⚡ electrical engineering

Obstacle-Aware Online Receiver Planning in Multistatic Ranging

This paper proposes a non-myopic receding-horizon framework for multistatic ranging that utilizes convex collision-avoidance constraints and a control objective focused on maintaining future line-of-sight conditions to enable effective receiver trajectory planning in obstacle-rich environments.

Original authors: Jingwei Hu, Dave Zachariah, Petre Stoica, Torbjörn Wigren

Published 2026-08-24

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CC BY 4.0

Original authors: Jingwei Hu, Dave Zachariah, Petre Stoica, Torbjörn Wigren

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of modern tracking, knowing where something is depends heavily on how you look at it. Imagine trying to find a lost hiker in a dense forest using only a few stationary radio towers. If the hiker moves behind a thick ridge, the signal from the towers might bounce off the ground or get blocked entirely, leaving the search team blind. This is the core challenge of multistatic ranging, a technique where separate transmitters send signals and separate receivers listen for the echoes. The accuracy of the location estimate relies on the geometry of the setup; the better the angles between the transmitters, the receiver, and the target, the sharper the picture. While stationary towers work well in open fields, they struggle when obstacles like buildings or hills block the direct path of the signal. To solve this, engineers have begun using mobile receivers, such as drones or ground robots, that can move around to keep a clear line of sight. However, simply moving a robot to avoid a wall is not enough; the robot must also anticipate where the target will go and ensure that the signal path remains unbroken by future obstacles, a task that requires looking ahead rather than just reacting to the present.

Researchers at Uppsala University have developed a new way to guide these mobile receivers through cluttered environments. Their work addresses a specific failure in current methods: many existing systems plan a robot's path by avoiding physical collisions but ignore the fact that the target itself might move behind an obstacle, cutting off the signal. The team created a planning framework that treats the physical safety of the robot and the clarity of the signal as a single, unified problem. Instead of just asking, "Is the path clear of walls?", their system asks, "Will the target be visible from this spot in the next few seconds?" By looking ahead, the system can steer the receiver to a position that maintains a clear view of the target even as the target maneuvers around corners or behind barriers.

The method works by constantly calculating a short-term plan for the receiver's movement, much like a driver checking the road a few seconds ahead to decide whether to turn or brake. The system considers the physical limits of the receiver, such as how fast it can accelerate and how far it can travel, while also mapping out the invisible lines of sight between the transmitters, the receiver, and the target. If the system predicts that the target will soon be hidden behind a building, it proactively moves the receiver to a new vantage point before the signal is lost. This approach uses a mathematical concept called a "receding horizon," where the plan is updated at every single moment. As the receiver moves and the target shifts, the system recalculates the best path forward, ensuring that the receiver is always positioned to catch the signal if a direct path exists.

To test this idea, the researchers ran computer simulations in a virtual environment containing two mobile receivers, four fixed transmitters, and two large obstacles. They compared their new method against two simpler approaches: one where the receivers stayed in fixed positions, and another where the receivers moved but ignored the possibility of the signal being blocked. In the simulation, the fixed receivers tracked the target accurately only as long as the target remained in a direct line of sight. The moment the target moved behind an obstacle, the tracking error spiked dramatically, and the system lost precision. The moving receivers that ignored future blockages fared even worse, often wandering into positions where they could not see the target at all, leading to long periods of large errors.

In contrast, the new obstacle-aware method kept the tracking error low and stable throughout the entire maneuver. The receiver successfully navigated around the physical obstacles while simultaneously repositioning itself to maintain a clear view of the target as it moved. The simulation showed that once the system locked onto the target, it could maintain accurate tracking even as the target moved between the obstacles. The researchers found that their approach required about two seconds to compute each new movement decision on a standard laptop, a speed that suggests the method could be practical for real-time use. The results indicate that simply avoiding physical collisions is insufficient for tracking in complex environments; the receiver must actively manage the visibility of the signal. By explicitly planning for future obstructions, the system ensures that the measurements remain useful, allowing for a continuous and accurate track of the target's location.

Technical Summary: Obstacle-Aware Online Receiver Planning in Multistatic Ranging

Problem Formulation

The paper addresses the challenge of tracking a moving target in cluttered environments using a multistatic ranging system. The system consists of $N$ static transmitters and $M$ mobile receivers (e.g., UAVs or UGVs) operating in a $d$ -dimensional space ( $d=2$ or $3$) containing static obstacles. The core difficulty lies in the fact that target state estimation accuracy (specifically Time-Difference-of-Arrival, or TDOA) is heavily dependent on sensor geometry. However, in environments with obstacles, maintaining the necessary Line-of-Sight (LOS) conditions between transmitters, receivers, and the target is non-trivial.

Existing approaches often decouple visibility from estimation informativeness, either assuming obstacle-free settings or handling occlusion via separate feasibility constraints that fail to anticipate future obstructions caused by target motion. The goal is to jointly determine receiver control inputs to plan trajectories that ensure accurate target state estimation while avoiding collisions and maintaining LOS signal paths.

Methodology

The authors propose a non-myopic receding-horizon framework that integrates collision avoidance with an active control objective focused on signal quality.

1. System Modeling

Target Dynamics: Modeled as a state-space system with position and velocity, driven by unknown acceleration modeled as a temporally white process.
Receiver Dynamics: Mobile receivers are modeled with position and velocity states, subject to physical constraints (acceleration limits, workspace boundaries) and collision-avoidance constraints.
Measurements: Receivers measure TDOA between direct signals from transmitters and reflected signals from the target. Under LOS, measurement variance is finite; under Non-LOS (NLOS) conditions, the measurement is treated as uninformative (infinite variance).

2. Tractable Constraint Formulation

To handle the non-convex nature of obstacle avoidance in a planning horizon, the method employs a convex relaxation strategy:

Collision Avoidance: For each obstacle (modeled as a convex polyhedron), the algorithm computes the closest point on the obstacle to the receiver's current position. This defines a supporting hyperplane. The intersection of half-spaces defined by these hyperplanes creates a local convex feasible set.
Sliding Horizon: The collision-free set is recomputed at each time step. By considering a sufficiently long planning horizon ( $k$ ), the sequence of overlapping convex sets ensures a collision-free path across the map without requiring global non-convex optimization.

3. Control Objective (Active Non-LOS Mitigation)

The core innovation is the control criterion $J(U_t)$ , which aims to minimize the future tracking error.

Lower Bound: The expected tracking error is lower-bounded by the Cramér-Rao Bound (CRB), which depends on the Fisher Information Matrix (FIM).
LOS Continuity: The standard FIM is discontinuous because measurement variance jumps to infinity when LOS is lost. To make the optimization tractable, the authors introduce a continuous LOS-margin function.
- They define a "LOS margin" based on the signed distance of the receiver and target from the separating planes of obstacles.
- A sigmoid function is used to map these margins to a continuous measure of measurement informativeness.
- The objective function incentivizes trajectories that maximize these margins, particularly between the receiver and the target, effectively proactively avoiding future occlusions.

4. Optimization

The problem is formulated as a constrained optimization over a sequence of control inputs $U_t$ within a sliding window. The objective function is approximated using deterministic sigma-point sampling of the target trajectory to handle the expectation over target dynamics. The resulting problem is solved using a standard interior-point method.

Key Contributions

The paper identifies two primary contributions:

Robust Obstacle-Aware Replanning: A non-myopic receding-horizon framework for multistatic tracking that utilizes convex collision-avoidance constraints to ensure feasible motion in cluttered environments.
Active Non-LOS Mitigation: A control objective specifically designed to maintain good LOS signal conditions by accounting for future obstructions, rather than merely reacting to current visibility.

Numerical Results

The method was evaluated using synthetic data with $M=2$ mobile receivers, $N=4$ static transmitters, and $O=2$ obstacles.

Baselines: The proposed method was compared against (1) static receivers and (2) mobile receivers that optimize for tracking but ignore future signal obstructions.
Performance:
- Static Receivers: Provided accurate tracking only when LOS was maintained. Once the target moved behind an obstacle, the Cramér-Rao Bound (CRB) and Root Mean Square Error (RMSE) increased sharply.
- Mobile (Non-Aware): Showed significant periods of large tracking errors when they failed to anticipate occlusions.
- Proposed Method: Demonstrated the ability to lock onto the target and maintain accurate tracking throughout maneuvers between obstacles. By planning collision-free trajectories that proactively preserve LOS, the method kept the estimation error low and stable.
Computation: On a standard laptop with non-optimized code, each control update (with a horizon of $k=15$ ) required approximately two seconds.

Significance and Claims

The paper claims that its significance lies in unifying sensor geometry optimization with obstacle avoidance in a way that explicitly anticipates future occlusions. The authors argue that collision avoidance alone is insufficient for target tracking in cluttered environments because it does not account for the loss of estimation quality due to signal blockage.

By explicitly incorporating LOS conditions into the planning horizon via a continuous margin function, the proposed method enables proactive receiver reorientation. This allows the system to maintain informative measurements and recover LOS following interruptions, a capability lacking in existing short-horizon or feasibility-constrained approaches. The work is presented as a step toward efficient, feasible motion control for multistatic active tracking in realistic, obstructed scenarios.