A correction is given to a previously published result concerned with the relationship between a suitably defined matrix seminorm for consensus analysis and a coefficient of ergodicity.

Accurate metabolite annotation and false discovery rate (FDR) control remain challenging in large-scale metabolomics. Recent progress leveraging proteomics experiences and interdisciplinary inspirations has provided valuable insights. While target-decoy strategies have been introduced, generating reliable decoy libraries is difficult due to metabolite complexity. Moreover, continuous bioinformatics innovation is imperative to improve the utilization of expanding spectral resources while reducing false annotations. Here, we introduce the concept of ion entropy for metabolomics and propose two entropy-based decoy generation approaches. Assessment of public databases validates ion entropy as an effective metric to quantify ion information in massive metabolomics datasets. Our entropy-based decoy strategies outperform current representative methods in metabolomics and achieve superior FDR estimation accuracy. Analysis of 46 public datasets provides instructive recommendations for practical application.

BACKGROUND: As a gold-standard quantitative technique based on mass spectrometry, multiple reaction monitoring (MRM) has been widely used in proteomics and metabolomics. In the analysis of MRM data, as no peak picking algorithm can achieve perfect accuracy, manual inspection is necessary to correct the errors. In large cohort analysis scenarios, the time required for manual inspection is often considerable. Apart from the commercial software that comes with mass spectrometers, the open-source and free software Skyline is the most popular software for quantitative omics. However, this software is not optimized for manual inspection of hundreds of samples, the interactive experience also needs to be improved. RESULTS: Here we introduce MRMPro, a web-based MRM data analysis platform for efficient manual inspection. MRMPro supports data analysis of MRM and schedule MRM data acquired by mass spectrometers of mainstream vendors. With the goal of improving the speed of manual inspection, we implemented a collaborative review system based on cloud architecture, allowing multiple users to review through browsers. To reduce bandwidth usage and improve data retrieval speed, we proposed a MRM data compression algorithm, which reduced data volume by more than 60% and 80% respectively compared to vendor and mzML format. To improve the efficiency of manual inspection, we proposed a retention time drift estimation algorithm based on similarity of chromatograms. The estimated retention time drifts were then used for peak alignment and automatic EIC grouping. Compared with Skyline, MRMPro has higher quantification accuracy and better manual inspection support. CONCLUSIONS: In this study, we proposed MRMPro to improve the usability of manual calibration for MRM data analysis. MRMPro is free for non-commercial use. Researchers can access MRMPro through http://mrmpro.csibio.com/ . All major mass spectrometry formats (wiff, raw, mzML, etc.) can be analyzed on the platform. The final identification results can be exported to a common.xlsx format for subsequent analysis.

MOTIVATION: Liquid chromatography coupled with high-resolution mass spectrometry is widely used in composition profiling in untargeted metabolomics research. While retaining complete sample information, mass spectrometry (MS) data naturally have the characteristics of high dimensionality, high complexity, and huge data volume. In mainstream quantification methods, none of the existing methods can perform direct 3D analysis on lossless profile MS signals. All software simplify calculations by dimensionality reduction or lossy grid transformation, ignoring the full 3D signal distribution of MS data and resulting in inaccurate feature detection and quantification. RESULTS: On the basis that the neural network is effective for high-dimensional data analysis and can discover implicit features from large amounts of complex data, in this work, we propose 3D-MSNet, a novel deep learning-based model for untargeted feature extraction. 3D-MSNet performs direct feature detection on 3D MS point clouds as an instance segmentation task. After training on a self-annotated 3D feature dataset, we compared our model with nine popular software (MS-DIAL, MZmine 2, XCMS Online, MarkerView, Compound Discoverer, MaxQuant, Dinosaur, DeepIso, PointIso) on two metabolomics and one proteomics public benchmark datasets. Our 3D-MSNet model outperformed other software with significant improvement in feature detection and quantification accuracy on all evaluation datasets. Furthermore, 3D-MSNet has high feature extraction robustness and can be widely applied to profile MS data acquired with various high-resolution mass spectrometers with various resolutions. AVAILABILITY AND IMPLEMENTATION: 3D-MSNet is an open-source model and is freely available at https://github.com/CSi-Studio/3D-MSNet under a permissive license. Benchmark datasets, training dataset, evaluation methods, and results are available at https://doi.org/10.5281/zenodo.6582912.

BACKGROUND: Plate design is a necessary and time-consuming operation for GC/LC-MS-based sample preparation. The implementation of the inter-batch balancing algorithm and the intra-batch randomization algorithm can have a significant impact on the final results. For researchers without programming skills, a stable and efficient online service for plate design is necessary. RESULTS: Here we describe InjectionDesign, a free online plate design service focused on GC/LC-MS-based multi-omics experiment design. It offers the ability to separate the position design from the sequence design, making the output more compatible with the requirements of a modern mass spectrometer-based laboratory. In addition, it has implemented an optimized block randomization algorithm, which can be better applied to sample stratification with block randomization for an unbalanced distribution. It is easy to use, with built-in support for common instrument models and quick export to a worksheet. CONCLUSIONS: InjectionDesign is an open-source project based on Java. Researchers can get the source code for the project from Github: https://github.com/CSi-Studio/InjectionDesign . A free web service is also provided: http://www.injection.design .

BACKGROUND: Liquid chromatography-mass spectrometry is widely used in untargeted metabolomics for composition profiling. In multi-run analysis scenarios, features of each run are aligned into consensus features by feature alignment algorithms to observe the intensity variations across runs. However, most of the existing feature alignment methods focus more on accurate retention time correction, while underestimating the importance of feature matching. None of the existing methods can comprehensively consider feature correspondences among all runs and achieve optimal matching. RESULTS: To comprehensively analyze feature correspondences among runs, we propose G-Aligner, a graph-based feature alignment method for untargeted LC-MS data. In the feature matching stage, G-Aligner treats features and potential correspondences as nodes and edges in a multipartite graph, considers the multi-run feature matching problem an unbalanced multidimensional assignment problem, and provides three combinatorial optimization algorithms to find optimal matching solutions. In comparison with the feature alignment methods in OpenMS, MZmine2 and XCMS on three public metabolomics benchmark datasets, G-Aligner achieved the best feature alignment performance on all the three datasets with up to 9.8% and 26.6% increase in accurately aligned features and analytes, and helped all comparison software obtain more accurate results on their self-extracted features by integrating G-Aligner to their analysis workflow. G-Aligner is open-source and freely available at https://github.com/CSi-Studio/G-Aligner under a permissive license. Benchmark datasets, manual annotation results, evaluation methods and results are available at https://doi.org/10.5281/zenodo.8313034 CONCLUSIONS: In this study, we proposed G-Aligner to improve feature matching accuracy for untargeted metabolomics LC-MS data. G-Aligner comprehensively considered potential feature correspondences between all runs, converting the feature matching problem as a multidimensional assignment problem (MAP). In evaluations on three public metabolomics benchmark datasets, G-Aligner achieved the highest alignment accuracy on manual annotated and popular software extracted features, proving the effectiveness and robustness of the algorithm.

Instance segmentation in videos, which aims to segment and track multiple objects in video frames, has garnered a flurry of research attention in recent years. In this paper, we present a novel weakly supervised framework with Spatio-Temporal Collaboration for instance Segmentation in videos, namely STC-Seg. Concretely, STC-Seg demonstrates four contributions. First, we leverage the complementary representations from unsupervised depth estimation and optical flow to produce effective pseudo-labels for training deep networks and predicting high-quality instance masks. Second, to enhance the mask generation, we devise a puzzle loss, which enables end-to-end training using box-level annotations. Third, our tracking module jointly utilizes bounding-box diagonal points with spatio-temporal discrepancy to model movements, which largely improves the robustness to different object appearances. Finally, our framework is flexible and enables image-level instance segmentation methods to operate the video-level task. We conduct an extensive set of experiments on the KITTI MOTS and YT-VIS datasets. Experimental results demonstrate that our method achieves strong performance and even outperforms fully supervised TrackR-CNN and MaskTrack R-CNN. We believe that STC-Seg can be a valuable addition to the community, as it reflects the tip of an iceberg about the innovative opportunities in the weakly supervised paradigm for instance segmentation in videos.

MOTIVATION: Peptide identification of data-independent acquisition (DIA) mass spectrometry applying the peptide-centric approach heavily relies on the spectral library matching, such as the fragment intensity similarity. If the intensity similarity is calculated through all possible fragment ions of a targeted peptide instead of just a few fragment ions provided by the spectral library, the matching will be more comprehensive and reliable, and thus the identification will be more confident. In addition, the emergence of high precision spectrum predictors, like Prosit, also makes it possible to capitalize on the predicted spectrum, which contains all possible fragment ion intensities, to calculate the intensity similarity for DIA data. RESULTS: In this work, we propose Alpha-Tri, a neural-network-based model to calculate intensity similarity as a post-processing score using the predicted spectrum, measured spectrum and correlation spectrum (triple-spectrum). The predicted spectrum is generated by Prosit, the measured spectrum is retrieved from the apex of the chromatograms of all possible fragment ions and the correlation spectrum is used to indicate the present probabilities of these fragment ions as the link between the precursor and its fragment ions is lost in DIA. By adopting a data-driven method, Alpha-Tri is able to learn the intensity similarity from the triple-spectrum. This learned value is appended to initial scores from DIA-NN, allowing the ensuing statistical validation tool to report more peptides at the same false discovery rate (FDR). In our evaluation of the HeLa dataset with gradient lengths ranging from 0.5 to 2 h, Alpha-Tri delivered 3.0-7.2% gains in peptide detections at 1% FDR. On LFQbench dataset, a mixed-species dataset with known ratios, Alpha-Tri identified more peptides and proteins fell within the valid ratio ranges by up to 8.6% and 7.6%, respectively, compared with DIA-NN solely. AVAILABILITY AND IMPLEMENTATION: The original datasets for benchmarks are downloaded from the ProteomeXchange with the identifiers PXD005573, PXD000954 and PXD002952. Source code is available at https://github.com/YuAirLab/Alpha-Tri.

BACKGROUND: With the precision of the mass spectrometry (MS) going higher, the MS file size increases rapidly. Beyond the widely-used open format mzML, near-lossless or lossless compression algorithms and formats emerged in scenarios with different precision requirements. The data precision is often related to the instrument and subsequent processing algorithms. Unlike storage-oriented formats, which focus more on lossless compression rate, computation-oriented formats concentrate as much on decoding speed as the compression rate. RESULTS: Here we introduce "Aird", an opensource and computation-oriented format with controllable precision, flexible indexing strategies, and high compression rate. Aird provides a novel compressor called Zlib-Diff-PforDelta (ZDPD) for m/z data. Compared with Zlib only, m/z data size is about 55% lower in Aird average. With the high-speed decoding and encoding performance of the single instruction multiple data technology used in the ZDPD, Aird merely takes 33% decoding time compared with Zlib. We have downloaded seven datasets from ProteomeXchange and Metabolights. They are from different SCIEX, Thermo, and Agilent instruments. Then we convert the raw data into mzML, mgf, and mz5 file formats by MSConvert and compare them with Aird format. Aird uses JavaScript Object Notation for metadata storage. Aird-SDK is written in Java, and AirdPro is a GUI client for vendor file converting written in C#. They are freely available at https://github.com/CSi-Studio/Aird-SDK and https://github.com/CSi-Studio/AirdPro . CONCLUSIONS: With the innovation of MS acquisition mode, MS data characteristics are also constantly changing. New data features can bring more effective compression methods and new index modes to achieve high search performance. The MS data storage mode will also become professional and customized. ZDPD uses multiple MS digital features, and researchers also can use it in other formats like mzML. Aird is designed to become a computing-oriented data format with high scalability, compression rate, and fast decoding speed.

In robotic applications, many pose problems involve solving the homogeneous transformation based on the special Euclidean group SE(n) . However, due to the nonconvexity of SE(n) , many of these solvers treat rotation and translation separately, and the computational efficiency is still unsatisfactory. A new technique called the SE(n)++ is proposed in this article that exploits a novel mapping from SE(n) to SO(n + 1) . The mapping transforms the coupling between rotation and translation into a unified formulation on the Lie group and gives better analytical results and computational performances. Specifically, three major pose problems are considered in this article, that is, the point-cloud registration, the hand-eye calibration, and the SE(n) synchronization. Experimental validations have confirmed the effectiveness of the proposed SE(n)++ method in open datasets.

MOTIVATION: The peptide-centric identification methodologies of data-independent acquisition (DIA) data mainly rely on scores for the mass spectrometric signals of targeted peptides. Among these scores, the coelution scores of peak groups constructed by the chromatograms of peptide fragment ions have a significant influence on the identification. Most of the existing coelution scores are achieved by artificially designing some functions in terms of the shape similarity, retention time shift of peak groups. However, these scores cannot characterize the coelution robustly when the peak group is in the circumstance of interference. RESULTS: On the basis that the neural network is more powerful to learn the implicit features of data robustly from a large number of samples, and thus minimizing the influence of data noise, in this work, we propose Alpha-XIC, a neural network-based model to score the coelution. By learning the characteristics of the coelution of peak groups derived from the being analyzed DIA data, Alpha-XIC is capable of yielding robust coelution scores even for peak groups with interference. With this score appending to initial scores generated by the accompanying identification engine DIA-NN, the ensuing statistical validation can report the identification result and recover the misidentified peptides. In our evaluation of the HeLa dataset with gradient lengths ranging from 0.5 to 2 h, Alpha-XIC delivered 9.4-16.2% improvements in the number of identified precursors at 1% false discovery rate. Furthermore, Alpha-XIC was tested on LFQbench, a mixed-species dataset with known ratios, and increased the number of peptides and proteins fell within valid ratios by up to 16.4% and 17.8%, respectively, compared to the initial identification by DIA-NN. AVAILABILITY AND IMPLEMENTATION: Source code is available at https://github.com/YuAirLab/Alpha-XIC.

This article discusses cooperative stabilization control of rigid formations via an event-based approach. We first design a centralized event-based formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the triggering condition, event function, and triggering behavior are discussed in detail, and the exponential convergence of the event-based formation system is guaranteed.

Vision and voice are two vital keys for agents' interaction and learning. In this paper, we present a novel indoor navigation model called Memory Vision-Voice Indoor Navigation (MVV-IN), which receives voice commands and analyzes multimodal information of visual observation in order to enhance robots' environment understanding. We make use of single RGB images taken by a rst-view monocular camera. We also apply a self-attention mechanism to keep the agent focusing on key areas. Memory is important for the agent to avoid repeating certain tasks unnecessarily and in order for it to adapt adequately to new scenes, therefore, we make use of meta-learning. We have experimented with various functional features extracted from visual observation. Comparative experiments prove that our methods outperform state-of-the-art baselines.

This paper studies the problem of distributed computation of higher order Voronoi partition over a bounded region by a group of robots with both range-limited visibility sensors and communication devices. We model the sensing and communication capabilities by discs with limited radius. Motivated by the concept of dominating region in higher-order Voronoi partition, we propose a detecting ray based algorithm, which computes the boundary points of the dominating region of a robot in an omnidirectional manner, with local position information of its neighbors within the communication range. Simulations are provided to demonstrate the performance of our proposed algorithm by using a thirteen-robot group.

This paper proposes three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We first propose two model-independent algorithms for a subclass of Euler-Lagrange agents without the vector of gravitational potential forces. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent self-dynamics. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work studying event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities, which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information, and bounds on the initial conditions. When the Euler-Lagrange agents have dynamics that include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain parameters associated with the agent self-dynamics. For each algorithm, a trigger function is proposed to govern the event update times. The controller is only updated at each event, which ensures that the control input is piecewise constant and thus saves energy resources. We analyze each controller and trigger function to exclude Zeno behavior.

This paper studies the distributed containment control problem of multiple rigid bodies with event-triggered controllers. An event-triggered cooperative strategy is proposed based on combinational measurements. In this framework, each agent is triggered only at its own triggering instants, which reduces the frequency of controller updates in practice. It is shown that the triggering time sequence of each agent is Zero-free. Finally, a modified event-triggered condition is designed to avoid continuous combinational measurements between neighboring agents. It is also shown that no agents will exhibit Zeno triggering in this case.

In this paper, we present a fast, non-iterative approach to smooth a noisy input on the Special Euclidean Group, SE(3) manifold. The translational part can be smoothed by a simple Gaussian convolution. We then proposed a novel approach to rotation smoothing. Unlike existing rotation smoothing methods using either iterative optimization methods or stochastic filtering methods, our method allows direct computation of the smoothing result and allows parallelization of the computation. Furthermore, we have done a comparative study on Jia and Evans's method published in 2014, and shown that our method can better smooth an input rotation sequence, with shorter computational time. The smoothed camera path is then used for video stabilisation, which shows fluid and smooth camera motion.

In this paper, three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator (LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost, because both the collective object (such as formation or consensus) and the individual goal of each agent are very important for the overall system. First, we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings. The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation (ARE). It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix. Next, for physically interconnected multi-agent systems, the optimal formation algorithm is presented, and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown. Finally, if the communication topology between agents is fixed, the local feedback gain is obtained from the solution to a quadratic equation with one unknown. The equation is derived from the derivative of the cost function with respect to the local feedback gain. Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.

In this paper we detail the implementation of a Differential GPS system using only low-cost GPS receivers. The nature of the errors generated by low-cost modules is investigated and contrasted against typical error models of traditional, commercial DGPS systems. It is found that the error profile unique to low-cost GPS modules leads to a system that offers particular advantage in the horizontal plane compared to uncorrected receivers and as such is especially suited for tasks such as mapping and field robotics. A particular incarnation is demonstrated on a mobile robot with experimental results from static and moving tests showing an accuracy in the plane on the order of one metre.

In this paper, methods to improve a practical Time Difference of Arrival (TDOA) based source localization system are investigated. Firstly, our previous work on the development of a TDOA based source localization system using reconfigurable Software Defined Radios (SDRs) is described in detail. The system can achieve less than 100m error in a coverage of several kilometers. However, the performance of the localization system is limited by many factors. In order to further improve the localization accuracy, a method to improve the resolution of TDOA measurements is proposed; and by investigating the synchronization error and sensor position error through experiments, their error distributions are obtained to reduce measurement error. When the measurement accuracy reaches a limit constrained by current hardware platforms, localization optimization algorithms are implemented. Instead of proving the effectiveness of the algorithms through simulation, all numerical results are obtained from real-world experiments and the results show great enhancement of the localization accuracy.

ABSTRACT Distance estimation is vital for localization and many other applications in wireless sensor networks. In this paper, we develop a method that employs a maximum‐likelihood estimator to estimate distances between a pair of neighboring nodes in a static wireless sensor network using their local connectivity information, namely the numbers of their common and non‐common one‐hop neighbors. We present the distance estimation method under a generic channel model, including the unit disk (communication) model and the more realistic log‐normal (shadowing) model as special cases. Under the log‐normal model, we investigate the impact of the log‐normal model uncertainty; we numerically evaluate the bias and standard deviation associated with our method, which show that for long distances our method outperforms the method based on received signal strength; and we provide a Cramér–Rao lower bound analysis for the problem of estimating distances via connectivity and derive helpful guidelines for implementing our method. Finally, on implementing the proposed method on the basis of measurement data from a realistic environment and applying it in connectivity‐based sensor localization, the advantages of the proposed method are confirmed. Copyright © 2012 John Wiley & Sons, Ltd.

We consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs. Different algorithms are proposed and analyzed for different settings, including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies, as well as the case with a group velocity reference signal under switching velocity interaction. It is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions. Such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify. Rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory, matrix analysis as well as the Lyapunov stability theory.

In this paper, we analyze the performance limit of sensor localization from a novel perspective. We consider distance-based single-hop sensor localization with noisy distance measurements by time of arrival (TOA). Differently from the existing studies, the anchors are assumed to be randomly deployed, with the result that the trace of the associated Cramer-Rao Lower Bound (CRLB) matrix becomes a random variable. We adopt this random variable as a scalar metric for the performance limit and then focus on its statistical attributes. By the Central Limit Theorems for U-statistics, we show that as the number of anchors goes to infinity, this scalar metric converges to a random variable which is an affine transformation of a chi-square random variable of degree 2. In addition, we provide the quantitative relationship among the mean, the standard deviation, the number of anchors, parameters of communication channels and the distribution of the anchors. Extensive simulations are carried out to confirm the theoretical results. On the one hand, our study reveals some fundamental features of sensor localization; on the other hand, the conclusions we draw can in turn guide us in the design of wireless sensor networks.

In this paper, our main concern is to study the influence of the number of edges on the convergence rate and the total communication cost in distributed average consensus problems. We begin with the case of regular networks, i.e. networks for which the associated graph (vertices corresponding to sensors and edges being defined by communicating sensor pairs) has the same vertex degree for all vertices. In regular graphs, the number of edges is effectively determined by the common vertex degree. Therefore the problem is converted to one of analyzing the influence of the common vertex degree on the convergence rate and total communication cost. To evaluate the convergence rate we use the ratio of two eigenvalues of the Laplacian matrix of the graph, for which we obtain lower and upper bounds in terms of the common vertex degree. Using the bounds, we can illustrate the intuitively reasonable property that the convergence rate will increase with increase in the common vertex degree. However the increment in the convergence rate drops dramatically as the common vertex degree becomes progressively large. At the same time the total communication cost of the consensus process will become large. Based on these two observations we define a type of `Magic Number' to help analyze the value or otherwise of adding more links to the network. The Monte Carlo simulation results are consistent with the theoretical analysis and demonstrate the existence of the magic number. Further we present the simulation results on irregular graphs in which the degree distribution is subject to a Poisson distribution. From the simulation results we observe that the magic number also exists in the irregular graphs. In general the magic number for irregular graphs is larger than the one for regular graphs.

This paper addresses a surveillance problem in which the goal is to achieve a circular motion around a target by a non-holonomic agent. The agent only knows its own position with respect to its initial frame, and the bearing angle of the target in that frame. It is assumed that the position of the target is unknown. An estimator and a controller are proposed to estimate the position of the target and make the agent move on a circular trajectory with a desired radius around it. The performance of the proposed algorithm is verified both through simulations and experiments. Robustness is also established in the face of noise and target motion.

This paper is concerned with the asynchronous consensus problem of discrete-time second-order multi-agent system under dynamically changing communication topology, in which the asynchrony means that each agent detects the neighbors' state information to update its state information by its own clock. It is not assumed that the agents' clocks are synchronized. Nor is it assumed that the time sequence over which each agent update its state information is evenly spaced. By using tools from graph theory and nonnegative matrix theory, particularly the product properties of row-stochastic matrices from an infinite set, we finally show that essentially the same result as that for the synchronous discrete-time system holds in the face of asynchronous setting. This generalizes the existing result to a very general case.

This paper focuses on finding a dual quaternion solution to attitude and position control for multiple rigid body coordination. Representing rigid bodies in 3-D space by unit dual quaternion kinematics, a distributed control strategy, together with a specified rooted-tree structure, are proposed to control the attitude and position of networked rigid bodies simultaneously with notion concision and nonsingularity. A property called pairwise asymptotic stability of the overall system is then analyzed and validated by an example of seven quad-rotor formation in the Urban Search And Rescue Simulation (USARSim) platform. As a separate but related issue, a maximum depth condition of the rooted tree is found with respect to error accumulation along each path using dual quaternion algebra, such that a given safety bound on attitude and position errors can be satisfied.

For the purposes of this paper, “gossiping” is a distributed process whose purpose is to enable the members of a group of autonomous agents to asymptotically determine, in a decentralized manner, the average of the initial values of their scalar gossip variables. This paper discusses several different deterministic protocols for gossiping which avoid deadlocks and achieve consensus under different assumptions. First considered is$T$-periodic gossiping which is a gossiping protocol which stipulates that each agent must gossip with the same neighbor exactly once every$T$time units. Among the results discussed is the fact that if the underlying graph characterizing neighbor relations is a tree, convergence is exponential at a worst case rate which is the same for all possible$T$-periodic gossip sequences associated with the graph. Many gossiping protocols are request based which means simply that a gossip between two agents will occur whenever one of the two agents accepts a request to gossip placed by the other. Three deterministic request-based protocols are discussed. Each is guaranteed to not deadlock and to always generate sequences of gossip vectors which converge exponentially fast. It is shown that worst case convergence rates can be characterized in terms of the second largest singular values of suitably defined doubly stochastic matrices.

Distance estimation is of great importance for localization and a variety of applications in wireless sensor networks. In this paper, we develop a simple and efficient method for estimating distances between any pairs of neighboring nodes in static wireless sensor networks based on their local connectivity information, namely the numbers of their common one-hop neighbors and non-common one-hop neighbors. The proposed method involves two steps: estimating an intermediate parameter through a Maximum-Likelihood Estimator (MLE) and then mapping this estimate to the associated distance estimate. In the first instance, we present the method by assuming that signal transmission satisfies the ideal unit disk model but then we expand it to the more realistic log-normal shadowing model. Finally, simulation results show that localization algorithms using the distance estimates produced by this method can deliver superior performances in most cases in comparison with the corresponding connectivity-based localization algorithms.

Error propagation is a greatly complicated problem arising in multihop sensor localization. In this paper, we focus on how certain key factors in a sensor network affect error propagation for a restricted range-based localization scenario and obtain the significant conclusion that localization errors measured by the Mean Squared Error are propagated at the rate of the cube of the minimal hop count to anchors. A simulation analysis based on actual localization processes and the Cramér-Rao Lower Bound verifies this result.

In previous work we proposed a method to determine the bias in localization algorithms using 2 or 3 sensors, whose location have been already identified, for targets in 2-dimensional space by mixing Taylor series and Jacobian matrices. In this paper we extend the bias-correction method to n-dimensional space with N sensors. To illustrate this approach, we analyze the proposed method in three situations using localization algorithms. Monte Carlo simulation results demonstrate the proposed bias-correction method can correct the bias very well in most situations.

Location information for sensors in wireless sensor networks (WSNs) is essential to many tasks. In the presence of noise, locations must be estimated and thus the errors are unavoidable. Moreover, the errors can propagate (i.e. increase) as sensors progressively more distant from anchors are localized. Understanding the rules governing error propagation is quite helpful to deploying WSNs and improving performances of localization systems. In this paper, we investigate error propagation measured by the Cramer-Rao Lower Bound (CRLB) in a type of regular 1-Dimensional WSNs whose Fisher Information Matrices are symmetric band Toeplitz matrices. Approximate analytic formulas for the CRLBs in the regular and almost regular WSNs are derived, and properties of error propagation are also obtained. In addition, we derive a magic number relating to the number of range measurements, which indicates a turning point as to system localization accuracies.

In this paper we introduce a new approach to determine the bias in localization algorithms by mixing Taylor series and Jacobian matrices, which results in an easily calculated analytical expression for the bias. To illustrate this approach, we analyze the proposed method in two situations using localization algorithms based on distance measurements. Monte Carlo simulations verify that the proposed method is consistent with the performance of localization algorithms, which means the bias-correction method can correct the bias in most situations except when there is a collinearity problem. Although the method is analyzed in distance-based localization algorithms, it can be extended to other kinds of localization algorithms.