Multi-UAV SAR Interferometry Advances

• Multi-UAV SAR Interferometry is a remote sensing method that uses coordinated UAVs to synthesize high-resolution digital elevation models via multi-baseline interferometry.
• It combines bistatic and multi-baseline formations with both wideband and Doppler-SAR techniques to enhance height sensitivity and reduce estimation errors.
• Optimized flight formation, resource allocation, and real-time data offloading enable sub-decimeter accuracy and scalable, robust terrain mapping.

Multi-UAV Synthetic Aperture Radar (SAR) Interferometry constitutes a class of remote sensing methodologies in which swarms or formations of unmanned aerial vehicles (UAVs) equipped with SAR sensors acquire multiple coherent observations for digital elevation model (DEM) generation via radar interferometry. Fusion of images from separate UAVs enables precise height mapping, coverage scalability, and near-real-time data offloading, with accuracy and coverage dictated by formation geometry, radiometric coherence, communication resources, and flight dynamics. Both wideband range-difference and Doppler-rate (ultra-narrowband) paradigms have been established, with critical advances in optimization frameworks enabling sub-decimeter vertical precision under operational constraints.

1. SAR Interferometry Principles in Multi-UAV Configurations

Multi-UAV SAR interferometry leverages spatio-temporal diversity from multiple aerial sensors for topographic mapping and surface change analysis. Key architectural paradigms include:

• Bistatic and Multi-baseline Formations: In typical bistatic InSAR, a “master” UAV transmits/receives, and one or more “slave” UAVs passively record echoes. Multi-baseline extension with $I \ge 3$ allows simultaneous acquisition of several baselines, improving height sensitivity and error reduction (Lahmeri et al., 15 Jul 2025, Lahmeri et al., 24 Oct 2024, Lahmeri et al., 9 Jul 2024).
• Baseline Definition: For UAVs with positions $\mathbf{q}_i = (x_i, z_i)^\mathrm{T}$ along a common azimuth plane, baseline lengths $b_{ij} = \| \mathbf{q}_i - \mathbf{q}_j \|_2$ and their perpendicular projections $b_{\perp,ij} = b_{ij} \cos(\theta_i - \alpha_{ij})$—where $\theta_i$ is the look angle and $\alpha_{ij}$ baseline orientation—are primary determinants of interferometric sensitivity and ambiguity.
• Interferometric Phase Model: The wrapped phase difference for baseline $(i,j)$ is

$\Delta\Phi_{ij} = \frac{4\pi}{\lambda}(r_i - r_j)$

where $r_i$ is the slant range from UAV $i$ to a ground point, and $\lambda$ is radar wavelength. Corresponding surface height after phase unwrapping is

$$h_{ij} = \frac{\lambda r_i \sin\theta_i}{4\pi b_{\perp,ij}} \Delta\Phi_{ij}$$

(Lahmeri et al., 15 Jul 2025, Lahmeri et al., 24 Oct 2024, Lahmeri et al., 9 Jul 2024).

2. Doppler-SAR Interferometry: Ultra-Narrowband Paradigm

Doppler-SAR interferometry utilizes ultra-narrowband continuous wave (CW) transmissions. In contrast to classical wideband SAR—which exploits range differences due to large instantaneous bandwidths—the Doppler-SAR modality reconstructs height from differences in Doppler frequencies and Doppler rates induced by velocity differences among UAVs:

• Received Field and Data Formation: Under start–stop and Born approximations, the scattered field at UAV $i$:

$$r_i(t) = \int_{\mathbb{R}^3} \frac{\omega_0^2}{(4\pi)^2} V(x) \exp\left\{-j\omega_0[t - 2|x - x_i(t)|/c]\right\} / |x - x_i(t)|^2\, dx$$

Data formation by CW correlation employs a window $\varphi$ and frequency-scaling parameter $\mu \approx 1$:

$$d_i(\mu, s) = \int r_i(t) e^{+j(\omega_0/c)\mu[t-sT_\varphi]} \varphi(t-sT_\varphi) dt$$

(Yazici et al., 2017).

• Interferometric Phase and Height Mapping:

$$\Phi^{\text{UNB}}(x) \approx 2s_d^1 T_\varphi [f_1^d(x, s_d^1) - f_2^d(x, s_d^2)]$$

Height estimation is performed by solving three algebraic constraints (iso-Doppler surface, iso-Doppler-rate surface, interferometric Doppler-rate), yielding the intersection point corresponding to true scatterer height (Yazici et al., 2017).

• Advantages and Limitations: Doppler-SAR enables very lightweight, low-power systems without wideband hardware, and velocity-differentiated UAVs can achieve fine height resolution—even when look directions nearly coincide. Significant limitations include need for highly accurate velocity control, phase stability, absence of direct range measurement, and increased layover risk if synthetic apertures are confined (Yazici et al., 2017).

3. Performance Metrics: Coherence, Height of Ambiguity, and Error Formulation

Several key metrics govern sensing accuracy and DEM quality:

• Interferometric Coherence ($\gamma$):

$$\gamma(x,y) = \frac{|\mathbb{E}\{s_1(x,y) s_2^*(x,y)\}|}{\sqrt{\mathbb{E}\{|s_1(x,y)|^2\} \mathbb{E}\{|s_2(x,y)|^2\}}}$$

Coherence loss is decomposed into SNR-decorrelation and baseline-decorrelation factors (Lahmeri et al., 15 Jul 2025, Lahmeri et al., 2023, Lahmeri et al., 9 Jul 2024).

• Height of Ambiguity (HoA):

$$h_{\rm amb,ij} = \frac{\lambda r_i \sin\theta_i}{b_{\perp,ij}}$$

Smaller HoA improves height precision but increases phase-unwrapping risk; larger baselines yield lower HoA but may reduce coherence (Lahmeri et al., 15 Jul 2025, Lahmeri et al., 2023, Lahmeri et al., 24 Oct 2024).

• Height Error and Fusion:

$$\sigma_{h,ij} = \frac{h_{\rm amb,ij}}{2\pi} \sigma_{\Phi,ij}, \qquad \sigma_h = \left( \sum_{i<j} \sigma_{h,ij}^{-2} \right)^{-1/2}$$

Fusion with inverse-variance weighting over $M$ independent baselines reduces vertical error as $1/\sqrt{M}$ in the homogeneous variance case (Lahmeri et al., 15 Jul 2025, Lahmeri et al., 24 Oct 2024).

4. Joint Sensing and Communication Optimization

Multi-UAV SAR interferometry requires simultaneous optimization of flight formation, sensor resource allocation, and communication link budget to maximize coverage and accuracy subject to operational constraints:

• Optimization Problem Statement (example for $I$ UAVs):

$$\min_{\mathcal{Q}, v_y, P_{\rm com}} \ \sigma_h(\mathcal{Q}, v_y)$$

Subject to:

$$\begin{aligned} & z_{\min} \leq z_i \leq z_{\max},\ \theta_{\min} \leq \theta_i \leq \theta_{\max}, \ v_{\min} \leq v_y \leq v_{\max} \ & 0 \leq P_{\rm com,i}[n] \leq P_{\rm com}^{\max}, \ b_{ij} \geq d_{\min}, \ C_{\rm tot}(\mathcal{Q}, v_y) \geq C_{\min} \ & h_{\rm amb, ij} \geq h_{\rm amb}^{\min},\ R_{i,n} \geq R_{\min,i},\ \sum_n P_{\rm com,i}[n] \leq E_{\max}-T(P_{\rm prop}+P_{\rm rad,i}) \end{aligned}$$

(Lahmeri et al., 15 Jul 2025, Lahmeri et al., 9 Jul 2024, Lahmeri et al., 24 Oct 2024, Lahmeri et al., 2023).

• Algorithmic Techniques: Solution frameworks employ alternating optimization (AO), particle swarm optimization (PSO) for non-smooth constraints (e.g., geometric positions), monotonic optimization for altitude selection, and successive convex approximation (SCA) for resource allocation and nonconvex constraint linearization (Lahmeri et al., 15 Jul 2025, Lahmeri et al., 9 Jul 2024, Lahmeri et al., 2023, Lahmeri et al., 24 Oct 2024).
• Resource Allocation: UAV positions and velocities are intertwined with communication power (FDMA channel), as real-time offloading must satisfy SNR, rate, and energy requirements, influencing both achievable coverage and sensing geometry (Lahmeri et al., 15 Jul 2025, Lahmeri et al., 9 Jul 2024, Lahmeri et al., 2023).

5. Height Error Reduction, Sensor Fusion, and Swarm Coordination

The benefit of multiple baselines is evident in precision and robustness:

• Dual- and Multi-Baseline Fusion: Weighted averaging of two independent DEMs from three UAVs achieves significant reduction in worst-case height estimation error; e.g., dual-baseline AO reduces error by 50% vs. the classical single-baseline method at $H_{amb}^{\min} = 1.2 \mathrm{m}$ ($\sigma_h \approx 0.11 \mathrm{m}$ vs. $0.22 \mathrm{m}$) (Lahmeri et al., 24 Oct 2024).
• Multi-UAV Scaling: For $I=5$ UAVs, fused height error $\sigma_h \approx 7$ cm is attainable, with diminishing returns above $I=8$ due to phase decorrelation limits (Lahmeri et al., 15 Jul 2025). A plausible implication is that swarm size should be matched to coverage, mission energy, and swath requirements for optimal cost-benefit.

Baseline Scheme	DEM Error Improvement	Data Offloading Requirement
Single-baseline	Reference	Moderate
Dual-baseline (AO)	30-50% vs. single	Higher rate, energy
Multi-baseline (swarm)	$1/\sqrt{M}$ scaling	FDMA, parallel offload

6. Trade-Offs and Practical Deployment Guidelines

Operational trade-offs and constraints are central to system design:

• HoA vs. Coverage: Reducing $h_{\rm amb}^{\max}$ by doubling $b_\perp$ improves height sensitivity but decreases coverage by $\sim 7.5\%$ due to reduced swath overlap (Lahmeri et al., 2023, Lahmeri et al., 15 Jul 2025).
• Comm. Power and Formation: Limited communication power compels tight UAV formation and short baselines to support required SAR data rate; high power permits greater separation and increased sensitivity (Lahmeri et al., 9 Jul 2024, Lahmeri et al., 2023).
• Velocity Effects: Low UAV velocity is preferable for InSAR, improving coherence and therefore height estimation accuracy; average speeds of a few m/s optimize DEM precision (Lahmeri et al., 9 Jul 2024). Higher speeds degrade SNR and coherence.
• Deployment Guidelines:
  • Pre-compute baseline and altitude bounds from coherence/HoA targets.
  • Select $I \geq 4$ UAVs for multi-baseline gain without undue coordination overhead (Lahmeri et al., 15 Jul 2025).
  • Place ground station to minimize maximum data offload distance, equip with sufficient FDMA bandwidth ($\geq1$ GHz recommended).
  • Update formation and resource allocation in real time under dynamic wind and battery constraints using distributed AO/PSO (Lahmeri et al., 15 Jul 2025, Lahmeri et al., 9 Jul 2024).

7. Practical System Design and Simulation Insights

Recent research demonstrates feasibility and performance of multi-UAV SAR interferometry under rigorous constraints:

• Simulation Results: For scenes $128 \times 128$ m at $1$ m ground spacing, UAV baselines $b=300$ m, $\lambda=0.12$ m, and velocities $v_y = 2$–$4.3$ m/s, centimeter-level vertical accuracy is attainable for multi-baseline swarms (Yazici et al., 2017, Lahmeri et al., 9 Jul 2024, Lahmeri et al., 15 Jul 2025, Lahmeri et al., 24 Oct 2024).
• Algorithmic Convergence: AO and co-evolutionary PSO converge within $25$–$50$ generations (multi-UAV, $I=5$) for formation optimization, with robust performance compared to genetic algorithms, simulated annealing, and deep reinforcement learning benchmarks (Lahmeri et al., 15 Jul 2025). AO+SCA reaches local optimum in $5$ outer iterations for two-UAV scenarios (Lahmeri et al., 2023).
• Processing Flow:

1. Acquire raw SAR/CW returns from all UAVs.
2. Extract Doppler, Doppler-rate, and phase metrics.
3. Backproject and register images onto reference surfaces.
4. Form interferograms and solve height equations or fuse DEMs via inverse-variance weighting.
5. Co-optimize formation and link resources to maintain real-time offload (Yazici et al., 2017, Lahmeri et al., 24 Oct 2024, Lahmeri et al., 9 Jul 2024, Lahmeri et al., 2023).

A plausible implication is that advances in multi-UAV SAR interferometry—particularly the fusion of sensing/communication optimization and multi-baseline error reduction—are enabling flexible, high-accuracy, and scalable earth observation systems suitable for rapidly changing or remote environments.