Real Data Testing of Model Parameter Estimation Methods for Macroscopic Traffic Flow Model

We study an adaptive estimation procedure called the Goldenshluger-Lepski method in the context of reproducing kernel Hilbert space (RKHS) regression. Adaptive estimation provides a way of selecting tuning parameters for statistical estimators using only the available data. This allows us to perform estimation without making strong assumptions about the estimand. In contrast to procedures such as training and validation, the Goldenshluger-Lepski method uses all of the data to produce non-adaptive estimators for a range of values of the tuning parameters. An adaptive estimator is selected by performing pairwise comparisons between these non-adaptive estimators. Applying the Goldenshluger-Lepski method is non-trivial as it requires a simultaneous high-probability bound on all of the pairwise comparisons. In the RKHS regression context, we choose our non-adaptive estimators to be clipped least-squares estimators constrained to lie in a ball in an RKHS. Applying the Goldenshluger-Lepski method in this context is made more complicated by the fact that we cannot use the $L^2$ norm for performing the pairwise comparisons as it is unknown. We use the method to address two regression problems. In the first problem the RKHS is fixed, while in the second problem we adapt over a collection of RKHSs.

This paper is concerned with an adaptive state estimation problem for a class of continuous-time nonlinear stochastic systems with unknown constant parameters. These nonlinear systems have a linear-in-parameter (affine) structure and the nonlinearity is assumed to be bounded in a Lipschitz-like manner. Using stochastic counterparts of Lyapunov stability theory, we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square. Sufficient conditions are given in terms of the solvability of LMIs. In addition, we introduce a suboptimal design approach. By a martingale method, we demonstrate that this suboptimal design procedure also minimizes an upper bound of estimation error in almost sure sense.

An adaptive freeway traffic state estimator

This paper investigates adaptive event-triggered state estimation for T-S fuzzy systems with multiple cyber-attacks. In order to reduce network load, the adaptive event-trigger mechanism is used to adjust the threshold of event triggering condition adaptively on the premise of ensuring system performance. Considering the influence of cyber-attacks, a T-S fuzzy model for the state estimation is established with the adaptive event-trigger mechanism. On the basis of the model, the sufficient conditions to guarantee the system asymptotically stability are obtained by using Lyapunov stability theory. In addition, the gains of the estimator are acquired in the form of linear matrix inequalities (LMIs). Finally, a simulated example is given to testify the feasibility of the proposed method.

This paper presents a method for real time adaptive hybrid state estimation of the power system states using the SCADA as well as limited synchronous phasor measurements. The proposed method can track the power system dynamics by periodically updating the sensitivities to the unobservable buses during the intervals between successive outputs of state estimator with SCADA measurements. The performance of the proposed method is evaluated on a number of standard test systems for different sets of un-observability. Simulation result shows that the proposed method can track the electromechanical dynamics of the system during the large disturbances in the system, it also improves the accuracy of the estimates and enhances the numerical stability of the estimation.

Measurement error is a crucial factor that determines the accuracy of state estimation (SE). Conventional estimators have fixed models, and can yield optimal performance only when the measurement error statistics exactly meet the assumptions. In reality, however, the error distribution is usually unknown and time-varying, resulting in suboptimal state estimates in most cases. This paper develops the concept of adaptive SE for power systems measured by phasor measurement units (PMUs). First, the Gaussian-Laplacian Mixture (GLM) model is developed to fit the body and tail of unknown measurement error distributions. Then, an adaptive estimation framework is proposed based on the Expectation-Maximization (EM) algorithm. It is capable of tracking the actual error statistics online, and adjusting the parameters of SE to maintain near-optimality of state estimates under complex measurement error conditions. Simulation results demonstrate that the proposed adaptive estimator yields more accurate state estimates than the well-known Weighted Least Squares (WLS) and Weighted Least Absolute Value (WLAV) estimators by adapting itself to the variations of measurement error statistics.

In many circumstances involving heat and mass transfer issues, it is considered impractical to measure the input flux and the resulting state distribution in the domain. Therefore, the need to develop techniques to provide solutions for such problems and estimate the inverse mass flux becomes imperative. Adaptive state estimator (ASE) is increasingly becoming a popular inverse estimation technique which resolves inverse problems by incorporating the semi-Markovian concept into a Bayesian estimation technique, thereby developing an inverse input and state estimator consisting of a bank of parallel adaptively weighted Kalman filters. The ASE is particularly designed for a system that encompasses independent unknowns and /or random switching of input and measurement biases. The present study describes the scheme to estimate the groundwater input contaminant flux and its transient distribution in a conjectural two-dimensional aquifer by means of ASE, which in particular is because of its unique ability to efficiently handle the process noise giving an estimation of keeping the relative error range within 10% in 2-dimensional problems. Numerical simulation results show that the proposed estimator presents decent estimation performance for both smoothly and abruptly varying input flux scenarios. Results also show that ASE enjoys a better estimation performance than its competitor, Recursive Least Square Estimator (RLSE) due to its larger error tolerance in greater process noise regimes. ASE’s inherent deficiency of being slower than the RLSE, resulting from the complexity of algorithm, was also noticed. The chosen input scenarios are tested to calculate the effect of input area and both estimators show improved results with an increase in input flux area especially as sensors are moved closer to the assumed input location.

Path planning over spatiotemporal models can be applied to a variety of applications such as UAVs searching for spreading wildfire in mountains or network of balloons in time-varying atmosphere deployed for inexpensive internet service. A notable aspect in such applications is the dynamically changing environment. However, path planning algorithms often assume static environments and only consider the vehicle’s dynamics exploring the environment. We present a spatiotemporal model that uses a cross-correlation operator to consider spatiotemporal dependence. Also, we present an adaptive state estimator for path planning. Since the state estimation depends on the vehicle’s path, the path planning needs to consider the trade-off between exploration and exploitation. We use a high-level decision-maker to choose an explorative path or an exploitative path. The overall proposed framework consists of an adaptive state estimator, a short-term path planner, and a high-level decision-maker. We tested the framework with a spatiotemporal model simulation where the state of each grid transits from normal, latent, and fire state. For the mission objective of visiting the grids with fire, the proposed framework outperformed the random walk (baseline) and the single-minded exploitation (or exploration) path.

In this paper, we model the generalized power system state estimation problem as a hybrid estimation problem in which the network configuration and voltage phasor states are treated as discrete and continuous states, respectively. We propose the Multiple model Adaptive Power system State Estimator (MAPSE), which implements a multiple model adaptive estimator with a bank of Unscented Kalman Filters (UKFs) to provide a running estimate of the voltage phasor states and a probability distribution for the candidate network configurations. The MAPSE updates the network configuration probability distribution by applying a Bayesian recursion to the measurement residuals from each of the UKFs at each timestep. Simulation on a modified version of the 33 node distribution network demonstrates successful network configuration detection and accurate voltage phasor state estimation.

The paper presents a review of methods for adaptive estimation of signals with unknown structures and parameters of models that determine the properties of both the signal itself and the errors of its measurement. The main approaches to solution of adaptive estimation problems are considered. One of them is aimed at designing algorithms with a learning sample, and the other one relies on the Bayesian approach and aims at solving the joint problem of signal estimation and identification of models used to describe the signal and measurement errors in real time. An adaptive estimation algorithm based on the Bayesian approach is described in detail. The problems in which the proposed algorithm is used are discussed. Its effectiveness is illustrated by the example of gravity anomaly estimation on a moving vehicle under model uncertainty of the signal and measurement errors.

ABSTRACTThis paper describes a method of extracting time-varyingfeatures that is effective for speech signals with high funda-mental frequencies. The proposed method adopts a speechproduction model that consists of a Time-Varying Auto-Regressive (TVAR) process for an articulatory filter and aHidden Markov Model (HMM) for an excitation source.The model represents waveform amplitude variations bytime-varying gain of the excitation source. The proposed algo-rithm is given by extending a Viterbi algorithm so that theproposed algorithm can adaptively estimate TVAR coeffi-cients and time-varying gain with decoding the state tran-sition of the excitation source HMM. We applied the pro-posed method to extracting time-varying features from bothsynthetic and natural speech, and confirmed its feasibility.1. INTRODUCTIONThe conventional Linear Prediction (LP) method is widelyused to analyze speech signals[1]. However, several prob-lems still remain to be solved[2]. One such problem is thatlocal peaks of the LP spectral estimate are strongly biasedtoward the harmonics, especially for high-pitched speech.Several methods have been designed to overcome this prob-lem [3, 4, 5, 6]. The authors have previously indicated thatan analysis method based on a speech production modelconsisting of an Auto-Regressive (AR) process for an artic-ulatoryfilterand a HiddenMarkov Model(HMM)for an ex-citationsource is robustforhighfundamental frequencies[7,8]. However, this method is not suitable for analyzing con-tinuous speech for the following reasons. First, the AR co-efficients and HMM are iteratively estimated within everyanalysis frame, so a large number of operations is needed.Second, the analysis frame size needs to be large in orderto guarantee stable learning of the excitation source HMM.Third, the model parameters are assumed to be constantwithin the analysis frame, so the resulting parameters areaveraged within such a long analysis frame. This makesit difficult to extract the dynamic characteristics of speechwhen features change rapidly, like in a singing voice.In this paper, we extend the speech production model in[7] so that the proposed model can represent time-varyingfeatures of continuous speech. We also describe an anal-ysis method that adaptively estimates Time-Varying Auto-Regressive (TVAR) coefficients and gain based on the newmodel. The proposed method can substantially reduce thenumber of operations by applying the learned HMM andcan also extract dynamic characteristics of continuous speechby estimating those time-varying features adaptively.2. SPEECH PRODUCTION MODEL BASED ONTVAR-HMMThe proposed method adopts a speech production modelthat consists of a TVAR process for an articulatory filterand an HMM for an excitation source. The nodes of theHMM are concatenated in a ring state in order to representperiodicity of voiced sounds. We have previously shownthat LP analysis incorporating the excitation source HMMcan precisely estimate the characteristics of both vocal tractand excitation source from high-pitched speech signal[7, 8].The proposed model represents the time-varying features ofnot only the vocal tract but also the waveform amplitude bymultiplying an excitation source emitted from the HMM bya time-varying gain.

Kalman filtering (KF) and hidden Markov model (HMM) signal processing techniques are coupled to demodulate signals transmitted through noisy fading channels. The demodulation scheme presented can be applied to both digital M-ary differential phase shift keyed (MDPSK) and analog frequency modulated (FM) signals. Adaptive state and parameter estimation algorithms are devised based on the assumption that the transmission channel introduces time-varying gain and phase changes, modelled by a stochastic linear system, and has additive Gaussian noise. Our technique is to use an HMM filter, for signal estimation, coupled with a KF, for channel parameter tracking. The approach taken can easily be generalised for other transmission schemes, such as continuous phase modulated (CPM) signals. >

The state of charge (SoC) estimation is the safety management basis of the packing lithium‐ion batteries (LIB), and there is no effective solution yet. An improved splice equivalent modeling method is proposed to describe its working characteristics by using the state‐space description, in which the optimization strategy of the circuit structure is studied by using the aspects of equivalent mode, analog calculation, and component distribution adjustment, revealing the mathematical expression mechanism of different structural characteristics. A novel particle adaptive unscented Kalman filtering algorithm is introduced for the iterative calculation to explore the working state characterization mechanism of the packing LIB, in which the incorporate multiple information is considered and applied. The adaptive regulation is obtained by exploring the feature extraction and optimal representation, according to which the accurate SoC estimation model is constructed. The state of balance evaluation theory is explored, and the multiparameter correction strategy is carried out along with the experimental working characteristic analysis under complex conditions, according to which the optimization method is obtained for the SoC estimation model structure. When the remaining energy varies from 10% to 100%, the tracking voltage error is <0.035 V and the SoC estimation accuracy is 98.56%. The adaptive working state estimation is realized accurately, which lays a key breakthrough foundation for the safety management of the LIB packs.

We simplify a general heuristic necessary condition of Stein's for adaptive estimation of a Euclidean parameter in the presence of an infinite dimensional shape nuisance parameter and other Euclidean nuisance parameters. We derive sufficient conditions and apply them in the construction of adaptive estimates for the parameters of linear models and multivariate elliptic distributions. We conclude with a review of issues in adaptive estimation.

Bickel and Ritov suggested an optimal estimator for the integral of the square of the kth derivative of a density when the unknown density belongs to a Lipschitz class of a given order $\beta$. In this context optimality means that the estimate is asymptotically efficient, that is, it has the best constant and rate of risk convergence, whenever $\beta > 2k + 1/4$, and it is rate optimal otherwise. The suggested optimal estimator crucially depends on the value of $\beta$ which is obviously unknown. Bickel and Ritov conjectured that the method of cross validation leads to a corresponding adaptive estimator which has the same optimal statistical properties as the optimal estimator based on prior knowledge of $\beta$. We show for probability densities supported over a finite interval that when $\beta > 2k + 1/4$ adaptation is not necessary for the construction of an asymptotically efficient estimator. On the other hand, it is not possible to construct an adaptive estimator which has the same rate of convergence as the optimal nonadaptive estimator as soon as $k < \beta \leq 2k + 1/4$.