# Adaptive Fading Extended Kalman Filtering for Mobile Robot Localization Using a Doppler–Azimuth Radar

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## Abstract

**:**

## 1. Introduction

- How to characterize the inaccurate odometer measurement-induced unknown bias in the kinematic model of a type (2,0) robot?
- How to consider the inaccurate odometer measurement-induced unknown bias in the D–AR measurement model?
- How to developed a on-line localization algorithm such that the given localization performance can be achieved?

- The inaccurate odometer measurement-induced unknown bias is considered in the kinematic model of a type (2,0) robot for the first time;
- The induced unknown bias is regarded in the D–AR measurement model;
- The AFEKF is adopted to reduce the impact of the modeling errors and achieving on-line localization;
- Thee comparative simulations have been conducted to testify the usefulness of the developed AFEKF by choosing three different types of modeling errors.

## 2. Problem Formulation

**Assumption**

**A1.**

**Assumption**

**A2.**

#### 2.1. Conventional Robot Kinematic Model

#### 2.2. Doppler-Azimuth Radar Measurement Model

**Remark**

**1.**

## 3. The Conventional EKF Algorithm

**Prediction**:

**Update**:

**Remark**

**2.**

## 4. Adaptive Fading EKF Algorithm

**Prediction**:

**Measurement Update**:

**Remark**

**3.**

## 5. Stability Analysis

**Definition**

**1.**

**Definition**

**2.**

**Theorem**

**1.**

**Remark**

**4.**

## 6. Simulation Results

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Li, B.; Lu, Y.; Karimi, H.R.
Adaptive Fading Extended Kalman Filtering for Mobile Robot Localization Using a Doppler–Azimuth Radar. *Electronics* **2021**, *10*, 2544.
https://doi.org/10.3390/electronics10202544

**AMA Style**

Li B, Lu Y, Karimi HR.
Adaptive Fading Extended Kalman Filtering for Mobile Robot Localization Using a Doppler–Azimuth Radar. *Electronics*. 2021; 10(20):2544.
https://doi.org/10.3390/electronics10202544

**Chicago/Turabian Style**

Li, Bin, Yanyang Lu, and Hamid Reza Karimi.
2021. "Adaptive Fading Extended Kalman Filtering for Mobile Robot Localization Using a Doppler–Azimuth Radar" *Electronics* 10, no. 20: 2544.
https://doi.org/10.3390/electronics10202544