arXiv subjects

Raj Thilak Rajan

Publications and source records attributed to Raj Thilak Rajan.

At least 19 recordsLinked to original sources

arXiv2026

Resource-Efficient Distributed Recursive Gaussian Processes

Gaussian processes (GPs) provide a flexible framework for learning unknown functions from noisy measurements while quantifying predictive uncertainty, making them well suited for estimation in multi-agent systems. However, when measurements are collected by multiple agents, maintaining a unified GP model without centralized processing requires efficient distributed algorithms that can operate using local measurements and communication with neighboring agents. In this work, we develop two distributed recursive GP (RGP) algorithms for multi-output GP regression: ADMM-RGP and PDMM-RGP. We analyze the stability and convergence of both algorithms and develop parameter selection strategies to accelerate convergence, thus reducing the communication burden. The proposed methods are validated on a real-world multi-output wind dataset, and their convergence behavior is examined across communication graphs with varying connectivity. Numerical experiments demonstrate that ADMM-RGP and PDMM-RGP can significantly reduce communication relative to the state of the art, while maintaining comparable estimation accuracy and network-wide consensus.

cs.LG↗

arXiv2026

Distributed Target Tracking using Radar Networks

Distributed target tracking is essential for scalable and robust sensing systems, as it enables multiple radar nodes to cooperatively estimate a target state without relying on a centralized fusion center. In this paper, we present a fully distributed framework for single-target tracking in frequency-modulated continuous-wave (FMCW) radar networks. Each monostatic radar node observes local range and Doppler measurements and exchanges information only with neighboring nodes. Two consensus optimization-based estimators are developed. First, a Distributed Maximum A Posteriori (D-MAP) estimator is formulated for batch-based tracking, where prior state information is incorporated and the resulting optimization problem is solved using consensus-based alternating direction method of multipliers (ADMM). Second, a Distributed Extended Kalman Filter (D-EKF) is proposed for recursive tracking, where each node performs local prediction and correction followed by consensus ADMM-based information exchange. We derive the posterior Cramér-Rao lower bound (PCRLB) as a theoretical performance benchmark. Our simulation results show that D-MAP improves the accuracy of the estimation over the distributed maximum-likelihood baseline. These results demonstrate that the proposed framework provides a scalable and robust alternative to centralized radar tracking, given only local inter-node communication.

eess.SP↗

arXiv2026

Multi-FEAT: Multi-Feature Edge Alignment for Targetless Camera-LiDAR Calibration

Multi-agent systems, e.g., automobiles and UAVs (Unmanned Ariel Vehicles), rely on the precision of onboard sensors to accurately perceive their environment, which in turn depends on the precision of onboard sensors and reliable in-field calibration. This paper introduces a novel targetless camera-LiDAR extrinsic calibration approach called Multi-FEAT (Multi-Feature Edge AlignmenT). Multi-FEAT uses the cylindrical projection model to encode the 3D LiDAR point cloud into a 2D panorama and exploits diverse LiDAR feature information in panoramic images to supplement the sparse LiDAR point cloud boundaries. Furthermore, camera edges are extracted using off-the-shelf segmentation solutions. In addition, a feature-matching function is designed to optimize the calibration parameters. The performance of the proposed Multi-FEAT algorithm is evaluated using the KITTI dataset, and our approach shows more reliable results than several existing targetless calibration methods. We conclude our analysis with directions for future work.

eess.SP↗

arXiv2026

Consensus-based Recursive Multi-Output Gaussian Process

Multi-output Gaussian Processes provide principled uncertainty-aware learning of vector-valued fields but are difficult to deploy in large-scale, distributed, and streaming settings due to their computational and centralized nature. This paper proposes a Consensus-based Recursive Multi-Output Gaussian Process (CRMGP) framework that combines recursive inference on shared basis vectors with neighbour-to-neighbour information-consensus updates. The resulting method supports parallel, fully distributed learning with bounded per-step computation while preserving inter-output correlations and calibrated uncertainty. Experiments on synthetic wind fields and real LiDAR data demonstrate that CRMGP achieves competitive predictive performance and reliable uncertainty calibration, offering a scalable alternative to centralized Gaussian process models for multi-agent sensing applications.

cs.LG↗

arXiv2026

Multicluster Design and Control of Large-Scale Affine Formations

Conventional affine formation control (AFC) empowers a network of agents with flexible but collective motions - a potential which has not yet been exploited for large-scale swarms. One of the key bottlenecks lies in the design of an interaction graph, characterized by the Laplacian-like stress matrix. Efficient and scalable design solutions often yield suboptimal solutions on various performance metrics, e.g., convergence speed and communication cost, to name a few. The current state-of-the-art algorithms for finding optimal solutions are computationally expensive and therefore not scalable. In this work, we propose a more efficient optimal design for any generic configuration, with the potential to further reduce complexity for a large class of nongeneric rotationally symmetric configurations. Furthermore, we introduce a multicluster control framework that offers an additional scalability improvement, enabling not only collective affine motions as in conventional AFC but also partially independent motions naturally desired for large-scale swarms. The overall design is compatible with a swarm size of several hundred agents with fast formation convergence, as compared to up to only a few dozen agents by existing methods. Experimentally, we benchmark the performance of our algorithm compared with several state-of-the-art solutions and demonstrate the capabilities of our proposed control strategies.

eess.SY↗

arXiv2026

A Covariance Matching Approach to Graph Topology Identification

Graph topology identification (GTI) is a central challenge in networked systems, where the underlying structure is often hidden, yet nodal data are available. Conventional solutions to address these challenges rely on probabilistic models or complex optimization formulations, commonly suffering from non-convexity or requiring restrictive assumptions on acyclicity or positivity. In this paper, we propose a novel covariance matching (CovMatch) framework that directly aligns the empirical covariance of the observed data with the theoretical covariance implied by an underlying graph. We show that as long as the data-generating process permits an explicit covariance expression, CovMatch offers a unified route to topology inference. We showcase our methodology on linear structural equation models (SEMs), showing that CovMatch naturally handles both undirected and general sparse directed graphs - whether acyclic or positively weighted - without explicit knowledge of these structural constraints. Through appropriate reparameterizations, CovMatch simplifies the graph learning problem to either a conic mixed integer program for undirected graphs or an orthogonal matrix optimization for directed graphs. Numerical results confirm that, even for relatively large graphs, our approach efficiently recovers the true topology and outperforms standard baselines in accuracy. These findings highlight CovMatch as a powerful alternative to log-determinant or Bayesian methods for GTI, paving the way for broader research on learning complex network topologies with minimal assumptions.

eess.SP↗

arXiv2025

Geometry-Aware Edge-State Tracking for Resilient Affine Formation Control

Affine formation control (AFC) is a subset of formation control methods that enables coordinated multiagent movement while preserving affine relationships, and has recently gained increasing popularity due to its broad applicability across diverse applications. AFC is inherently distributed, where each agent's local controller relies on the relative displacements of neighboring agents. The unavailability of these measurements in practice, due to node or communication failures, leads to a change in the underlying graph topology and subsequently causes instability or sub-optimal performance. In this work, each edge in the graph is modeled using a state-space framework, allowing the corresponding edge-states to be estimated with or without up-to-date measurements. We then propose a Kalman-based estimation framework where we fuse both temporal information from agents' dynamics and spatial information, which is derived from the geometry of the affine formations. We give convergence guarantees and optimality analysis on the proposed algorithm, and numerical validations show the enhanced resilience of AFC against these topology changes in several practical scenarios.

eess.SP↗

arXiv2025

Fast Multiagent Formation Stabilization with Sparse Universally Rigid Frameworks

Affine formation control (AFC) is a distributed networked control system that has recently received increasing attention in various applications. AFC is typically achieved using a generalized consensus system where the stress matrix, which encodes the graph structure, is used instead of a graph Laplacian. Universally rigid frameworks (URFs) guarantee the existence of the stress matrix and have thus become the guideline for such a network design. In this work, we propose a convex optimization framework to design the stress matrix for AFC without predefining a rigid graph. We aim to find a resulting network with a reduced number of communication links, but still with a fast convergence speed. We show through simulations that our proposed solutions can yield a more sparse graph, while admitting a faster convergence compared to the state-of-the-art solutions.

eess.SY↗

arXiv2025

Autonomous Navigation of Quadrupeds Using Coverage Path Planning with Morphological Skeleton Map

This paper proposes a novel method of coverage path planning for the purpose of scanning an unstructured environment autonomously. The method uses the morphological skeleton of the prior 2D navigation map via SLAM to generate a sequence of points of interest (POIs). This sequence is then ordered to create an optimal path given the robot's current position. To control the high-level operation, a finite state machine is used to switch between two modes: navigating towards a POI using Nav2, and scanning the local surrounding. We validate the method in a leveled indoor obstacle-free non-convex environment on time efficiency and reachability over five trials. The map reader and the path planner can quickly process maps of width and height ranging between [196,225] pixels and [185,231] pixels in 2.52 ms/pixel and 1.7 ms/pixel, respectively, where their computation time increases with 22.0 ns/pixel and 8.17 $μ$s/pixel, respectively. The robot managed to reach 86.5% of all waypoints over all five runs. The proposed method suffers from drift occurring in the 2D navigation map.

cs.RO↗

arXiv2024

On the Stability of Consensus Control under Rotational Ambiguities

Consensus control of multiagent systems arises in various robotic applications such as rendezvous and formation control. For example, to compute the control inputs of individual agents, the difference in the positions in aligned coordinate frames i.e., the pairwise displacements are typically measured. However, the local coordinate frames might be subject to rotational ambiguities, such as a rotation or a reflection, particularly if the positions of the agent are not directly observed but reconstructed from e.g. pairwise Euclidean distances. This rotational ambiguity causes stability issues in practice, as agents have rotated perceptions of the environment. In this work, we conduct a thorough analysis of the stability in the presence of rotational ambiguities in several scenarios including e.g., proper and improper rotation, and the homogeneity of rotations. We give stability criteria and stability margin on the rotations, which are numerically verified with two traditional examples of consensus control.

eess.SY↗

arXiv2024

RAPF: Efficient path planning for lunar microrovers

Efficient path planning is key for safe autonomous navigation over complex and unknown terrains. Lunar Zebro (LZ), a project of the Delft University of Technology, aims to deploy a compact rover, no larger than an A4 sheet of paper and weighing not more than 3 kilograms. In this work, we introduce a Robust Artificial Potential Field (RAPF) algorithm, a new path-planning algorithm for reliable local navigation solution for lunar microrovers. RAPF leverages and improves state of the art Artificial Potential Field (APF)-based methods by incorporating the position of the robot in the generation of bacteria points and considering local minima as regions to avoid. We perform both simulations and on field experiments to validate the performance of RAPF, which outperforms state-of-the-art APF-based algorithms by over 15% in reachability within a similar or shorter planning time. The improvements resulted in a 200% higher success rate and 50% lower computing time compared to the conventional APF algorithm. Near-optimal paths are computed in real-time with limited available processing power. The bacterial approach of the RAPF algorithm proves faster to execute and smaller to store than path planning algorithms used in existing planetary rovers, showcasing its potential for reliable lunar exploration with computationally constrained and energy constrained robotic systems.

cs.RO↗

arXiv2024

Joint Ranging and Phase Offset Estimation for Multiple Drones using ADS-B Signatures

A new method for joint ranging and Phase Offset (PO) estimation of multiple drones/aircrafts is proposed in this paper. The proposed method employs the superimposed uncoordinated Automatic Dependent Surveillance Broadcast (ADS-B) packets broadcasted by drones/aircrafts for joint range and PO estimation. It jointly estimates range and PO prior to ADS-B packet decoding; thus, it can improve air safety when packet decoding is infeasible due to packet collision. Moreover, it enables coherent detection of ADS-B packets, which can result in more reliable multiple target tracking in aviation systems using cooperative sensors for detect and avoid (DAA). By minimizing the Kullback Leibler Divergence (KLD) statistical distance measure, we show that the received complex baseband signal coming from K uncoordinated drones corrupted by Additive White Gaussian Noise (AWGN) at a single antenna receiver can be approximated by an independent and identically distributed Gaussian Mixture (GM) with 2 power K mixture components in the two dimensional (2D) plane. While direct joint Maximum Likelihood Estimation (MLE) of range and PO from the derived GM Probability Density Function (PDF) leads to an intractable maximization, our proposed method employs the Expectation Maximization (EM) algorithm to estimate the modes of the 2D Gaussian mixture followed by a reordering estimation technique through combinatorial optimization to estimate range and PO. An extension to a multiple antenna receiver is also investigated in this paper. While the proposed estimator can estimate the range of multiple drones with a single receive antenna, a larger number of drones can be supported with higher accuracy by the use of multiple antennas at the receiver. The effectiveness of the proposed estimator is supported by simulation results. We show that the proposed estimator can jointly estimate the range of three drones accurately.

eess.SY↗

arXiv2024

Cooperative Sense and Avoid for UAVs using Secondary Radar

A cooperative Sense and Avoid (SAA) algorithm for safe navigation of small-sized UAVs within an airspace is proposed in this paper. The proposed method relies upon cooperation between the UAV and the surrounding transponder-equipped aviation obstacles. To do so, the aviation obstacles share their altitude and identification code with the UAV by using a Mode S operation of the Secondary Surveillance Radar (SSR) after interrogation. The proposed SAA algorithm benefits from the estimate of the aviation obstacle's elevation angle for ranging. This results in more accurate ranging compared to the round-trip time-based ranging, which is currently used in existing SAA systems. We also propose a low-complexity and accurate radial velocity estimator for the Mode S operation of the SSR which is employed in the proposed SAA system. Furthermore, by considering the Pulse-Position Modulation (PPM) of the transponder reply as a waveform of pulse radar with random pulse repetition intervals, the maximum unambiguous radial velocity is obtained. The proposed SAA is equipped with an intruder identification method that determines the risk level ofthe surrounding transponder-equipped aviation obstacles. Given the estimated parameters, the intruder identification method classifies the aviation obstacles into high-, medium-, and low-risk intruders. The output of the classifier enables the UAV to plan its path or maneuver for safe navigation accordingly. The root mean square error (RMSE) of the proposed estimators are analytically derived, and the effectiveness of our SAA solution is confirmed through simulation experiments.

eess.SP↗

arXiv2024

GPS-VIO Fusion with Online Rotational Calibration

Accurate global localization is crucial for autonomous navigation and planning. To this end, various GPS-aided Visual-Inertial Odometry (GPS-VIO) fusion algorithms are proposed in the literature. This paper presents a novel GPS-VIO system that is able to significantly benefit from the online calibration of the rotational extrinsic parameter between the GPS reference frame and the VIO reference frame. The behind reason is this parameter is observable. This paper provides novel proof through nonlinear observability analysis. We also evaluate the proposed algorithm extensively on diverse platforms, including flying UAV and driving vehicle. The experimental results support the observability analysis and show increased localization accuracy in comparison to state-of-the-art (SOTA) tightly-coupled algorithms.

cs.RO↗

arXiv2023

On the choice of reference in offset calibration

Sensor calibration is an indispensable task in any networked cyberphysical system. In this paper, we consider a sensor network plagued with offset errors, measuring a rank-1 signal subspace, where each sensor collects measurements under a linear model with additive zero-mean Gaussian noise. Under varying assumptions on the underlying noise covariance, we investigate the effect of using an arbitrary reference for estimating the sensor offsets, in contrast to the `average of all the unknown offsets' as a reference. We first show that the \emph{average} reference yields an efficient minimum variance unbiased estimator. If the underlying noise is homoscedastic in nature, then we prove the \emph{average} reference yields a factor $2$ improvement on the variance, as compared to any arbitrarily chosen reference within the network. Furthermore, when the underlying noise is independent but not identical, we derive an expression for the improvement offered by the \emph{average} reference. We demonstrate our results using the problem of clock synchronization in sensor networks, and discuss directions for future work.

eess.SP↗

arXiv2023

Artificial Potential Field-Based Path Planning for Cluttered Environments

In this paper, we study path planning algorithms of resource constrained mobile agents in unknown cluttered environments, which include but are not limited to various terrestrial missions e.g., search and rescue missions by drones in jungles, and space missions e.g., navigation of rovers on the Moon. In particular, we focus our attention on artificial potential field (APF) based methods, in which the target is attractive while the obstacles are repulsive to the mobile agent. In this paper, we propose two major updates to the classical APF algorithm which significantly improve the performance of path planning using APF. First, we propose to improve an existing classical method that replaces the gradient descent optimization of the potential field cost function on a continuous domain with a combinatorial optimization on a set of predefined points (called bacteria points) around the agent's current location. Our proposition includes an adaptive hyperparameter that changes the value of the potential function associated to each bacteria point based on the current environmental measurements. Our proposed solution improves the navigation performance in terms of convergence to the target at the expense of minimal increase in computational complexity. Second, we propose an improved potential field cost function of the bacteria points by introducing a new branching cost function which further improves the navigation performance. The algorithms were tested on a set of Monte Carlo simulation trials where the environment changes for each trial. Our simulation results show 25% lower navigation time and around 300% higher success rate compared to the conventional potential field method, and we present future directions for research.

eess.SY↗

arXiv2022

Performance Bounds for Cooperative Localisation in the Starlink Network

Mega-constellations in Low Earth Orbit have the potential to revolutionise worldwide internet access. The concomitant potential of these mega-constellations to impact space sustainability, however, has prompted concern from space actors as well as provoking concern in the ground-based astronomy community. Increasing the knowledge of the orbital state of satellites in mega-constellations improves space situations awareness, reducing the need for collision avoidance manoeuvres and allowing astronomers to prepare better observational mitigation strategies. In this paper, we create a model of Phase 1 of Starlink, one of the more well-studied megaconstellations, and investigate the potential of cooperative localisation using time-ofarrival measurements from the optical inter-satellite links in the constellation. To this end, we study the performance of any unbiased estimator for localisation, by calculating the instantaneous Cram$\acute{\text{e}}$r-Rao bound for two situations; one in which inter-satellite measurements and measurements from ground stations were considered, and one in which only relative navigation from inter-satellite measurements were considered. Our results show that localisation determined from a combination of inter-satellite measurements and ground stations can have at best an an average RMSE of approximately 10.15 metres over the majority of a satellite's orbit. Relative localisation using only inter-satellite measurements has a slightly poorer performance with an average RMSE of 10.68 metres. The results show that both anchored and anchorless inter-satellite cooperative localisation are dependent on the constellation's geometry and the characteristics of the inter-satellite links, both of which could inform the use of relative navigation in large satellite constellations in future.

eess.SY↗

arXiv2022

Relative Kinematics Estimation Using Accelerometer Measurements

Given a network of $N$ static nodes in $D$-dimensional space and the pairwise distances between them, the challenge of estimating the coordinates of the nodes is a well-studied problem. However, for numerous application domains, the nodes are mobile and the estimation of relative kinematics (e.g., position, velocity and acceleration) is a challenge, which has received limited attention in literature. In this paper, we propose a time-varying Grammian-based data model for estimating the relative kinematics of mobile nodes with polynomial trajectories, given the time-varying pairwise distance measurements between the nodes. Furthermore, we consider a scenario where the nodes have on-board accelerometers, and extend the proposed data model to include these accelerometer measurements. We propose closed-form solutions to estimate the relative kinematics, based on the proposed data models. We conduct simulations to showcase the performance of the proposed estimators, which show improvement against state-of-the-art methods.

eess.SP↗