Suboptimal Estimation Research Articles

X*: Anytime Multi-Agent Path Finding for Sparse Domains using Window-Based Iterative Repairs

Real-world multi-agent systems such as warehouse robots operate under significant time constraints – in such settings, rather than spending significant amounts of time solving for optimal paths, it is instead preferable to find valid, collision-free paths quickly, even if suboptimal, and given additional time, to iteratively refine such paths to improve their cost. In such domains, we observe that agent-agent collisions are sparse – they involve small local subsets of agents, and are geographically contained within a small region of the overall space. Leveraging this insight, we can first plan paths for each agent individually, and in the cases of collisions between agents, perform small local repairs limited to local subspace windows. As time permits, these windows can be successively grown and the repairs within them refined, thereby improving the path quality, and eventually converging to the global joint optimal solution. Using these insights, we present two algorithmic contributions: 1) the Windowed Anytime Multiagent Planning Framework (WAMPF) for a class of anytime planners that quickly generate valid paths with suboptimality estimates and generate optimal paths given sufficient time, and 2) X*, an efficient WAMPF-based planner. X* is able to efficiently find successive valid solutions by employing re-use techniques during the repair growth step of WAMPF. Experimentally, we demonstrate that in sparse domains: 1) X* outperforms state-of-the-art anytime or optimal MAPF solvers in time to valid path, 2) X* is competitive with state-of-the-art anytime or optimal MAPF solvers in time to optimal path, 3) X* quickly converges to very tight suboptimality bounds, and 4) X* is competitive with state-of-the-art suboptimal MAPF solvers in time to valid path for small numbers of agents while providing much higher quality paths.

Low‐complexity sub‐optimal cell ID estimation in NB‐IoT system

The cell identity (ID) estimation is one of the essential steps performed by the narrowband-internet of things (NB-IoT) user equipment (UE) during its initial access to the network. The cell ID value is carried by the narrowband secondary synchronisation signal (NSSS) that is periodically transmitted in even radio frames. In this study, the authors proposed a novel technique of cell ID estimation for the NB-IoT UE. The proposed technique is based on a sub-optimal estimator that applies auto-correlation over the received observations and which is 30 times less complex than the optimal maximum likelihood (ML) estimator based on cross-correlation. In addition, they presented three methods that allow the receiver to take advantage of the periodicity of the NSSS. Finally, the advantages and the drawbacks of the presented methods are discussed with a performance analysis through simulation results. Results show that these methods reach the performance of ML with lower overall complexity.

Spectral subdomains and prior estimation of leaf structure improves PROSPECT inversion on reflectance or transmittance alone

Leaf biochemical and structural traits are vegetation characteristics related to various physiological processes. Taking advantage of the physical relationship between optical properties and leaf biochemistry, field-based spectroscopy has allowed for the rapid estimation of leaf biochemical constituents and repeated non-destructive measurements through time. Leaf constituent retrieval from leaf optical properties following inversion of the physically-based radiative transfer model PROSPECT is now a popular method, but some cases prompt poor retrieval success and this approach requires a strict inversion procedure. We investigated the performances of different inversion procedures for the estimation of leaf constituents, specifically chlorophyll a and b, carotenoids, water (EWT), and dry matter (LMA) from >1400 broadleaf samples, including the definition of optimal spectral subdomains, and the use of leaf reflectance or transmittance alone. We also developed a strategy to obtain prior information on the leaf structure parameter (N) in PROSPECT, when only reflectance or transmittance is measured, and examined the influence of this prior information in combination with different inversion procedures. We found that using the full domain of reflectance or transmittance only systematically leads to suboptimal estimation of chlorophyll a and b, carotenoids, EWT, and LMA, due to either the combined absorption of multiple constituents or inaccurate estimation of the N parameter. Our study confirms that the selection of optimal spectral subdomains leads to improved estimation of all leaf constituents, from 700 to 720 nm for chlorophyll a and b, 520–560 nm for carotenoids, and from 1700 to 2400 nm for EWT and LMA. Prior information on N, computed directly from the spectra, leads to systematic improved estimation of leaf constituents when only reflectance or transmittance is measured, with reductions in normalized root mean square error from 8 to 37%. We strongly recommend using optimal subdomains when inverting PROSPECT to retrieve leaf constituents, and with the availability of only reflectance or transmittance we further recommend the use of prior information on the N parameter.

Error Analysis of Euler Semi-implicit Scheme for the Nonstationary Magneto-hydrodynamics Problem with Temperature Dependent Parameters

In this article we consider a fully discrete Euler semi-implicit scheme for the nonstationary electromagnetically and thermally driven flow, which is describing the motion of a nonisothermal incompressible magneto-hydrodyna-mics fluid subject to generalized Boussinesq problem with temperature dependent parameters. A prototypical time-stepping scheme, which is comprised of the Euler semi-implicit discretization in time and conforming mixed finite element approximation in space is studied in detail. We obtain that the proposed scheme is unconditionally stable and derive some optimal error estimates for the fluid velocity, the fluid magnetic and the fluid temperature. Moreover, a suboptimal error estimate for the fluid pressure is proved. Numerical results are provided to verify the theoretical rates of the scheme.

State estimation of CPSs with deception attacks: Stability analysis and approximate computation

This paper is concerned with the state estimation problems of cyber-physical systems (CPSs) under unobservable deception attacks. First, the optimal state estimator is provided based on the derived state probability density function, which consists of an exponentially increasing number of linear Gaussian hypotheses. The exponentially growing number of components will lead to high computational cost. Therefore, a suboptimal state estimator based on the IMM algorithm is proposed, which is computationally more efficient than the optimal estimator. Finally, numerical results are given to verify the effectiveness and superiority of the proposed suboptimal estimator, rendering an efficient and stable state estimation when the privacy of sensor measurements is attacked.

On stability and convergence of suboptimal estimation for systems over lossy networks without acknowledgement

This paper concentrates on the suboptimal state estimation problem for systems without acknowledgement (ACK). The ACK signal is used for informing the estimator of whether control-input packets have been lost during the transmission or not. For such systems, which are usually regarded as NACK systems, the optimal estimator has been proved to be beset by exponentially increasing computational burden so that it is scarcely possible to be implemented in practice and then the suboptimal estimation becomes a necessary need. Inspired by the idea of multiple-model approaches, we first design an efficient suboptimal estimator for NACK systems to significantly improve computational efficiency. More importantly, we obtained a sufficient and necessary condition to characterise the stability of this proposed suboptimal estimator, which depends only on the packet loss rate (PLR) of the observation regardless of the control-input PLR. We also prove that its estimation error will converge to that of the optimal estimator under a certain condition. A distinguishing feature of the suboptimal estimator proposed in this paper is that not only its stability and convergence can be determined theoretically, but also they are proved to be the same as those of the optimal one for NACK systems.

Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems

AbstractThe focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.

Calibration of MEMS Triaxial Accelerometers Based on the Maximum Likelihood Estimation Method

As a widely used inertial device, a MEMS triaxial accelerometer has zero-bias error, nonorthogonal error, and scale-factor error due to technical defects. Raw readings without calibration might seriously affect the accuracy of inertial navigation system. Therefore, it is necessary to conduct calibration processing before using a MEMS triaxial accelerometer. This paper presents a MEMS triaxial accelerometer calibration method based on the maximum likelihood estimation method. The error of the MEMS triaxial accelerometer comes into question, and the optimal estimation function is established. The calibration parameters are obtained by the Newton iteration method, which is more efficient and accurate. Compared with the least square method, which estimates the parameters of the suboptimal estimation function established under the condition of assuming that the mean of the random noise is zero, the parameters calibrated by the maximum likelihood estimation method are more accurate and stable. Moreover, the proposed method has low computation, which is more functional. Simulation and experimental results using the consumer low-cost MEMS triaxial accelerometer are presented to support the abovementioned superiorities of the maximum likelihood estimation method. The proposed method has the potential to be applied to other triaxial inertial sensors.

Closed-Form Distance Estimators under Kalman Filtering Framework with Application to Object Tracking

In this paper, the minimum mean square error (MMSE) estimation problem for calculation of distances between two signals via the Kalman filtering framework is considered. The developed algorithm includes two stages: the Kalman estimate of a state vector computed at the first stage is nonlinearly transformed at the second stage based on a distance function and the MMSE criterion. In general, the most challenging aspect of application of the distance estimator is calculation of the multivariate Gaussian integral. However, it can be successfully overcome for the specific metrics between two points in line, between point and line, between point and plane, and others. In these cases, the MMSE estimator is defined by an analytical closed-form expression. We derive the exact closed-form bilinear and quadratic MMSE estimators that can be effectively applied for calculation of an inner product, squared norm, and Euclidean distance. A novel low-complexity suboptimal estimator for special composite functions of linear, bilinear, and quadratic forms is proposed. Radar range-angle responses are described by the functions. The proposed estimators are validated through a series of experiments using real models and metrics. Experimental results show that the MMSE estimators outperform existing estimators that calculate distance and angle in nonoptimal manner.

Remote State Estimation With Stochastic Event-Triggered Sensor Schedule and Packet Drops

This article studies the remote state estimation problem of linear time-invariant systems with stochastic event-triggered sensor schedules in the presence of packet drops between the sensor and the estimator. Due to the existence of packet drops, the Gaussianity at the estimator side no longer holds. It is proved that the system state conditioned on the available information at the estimator side is Gaussian mixture distributed. The minimum-mean-square-error (MMSE) estimator can be obtained from the bank of Kalman filters. Since the optimal estimators require exponentially increasing computation and memory with time, suboptimal estimators to reduce computational complexities by limiting the length and numbers of hypotheses are further provided. In the end, simulations are conducted to illustrate the performance of the optimal and suboptimal estimators.

State estimate for stochastic systems with dual unknown interference inputs

Stochastic system state estimation subject to the unknown interference input widely exists in many fields, such as the control, communication, signal processing, and fault diagnosis. However, the research results are mostly limited to the stochastic system in which only the dynamic state model or the measurement model concerns the individual unknown interference input, and the state model and the measurement model are both with the same unknown interference input. State estimate of the stochastic systems where the state model and the measurement model contain dual Unknown Interference inputs (dual-UI) with different physical meanings and mathematical definitions is concerned here. Firstly, the decoupling condition with the Unknown Interference input in the State model (S-UI) is shown, which introduces the decoupled system with the adjacent Measurement concerned Unknown Interference inputs (M-UI) appearing in the state model and the measurement model. Then, through defining the Differential term of the adjacent M-UI (M-UID), the equivalent system with only M-UID in the state model is obtained. Finally, considering the design freedom of the equivalent system, the decoupling filter in the minimum mean square error sense and the adaptive minimum upper filter with different applicable conditions are represented to obtain the optimal and sub-optimal state estimate, respectively. Two simulation cases verify the effectiveness and superiority compared with the traditional methods.

Distributed optimal linear fusion estimators

This paper is concerned with the distributed information fusion estimation problem in multi-sensor environments. A universal distributed optimal linear fusion estimation (DOLFE) algorithm, which has a Kalman-type structure with matrix gains, is presented under the linear unbiased minimum variance criterion. To reduce the computational burden, two suboptimal linear fusion estimation algorithms with diagonal-matrix gains and scalar gains are also presented. Based on the proposed DOLFE algorithm, a distributed optimal linear fusion filter (DOLFF) is presented for multi-sensor linear discrete-time stochastic systems. It has better accuracy than that based on the matrix-weighted fusion of local estimators but worse accuracy than the centralized fusion filter (CFF). The stability and steady-state property of the proposed DOLFF are analyzed. Then, the corresponding multi-step predictor and smoother are also developed based on DOLFF. To obtain the distributed fusion estimators, some estimation error cross-covariance matrices that are used to compute the gains are derived. At last, distributed optimal linear fusion estimators with feedback are also presented. Furthermore, it is strictly proved that the proposed distributed optimal linear fusion filter with feedback (DOLFFWF) has the same accuracy as the CFF. Two simulation examples show the effectiveness of the proposed algorithms.

Methodological considerations for investigating oral anticoagulation persistence in atrial fibrillation.

Aims Reports of long-term oral anticoagulant (OAC) therapy for atrial fibrillation (AF) reveal highly variable, and generally suboptimal estimates of medication persistence. The objective of this review is to summarize current literature and highlight important methodological considerations for interpreting persistence research and designing studies of persistence on OAC treatment.Methods and results We summarize differences in study methodology, setting, timing, treatment, and other factors associated with reports of better or worse persistence. For example, prospective compared with retrospective study designs are associated with higher reported persistence. Similarly, patient factors such as permanent AF or high stroke risk, and treatment with non-vitamin K oral antagonists relative to vitamin K antagonists are associated with higher persistence. Persistence has also been reported to be higher in Europe compared with North America and higher when the treating physician is a general practitioner compared with a specialist. We propose a framework for assessing and designing persistence studies. This framework includes aspects of patient selection, reliability and validity of measures, persistence definitions, clinical utility of measurements, follow-up periods, and analytic approaches.Conclusions Differences in study design, patient selection, treatments, and factors such as the countries/regions where studies are conducted or the type of treating physician may help explain the variability in OAC persistence estimates. A framework is proposed to assess persistence studies. This may have utility to compare and interpret published studies as well as for planning of future studies.

Recursive Approach of Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation

Optimal Input Design (OID) methodologies are developed to find a signal that could best estimate a set of parameters of a given model. Their application in constrained nonlinear systems, especially when the search space limits or the initial conditions are unknown, may present several difficulties due to the numerical instability related to the optimization processes. A good choice over the parameters possible ranges is a trade-off among numerical stability, search space size, and effectiveness, and it is hardly found. To deal with this problem, this paper proposes a series of changes in the Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation (SOESGOPE) methodology. First, the limits over the parameters are tightly adjusted according to their confidence. A recursive approach runs the optimization methodology, analyzes the solution’s feasibility and marginal costs given by the Lagrange Multipliers, and selects a direction that could improve the system’s response. This approach improves the convergence and the assertiveness of the estimation process. To validate this approach, some cases, including a parameters estimation of a mobile robot nonlinear system, are tested.

Non-fragile Suboptimal Set-membership Estimation for Delayed Memristive Neural Networks with Quantization via Maximum-error-first Protocol

This paper is concerned with the non-fragile protocol-based set-membership estimation problem for a class of discrete memristive neural networks (MNNs) with mixed time-delays, quantization and unknown but bounded noises. The nonlinear neural activation function satisfies the sector-bounded condition and the logarithmic quantization error is transformed to the norm-bounded uncertainty. In order to save the networks resources, the maximum-error-first (MEF) protocol is introduced to allocate the utilization order of the network channel. The focus is on the design of non-fragile state estimator to ensure such that, in the simultaneous presence of the mixed time-delays, quantization errors and estimator gain perturbations, real state is confined to the ellipsoid. In particular, a minimization problem is given to determine the radius of the designed ellipsoid and the estimator gain matrix by testifying the feasibility of some recursive matrix inequalities. Finally, some simulations are used to show the feasibility of the developed non-fragile suboptimal state estimation strategy.

Discontinuous Galerkin Methods for Nonlinear Scalar Conservation Laws: Generalized Local Lax--Friedrichs Numerical Fluxes

In this paper, we study the discontinuous Galerkin (DG) method with a class of generalized numerical fluxes for one-dimensional scalar nonlinear conservation laws. The generalized local Lax--Friedrichs (GLLF) fluxes with two weights, which may not be monotone, are proposed and analyzed. Under a condition for the weights, we first show the monotonicity for the flux and thus the $L^2$ stability of the scheme. Then, by constructing and analyzing a special piecewise global projection which commutes with the time derivative operator, we are able to show optimal error estimates for the DG scheme with GLLF fluxes. The result is sharp for monotone numerical fluxes, for which only suboptimal estimates can be proved in previous work. Moreover, optimal error estimates are still valid for fluxes that are not monotone, allowing us to choose some suitable weights to achieve less numerical dissipation and thus to better resolve shocks. Numerical experiments are provided to show the sharpness of theoretical results.

Exploring $Bona~Fide$ Optimal Noise for Bayesian Parameter Estimation

In this paper, we investigate the benefit of intentionally added noise to observed data in various scenarios of Bayesian parameter estimation. For optimal estimators, we theoretically demonstrate that the Bayesian Cramer-Rao bound for the case with added noise is never smaller than for the original data, and the updated minimum mean-square error (MSE) estimator performs no better. This motivates us to explore the feasibility of noise benefit in some useful suboptimal estimators. Several Bayesian estimators established from one-bit-quantizer sensors are considered, and for different types of pre-existing background noise, optimal distributions are determined for the added noise in order to improve the performance in estimation. With a single sensor, it is shown that the optimal added noise for reducing the MSE is actually a constant bias. However, with parallel arrays of such sensors, bona fide optimal added noise, no longer a constant bias, is shown to reduce the MSE. Moreover, it is found that the designed Bayesian estimators can benefit from the optimal added noise to effectively approach the performance of the minimum MSE estimator, even when the assembled sensors possess different quantization thresholds.

Tuning of Standing Postural Responses to Instability and Cost Function

Whole-body movements are performed daily, and humans must constantly take into account the inherent instability of a standing posture. At times these movements may be performed in risky environments and when facing different costs of failure. The aim of the study was to test the hypothesis that in upright stance participants continuously estimate both probability of failure and cost of failure such that their postural responses will be based on these estimates. We designed a snowboard riding simulation experiment where participants were asked to control the position of a moving snowboard within a snow track in a risky environment. Cost functions were provided by modifying the penalty of riding in the area adjacent to the snow track. Uncertainty was modified by changing the gain of postural responses while participants were standing on a rocker board. We demonstrated that participants continually evaluated the environmental cost function and compensated for additional risk with feedback-based postural changes, even when probability of failure was negligible. Results showed also that the participants’ estimates of the probability of failure accounted for their own inherent instability. Moreover, participants showed a tendency to overweight large probabilities of failure with more biomechanically constrained standing postures that results in suboptimal estimates of risky environments. Overall, our results suggest that participants tune their standing postural responses by empirically estimating the cost of failure and the uncertainty level in order to minimize the risk of falling when cost is high.

Smart Collaborative Tracking for Ubiquitous Power IoT in Edge-Cloud Interplay Domain

Ubiquitous power Internet of Things (IoT) is suffering unprecedented constraints and reliable tracing is a typical example. Motivated by software-defined and function virtualization capabilities of edge-cloud interplay, we propose a smart collaborative tracking scheme by investigating advanced parameter prediction skills and improved particle filter approaches. First, the range-based positioning issues are transformed into the vector nonlinear suboptimal estimation problem based on information fusion. Second, the importance of density function is provisioned to calculate locations and trajectories of the mobile node by obtaining cubature points, updating state estimation, and revising vector estimation. The Gauss–Newton iterative method has been utilized to achieve higher accuracy. Third, we implement our scheme into the simulation platform and prototype system. The practical deployment has been validated from multiple perspectives. Comparing with existing candidates, experimental results illustrate that the proposed algorithm is able to enhance the performance and demonstrate acceptable reliability. Potential usages are being expected in dynamic surveillance, equipment maintenance, and other emerging IoT scenarios.

Multi-level rate-constrained successive elimination algorithm tailored to suboptimal motion estimation in HEVC

In the context of motion estimation for video coding, successive elimination algorithms (SEAs) significantly reduce the number of candidates evaluated during motion estimation without altering the resulting optimal motion vector. Nevertheless, SEA is often only used in conjunction with exhaustive search algorithms (e.g., full search). In this paper, we combine the multi-level successive elimination algorithm (ML-SEA) and the rate-constrained successive elimination algorithm (RCSEA) and show that they can be advantageously applied to suboptimal search algorithms. We demonstrate that the savings brought about by the new multi-level RCSEA (ML-RCSEA) outweigh the pre-computational costs of this approach for the Test Zonal (TZ) Search algorithm found in the HM reference encoder. We propose a novel multi-level composition pattern for performing RCSEA on an asymmetric partitioning. We introduce a double-check mechanism for RCSEA, and show that on average, it avoids computing 71% of motion vector (MV) costs. We also apply the proposed ML-RCSEA to bi-predictive refinement search and leverage a cost-based search ordering to remove 56% of error metric computations, on average. When compared to the HM reference encoder, our experiments show that the proposed solution reduces the TZ Search time by approximately 45%, contributing to an average encoding time reduction of about 7%, without increasing the Bjøntegaard delta rate (BD-Rate).