Matrix Uncertainty Research Articles

OKPS: A Reactive/Cooperative Multi-Sensors Data Fusion Approach Designed for Robust Vehicle Localization

This paper presents the Optimized Kalman Particle Swarm (OKPS) filter. This filter results from two years of research and improves the Swarm Particle Filter (SPF). The OKPS has been designed to be both cooperative and reactive. It combines the advantages of the Particle Filter (PF) and the metaheuristic Particle Swarm Optimization (PSO) for ego-vehicles localization applications. In addition to a simple fusion between the swarm optimization and the particular filtering (which leads to the Swarm Particle Filter), the OKPS uses some attributes of the Extended Kalman filter (EKF). The OKPS filter innovates by fitting its particles with a capacity of self-diagnose by means of the EKF covariance uncertainty matrix. The particles can therefore evolve by exchanging information to assess the optimized position of the ego-vehicle. The OKPS fuses data coming from embedded sensors (low cost INS, GPS and Odometer) to perform a robust ego-vehicle positioning. The OKPS is compared to the EKF filter and to filters using particles (PF and SPF) on real data from our equipped vehicle.

On Known-Plaintext Attacks to a Compressed Sensing-Based Encryption: A Quantitative Analysis

Despite the linearity of its encoding, compressed sensing (CS) may be used to provide a limited form of data protection when random encoding matrices are used to produce sets of low-dimensional measurements (ciphertexts). In this paper, we quantify by theoretical means the resistance of the least complex form of this kind of encoding against known-plaintext attacks. For both standard CS with antipodal random matrices and recent multiclass encryption schemes based on it, we show how the number of candidate encoding matrices that match a typical plaintext-ciphertext pair is so large that the search for the true encoding matrix inconclusive. Such results on the practical ineffectiveness of known-plaintext attacks underlie the fact that even closely related signal recovery under encoding matrix uncertainty is doomed to fail. Practical attacks are then exemplified by applying CS with antipodal random matrices as a multiclass encryption scheme to signals such as images and electrocardiographic tracks, showing that the extracted information on the true encoding matrix from a plaintext-ciphertext pair leads to no significant signal recovery quality increase. This theoretical and empirical evidence clarifies that, although not perfectly secure, both standard CS and multiclass encryption schemes feature a noteworthy level of security against known-plaintext attacks, therefore increasing its appeal as a negligible-cost encryption method for resource-limited sensing applications.

Robust sensor placement for leak location: analysis and design

In this paper, a nominal sensor placement methodology for leak location in water distribution networks is presented. To reduce the size and the complexity of the optimization problem a clustering technique is combined with the nominal sensor placement methodology. Some of the pressure sensor placement methods for leak detection and location in water distribution networks are based on the pressure sensitivity matrix analysis. This matrix depends on the network demands, which are nondeterministic, and the leak magnitudes, that are unknown. The robustness of the nominal sensor placement methodology is investigated against the fault sensitivity matrix uncertainty. Providing upon the dependency of the leak location procedure on the network operating point, the nominal sensor placement problem is then reformulated as a multi-objective optimization for which Pareto optimal solutions are generated. The robustness study as well as the resulting robust sensor placement methodology are illustrated by means of a small academic network as well as a district metered area in the Barcelona water distribution network.

Quantum-mechanical cumulant expansions and their application to phase-space and to phase distributions

Starting from the characteristic function of an operator, we investigate cumulant expansions in quantum optics and apply them to two-dimensional distributions for the canonical variables of the phase space in the case of one degree of freedom (Wigner quasiprobability and its Fourier transform, uncertainty matrix) and to one-dimensional distributions (phase operator, time evolution operator to Hamiltonian). In the relations between cumulants and moments, we make emphasis on the central moments of an operator. It is shown that the determinant of the uncertainty matrix (modified uncertainty product) is invariant with respect to rotation and squeezing of the state in the phase space, whereas the uncertainty sum is only invariant with respect to rotations. We examine some problems for exponentials of the phase operator and show how mean values and variances are connected with the cumulants. The Hilbert–Schmidt distance of a state during time evolution to an initial state is discussed by cumulants.

Anti-unwinding constrained attitude control for flexible spacecraft with actuator saturation

In this paper, two novel anti-unwinding constrained attitude controllers for flexible spacecraft are designed based on inverse optimal approach and unit quaternion representation of attitude subjected to inertia matrix uncertainty and external disturbance. One accounts for actuator amplitude constraint and the other considers actuator amplitude and rate constraints at length. A new saturation compensator is designed and embedded into the controllers to eliminate the effect of actuator saturation. The proposed controllers can avoid the issue of attitude slewing unwinding due to the double values of unit quaternions. The stability of the resulting closed-loop systems by the proposed controllers is guaranteed by Lyapunov-based approach. Simulation results are presented to assess the performance of the proposed methods.

Uncertainty decomposition-based fault-tolerant adaptive control of flexible spacecraft

A fault-tolerant adaptive control scheme is developed for attitude tracking of flexible spacecraft with unknown inertia parameters, external disturbance, and actuator faults. The uncertainties of flexibility and dynamics are parameterized, and the control gain matrix uncertainty is handled using an uncertainty decomposition. The control scheme, with adaptive laws of the overall system uncertain parameter estimates, guarantees the system stability and asymptotic attitude tracking properties. Simulation results illustrate the effectiveness of the proposed control scheme.

Estimates of the attraction domain of linear systems under L 2-bounded control

Using the linear matrix inequality technique, in this paper we construct a convex estimate of the attraction domain for a linear system with L 2-bounded control in the form of linear static state feedback. A robust statement of the problem is also studied, when the control system contains structured matrix uncertainty. The results of numerical simulations are presented.

Using the in-line component for fixed-wing EM 1D inversion

Numerous authors have discussed the utility of multicomponent measurements. Generally speaking, for a vertical-oriented dipole source, the measured vertical component couples to horizontal planar bodies while the horizontal in-line component couples best to vertical planar targets. For layered-earth cases, helicopter EM systems have little or no in-line component response and as a result much of the in-line signal is due to receiver coil rotation and appears as noise. In contrast to this, the in-line component of a fixed-wing airborne electromagnetic (AEM) system with large transmitter–receiver offset can be substantial, exceeding the vertical component in conductive areas. This paper compares the in-line and vertical response of a fixed-wing airborne electromagnetic (AEM) system using a half-space model and calculates sensitivity functions. The a posteriori inversion model parameter uncertainty matrix is calculated for a bathymetry model (conductive layer over more resistive half-space) for two inversion cases; use of vertical component alone is compared to joint inversion of vertical and in-line components. The joint inversion is able to better resolve model parameters. An example is then provided using field data from a bathymetry survey to compare the joint inversion to vertical component only inversion. For each inversion set, the difference between the inverted water depth and ship-measured bathymetry is calculated. The result is in general agreement with that expected from the a posteriori inversion model parameter uncertainty calculation.

A Selection Method Based on MAGDM with Interval-Valued Intuitionistic Fuzzy Sets

As the cloud computing develops rapidly, more and more cloud services appear. Many enterprises tend to utilize cloud service to achieve better flexibility and react faster to market demands. In the cloud service selection, several experts may be invited and many attributes (indicators or goals) should be considered. Therefore, the cloud service selection can be regarded as a kind of Multiattribute Group Decision Making (MAGDM) problems. This paper develops a new method for solving such MAGDM problems. In this method, the ratings of the alternatives on attributes in individual decision matrices given by each expert are in the form of interval-valued intuitionistic fuzzy sets (IVIFSs) which can flexibly describe the preferences of experts on qualitative attributes. First, the weights of experts on each attribute are determined by extending the classical gray relational analysis (GRA) into IVIF environment. Then, based on the collective decision matrix obtained by aggregating the individual matrices, the score (profit) matrix, accuracy matrix, and uncertainty (risk) matrix are derived. A multiobjective programming model is constructed to determine the attribute weights. Subsequently, the alternatives are ranked by employing the overall scores and uncertainties of alternatives. Finally, a cloud service selection problem is provided to illustrate the feasibility and effectiveness of the proposed methods.

Ecogeographically and Non-Ecogeographically Forecasting Discontinuous Canopied Simulium damnosum s.l. Habitats by Interpolating Metrizable Sub-Mixel Mean Solar Exoatmospheric Quantum Scalar Irradiance where θi is a Zenith Angle and Diatomically Etiolated Xanthophylls with Azimutually Isotropic Sources of Chloroplastic Carotenoid Zeaxanthins Spectrally Extracted from a Decomposed RapidEye™ Red Edge Normalized Difference Vegetation Index Reference Targeted Biosignature: A Case Study in Burkina Faso and

We interpolated a geospectrally decomposed 5 meter (m) RapidEye™,Red Edge, Normalized Difference Vegetation Index (NDVI), unmixed, endmember, biosignature of a georeferenced, larval habitat of Similium damnosum s.l.,a black fly vector of onchocerciasis. We did so to identify unknown, unsampled, prolific, habitats in African riverine environments. The S. damnosum s.l.larval habitat was initially geosampled in a riverine village in Burkina Faso and overlaid onto the 5m resolution data. The Band Mathfunction of ENVI 4.8TM was employed to calculate the RedEdge NDVI. Before applying the spectral index to the imagery raw mixel (“mixed pixel”) values, digital numbers(DN)] were converted into physically meaningful units to differentiate absorption reflectance spectra and immature Similium productivity based on habitat size.Linear regression was used to equate and quantitate band data to DN and the reflectance values which in the geospectral,sub-mixel, risk analysis was equivalent to removing the solar irradiance and the atmospheric path radiance in the object-based classifier. A radiometric calibration tool then calibrated the spaceborne sensor data to radiance and top-of-atmosphere (ToA) reflectance.Additionally,Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH®)removed the effects of multiscattering in the scene.We calculated the internal relative reflectance which normalized the image to a scene average spectrum. ENVI’s Log Residuals Correction Tool removed the instrument gain, topographic effects, and albedo effects from the reflectance, transmittance, wavelength emissitivities. The instantaneous fraction of direct beam radiation intercepted by the habitat canopy was calculated and described as fPAR = 1 - exp (-k (leaf area index)/cosθs) where the extinction coefficient k was a function of leaf angle distribution.We employed a successive progressive algorithm, a two stream radiative atmospheric transfer analyses, a geometric-optical model and a bidirectional reflectance distribution function to unmix the S. damnosum s.l., larval habitat,canopied endmembers.The non-parametric, residual, explanatorial, decomposed, sub-mixel estimators derived from the RapidEye™data were then used to construct a Boolean model.Therefater,the imaged larval habitat and its geospatially, ecohydrological, within-canopy pigments (e.g., chorophyll, zeathinins) were defined and a Red Edge,NDVI, endmember biosignature was decomposed in ENVI. An autocorrelation uncertainty matrix was deconvolved into combinations of the unmixed canopied endmembers.Subsequently, the NDVI, endmember biosignature, decomposed, canopied endmembers with its multiple ToA noise-adjusted coefficients were kriged in Geospatial Analyst of ArcGIS 10.3®to identify unknown, unsampled, prolific, S. damnosum s.l., georeferencable, larval habitats along a northern Ugandan riverine ecosystem. Of the forecasted prolific, shaded, larval habitats by the canopy model, 72% were found to contain S. damnosum s.l. larvae when field verified. The sensitivity of the test was 78.26 while the specifity was 100.

New generalizations of the Petersen lemma

Consideration was given to the generalizations of the Petersen lemma of matrix uncertainty which is one of the main technical facilities for handling the structured matrix uncertainties used to advantage in various robust formulations of the problems of stabilization and control.

Continuous time-varying sliding mode based attitude control for reentry vehicle

The attitude control for reentry vehicle is responsible for the robust operation to avoid the major deterioration from parametric uncertainties and external disturbances. Targeting these practical issues, both the cases with and without a priori knowledge of upper bound on the lumped uncertainty (i.e. the joint effect caused by external disturbance and inertia matrix uncertainty) are addressed, and correspondingly two continuous time-varying sliding mode based attitude controller design strategies are proposed to achieve the robust tracking of the attitude commands while alleviating the control chattering. Firstly, to deal with the case where the upper bound on the second derivative of the lumped uncertainty is known in advance, a nonlinear disturbance observer based continuous time-varying sliding mode control algorithm is developed so that the asymptotic stability of the closed system is guaranteed. Furthermore, in order to address the more practical case that the upper bound on the lumped uncertainty is unavailable, a continuous adaptive time-varying sliding mode control algorithm is derived with the related switching gains adjusted on-line, by which the trajectories of the closed-loop system are guaranteed to be uniformly ultimately bounded. Finally, the proposed strategies are applied to the attitude control of X-33 RLV in the reentry phase to illustrate the effectiveness of the theoretical results.

Robustness Analysis of Sensor Placement for Leak Detection and Location under Uncertain Operating Conditions

Some pressure sensor placement methods for leak detection and location in water distribution networks are based on the pressure sensitivity matrix analysis. This matrix depends on the network demands, which are nondeterministic, and the leak magnitudes, which are unknown. In this paper, the robustness of a sensor placement methodology against the fault sensitivity matrix uncertainty is studied. The robustness study is illustrated by means of a small academic network as well as a district metered area in the Barcelona water distribution network. Results reveal that this uncertainty should be taken into account in the sensor placement methodology.

LMI-based robust admissible control for uncertain singular delta operator systems

This paper investigates the problem of state feedback robust admissible control for singular delta operator systems with norm-bounded coefficient matrix uncertainties. A necessary and sufficient condition is derived to ensure the admissibility of the closed-loop singular delta operator system for all allowable uncertainties. Then, by specifying the structure of some matrix variables, the existence condition and explicit expression of a robust admissible controller are obtained in terms of strict linear matrix inequalities. Moreover, from the relation between singular discrete systems and singular delta operator systems, the corresponding results are also presented for uncertain singular discrete systems. Finally, some numerical examples are provided to demonstrate the effectiveness of the results in this paper.

Radar Detection of Distributed Targets in Homogeneous Interference Whose Inverse Covariance Structure is Defined via Unitary Invariant Functions

In this paper we deal with the problem of detecting an extended target embedded in homogeneous Gaussian interference with unknown but structured covariance matrix. We model the possible target echo, from each range bin under test, as a deterministic signal with an unknown scaling factor accounting for the target response. At the design stage, we exploit some a-priori knowledge about the operating environment enforcing the inverse interference plus noise covariance matrix to belong to a set described via unitary invariant continuous functions. Hence, we derive the constrained Maximum Likelihood (ML) estimates of the unknown parameters, under both the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> hypotheses, and design the Generalized Likelihood Ratio Test (GLRT) for the considered decision problem. At the analysis stage, we assess the performance of the devised GLRT for some covariance matrix uncertainty sets of practical relevance both for spatial and Doppler processing. The results highlight that correct use of the a-priori knowledge can lead to a detection performance quite close to the optimum receiver which supposes the perfect knowledge of the interference plus noise covariance matrix.

H2 control of linear uncertain systems considering input quantization with encoder/decoder mismatch

In this paper, an H2 control design for linear uncertain systems with input quantization in the presence of more general encoder/decoder mismatch is investigated. The construction of the control law includes two parts: linear part and nonlinear part. The gain of the linear part is derived from linear matrix inequalities (LMIs), and the linear part of the control law is designed for achieving the H2 performance against system characteristic matrix uncertainty and encoder/decoder mismatch. The nonlinear part is designed to eliminate the influence of external disturbance and quantization error. Finally, examples are provided to illustrate the effectiveness of the proposed method.

Time series inversion of spectra from ground-based radiometers

Abstract. Retrieving time series of atmospheric constituents from ground-based spectrometers often requires different temporal averaging depending on the altitude region in focus. This can lead to several datasets existing for one instrument, which complicates validation and comparisons between instruments. This paper puts forth a possible solution by incorporating the temporal domain into the maximum a posteriori (MAP) retrieval algorithm. The state vector is increased to include measurements spanning a time period, and the temporal correlations between the true atmospheric states are explicitly specified in the a priori uncertainty matrix. This allows the MAP method to effectively select the best temporal smoothing for each altitude, removing the need for several datasets to cover different altitudes. The method is compared to traditional averaging of spectra using a simulated retrieval of water vapour in the mesosphere. The simulations show that the method offers a significant advantage compared to the traditional method, extending the sensitivity an additional 10 km upwards without reducing the temporal resolution at lower altitudes. The method is also tested on the Onsala Space Observatory (OSO) water vapour microwave radiometer confirming the advantages found in the simulation. Additionally, it is shown how the method can interpolate data in time and provide diagnostic values to evaluate the interpolated data.

Uncertainty in developing supervisory demand-side controls in buildings: A framework and guidance

Successful demand-side control depends on the accuracy of the prediction of the power demand. This prediction should express margins of expected ranges of the power demand. Therefore, uncertainty is an unavoidable ingredient that has to be explicitly considered when evaluating performance of demand-side control. However, there is at present neither serious attention to system uncertainty nor to human-introduced uncertainty in developing the supervisory controls of building and HVAC&R systems. There is, in fact, neither a commonly shared terminology nor an agreement on a generic typology of uncertainty. Apart from introducing a common terminology and typology of uncertainty, this study provides a conceptual framework for systemic management of uncertainty, along with a process of developing the supervisory demand-side controls. This study reviews relevant uncertainty sources. Surveyed sources are classified according to the typology, and then encoded into the uncertainty matrix as part of the framework. The uncertainty matrix is used for a priori uncertainty assessment that enables model developers to identify, articulate, and prioritize critical uncertainty; it is a crucial step for gathering more adequate identification and for proper treatment of uncertainty before developing a significant model. The a priori uncertainty assessment identified that heuristic uncertainty and scenario uncertainty tend to introduce higher risks for the demand-side control in meeting its objectives. Upon this assessment, this study suggests a theoretical guide to manage and reduce risks due to uncertainty: heuristic uncertainty can be preventable if models are constructed through the formal modeling framework; physical uncertainty including both scenario uncertainty and statistical uncertainty can be compiled into model in order to render the model immune to uncertainty. • Uncertainty is an unavoidable complication for performance of the demand-side control. • Neither a commonly shared terminology nor typology of uncertainty is available. • A priori uncertainty assessment gathers more adequate identification of uncertainty. • A priori uncertainty assessment also suggests proper treatment of uncertainty. • This study presents a general guide to manage and reduce the risk due to uncertainty.

Broadband Measurements of $S$-Parameters Utilizing 4$\,\times\,$4 Butler Matrices

A novel application of 4 $\,\times\,$ 4 Butler matrices in a multiport measurement technique has been investigated. The proposed measuring system consists of two standard Butler matrices. By application of numerical procedure in measurement system calibration, an enhanced accuracy has been achieved. An influence of power detectors' uncertainty and imperfect Butler matrix parameters on calibration procedure and measurement results has been investigated. The proposed measuring system has been verified by measurements of scattering parameters of two attenuators and a narrowband bandpass filter in frequency range of 2–3 GHz. It has been shown that the proposed system allows for achieving results corresponding closely to the measurements obtained with the commercial vector network analyzer.

A Robust Sparse Signal Recovery Method with Matrix Uncertain by Using $l_2$-norm

Traditional sparse reconstruction algorithms require that the dictionary is accurately known, and the sparse recovery performance would degrade significantly with the measurement matrix uncertainty. In order to eliminate the effects of measurement matrix uncertainty, this paper proposed a robust reconstruction algorithm. Through the variance of additive errors, this algorithm incorporates the sparsity constraint and the effect of the additive errors from the statistical point at the same time. Numerical simulations demonstrated that the proposed method has a better reconstructing performance than the traditional methods.