# An Advanced Data Processing Algorithm for Extraction of Polarimetric Radar Signatures of Moving Automotive Vehicles Using the H/A/α Decomposition Technique

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Fully Polarimetric Radar

^{−1}, which is equivalent to $0.31$ km h

^{−1}, as the number of sweeps per burst ${N}_{Sweeps}$ is usually 512 [34]. This is equivalent to an integration time ${T}_{i}$ of approximately $0.52$ $\mathrm{s}$. Moreover, this radar has a maximum unambiguous radial velocity of ${v}_{r}^{max}$ of ±$22.1$ ms

^{−1}, which is equivalent to ±$79.8$ km h

^{−1}and which might be a limitation of the tracking performance, as the actual velocity measurement may be incorrect. As the radar utilizes this FMCW waveform, ambiguity issues in the range domain will not occur within the operational ranges in this research.

#### 2.2. Data Acquisition

^{−1}.

#### 2.3. Signal and Data Processing Chain

#### 2.3.1. Range-Doppler Processing

^{−1}, a sixth-order Butterworth high-pass filter (HPF) with its cut-off frequency at 122 Hz, equivalent to 20 km h

^{−1}, was applied [1]. From prior knowledge of the area of interest, it was assumed that the targets were not moving orthogonal to the radar view angle such that the radial velocity of the moving vehicles was near 0 km h

^{−1}and filtered out as well. After the Doppler processing steps of 512 pulses per time frame, the strong reflections of the moving vehicles can clearly be seen in the range-Doppler map, as shown in Figure 5.

#### 2.3.2. Polarimetric Data Fusion

#### 2.3.3. Target Detection and Clustering

#### 2.3.4. Multi-Target Tracking

#### 2.4. H/A/α Decomposition

## 3. Results

#### 3.1. Tracking Performance

^{−1}to 100 km h

^{−1}and from −60 km h

^{−1}to 100 km h

^{−1}. Its acceleration was initialized by following a normal distribution with a mean of 0 and a standard deviation of $0.1$. Each target’s true state was updated according to a dynamic model while assuming constant acceleration. Additive white Gaussian noise was added to the target’s centroid at each time frame, resulting in a noisy track of a point target in the range-velocity domain. In order to mimic real-world targets, each point target was dilated with a disk-shaped element. The simulation results are presented in Figure 8, showing the true trajectory and output of the tracking algorithm.

^{−1}, respectively.

#### 3.2. Analysis of Polarimetric Signatures

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CA-CFAR | Cell averaging CFAR |

CFAR | Constant false alarm rate |

DBSCAN | Density-based spatial clustering of applications with noise |

FFT | Fast Fourier transform |

FMCW | Frequency-modulated continuous-wave |

FPGA | Field-programmable gate array |

GOCA-CFAR | Greatest of cell averaging CFAR |

GNN | Global nearest neighbor |

HPF | High-pass filter |

LFM | Linear frequency modulated |

LRT | Likelihood ratio test |

MHT | Multiple hypothesis tracking |

MTT | Multi-target tracking |

OPD | Optimal polarimetric detector |

OS-CFAR | Ordered statistics CFAR |

PMF | Polarimetric matched filter |

PMSD | Polarimetric maximization synthesis detector |

PSM | Polarization scattering matrix |

PWF | Polarization whitening filter |

RCS | Radar cross-section |

RMSE | Root mean square error |

SAR | Synthetic aperture radar |

SD | Span detector |

SNR | Signal-to-noise ratio |

SOCA-CFAR | Smallest of cell averaging CFAR |

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**Figure 1.**A pair of time-shifted LFM signals transmitted with horizontal and vertical polarization, illustrated in the chirp frequency domain (with the sounding signals indicated by solid thick red and blue lines, the received signals by thin solid lines, and the received signals with the maximum delay/distance from the radar by dashed lines). More details can be found in [37].

**Figure 2.**A map illustrating the location of the PARSAX radar and the illuminated area. The area of interest used for this analysis is indicated by black lines.

**Figure 3.**Signal and data processing chain for the four polarization receiver channels, where ${s}_{H}\left(t\right)$ and ${s}_{V}\left(t\right)$ represent the transmitted waveforms used for deramping the received signals for further processing.

**Figure 4.**A range-Doppler map of real-world data representing a dense highway, visualizing moving vehicles and static clutter. This map originated from the HH channel, the other polarization channels (HV, VH, and VV) showed similar results. The red box around zero Doppler velocity shows the area of analyzed clutter signals.

**Figure 5.**A range-Doppler map of real-world data representing a dense highway, visualizing only moving vehicles. This map originated from the HH channel, and the other polarization channels (HV, VH, and VV) showed similar results.

**Figure 6.**Resulting detection map and clusters (indicated by red boxes) after applying polarimetric data fusion and the OS-CFAR detector.

**Figure 8.**Synthesized trajectories (indicated in black) and their corresponding estimations (indicated in red) as a result of the proposed multi-target tracking algorithm in the range-velocity domain of ${N}_{T}=20$ targets for ${T}_{sim}\approx 15\mathrm{s}$.

**Figure 9.**(

**a**) The true and estimated range of target ${T}_{5}$ over time with (

**b**) the corresponding RMSE, expressed in terms of the range resolution $\Delta R$, as well as (

**c**) the true and estimated velocity of target ${T}_{5}$ over time with (

**d**) the corresponding RMSE, expressed in terms of the velocity resolution $\Delta {v}_{r}$.

**Figure 10.**Estimated trajectories in the range-velocity domain of vehicles on a highway after 20 time frames. For each target, the estimated trajectory, estimated current state ${\widehat{\mathbf{x}}}_{k|k}$, predicted state ${\widehat{\mathbf{x}}}_{k|k-1}$, and corresponding associated measurement ${\mathbf{z}}_{k}^{i}$ are plotted.

**Figure 11.**Two-dimensional histogram in the H/$\alpha $ plane, based on time averaging of the coherency matrix ${\mathbf{T}}_{time}$ of (

**a**) moving automotive vehicles and (

**b**) static clutter.

**Figure 12.**Two-dimensional histogram in the H/$\alpha $ plane, based on spatial averaging of the coherency matrix ${\mathbf{T}}_{space}$ of (

**a**) moving automotive vehicles and (

**b**) static clutter.

**Figure 13.**Feature space with the mean entropy H against the mean angle $\alpha $, based on spatial averaging of the coherency matrix ${\mathbf{T}}_{space}$ of target scattering and static clutter scattering.

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

System characteristics | Center frequency (${f}_{c}$) | $3.315$ GHz |

Modulation bandwidth (B) | up to 50 MHz | |

Sweep time (${T}_{s}$) | 1 $\mathrm{m}$$\mathrm{s}$ | |

Effective bandwidth (${B}_{eff}$) | up to 45 MHz | |

Range resolution ($\Delta R$) | up to 3.3 m | |

Power characteristics | Maximum power per channel | 100 W |

Transmitter attenuation | up to 80 dB | |

Transmitter parabolic antenna | Antenna diameter | $4.28$ m |

Antenna beamwidth | 1.8° | |

Antenna gain | $40.0$ dB | |

Receiver parabolic antenna | Antenna diameter | $2.12$ m |

Antenna beamwidth | 4.6° | |

Antenna gain | $32.8$ dB | |

TX-RX isolation | HH-polarized | $-100$ dB |

VV-polarized | $-85$ dB | |

ADC characteristics | Maximum sampling frequency | 400 MHz |

ADC resolution | 14-bit | |

Spur-free dynamic range | ≥70 dB |

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**MDPI and ACS Style**

Bosma, D.A.; Krasnov, O.A.; Yarovoy, A.
An Advanced Data Processing Algorithm for Extraction of Polarimetric Radar Signatures of Moving Automotive Vehicles Using the *H*/*A*/*α* Decomposition Technique. *Remote Sens.* **2023**, *15*, 1060.
https://doi.org/10.3390/rs15041060

**AMA Style**

Bosma DA, Krasnov OA, Yarovoy A.
An Advanced Data Processing Algorithm for Extraction of Polarimetric Radar Signatures of Moving Automotive Vehicles Using the *H*/*A*/*α* Decomposition Technique. *Remote Sensing*. 2023; 15(4):1060.
https://doi.org/10.3390/rs15041060

**Chicago/Turabian Style**

Bosma, Detmer A., Oleg A. Krasnov, and Alexander Yarovoy.
2023. "An Advanced Data Processing Algorithm for Extraction of Polarimetric Radar Signatures of Moving Automotive Vehicles Using the *H*/*A*/*α* Decomposition Technique" *Remote Sensing* 15, no. 4: 1060.
https://doi.org/10.3390/rs15041060