# An Indoor Positioning and Tracking Algorithm Based on Angle-of-Arrival Using a Dual-Channel Array Antenna

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## Abstract

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## 1. Introduction

## 2. Array Antenna Angle-of-Arrival Positioning Algorithm

## 3. Proposed Tracking Algorithm

#### 3.1. Strong Tracking Kalman Filter

#### 3.2. Improved Tracking Algorithm

- (1)
- Calculate the one-step state prediction value according to Equation (19).
- (2)
- Calculate innovation vector according to ${r}_{k}={Z}_{k}-{H}_{k}{X}_{k,k-1}$.
- (3)
- Calculate the prediction error covariance matrix according to Equation (23).
- (4)
- Calculate the SVD factorization of ${P}_{k,k-1}$.
- (5)
- Calculate Kalman gain matrix according to Equation (31).
- (6)
- Status updates according to Equation (23).
- (7)
- Test information is constructed based on innovation vector and its covariance matrix according to Equation (32).
- (8)
- Huber function is used to construct adaptive factors according to Equation (33).
- (9)
- Update error covariance matrix according to Equation (23).

## 4. Experimental Validation

#### 4.1. Experimental Environment

#### 4.2. Empirical Positioning Algorithm

#### 4.3. Empirical Tracking Algorithm

#### 4.3.1. Empirical Source Rotation Positioning

#### 4.3.2. Empirical Dynamic Positioning

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Amplitude and phase of the single–-frame data after compensation. (

**a**) Amplitude after compensation. (

**b**) Phase after compensation.

**Figure 7.**The static test location results for the source location of (0, −1). (

**a**) Average error in the x-direction. (

**b**) Average error in the z-direction. (

**c**) Location distribution. (

**d**) CDF.

**Figure 8.**The static test location results for the source location of (2, 0). (

**a**) Average error in the x-direction. (

**b**) Average error in the z-direction. (

**c**) Location distribution. (

**d**) CDF.

**Figure 9.**The static test location results for the source location of (2, −1.5). (

**a**) Average error in the x-direction. (

**b**) Average error in the z-direction. (

**c**) Location distribution. (

**d**) CDF.

**Figure 10.**The source rotation test positioning results at the point (0, 0). (

**a**) Error in the x-direction. (

**b**) Error in the z-direction. (

**c**) CDF.

**Figure 11.**The source rotation test positioning results at the point (2, −1.5). (

**a**) Error in the x-direction. (

**b**) Error in the z-direction. (

**c**) CDF.

**Figure 12.**The strong tracking kalman filter (STKF) positioning results under the source rotation for the point (0, 0). (

**a**) Error in the x-direction. (

**b**) Error in the z-direction.

**Figure 13.**The STKF positioning results under the source rotation for the point (2, −1.5). (

**a**) Error in the x-direction. (

**b**) Error in the z-direction.

**Figure 14.**The singular value decomposition SVD–STKF positioning results under the source rotation for the point (0, 0). (

**a**) Error in the x-direction. (

**b**) Error in the z-direction.

**Figure 15.**The SVD–STKF positioning results under the source rotation for the point (2, −1.5). (

**a**) Error in the x-direction. (

**b**) Error in the z-direction.

**Figure 16.**Distribution of rotation anchor points of the source. (

**a**) (0, 0) location distribution. (

**b**) (2, −1.5) location distribution.

Point | Direction Component | Frequency (kHz) | Maximum Error (m) |
---|---|---|---|

(0, 0) | X | 254 | 0.208 |

256 | 0.415 | ||

252 | 0.377 | ||

Z | 254 | 0.125 | |

256 | 0.269 | ||

252 | 0.306 |

Point | Direction Component | Filter Method | Maximum Error (m) | RMS |
---|---|---|---|---|

(0, 0) | x | Raw Output | 0.21765 | 0.124 |

STKF | 0.215 | 0.122 | ||

SVD-STKF | 0.215 | 0.12 | ||

z | Raw output | 0.21765 | 0.109 | |

STKF | 0.191 | 0.107 | ||

SVD-STKF | 0.189 | 0.104 | ||

(2,−1.5) | x | Raw output | 0.541 | 0.255 |

STKF | 0.532 | 0.249 | ||

SVD-STKF | 0.47 | 0.223 | ||

z | Raw output | 0.247 | 0.125 | |

STKF | 0.227 | 0.119 | ||

SVD-STKF | 0.204 | 0.11 |

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**MDPI and ACS Style**

Li, C.; Zhen, J.; Chang, K.; Xu, A.; Zhu, H.; Wu, J.
An Indoor Positioning and Tracking Algorithm Based on Angle-of-Arrival Using a Dual-Channel Array Antenna. *Remote Sens.* **2021**, *13*, 4301.
https://doi.org/10.3390/rs13214301

**AMA Style**

Li C, Zhen J, Chang K, Xu A, Zhu H, Wu J.
An Indoor Positioning and Tracking Algorithm Based on Angle-of-Arrival Using a Dual-Channel Array Antenna. *Remote Sensing*. 2021; 13(21):4301.
https://doi.org/10.3390/rs13214301

**Chicago/Turabian Style**

Li, Chenhui, Jie Zhen, Kanglong Chang, Aigong Xu, Huizhong Zhu, and Jianxin Wu.
2021. "An Indoor Positioning and Tracking Algorithm Based on Angle-of-Arrival Using a Dual-Channel Array Antenna" *Remote Sensing* 13, no. 21: 4301.
https://doi.org/10.3390/rs13214301