# Energy Efficient Received Signal Strength-Based Target Localization and Tracking Using Support Vector Regression

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## Abstract

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## 1. Introduction

- An SVR-based L&T model fed with RSSI measurements was proposed to solve the problem of dynamicity in RSSI measurements as well as indoor environments, and it was compared with a well-known trilateration-based L&T scheme for the same RSSI measurements through rigorous localization accuracy simulations. Here, the trilateration and the proposed SVR-based scheme were fed with six and three RSSI measurements, respectively. The energy consumption during the target L&T for these two approaches were also compared.
- Further, the target location estimations obtained using the proposed SVR scheme were run through a standard Kalman Filter (KF) for further refinement, and named as SVR+KF. The proposed SVR+KF framework was evaluated against trilateration and plain SVR-based schemes. Out of these three schemes, the SVR+KF-based scheme provided the lowest error in estimating the target location.
- We also tested the impact of the kernel function on target-tracking accuracy with the proposed SVR+KF algorithm. In this work, we tested four popular SVM kernel functions, namely, linear, sigmoid, RBF, and polynomial, during simulations in case I to case IV, respectively. In the target motion in all of these cases, the target was assumed to have high variation in the target velocity during its motion, and high maneuverability in trajectory. The noise in the RSSI measurements was kept the same for all four cases. The simulation results showed that the fusion of SVR and KF (i.e., the SVR+KF localization scheme) was highly accurate, consistent, and reliable in estimating target locations with the four considered types of kernels.

## 2. Related Work

## 3. SVR for the Target L&T

_{,}and $w$ are the SVR coefficients, and $z$ is any given RSSI input vector. The optimized model corresponding to Equation (2) is given below [12]:

- (i)
- Linear Kernel

- (ii)
- Sigmoid Kernel

- (iii)
- RBF Kernel

- (iv)
- Polynomial Kernel

## 4. System Design and Assumptions of the Proposed SVR-Based L&T System

_{1}to RSSI

_{6}. The key simulation parameters for this study are given in Table 2.

^{t}RSSI and N ACKs with bit duration

^{t}ACK, the energy consumption for the estimation of the distance for one anchor node is given as follows [14]:

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Case I: the impact of linear kernel on SVR-based target localization. (

**a**) Location estimates with trilateration, SVR, and SVR+KF against actual target trajectory, (

**b**) localization error with trilateration, SVR, and SVR+KF along the x direction, (

**c**) localization error with trilateration, SVR, and SVR+KF along the y direction, (

**d**) localization error with trilateration, SVR, and SVR+KF along the x–y direction estimates of the mobile target obtained with trilateration, SVR, and SVR+KF.

**Figure 5.**Case II: impact of the sigmoid kernel on SVR-based target localization. (

**a**) Location estimates with trilateration, SVR, and SVR+KF against the actual target trajectory, (

**b**) localization error with trilateration, SVR, and SVR+KF along the x direction, (

**c**) localization error with trilateration, SVR, and SVR+KF along the y direction, (

**d**) localization error with trilateration, SVR, and SVR+KF along the x–y direction.

**Figure 6.**Case III: impact of the RBF Kernel on SVR-based target localization. (

**a**) Location estimates with trilateration, SVR, and SVR+KF against the actual target trajectory, (

**b**) localization error with trilateration, SVR, and SVR+KF along the x direction, (

**c**) localization error with trilateration, SVR, and SVR+KF along the y direction, (

**d**) localization error with trilateration, SVR, and SVR+KF along the x–y direction.

**Figure 7.**Case IV: impact of polynomial kernel on SVR-based target localization. (

**a**) Location estimates with trilateration, SVR, and SVR+KF against the actual target trajectory, (

**b**) localization error with trilateration, SVR, and SVR+KF along the x direction, (

**c**) localization error with trilateration, SVR, and SVR+KF along the y direction, (

**d**) localization error with trilateration, SVR, and SVR+KF along the x–y direction.

Anchor Node Number | 2-D Location | Anchor Node Number | 2-D Location |
---|---|---|---|

AN1 | (30, 25) | AN4 | (30, 90) |

AN2 | (10, 60) | AN5 | (80, 60) |

AN3 | (50, 50) | AN6 | (70, 90) |

Parameter | Value |
---|---|

Initial Target State X_{0} at k = 0 | (12, 16) |

receiver and transmitter antenna gains | 1 dB |

AN communication radius | 30 m |

Transmission power | 1 mW |

Path Loss Exponent $\eta $ | 3 |

Discretization time step dt | 1 s |

${X}_{\sigma}$ | ~N(3, 1) |

Sigmoid Kernel Function Constant 𝛾 | 1/17 |

Sigmoid Kernel Function Constant 𝛽 | 0 |

Polynomial Kernel Function Constant 𝛾 | 1/17 |

Polynomial Kernel Function Constant 𝑐 | 0 |

Degree of the polynomial for Polynomial Kernel Function 𝑑 | 3 |

Microcontroller | ||
---|---|---|

Parameter | Value | Unit |

Current draw in active state | 8 | mA |

Wake up time | 1 | ms |

Transceiver | ||

Current draw RX | 16 | mA |

Current draw TX, 3 dB | 17 | mA |

Current draw TX, −17 dB | 10 | mA |

Wake up time | 1 | ms |

Bit Rate | 250 | kbps |

L&T Scheme | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{x}}$ (in Meters) | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{y}}$ (in Meters) | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{a}\mathit{v}\mathit{g}}$ (in Meters) | $\mathit{A}\mathit{v}\mathit{e}\mathit{r}\mathit{a}\mathit{g}\mathit{e}\text{}\mathit{L}\mathit{o}\mathit{c}\mathit{a}\mathit{l}\mathit{i}\mathit{z}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\text{}\mathit{E}\mathit{r}\mathit{r}\mathit{o}\mathit{r}$ (in Meters) | Total Energy Consumption |
---|---|---|---|---|---|

Trilateration | 21.62 | 14.16 | 17.89 | 11.65 | 2.50 J |

SVR (Proposed) | 5.95 | 5.55 | 5.75 | 3.92 | 1.89 mJ |

SVR+KF (Proposed) | 0.13 | 0.09 | 0.11 | 0.1 | 2.22 mJ |

L&T Scheme | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{x}}$ (in Meters) | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{y}}$ (in Meters) | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{a}\mathit{v}\mathit{g}}$ (in Meters) | $\mathit{A}\mathit{v}\mathit{e}\mathit{r}\mathit{a}\mathit{g}\mathit{e}\text{}\mathit{L}\mathit{o}\mathit{c}\mathit{a}\mathit{l}\mathit{i}\mathit{z}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\text{}\mathit{E}\mathit{r}\mathit{r}\mathit{o}\mathit{r}$ (in Meters) | Total Energy Consumption |
---|---|---|---|---|---|

Trilateration | 16.61 | 10.96 | 13.79 | 10.70 | 2.50 J |

SVR (Proposed) | 18.01 | 15.71 | 16.86 | 12.93 | 2.31 mJ |

SVR+KF (Proposed) | 0.39 | 0.05 | 0.22 | 1.22 | 2.78 mJ |

L&T Scheme | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{x}}$ (in Meters) | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{y}}$ (in Meters) | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{a}\mathit{v}\mathit{g}}$ (in Meters) | $\mathit{A}\mathit{v}\mathit{e}\mathit{r}\mathit{a}\mathit{g}\mathit{e}\text{}\mathit{L}\mathit{o}\mathit{c}\mathit{a}\mathit{l}\mathit{i}\mathit{z}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\text{}\mathit{E}\mathit{r}\mathit{r}\mathit{o}\mathit{r}$ (in Meters) | Total Energy Consumption |
---|---|---|---|---|---|

Trilateration | 15.03 | 10.30 | 12.67 | 10.15 | 2.50 J |

SVR (Proposed) | 18.77 | 16.63 | 17.70 | 13.56 | 2.56 mJ |

SVR+KF (Proposed) | 0.64 | 0.14 | 0.39 | 1.52 | 2.95 mJ |

L&T Scheme | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{x}}$ (in Meters) | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{y}}$ (in Meters) | $\mathit{R}\mathit{M}\mathit{S}{\mathit{E}}_{\mathit{a}\mathit{v}\mathit{g}}$ (in Meters) | Total Energy Consumption | |
---|---|---|---|---|---|

Trilateration | 16.07 | 10.94 | 13.50 | 10.71 | 2.50 J |

SVR (Proposed) | 3.95 | 13.45 | 8.70 | 7.05 | 1.68 mJ |

SVR+KF (Proposed) | 0.11 | 0.03 | 0.07 | 0.95 | 2.12 mJ |

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**MDPI and ACS Style**

Molla, J.P.; Dhabliya, D.; Jondhale, S.R.; Arumugam, S.S.; Rajawat, A.S.; Goyal, S.B.; Raboaca, M.S.; Mihaltan, T.C.; Verma, C.; Suciu, G.
Energy Efficient Received Signal Strength-Based Target Localization and Tracking Using Support Vector Regression. *Energies* **2023**, *16*, 555.
https://doi.org/10.3390/en16010555

**AMA Style**

Molla JP, Dhabliya D, Jondhale SR, Arumugam SS, Rajawat AS, Goyal SB, Raboaca MS, Mihaltan TC, Verma C, Suciu G.
Energy Efficient Received Signal Strength-Based Target Localization and Tracking Using Support Vector Regression. *Energies*. 2023; 16(1):555.
https://doi.org/10.3390/en16010555

**Chicago/Turabian Style**

Molla, Jahir Pasha, Dharmesh Dhabliya, Satish R. Jondhale, Sivakumar Sabapathy Arumugam, Anand Singh Rajawat, S. B. Goyal, Maria Simona Raboaca, Traian Candin Mihaltan, Chaman Verma, and George Suciu.
2023. "Energy Efficient Received Signal Strength-Based Target Localization and Tracking Using Support Vector Regression" *Energies* 16, no. 1: 555.
https://doi.org/10.3390/en16010555