#
Usage of Geometric Altitude for Radar Plot Position Improvements^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

#### 1.1. Barometric Altitude

#### 1.2. Geometric Altitude in ADS-B

#### 1.3. Three-Dimensional Height in Radars

#### 1.4. Radar Plot Positioning

#### 1.5. Geometric Altitude for Non-ADSB Aircraft

#### 1.6. Scope

- Analysis of geometric/barometric altitude offsets to estimate possible Radar plot position offsets.
- Evaluation of reconstruction of geometric altitudes for all aircraft (also without ADS-B capabilities).
- Comparison of a pressure/temperature-based reconstruction model to real-life meteorological data.
- Assessment of potential benefits by calculating the change in radar position accuracy comparing usage of barometric, reconstructed geometric, and 3D height information (as measured by the used Radar).

## 2. Results

#### 2.1. Geometric/Barometric Altitude Offsets

#### 2.2. Geometric Altitude Reconstruction

#### 2.3. Pressure/Temperature Reconstruction Assessment

#### 2.4. Comparison of Radar Plot Position Accuracy

## 3. Discussion

#### 3.1. Reconstruction Model

#### 3.2. Comparison of Radar Plot Position Accuracy

#### 3.3. Radar 3D Height

#### 3.4. Future Work

## 4. Methods

#### 4.1. Dataset

#### 4.2. Data Filtering

#### 4.2.1. ADS-B Filtering

- MOPS version of 2, NACp ≥ 4,
- Mode C code present, geometric altitude present and valid value (not 204793.75),
- Emitter category 3 or 5 (medium or heavy aircraft).

#### 4.2.2. Radar Filtering

- Data source is the analyzed Radar,
- Mode C code present, Mode C code not garbled, Mode C code valid,
- Three-dimensional height present,
- Mode C code > 100 (FL), range < 62.5 (nm).

#### 4.2.3. Loaded Data Counts

#### 4.3. ADS-B Binning

#### 4.4. Reconstruction Model

#### 4.5. Reconstruction Model Consistency

#### 4.6. Reference Data

#### 4.7. Position Accuracy Measurement

#### 4.8. Source Code

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- GPS Product Team. Global Positioning System (GPS) Standard Positioning Service (SPS) Performance Analysis Report; GPS Product Team: Washington, DC, USA, 2014. [Google Scholar]
- Barton, D.K.; Leonov, S.A. Radar Technology Encyclopedia; Artech House: Norwood, MA, USA, 1998. [Google Scholar]
- International Civil Aviation Organization. Manual on Automatic Meteorological Observing Systems at Aerodromes, 2nd ed.; International Civil Aviation Organization: Montreal, QC, Canada, 2011; Volume 9837. [Google Scholar]
- International Civil Aviation Organization. Manual of the ICAO Standard Atmosphere: Extended to 80 kilometres (262,500 feet); International Civil Aviation Organization: Montreal, QC, Canada, 1993; Volume 7488. [Google Scholar]
- Cavcar, M. The international standard atmosphere (ISA). Anadolu Univ. Turk.
**2000**, 30, 1–6. [Google Scholar] - Moré, J.J. The Levenberg-Marquardt algorithm: Implementation and theory. In Numerical Analysis; Springer: Berlin/Heidelberg, Germany, 1978; pp. 105–116. [Google Scholar]
- Specification for Surveillance Data Exchange ASTERIX, Part 12 Category 021, ADS-B Target Reports, 2.6 ed.; EUROCONTROL: Brussels, Belgium, 2021.

**Figure 1.**Geometric/Barometric Altitude Offsets. (

**a**) Altitude Error Distribution. (

**b**) Altitude Error Distribution over Barometric Flight Level.

**Figure 3.**Altitude Error Distributions and Vienna Airport Model Cell. (

**a**) Error Distributions. (

**b**) Vienna Airport Altitude Data and Reconstructed Model ${p}_{0},{t}_{0}$.

**Figure 4.**Vienna Airport Reconstructed Parameters Comparison. (

**a**) Pressure ${p}_{0}$ Comparison. (

**b**) Temperature ${t}_{0}$ Comparison.

**Figure 5.**Offset (connected points) and Standard Deviation (dashed lines) Comparison (in 30 min Intervals). (

**a**) Cartesian Offsets. (

**b**) Ground Range Offsets.

Term | Description | Comment |
---|---|---|

p | Pressure at altitude | hPa |

${p}_{0}$ | Standard pressure at MSL | 1013.25 hPa |

$\alpha $ | Temperature gradient over altitude | 0.0065 K/m |

${t}_{0}$ | Standard temperature at MSL | 273.15 + 15 °K |

h | Altitude | m |

${g}_{0}$ | Acceleration of gravity | 9.81 m/s^{2} |

R | Gas constant | 287 J/(kg K) |

**Table 2.**Gaussian Parameters of Error Distributions in Figure 3a.

Parameter | Mean (m) | Std.Dev. (m) |
---|---|---|

Geo-Baro | 379.24 | 85.20 |

Geo-Reconst | 7.95 | 6.82 |

**Table 3.**Gaussian Parameters of Full Series in Figure 5.

Offset Type | Altitude Source | Mean | Std.Dev. |
---|---|---|---|

Cartesian (m) | Barometric | 90.97 | 40.75 |

Geometric | 49.30 | 32.77 | |

3D Height | 147.30 | 440.20 | |

Azimuth (deg) | (same for all) | 0.0122 | 0.0382 |

Ground Range (m) | Barometric | −75.60 | 42.96 |

Geometric | −15.81 | 29.68 | |

3D Height | −83.43 | 454.02 |

Data Source | ASTERIX | Usage |
---|---|---|

ADS-B | CAT021 | Generate reconstruction model |

Analyzed Radar | CAT048 | Accuracy improvement assessment test data |

Tracker | CAT062 | Accuracy improvement assessment reference |

Data Source | ASTERIX | Count |
---|---|---|

Analyzed Radar | CAT048 | 392,040 |

ADS-B | CAT021 | 4,217,366 |

Tracker | CAT062 | 3,057,776 |

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**MDPI and ACS Style**

Puhr, H.
Usage of Geometric Altitude for Radar Plot Position Improvements. *Eng. Proc.* **2022**, *28*, 8.
https://doi.org/10.3390/engproc2022028008

**AMA Style**

Puhr H.
Usage of Geometric Altitude for Radar Plot Position Improvements. *Engineering Proceedings*. 2022; 28(1):8.
https://doi.org/10.3390/engproc2022028008

**Chicago/Turabian Style**

Puhr, Helmut.
2022. "Usage of Geometric Altitude for Radar Plot Position Improvements" *Engineering Proceedings* 28, no. 1: 8.
https://doi.org/10.3390/engproc2022028008