Sensing Accuracy Optimization for Communication-assisted Dual-baseline UAV-InSAR

Dual-baseline InSAR sensing system comprising one master and two slave UAV-SAR systems as well as a ground station (GS) for real-time data offloading.

Sensing Accuracy Optimization for Communication-assisted Dual-baseline UAV-InSAR

Mohamed-Amine Lahmeri∗, Vıctor Mustieles-Perez∗†, Martin Vossiek∗, Gerhard Krieger∗†,
and Robert Schober∗
∗Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg (FAU), Germany
†German Aerospace Center (DLR), Microwaves and Radar Institute, Weßling, Germany

Electrical Engineering and Systems Science > Signal Processing

[Submitted on 24 Oct 2024 (v1), last revised 2 Nov 2024 (this version, v2)]

Mohamed-Amine Lahmeri, Víctor Mustieles-Pérez, Martin Vossiek, Gerhard Krieger, Robert Schober

In this paper, we study the optimization of the sensing accuracy of unmanned aerial vehicle (UAV)-based dual-baseline interferometric synthetic aperture radar (InSAR) systems. A swarm of three UAV-synthetic aperture radar (SAR) systems is deployed to image an area of interest from different angles, enabling the creation of two independent digital elevation models (DEMs). To reduce the InSAR sensing error, i.e., the height estimation error, the two DEMs are fused based on weighted averaging techniques into one final DEM. The heavy computations required for this process are performed on the ground. To this end, the radar data is offloaded in real time via a frequency division multiple access (FDMA) air-to-ground backhaul link. In this work, we focus on improving the sensing accuracy by minimizing the worst-case height estimation error of the final DEM. To this end, the UAV formation and the power allocated for offloading are jointly optimized based on alternating optimization (AO), while meeting practical InSAR sensing and communication constraints. Our simulation results demonstrate that the proposed solution can significantly improve the sensing accuracy compared to classical single-baseline UAV-InSAR systems and other benchmark schemes.

Subjects:	Signal Processing (eess.SP)
Cite as:	arXiv:2410.18848 [eess.SP]
	(or arXiv:2410.18848v2 [eess.SP] for this version)
	https://doi.org/10.48550/arXiv.2410.18848

Submission history

From: Mohamed-Amine Lahmeri [view email]
[v1] Thu, 24 Oct 2024 15:29:13 UTC (963 KB)
[v2] Sat, 2 Nov 2024 11:41:41 UTC (1,283 KB)

Summary

Here's a summary of this research paper on optimizing UAV-based interferometric synthetic aperture radar (InSAR) systems:

1. Research Focus:

• - Studies optimization of sensing accuracy for dual-baseline UAV-InSAR systems
• - Uses three UAVs (one master, two slaves) to create two independent digital elevation models (DEMs)
• - The DEMs are fused into a final model using weighted averaging techniques

2. Technical Approach:

• - Employs frequency division multiple access (FDMA) for real-time data transmission to ground
• - Optimizes both UAV formation and power allocation for communication
• - Aims to minimize worst-case height estimation error while meeting various constraints
• - Uses alternating optimization (AO) and successive convex approximation (SCA) techniques

3. Key Innovations:

• - Develops an approximate bi-static SNR expression
• - Derives a tractable upper bound for height error in the final DEM
• - Creates a joint optimization solution for UAV positioning and power allocation
• - Proposes algorithms that handle both communication and sensing constraints

4. Results:

• - The proposed solution significantly outperforms classical single-baseline UAV-InSAR systems
• - Achieves at least 49% improvement compared to single-baseline systems
• - Shows 23.6% better performance compared to fixed master UAV position
• - Demonstrates 8.2% improvement over static power allocation schemes

5. Practical Implications:

• - Enables better 3D radar imaging for applications like mapping and monitoring
• - Improves accuracy of height measurements in challenging conditions
• - Provides real-time data processing capabilities
• - Offers flexible deployment options for various remote sensing tasks

The research represents a significant advancement in UAV-based radar imaging systems, particularly for applications requiring precise height measurements and real-time data processing.

Authors

• - Mohamed-Amine Lahmeri (Linkedin)
  
• - Víctor Mustieles-Pérez
• - Martin Vossiek
• - Gerhard Krieger
• - Robert Schober

Institutions:

1. Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany   - All authors are affiliated with FAU
2. German Aerospace Center (DLR), Microwaves and Radar Institute, Weßling, Germany   - Víctor Mustieles-Pérez and Gerhard Krieger have dual affiliations with DLR

Prior Related Works:
The authors cite several of their own recent related works:

1. M.-A. Lahmeri et al.:
- "Robust trajectory and resource optimization for communication-assisted UAV SAR sensing" (2024)
- "Trajectory and resource optimization for UAV synthetic aperture radar" (2022)
- "UAV formation optimization for communication-assisted InSAR sensing" (2024)

2. V. Mustieles-Perez et al.:
- "New insights into wideband synthetic aperture radar interferometry" (2024)

3. G. Krieger was involved in seminal work on satellite SAR:
- "TanDEM-X: A satellite formation for high-resolution SAR interferometry" (2007)

The authors appear to be building on their previous work in UAV-based radar systems, trajectory optimization, and interferometry. The combination of authors from both a university (FAU) and a major aerospace research center (DLR) suggests a strong mix of academic and practical expertise in radar systems and UAV technology.

This research was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 437847244.

Figures and Tables

Here are the figures and tables from the paper, along with their purpose:

Figures:

1. Figure 1: Dual-baseline InSAR sensing system diagram
- Shows the physical setup of the system
- Illustrates one master and two slave UAVs
- Includes ground station for real-time data offloading
- Demonstrates the geometric relationships between components

2. Figure 2: Block diagram of the proposed solution
- Shows the structure of the alternating optimization (AO) algorithm
- Illustrates how the problem is broken down into sub-problems
- Demonstrates the flow between optimization steps for different UAVs
- Shows relationships between different optimization components

3. Figure 3: Height error vs minimum Height of Ambiguity (HoA)
- Compares performance of proposed scheme against benchmarks
- Shows how height error changes with different HoA requirements
- Demonstrates advantages of proposed solution
- Includes both actual height error and its upper bound

4. Figure 4: Height error vs minimum data rate
- Shows how sensing accuracy changes with data rate requirements
- Compares different schemes' performance under varying data rates
- Demonstrates communication-sensing trade-offs
- Illustrates feasibility regions for different approaches

Table:

1. Table I: System Parameters
- Lists all key system parameters and their values
- Includes communication parameters (bandwidth, data rates, etc.)
- Contains radar parameters (wavelength, pulse duration, etc.)
- Specifies geometric constraints and other operational limits
- Provides optimization parameters and thresholds

Each figure and table serves to either illustrate the system architecture, demonstrate the solution approach, or validate the performance improvements achieved by the proposed method. The paper uses these visualizations effectively to show both the theoretical framework and practical performance benefits of their approach.

Figure 2 in detail

Let me break down Figure 2 and explain how the proposed solution works in detail.

Figure 2 shows the block diagram of the alternating optimization (AO) solution, which breaks down the complex main problem (P) into three manageable sub-problems:

1. Master UAV Optimization - (P.0):
- Takes as input the fixed positions and powers of slave UAVs (q₁, q₂, Pcom,1, Pcom,2)
- Optimizes master UAV position (q₀) and power allocation (Pcom,0)
- Uses successive convex approximation (SCA) to solve a convex approximation of the problem

2. First Slave UAV Optimization - (P.1):
- Takes fixed values for master and second slave (q₀, q₂, Pcom,0, Pcom,2)
- Optimizes first slave position (q₁) and power (Pcom,1)
- Splits into two sub-problems due to baseline decorrelation constraints:
   * (P.1.a): Handles case where θ₀ ≥ θ₁ (master look angle ≥ slave look angle)
   * (P.1.b): Handles case where θ₀ < θ₁
- Both sub-problems are solved and best result is chosen

3. Second Slave UAV Optimization - (P.2):
- Similar structure to (P.1)
- Takes fixed values for master and first slave
- Optimizes second slave position (q₂) and power (Pcom,2)
- Also splits into two cases (P.2.a) and (P.2.b)

The solution process works as follows:

1. Initialize:
- Start with feasible positions for all UAVs
- Set initial communication power allocations
- Set iteration counters and error tolerance

2. Iterative Process:
- Optimize master UAV parameters while keeping slave parameters fixed
- Then optimize first slave parameters while keeping others fixed
- Then optimize second slave parameters while keeping others fixed
- Repeat this cycle until convergence (when height error improvement falls below threshold)

3. Key Features:
- Each sub-problem is solved using convex optimization techniques
- The solution handles both communication and sensing constraints simultaneously
- The approach breaks down a complex non-convex problem into manageable pieces
- The algorithm converges to a local optimum of the worst-case height error

The arrows in the diagram show the information flow between sub-problems and how the solutions are iteratively refined. This approach allows the system to find good solutions to a complex optimization problem that would be intractable if solved directly.

The computational complexity of the complete solution is O(M₂(2M₁ + M₀)(N + 2)³·⁵), where:
- M₂ is the number of main AO iterations
- M₁ is the number of iterations for slave optimization
- M₀ is the number of iterations for master optimization
- N is the number of time slots

This solution structure effectively balances computational feasibility with optimization performance, allowing the system to find good solutions in a reasonable time frame.

Artifacts

This appears to be a theoretical/simulation paper rather than an experimental one, so no physical artifacts or equipment were directly used. However, the paper describes a theoretical system design that would include the following components:

System Components (Theoretical):

1. UAV Platform:

- Three rotary-wing UAVs forming a swarm
- One master UAV (transmits and receives radar signals)
- Two slave UAVs (receive-only)
- Each UAV equipped with SAR capabilities

2. Radar Equipment (Specifications from Table I):

- Operating wavelength: 0.12m
- Radar center frequency: 2.5 GHz
- Bandwidth: 3 GHz
- Transmit power: 26.02 dBm
- Antenna gains: 5 dBi
- System temperature: 400 K

3. Communication System:

- FDMA air-to-ground backhaul link
- Communication bandwidth: 1 GHz per UAV
- Maximum transmit power: 10.1 dB
- Ground station for data reception

Outputs (Simulation Results):

- Digital Elevation Models (DEMs) - two independent models that are fused into one final DEM
- Height error measurements and comparisons
- Performance metrics for different optimization approaches

The work is validated through simulation rather than physical implementation, using parameters that match realistic system specifications. All results shown are from computational simulations rather than physical measurements.

The authors used Python with the CVXPY library for implementing their optimization algorithms and generating the simulation results.

Python code generated by Claude AI

Background of the study:

The study focuses on optimizing the sensing accuracy of a dual-baseline unmanned aerial vehicle (UAV)-based interferometric synthetic aperture radar (InSAR) system. The authors deploy a swarm of three UAV-synthetic aperture radar (SAR) systems to image an area of interest from different angles, enabling the creation of two independent digital elevation models (DEMs). The radar data is offloaded in real-time to a ground station using a frequency division multiple access (FDMA) air-to-ground backhaul link.

Research objectives and hypotheses:

The main objective is to improve the sensing accuracy by minimizing the worst-case height estimation error of the final DEM. The authors jointly optimize the UAV formation and the power allocated for offloading, while meeting practical InSAR sensing and communication constraints.

Methodology:

The authors first propose an approximate bi-static signal-to-noise ratio (SNR) expression for the sensing application. They then derive a tractable upper bound for the complex expression of the height error of the final DEM based on the Cramér–Rao bound of the phase error. The authors formulate and solve a joint optimization problem for UAV formation and communication power allocation to minimize the derived upper bound on the height error, while satisfying sensing and communication constraints.

Results and findings:

The simulation results demonstrate that the proposed solution can significantly improve the sensing accuracy compared to classical single-baseline UAV-InSAR systems and other benchmark schemes. The proposed scheme consistently achieves a gain of at least 49% compared to the benchmark scheme 1 (single-baseline UAV-InSAR system). It also outperforms benchmark scheme 2 (fixed master UAV position) and benchmark scheme 3 (static power allocation) with minimum gains of 23.6% and 8.2%, respectively.

Discussion and interpretation:

The improved sensing accuracy of the proposed dual-baseline scheme is due to the averaging of the height error, which helps to enhance the overall precision. Additionally, the optimization of the UAV formation enables the proposed solution to outperform the benchmark schemes by finding the best positioning of the UAVs to minimize the height error.

Contributions to the field:

The key contributions of this study include: 1) Proposing an approximate bi-static SNR expression for the considered sensing application, 2) Deriving a tractable upper bound for the complex expression of the height error of the final DEM, and 3) Formulating and solving a joint optimization problem for UAV formation and communication power allocation to minimize the height error, while satisfying practical constraints.

Achievements and significance:

The proposed scheme significantly improves the sensing accuracy of the dual-baseline UAV-InSAR system compared to single-baseline systems and other benchmark schemes. This demonstrates the importance of using multiple UAVs for data acquisition and the benefits of optimizing the UAV formation and communication resources to enhance the overall InSAR performance.

Limitations and future work:

The study focuses on a specific dual-baseline UAV-InSAR system, and the results may not directly apply to other InSAR configurations or sensing applications. Future work could explore the extension of the proposed optimization framework to more general multi-baseline InSAR systems or the incorporation of additional practical constraints, such as collision avoidance or energy consumption minimization.