# An SOCP Estimator for Hybrid RSS and AOA Target Localization in Sensor Networks

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## Abstract

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## 1. Introduction

## 2. Problem Formulation

## 3. The Proposed SOCP Estimator

## 4. Complexity Analysis

## 5. Numerical Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Illustration of a target and anchor in three-dimensional space, and the distance and bearing information between them.

**Figure 3.**RMSE versus number of anchors, N, when $\gamma =2.5$, ${\gamma}_{i}\sim \mathcal{U}[2.2,2.8]$, $B=25$ m, $Mc=5000$. (

**a**) ${\sigma}_{{n}_{i}}=4$ dB, ${\kappa}_{i}=45.8447$ (i.e., ${\sigma}_{{m}_{i}}={\sigma}_{{\mathit{v}}_{i}}=6$ deg); (

**b**) ${\sigma}_{{n}_{i}}=5$ dB, ${\kappa}_{i}=25.9034$ (i.e., ${\sigma}_{{m}_{i}}={\sigma}_{{\mathit{v}}_{i}}=8$ deg); (

**c**) ${\sigma}_{{n}_{i}}=6$ dB, ${\kappa}_{i}=16.6760$ (i.e., ${\sigma}_{{m}_{i}}={\sigma}_{{\mathit{v}}_{i}}=10$ deg).

**Figure 4.**CDF versus LE (m), when $N=6$, $\gamma =2.5$, ${\gamma}_{i}\sim \mathcal{U}[2.2,2.8]$, $B=25$ m, $Mc=5000$. (

**a**) ${\sigma}_{{n}_{i}}=4$ dB, ${\kappa}_{i}=45.8447$ (i.e., ${\sigma}_{{m}_{i}}={\sigma}_{{\mathit{v}}_{i}}=6$ deg). (

**b**) ${\sigma}_{{n}_{i}}=5$ dB, ${\kappa}_{i}=25.9034$ (i.e., ${\sigma}_{{m}_{i}}={\sigma}_{{\mathit{v}}_{i}}=8$ deg). (

**c**) ${\sigma}_{{n}_{i}}=6$ dB, ${\kappa}_{i}=16.6760$ (i.e., ${\sigma}_{{m}_{i}}={\sigma}_{{\mathit{v}}_{i}}=10$ deg).

Algorithm | Complexity |
---|---|

SOCP in (11) | $\mathcal{O}\left({N}^{3.5}\right)$ |

ECWLS in [24] | $2\mathcal{O}\left(N\right)$ |

RLS-SDP in [27] | $2\mathcal{O}\left({N}^{4.5}\right)$ |

SRLS-SDP in [27] | $2\mathcal{O}\left({N}^{4.5}\right)$ |

SD-SOCP in [28] | $\mathcal{O}\left({N}^{3.5}\right)$ |

SOCP1 in [30] | $\mathcal{O}\left({N}^{3.5}\right)$ |

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**MDPI and ACS Style**

Costa, M.S.; Tomic, S.; Beko, M.
An SOCP Estimator for Hybrid RSS and AOA Target Localization in Sensor Networks. *Sensors* **2021**, *21*, 1731.
https://doi.org/10.3390/s21051731

**AMA Style**

Costa MS, Tomic S, Beko M.
An SOCP Estimator for Hybrid RSS and AOA Target Localization in Sensor Networks. *Sensors*. 2021; 21(5):1731.
https://doi.org/10.3390/s21051731

**Chicago/Turabian Style**

Costa, Marcelo Salgueiro, Slavisa Tomic, and Marko Beko.
2021. "An SOCP Estimator for Hybrid RSS and AOA Target Localization in Sensor Networks" *Sensors* 21, no. 5: 1731.
https://doi.org/10.3390/s21051731