Gaussian process state-space models are a widely used modeling paradigm for learning and estimation in dynamical systems. Reduced-rank Gaussian process state-space models combine spectral characterization of dynamical systems with Hilbert space methods to enable learning, which scale linearly with the length of the time series. However, the current state of the art algorithms struggle to deal efficiently with the dimensionality of the state-space itself. In this work, we propose a novel algorithm, referred to as Domain-Aware reduced-rank Gaussian Process State-Space Model (DA-GPSSM), which exploits the relationship between state dimensions to model only necessary dynamics resulting in reduced computational cost, by potentially orders of magnitude in comparison to the state-of-the-art. The proposed approach grants modeling flexibility while maintaining comparable performance and thus increasing the applicability of these models. We present implications of the proposed approach and discuss applications where DA-GPSSM can be beneficial. Finally, we conduct simulations to demonstrate the performance and reduced computational cost of our proposed method, compared to the state-of-the-art learning method, and propose future research directions.

Estimation of the relative positions of N static nodes in D-dimensional space given the pairwise distances between them is a well-studied problem in literature. However, for a network of mobile nodes, the existing solutions proposed in literature rely either on the knowledge of absolute positions of some nodes or enforce constraints on the motion of individual nodes to achieve a unique solution. In this work, we consider an anchorless environment and propose a time-varying Grammian-based data model which relates the relative positions of the mobile nodes to the pairwise distances between them. Given the data model, we propose algorithms to estimate the relative positions, velocity and other higher order derivatives, referred to as relative kinematics, associated with the network of mobile nodes. We further consider a scenario where accelerometers are on-board on all the mobile nodes, and investigate the inclusion the accelerometer measurements in the proposed model. The Cramér-Rao lower bound for the proposed data models are derived and compared with the performance of the estimators using Monte-Carlo simulations. We further compare and analyze the performance of the proposed estimators against the state-of-the-art methods, and present research directions for future work to further improve the proposed approach.

Traditional target tracking using monostatic radar systems typically rely on centralized or decentralized architectures, where all data is transmitted to a fusion center for estimating the position and velocity of mobile agents. This approach introduces a single point of failure and can significantly increase communication costs, particularly when the fusion center is far from individual radar nodes. To overcome these issues, we introduce a distributed Alternating Direction Method of Multipliers (ADMM) for target localization using a radar network, wherein each radar node shares its observed data only with its immediate neighboring nodes, and achieves consensus with the radar network on the estimated target locations and velocities. We perform simulations incorporating critical system parameters such as the number of radar nodes and Signal-to-Noise Ratio (SNR) to assess their impact of estimation accuracy and convergence speed of the proposed distributed ADMM algorithm. We highlight the additional benefits of our proposed solution, and present directions for future work.

One of the key challenges for multi-agent systems is collision free navigation in an unknown environment. In this work, we propose a unified framework for joint localization, control, and collision avoidance of multi-agent systems navigating in an unknown environment in the presence of dynamic obstacles. The cooperative agents rely on information from immediate neighboring agents within their communication neighborhood, and the dynamic obstacles are modelled as non-cooperative agents. The agents achieve localization by exploiting the individual agent dynamics, and pairwise distance measurements with agents in the sensing neighborhood of each cooperative agent. To ensure collision-free navigation, we exploit a Model Predictive Control (MPC) for each agent, with avoidance constraints using safety radius between pairwise agents. Futhermore, to avoid single point of failure, we propose Cooperative Positioning, Control and Collision Avoidance (CPCCA), which is based on distributed Method of Multipliers methods. We validate our framework and algorithms through simulations, demonstrating its effectiveness in real world scenarios, and propose directions for future work.

This article proposes a novel method of coverage path planning for the purpose of scanning an unstructured environment autonomously. The method uses the morphological skeleton of a 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 based on the robot’s current position. To control the high-level operation, a finite state machine (FSM) is used to switch between two modes: navigating toward a POI using Nav2 and scanning the local surroundings. We validate the method in a leveled, indoor, obstacle-free, non-convex environment, evaluating time efficiency and reachability over five trials. The map reader and path planner can quickly process maps of widths and heights ranging between [196,225] pixels and [185,231] pixels in 2.52ms and 1.7ms, respectively. Their computation time increases with 22.0ns/pixel and 8.17 μs/pixel, respectively. The robot managed to reach 86.5% of all waypoints across the five runs. The proposed method suffers from drift occurring in the 2D navigation map.

Tensor decomposition methods for signal processing applications are an active area of research. Real data are often low-rank, noisy, and come in a higher-order format. As such, low-rank tensor approximation methods that account for the high-order structure of the data are often used for denoising. One way to represent a tensor in a low-rank form is to decompose the tensor into a set of orthonormal factor matrices and an all-orthogonal core tensor using a higher-order singular value decomposition. Under noisy measurements, the lower bound for recovering the factor matrices and the core tensor is unknown. In this paper, we exploit the well-studied constrained Cramér-Rao bound to calculate a lower bound on the mean squared error of the unbiased estimates of the components of the multilinear singular value decomposition under additive white Gaussian noise, and we validate our approach through simulations.

In this paper, we propose a new method for joint ranging and Phase Offset (PO) estimation of multiple transponder-equipped aviation vehicles (TEAVs), including Manned Aerial Vehicles (MAVs) and Unmanned Aerial Vehicles (UAVs). The proposed method employs the overlapping uncoordinated Automatic Dependent Surveillance-Broadcast (ADS-B) packets broadcasted by the TEAVs for joint range and PO estimation 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 sense and avoid. By minimizing the Kullback-Leibler Divergence (KLD), we show that the received complex baseband signal, coming from K uncoordinated TEAVs, which is corrupted by Additive White Gaussian Noise (AWGN) at a single antenna receiver can be approximated by an independent and identically distributed (i.i.d.) Gaussian Mixture (GM) with 2^K mixture components in the two-dimensional plane. The proposed estimator employs the Expectation-Maximization (EM) algorithm to estimate the modes of the 2D Gaussian mixture followed by a reordering estimation technique to jointly estimate range and PO. Simulation results show that the proposed joint estimator outperforms excising methods, such as the time segmentation method and the blind adaptive beamforming.

Consensus control of multiagent systems arises in various applications such as rendezvous and formation control. The input to these algorithms, e.g., the (relative) positions of neighboring agents need to be measured using various sensors. Recent works aim to reconstruct these positions, i.e., achieve localization using Euclidean distance measurements instead of displacements, for cost efficiency and scalability. However, this approach inherently introduces ambiguities, such as a rotation or a reflection, which can cause stability issues in practice without corrections by some anchors. In this letter, we conduct a thorough analysis of the stability of consensus control in the presence of localization-induced 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.

A cooperative sense and avoid (SAA) algorithm for safe navigation of small-sized unmanned aerial vehicles (UAVs) within an airspace is proposed in this article. 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 the 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 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 of the 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 of the proposed estimators are analytically derived, and the effectiveness of our SAA solution is confirmed through simulation experiments.

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/aircrafts corrupted by Additive White Gaussian Noise (AWGN) at a single antenna receiver can be approximated by an independent and identically distributed (i.i.d.) Gaussian Mixture (GM) with 2^{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 article. While the proposed estimator can estimate the range of multiple drones/aircrafts with a single receive antenna, a larger number of drones/aircrafts 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 multiple drones/aircrafts accurately.

Gaussian process regression (GPR), is a powerful non-parametric approach for data modeling, which has garnered considerable interest in the past decade, however its widespread application is impeded by the significant computational burden for larger datasets. The computational complexity for both inference and hyperparameter learning in GPs lead to O(N³) for N training points. The current state-of-the-art approximations, such as structured kernel interpolation (SKI)-based methods e.g., Kernel Interpolation for Scalable Structured Gaussian Process (KISSGP), have emerged to mitigate this challenge by providing a scalable inducing point alternatives. However, the choice of the optimal number of grid points, which influences the accuracy and efficiency of the model, typically remains fixed and is chosen arbitrarily. In this work, we introduce a novel approximation framework, Malleable KISSGP (MKISSGP), which dynamically adjusts grid points using a new hyperparameter of the model called density, which adapts to the changes in the kernel hyperparameters in each training iteration. In comparison with the state-of-the-art KISSGP and irrespective of changes in hyperparameters, our proposed MKISSGP algorithm exhibits consistent error levels in the reconstruction of the kernel matrix, and offers reduced computational complexity. We present extensive simulations to validate the improved performance of the proposed MKISSGP, and give directions for future research.

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.

Unmanned Aerial Systems (UAS) have rapidly gained attraction in recent years as a promising solution to revolutionize numerous applications and meet the growing demand for efficient and timely delivery services due to their highly automated operation framework. Beyond Visual Line of Sight (BVLOS) operations, in particular, offer new means of delivering added-value services via a wide range of applications. This "plateau of productivity" holds enormous promise, but it is challenging to equip the drone with affordable technologies which support the BVLOS use case. To close this gap, this work showcases the convergence of the automotive and aviation industries to advance BVLOS aviation for UAS in a practical setting by studying a combination of Commercial Off-The-Shelf (COTS) technologies and systems. A novel risk-based approach of investigating the key technological components, architectures, algorithms, and protocols is proposed that facilitate highly reliable and autonomous BVLOS operations, aiming to enhance the alignment between market and operational needs and to better identify integration requirements between the different capabilities to be developed.

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.

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.

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 average reference yields an efficient minimum variance unbiased estimator. If the underlying noise is homoscedastic in nature, then we prove the 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 average reference. We demonstrate our results using the problem of clock synchronization in sensor networks, and discuss directions for future work.

Gaussian Process (GP) is a flexible non-parametric method which has a wide variety of applications e.g., field estimation using multi-agent systems. However, the training of the hyperparameters suffers from high computational complexity. Recently, distributed hyperparameter optimization with proximal gradients has been proposed to reduce complexity, however only for a network with a central station. In this work, exploiting edge-based constraints, we propose two fully-distributed algorithms pxADMMfd and pxADMMfd,fast for a network of multi-agent systems, which do not rely on a central station. In addition, asynchronous versions of the algorithms are also proposed to reduce the synchronization overhead in heterogeneous networks. Simulations are conducted for a field estimation problem, using both artificial, and real-world datasets, which show that the proposed fully-distributed algorithms successfully converge, at the cost of an increased number of iterations.