Mono-Static Target Localization

• Mono-static target localization is a method that uses a co-located transmitter and receiver to estimate a target’s position via round-trip echoes, RSSI, or full waveform acquisition.
• It leverages advanced array processing and beamforming to achieve high-resolution angular localization and optimize performance under hardware constraints.
• Algorithmic approaches, including RSSI-based trilateration and Bayesian shape inference, offer robust, accurate localization while balancing sensing accuracy and communication throughput.

Mono-static target localization refers to the estimation of a target’s position (and potentially its geometry) using sensing data collected by a single platform that acts as both transmitter and receiver, or by bidirectional communications/sensing agents at the same site. This paradigm, foundational in radar and integrated sensing/communications (ISAC), leverages round-trip echoes, received signal strength, or detailed array responses. It encompasses configurations ranging from radar arrays at fixed sites to mobile platforms such as UAVs or vehicular nodes, and extends to networks of distributed mono-static nodes under angular or beamforming constraints.

1. Mono-Static Sensing Principles and System Models

Mono-static sensing hinges on the co-location of transmitting and receiving elements. The canonical model involves:

• A half-duplex antenna array for transmission (e.g., at a communications base-station or UAV), paired with a receive array for echo capture (Felix et al., 19 Feb 2024).
• Signal models such as round-trip time-of-flight (TOF), received signal strength indicator (RSSI), or full waveform acquisition.
• Array-based mono-static radar: Transmission and reception are physically separated into distinct (but co-located) antennas or arrays, necessitated by half-duplex hardware constraints in ISAC systems.
• Mobile mono-static platforms: A UAV or robot collects sequential measurements as it moves, effectively synthesizing geometry via its airtrack (Yucer et al., 2020, Jing et al., 2022).

The measurement function for TOF-based systems is typically:

$\tau = \frac{2\|p_\text{rx} - p_\text{tg}\|}{c}$

where $p_\text{rx}$ is the mono-static node position, $p_\text{tg}$ the target, and $c$ the propagation speed. For RSSI-based measurements, the log-distance path-loss model governs the received power as a function of unknown distance and random fading (Yucer et al., 2020, Nozari et al., 15 Nov 2025).

In the array case, the system model involves beamforming via a communications transmit array (with element count $N_c$, spacing $d_c$) and a sensing receive array ($N_s$, $d_s$), forming a “virtual” sum-coarray that dictates angular localization performance (Felix et al., 19 Feb 2024).

2. Array Processing and Angular Localization

Mono-static arrays enable high-resolution angular localization by exploiting the sum-coarray principle:

• The joint Tx/Rx array is equivalent to a virtual array of size $N^+$ and spacing $d^+ = \min(d_c, d_s)$.
• The array’s point spread function (PSF) and array factor (AF) directly determine angular resolution and sidelobe levels, with explicit expressions for beamwidth and peak-to-sidelobe ratio (PSLR) (Felix et al., 19 Feb 2024).
• For a uniform Chebyshev-windowed array of $N^+$ elements:

$$\Delta\theta \approx \frac{\lambda\,\omega_{1/2}}{\pi\,d^+}$$

where $\omega_{1/2}$ is the half-power main-lobe width parameter.

• The localization Cramér–Rao Bound (CRB) for bearing estimation is governed by the array topology and SNR:

$$\mathrm{CRB}(\theta) = \frac{\sigma^2}{k^2\cos^2\theta \sum_{m=1}^{N^+} d^+_m{}^2|s_m(\theta)|^2}$$

where $k=2\pi/\lambda$ (Felix et al., 19 Feb 2024).

Sparse Rx array designs—where element spacing $d_s \gg \lambda/2$ and array length is kept fixed—can provide sub-degree resolution at a fraction of the cost of dense uniform rectangular arrays (URA), enabled via alternating-minimization algorithms that optimize for a Chebyshev-shaped PSF matching angular specifications under hardware constraints (Felix et al., 19 Feb 2024).

3. Algorithmic Approaches for Target Position Estimation

Mono-static localization algorithms are structured according to the measurement type and modality.

RSSI / Range-based Trilateration:

• Nodes or mobile agents estimate the distance $\hat d_i$ from RSSI, inverting the logarithmic path-loss model. Distance estimates are then fused using weighted least squares (WLS) or singular value decomposition (SVD)-based multilateration, with robustification via clustering to mitigate outlier impact (Yucer et al., 2020, Nozari et al., 15 Nov 2025).
• For an ensemble of anchor points $(x_i, y_i, \hat d_i)$, the non-linear system:

$(x-x_i)^2 + (y-y_i)^2 = \hat d_i^2$

is linearized and solved for position. Iterative refinement and windowed sample clustering enhance accuracy (Yucer et al., 2020).

ISAC Subnetwork Node Selection:

• In ISAC subnetworks with distributed mono-static agents, collaborative estimation is structured around WLS fusion of distance estimates from selected subnetworks. The subset of agents is iteratively optimized (e.g., via minimizing the weighted geometric dilution of precision, WGDOP) to enhance localization while balancing communication throughput (Nozari et al., 15 Nov 2025).

Mono-static Bayesian Shape Inference:

• For extended targets, such as in acoustic or electromagnetic imaging, Bayesian MCMC approaches estimate both target position and boundary geometry directly from mono-static multi-angle far-field data. The model leverages shape derivatives to construct a specialized basis for efficient MCMC exploration, with robust convergence even under model noise (Hong et al., 2023).

Trajectory-Optimized Mono-static UAV Sensing:

• For UAV-based ISAC, joint optimization of the sensing trajectory and communication schedule is carried out, balancing CRB-driven sensing objectives against communication rate. Successive convex approximation (SCA) and multi-stage replanning allow for adaptive trajectory adjustment based on incremental target localization updates (Jing et al., 2022).

4. Analytical Performance Bounds and Practical Trade-Offs

The fundamental performance limit for unbiased position estimation is established by the Cramér–Rao Bound (CRB), which subsumes the effect of geometry, SNR, bandwidth, and array configuration.

• Resolution vs. Hardware Cost: Sparse mono-static Rx arrays, designed with large element spacing but a fixed aperture, achieve angular resolutions down to $\Delta\theta\approx1^\circ$ at mmWave for as few as 3–5 Rx elements—resulting in substantial hardware savings relative to dense URAs (Felix et al., 19 Feb 2024).
• Diversity and Robustness: Spatial diversity via multiple antennas or collaborating subnetworks accelerates error reduction, with demonstrable robustness to fading and outlier measurements (Nozari et al., 15 Nov 2025).
• Sensing–Communication Trade-off: Resource allocation within ISAC networks induces a quantifiable trade-off between sensing accuracy and communication throughput. Throughput loss is proportional to the number of sensing resource blocks reserved, while localization error scales inversely with the product of the number of participants, antenna elements, and measurement repetitions (Nozari et al., 15 Nov 2025).
• Reflectivity and RCS Augmentation: In vehicular localization, electromagnetic skins (EMS/RIS/SP-EMS) affixed to the target can increase radar cross-section (RCS) by more than 10 dB, sharply reducing localization error by shrinking the CRB. RIS-equipped vehicles enable precise point-target behavior and dynamic retro-reflection, at the expense of additional hardware and control complexity (Tagliaferri et al., 2023).
• Bias Suppression via Retro-reflectors: Vehicles with extended, complex geometry induce aspect- and range-dependent localization biases. A planar EMS eliminates these by ensuring the maximal back-scatter and localization peak correspond to the EMS phase center, suppressing foreshortening and layover artifacts (Tagliaferri et al., 2023).

5. Representative Case Studies and Simulation Results

A selection of technical results exemplifies the state of mono-static target localization:

Approach	Error/Resolution	Key Findings
Sparse mono-static ISAC arrays (Felix et al., 19 Feb 2024)	Sub-degree $\Delta\theta$	Sparse Rx (3–5 el., $d_s=2\lambda$) $>$ dense URA
ISAC subnetworks, iterative selection (Nozari et al., 15 Nov 2025)	$<$7 cm (3 iterations, AWGN)	97% gain vs. random; spatial diversity reduces error
RSSI-based UAV mono-static (Yucer et al., 2020)	7–43 m campus (8 it.)	Clustering+SVD reduces error $\sim 5\times$ rel. to SVD only
UAV-ISAC trajectory-optimized (Jing et al., 2022)	0.2 m RMSE	ISAC trajectory yields $10\times$ improvement over comm. only
RIS-aided vehicular mono-static (Tagliaferri et al., 2023)	2–10$\times$ PEB gain	Point EMS suppresses geometric bias, improves CRB

These studies demonstrate that well-designed mono-static architectures can provide sub-meter to sub-centimeter accuracy in practical (urban or fading) environments, with hardware cost, communications impact, and environmental constraints all being tunable design dimensions.

6. Extensions: Geometric, Bayesian, and Constrained Formulations

Mono-static frameworks extend readily to higher-dimensional (3D) localization, extended-target imaging, and contexts with geometric or physical constraints.

• Constrained least-squares with array pattern priors: Imposing monostatic beamwidth inequalities in 3D leads to nonconvex LS problems solvable via Karush–Kuhn–Tucker (KKT) conditions, with a finite candidate set and a global minimum identified at low computational cost (Aubry et al., 2021).
• Bayesian shape-based inference: For extended or nontrivial targets, the mono-static measurement function serves as the forward operator in a Bayesian inversion, with shape regularization, adaptive bases, and efficient Markov Chain Monte Carlo (MCMC) transdimensional sampling for full posterior quantification (Hong et al., 2023).
• Integration with communications and ISAC: Mono-static sensing is being fused with next-generation communications, yielding architectures that inherently balance localization and channel quality, with ISAC array design now a central research theme (Felix et al., 19 Feb 2024, Jing et al., 2022, Nozari et al., 15 Nov 2025).

7. Practical Guidelines and Future Directions

A set of design recommendations is distilled from the current mono-static localization literature:

• Sparse and adaptive Rx topology: For systems with half-duplex constraints, sparse receive arrays provide flexible angular coverage and cost-efficient sub-degree resolution, supporting ISAC integration (Felix et al., 19 Feb 2024).
• Spatial diversity and subset selection: Selecting a minimal subset ($K\approx3$) of well-placed mono-static nodes suffices for sub-decimeter accuracy in AWGN, while additional diversity buffers against fading and outliers (Nozari et al., 15 Nov 2025).
• Retro-reflectors for bias suppression: EMS/RIS-equipped targets eliminate perspective and ranging bias, with hardware trade-offs between dynamic control (RIS) and low-cost passive coverage (SP-EMS) (Tagliaferri et al., 2023).
• Algorithmic robustness: Clustering, Bayesian, or iterative WLS approaches are critical to mitigate measurement noise, NLOS conditions, and geometric dilution, particularly in mobile or single-agent mono-static paradigms (Yucer et al., 2020, Nozari et al., 15 Nov 2025).
• ISAC-driven trajectory planning: Multi-stage SCA-based trajectory optimization enables simultaneous near-centimeter localization and high data rates for UAV ISAC missions (Jing et al., 2022).
• Hardware/throughput trade-offs: Sensing–communication trade-off curves and adaptive resource allocation protocols support dynamically tunable operation in networked ISAC deployment (Nozari et al., 15 Nov 2025).

Future mono-static localization research encompasses robust multi-band operation, multi-target discrimination, fusion of dynamic and static sensors, hybrid active/passive retro-reflectors (active-RIS), and deeper integration with vehicular and urban wireless infrastructures.