman filter, Sage filter, extended Kalman filter, and improved robust adaptive Kalman filter.

**Figure 7.**The real-time horizontal position error, velocity error, and heading error subfigures of conventional robust adaptive Kalman filter, Sage filter, extended Kalman filter, and improved robust adaptive Kalman filter.

**Figure 8.**The positioning errors of conventional robust adaptive Kalman filter, Sage filter, extended Kalman filter, improved robust adaptive Kalman filter, and GNSS in the boulevard scene.

**Figure 9.**The positioning errors of conventional robust adaptive Kalman filter, Sage filter, extended Kalman filter, improved robust adaptive Kalman filter, and GNSS in the tunnel scene.

**Figure 10.**The real-time position errors of the CRAKF, Sage filter, extended Kalman filter, and IRAKF in the North, East, and Down directions in the whole experimental route.

**Figure 11.**The real-time velocity errors of the CRAKF, Sage filter, extended Kalman filter, and IRAKF in the North, East, and Down directions in the whole experimental route.

**Figure 12.**The real-time attitude errors of the CRAKF, Sage filter, extended Kalman filter, and IRAKF in the Roll, Pitch, and Yaw in the whole experimental route.

**Figure 13.**The real-time position errors subfigures of the CRAKF, Sage filter, extended Kalman filter, and IRAKF in the North, East, and Down directions.

**Figure 14.**The real-time velocity errors subfigures of the CRAKF, Sage filter, extended Kalman filter, and IRAKF in the North, East, and Down directions.

**Figure 15.**The real-time attitude errors subfigures of the CRAKF, Sage filter, extended Kalman filter, and IRAKF in the Roll, Pitch, and Yaw.

**Figure 16.**The real-time power consumption of IRAKF, CRAKF, extended Kalman filter, and Sage filter in the experimental route.

Module | SPAN CPT6 | ||
---|---|---|---|

Gyro | Bias (deg/h) | 10 | 0.027 |

ARW (deg/sqrt(h)) | 0.27 | 0.0667 | |

Accelerometer | Bias (mGal) | 1800 | 50 |

VRW (m/s/sqrt(h)) | 0.042 | 0.03 |

**Table 2.**The RMS and maximum errors of the horizontal position, forward velocity, and heading of the CRAKF, Sage filter, extended Kalman filter, and IRAKF.

CRAKF | Sage Filter | Extended Kalman Filter | IRAKF | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Pos (m) | Vel (m/s) | Heading (deg) | Pos (m) | Vel (m/s) | Heading (deg) | Pos (m) | Vel (m/s) | Heading (deg) | Pos (m) | Vel (m/s) | Heading (deg) | |

RMS | 0.26 | 0.038 | 0.44 | 0.28 | 0.039 | 0.46 | 1.3 | 0.22 | 0.77 | 0.25 | 0.035 | 0.43 |

MAX | 1.67 | 0.18 | 4.06 | 1.7 | 0.18 | 4.1 | 17.1 | 3.4 | 7.8 | 1.65 | 0.14 | 4.06 |

**Table 3.**The horizontal position error of CRAKF, Sage filter, extended Kalman filter, and IRAKF at the moment of gross error.

CRAKF | Sage Filter | Extended KF | IRAKF | Improvement (%) | |||
---|---|---|---|---|---|---|---|

horizontal position (m) | 0.15 | 0.14 | 3.8 | 0.12 | 20 | 14.3 | 96.8 |

**Table 4.**The horizontal position errors of the CRAKF, Sage filter, extended Kalman filter, and IRAKF at the moment of GNSS RTK pseudo-fixed solution in the tunnel scene.

CRAKF | Sage Filter | Extended KF | IRAKF | Improvement (%) | |||
---|---|---|---|---|---|---|---|

horizontal position (m) | 0.16 | 0.165 | 2.1 | 0.14 | 12.5 | 15.2 | 93.3 |

**Table 5.**The RMS errors of the position, velocity, and attitude of the CRAKF, Sage filter, extended Kalman filter, and IRAKF in the whole experimental route.

Position (m) | Velocity (m/s) | Attitude (deg) | |||||||
---|---|---|---|---|---|---|---|---|---|

North | East | Down | North | East | Down | Roll | Pitch | Yaw | |

CRAKF | 0.21 | 0.16 | 0.74 | 0.035 | 0.034 | 0.045 | 0.53 | 0.214 | 0.432 |

Sage filter | 0.2 | 0.19 | 0.68 | 0.036 | 0.036 | 0.044 | 0.55 | 0.22 | 0.45 |

Extended Kalman filter | 1.11 | 0.66 | 1.02 | 0.19 | 0.2 | 0.23 | 0.65 | 0.60 | 0.774 |

IRAKF | 0.18 | 0.14 | 0.56 | 0.033 | 0.032 | 0.043 | 0.51 | 0.2 | 0.43 |

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**MDPI and ACS Style**

Yan, P.; Jiang, J.; Zhang, F.; Xie, D.; Wu, J.; Zhang, C.; Tang, Y.; Liu, J.
An Improved Adaptive Kalman Filter for a Single Frequency GNSS/MEMS-IMU/Odometer Integrated Navigation Module. *Remote Sens.* **2021**, *13*, 4317.
https://doi.org/10.3390/rs13214317

**AMA Style**

Yan P, Jiang J, Zhang F, Xie D, Wu J, Zhang C, Tang Y, Liu J.
An Improved Adaptive Kalman Filter for a Single Frequency GNSS/MEMS-IMU/Odometer Integrated Navigation Module. *Remote Sensing*. 2021; 13(21):4317.
https://doi.org/10.3390/rs13214317

**Chicago/Turabian Style**

Yan, Peihui, Jinguang Jiang, Fangning Zhang, Dongpeng Xie, Jiaji Wu, Chao Zhang, Yanan Tang, and Jingnan Liu.
2021. "An Improved Adaptive Kalman Filter for a Single Frequency GNSS/MEMS-IMU/Odometer Integrated Navigation Module" *Remote Sensing* 13, no. 21: 4317.
https://doi.org/10.3390/rs13214317