# Improved 2D Ground Target Tracking in GPS-Based Passive Radar Scenarios

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## Abstract

**:**

## 1. Introduction

## 2. System Operation Principle

#### 2.1. GPS Passive Radar Geometry

#### 2.2. GPS Passive Radar Signal Processing

## 3. Ground Target 2D Localization Scheme

#### 3.1. First Stage Spatial Filtering

- To form the first set of simultaneous beams, digital beamforming techniques were selected under the requirement of sidelobe level control to generate orthogonal beams along with the azimuth sector of the single radiating element. An iterative process was followed to define the N orthogonal beam steering angles, ${\mathrm{\Phi}}_{SLL}=\{{\varphi}_{SLL,1},{\varphi}_{SLL,2},\dots ,{\varphi}_{SLL,N}\}$. The process starts with the first lobe steered to the broadside, then the steering direction of the adjacent lobes is adjusted to the first null of the initial beam. The process continues with the following adjacent lobes until the entire azimuthal sector of a single radiating element is covered.
- The orthogonal beams design procedure reduces the contribution to signal power in the current beam of targets whose DoAs are the steering directions of adjacent beams. However, the decrease in gain with respect to the maximum at the intersection points of the beams can be greater than 3 dB, negatively affecting the echoes of the targets in those directions (Figure 4). As the main objective of this first stage of spatial filtering is to improve target echoes SNR to allow their detection, beamforming gain losses should be minimized along the whole coverage area. Therefore, a second set of N − 1 steering angles, ${\mathrm{\Phi}}_{LI}=\{{\varphi}_{LI,1},{\varphi}_{LI,2},\dots ,{\varphi}_{LI,N-1}\}$, was defined according to the crossing points of the previous orthogonal beams. Both steering angle sets are merged together in a steering vector to continue the design process, ${\mathrm{\Phi}}_{D}=[{\mathrm{\Phi}}_{SLL},{\mathrm{\Phi}}_{LI}]$.
- The optimization problem was solved for each steering direction and Doppler shift pair (${\varphi}_{D,i}$,p) to compute the weight vector ${\mathbf{w}}_{D}(p,{\varphi}_{D,i})$. Applying the weight vectors to the corresponding snapshots in the transformed domain (6), a three dimensional matrix, ${\mathbf{S}}_{\mathbf{CAF}}[m,p,{\varphi}_{D,i}]$ is obtained.$$\begin{array}{c}{\mathbf{S}}_{\mathbf{CAF}}[m,p,{\varphi}_{D,i}]={\mathbf{w}}_{D}{(p,{\varphi}_{D,i})}^{H}\xb7{\mathbf{s}}_{s}[m,p]\\ \phantom{\rule{1.em}{0ex}}i=1,\cdots ,2N-1\end{array}$$

#### 3.2. Detection Stage

#### 3.3. Second Stage Spatial Filtering

#### 3.4. Target Localization

#### 3.5. Estimation of the Initial Target Velocity

## 4. Target Tracking

## 5. Simulation Results

## 6. Results with Real Data

#### 6.1. Radar Scenario

#### 6.2. Results

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**PR scenario based on satellite IoO, consisting of a hemispherical reference antenna to allow acquisition of all GPS signals in line of sight, and a surveillance array to acquire targets echoes.

**Figure 5.**Target’s range estimation by means of 5 points around the maximum. The real target range is 125 m, while the maximum of the CAF is obtained at 132 m. The estimated range with this approach is 124.1 m.

**Figure 8.**Results for the simulated radar scenario: (

**a**) confirmed detections and associated tracks in the measurement space (range-Doppler); (

**b**) Cartesian space tracking results (+ marker) and reference targets’ path presented in Figure 7 (solid line).

**Figure 10.**Trials radar scenario: (

**a**) top view with PR location, satellite direction (PRN32), area of interest (green area), cooperative target trajectory from GPS data (purple line), buildings and sport facilities details are shown in pictures with their associated area; (

**b**) ground view of the AoI, cooperative vehicle and PR receiver deployment.

**Figure 11.**Real radar data results: first stage spatial filtering. (

**a**) RDM from single array element. (

**b**) RDM after beamforming (12.5${}^{\circ}$ beam).

**Figure 12.**Real radar data results: Cumulative detection output in measurement and tracking domain. (

**a**) RDM. (

**b**) Local Cartesian space.

**Figure 13.**Localization results for a cooperative target: (

**a**) Google Earth view of the cooperative target’s estimated position (green) versus target GPS data (purple); (

**b**) Estimated localization error for the cooperative target.

**Figure 14.**Localization results for non-cooperative targets moving away from PR location (blue and red). (

**a**) First non-cooperative target. (

**b**) Second non-cooperative target.

Simulated Data | Real Data | |||||||
---|---|---|---|---|---|---|---|---|

Targ 1 | Targ 2 | Targ 3 | Targ 4 | Targ 5 | Targ 6 | Total | Coop. Targ | |

$\mu $ [m] | 4.44 | 10.76 | 6.65 | 2.96 | 3.09 | 11.19 | 7.46 | 2.38 |

$\sigma $ [m] | 3.5 | 10.76 | 5.57 | 7.86 | 5.38 | 9.31 | 7.77 | 1.58 |

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**MDPI and ACS Style**

Gomez-del-Hoyo, P.; del-Rey-Maestre, N.; Jarabo-Amores, M.-P.; Mata-Moya, D.; Benito-Ortiz, M.-d.-C.
Improved 2D Ground Target Tracking in GPS-Based Passive Radar Scenarios. *Sensors* **2022**, *22*, 1724.
https://doi.org/10.3390/s22051724

**AMA Style**

Gomez-del-Hoyo P, del-Rey-Maestre N, Jarabo-Amores M-P, Mata-Moya D, Benito-Ortiz M-d-C.
Improved 2D Ground Target Tracking in GPS-Based Passive Radar Scenarios. *Sensors*. 2022; 22(5):1724.
https://doi.org/10.3390/s22051724

**Chicago/Turabian Style**

Gomez-del-Hoyo, Pedro, Nerea del-Rey-Maestre, María-Pilar Jarabo-Amores, David Mata-Moya, and María-de-Cortés Benito-Ortiz.
2022. "Improved 2D Ground Target Tracking in GPS-Based Passive Radar Scenarios" *Sensors* 22, no. 5: 1724.
https://doi.org/10.3390/s22051724