Error growth in position estimation from noisy relative pose measurements

We examine how the estimation error grows with time when a mobile robot estimates its location from relative pose measurements without global position or orientation sensors. We show that, in both two-dimensional and three-dimensional space, both the bias and the variance of the position estimation error grows at most linearly with time asymptotically. Non-asymptotic bounds on the bias and variance are obtained, which provide insight into the mechanism of error growth. The bias is crucially dependent on the trajectory of the robot. Conclusions on the asymptotic growth rate of the bias continue to hold even with unbiased measurements or error-free translation measurements. Exact formulas for the bias and the variance of the position estimation error are provided for two specific two-dimensional trajectories–straight line and periodic. Experiments with a P3-DX wheeled robot and Monte Carlo simulations are provided to verify the theoretical predictions. A method to reduce the bias is proposed based on the lessons learned.     

Distributed clock skew and offset estimation from relative measurements in mobile networks with Markovian switching topology

We analyze a distributed algorithm for the estimation of scalar parameters belonging to nodes in a mobile network from noisy relative measurements. The motivation comes from the problem of clock skew and offset estimation for the purpose of time synchronization. The time variation of the network was modeled as a Markov chain. The estimates are shown to be mean square convergent under fairly weak assumptions on the Markov chain, as long as the union of the graphs is connected. Expressions for the asymptotic mean and correlation are also provided.     

Estimation From Relative Measurements: Electrical Analogy and Large Graphs

We examine the problem of estimating vector-valued variables from noisy measurements of the difference between certain pairs of them. This problem, which is naturally posed in terms of a measurement graph, arises in applications such as sensor network localization, time synchronization, and motion consensus. We obtain a characterization on the minimum possible covariance of the estimation error when an arbitrarily large number of measurements are available. This covariance is shown to be equal to a matrix-valued effective resistance in an infinite electrical network. Covariance in large finite graphs converges to this effective resistance as the size of the graphs increases. This convergence result provides the formal justification for regarding large finite graphs as infinite graphs, which can be exploited to determine scaling laws for the estimation error in large finite graphs. Furthermore, these results indicate that in large networks, estimation algorithms that use small subsets of all the available measurements can still obtain accurate estimates.     

Self-assembly through hydrogen-bonding and C–Hπ interactions in metal complexes of N-functionalised glycine

The complex [Ni(L1)₂(py)₂]. toluene (L1 is N-phthaloylglycinato and py is pyridine) was prepared from solid state reaction whereas co-crystals having composition 2[Ni(L1)₂(py)₃(H₂O)] · [Ni(L1)₂(py)₂(H₂O)₂] · 2py · 2H₂O was obtained from solution state reaction.     

Structure-preserving model reduction of nonlinear building thermal models

This paper proposes an aggregation-based model reduction method for nonlinear models of multi-zone building thermal dynamics. The full-order model, which is already a lumped-parameter approximation, quickly grows in state space dimension as the number of zones increases. An advantage of the proposed method, apart from being applicable to the nonlinear thermal models, is that the reduced model obtained has the same structure and physical intuition as the original model. The key to the methodology is an analogy between a continuous-time Markov chain and the linear part of the thermal dynamics. A recently developed aggregation-based method of Markov chains is employed to aggregate the large state space of the full-order model into a smaller one. Simulations are provided to illustrate tradeoffs between modeling error and computation time.     

An architectural framework for seamless handoff between IEEE 802.11 and UMTS networks

In recent years, Cellular wireless technologies like GPRS, UMTS, CDMA and Wireless Local Area Network (WLAN) technologies like IEEE 802.11 have seen a quantum leap in their growth. Cellular technologies can provide data services over a wide area, but with lower data rates. WLAN technologies offer higher data rates, but over smaller areas, popularly known as ‘Hot Spots’. The demand for an ubiquitous data service can be fulfilled, if it is possible for the end-user to seamlessly roam between these heterogeneous technologies. In this paper, a novel framework is proposed consisting of intra-ISP network called ‘Intermediate Switching Network’(ISN) fused between UMTS and WLAN networks as well as data (Internet) services for providing seamless mobility without affecting user’s activities. The ISN uses MPLS and Multiprotocol-BGP to switch the data traffic between UMTS to IEEE 802.11 networks, as per the movements of the user. The ISN is integrated with the UMTS network at the GGSN-3G and at the Access Point for IEEE 802.11 network respectively. The simulation result shows the improved performance of the ISN based framework over existing schemes.     

An Algorithm for Accurate Distributed Time Synchronization in Mobile Wireless Sensor Networks from Noisy Difference Measurements

We propose a distributed algorithm for time synchronization in mobile wireless sensor networks. The problem of time synchronization is formulated as nodes estimating their skews and offsets from noisy difference measurements of offsets and logarithm of skews; the measurements acquired by time‐stamped message exchanges between neighbors. The algorithm ensures that the estimation error is mean square convergent (variance converging to 0) under certain conditions. A sequence of scheduled update instants is used to meet the requirement of decreasing time‐varying gains that need to be synchronized across nodes with unsynchronized clocks. Moreover, a modification on the algorithm is also presented to improve the initial convergence speed. Simulations indicate that highly accurate global time estimates can be achieved with the proposed algorithm for long time durations, while the errors in competing algorithms increase over time.     

Approximation error in PDE-based modelling of vehicular platoons

We study the problem of how much error is introduced in approximating the dynamics of a large vehicular platoon by using a partial differential equation, as was done in Barooah, Mehta, and Hespanha [Barooah, P., Mehta, P.G., and Hespanha, J.P. (2009 Barooah, P, Mehta, PG and Hespanha, JP. 2009. Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability. IEEE Transactions on Automatic Control, 54: 2100–2113. [Crossref], [Web of Science ®] , [Google Scholar]), ‘Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability’, IEEE Transactions on Automatic Control, 54, 2100–2113], Hao, Barooah, and Mehta [Hao, H., Barooah, P., and Mehta, P.G. (2011), ‘Stability Margin Scaling Laws of Distributed Formation Control as a Function of Network Structure’, IEEE Transactions on Automatic Control, 56, 923–929]. In particular, we examine the difference between the stability margins of the coupled-ordinary differential equations (ODE) model and its partial differential equation (PDE) approximation, which we call the approximation error. The stability margin is defined as the absolute value of the real part of the least stable pole. The PDE model has proved useful in the design of distributed control schemes (Barooah et al. 2009 Barooah, P, Mehta, PG and Hespanha, JP. 2009. Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability. IEEE Transactions on Automatic Control, 54: 2100–2113. [Crossref], [Web of Science ®] , [Google Scholar]; Hao et al. 2011 Hao, H, Barooah, P and Mehta, PG. 2011. Stability Margin Scaling Laws of Distributed Formation Control as a Function of Network Structure. IEEE Transactions on Automatic Control, 56: 923–929. [Crossref], [Web of Science ®] , [Google Scholar]); it provides insight into the effect of gains of local controllers on the closed-loop stability margin that is lacking in the coupled-ODE model. Here we show that the ratio of the approximation error to the stability margin is O(1/N), where N is the number of vehicles. Thus, the PDE model is an accurate approximation of the coupled-ODE model when N is large. Numerical computations are provided to corroborate the analysis.     

Enhanced CO2 separation performance of mixed matrix membrane by incorporating amine-functionalized silica filler

Mixed matrix membranes (MMMs) owing to the tunable characteristics and functionalization ability can effectively substitute the highly intensive conventional membranes for industrial-scale CO₂ separation. Further, to strengthen the interfacial polymer-filler interaction, an interfacial design strategy incorporating active functional groups in the filler surface can be demonstrated. In this study, as-synthesized silica nanoparticles (SNPs) was surface functionalized by (3-aminopropyl) trimethoxysilane silica modifier (AFSNP). The CO₂ separation of poly (vinyl alcohol)/polyethylene glycol based MMM infused with surface-functionalized SNP (AFSNP) was conducted. The comparative study highlighted in-depth analysis of intrinsic physicochemical properties of as-synthesized membranes and nanoparticles. Detailed characterization such as advanced microscopic analysis, X-ray photoelectron spectroscopy (XPS) analysis and ninhydrin assay validated the successful grafting of amino groups onto the silica surface. The morphological inspection corroborated the consistent dispersion ability of the nanoparticles in the membrane matrix. The effect of the operating conditions on the membrane selectivity and CO₂ permeance were statistically analyzed by ANOVA. The CO₂ permeation result (CO₂ permeance and CO₂/N₂ selectivity) exhibited many fold increment with surface functionalization of SNPs compared to undoped silica MMM. The defect-free, performance-oriented CO₂-selective membrane thus opened up the possibility of this combination as a prospective contender for large-scale carbon capture studies.