Incidence vs Cumulative Cases (ICC) curves are introduced and shown to provide a simple framework for parameter identification in the case of the most elementary epidemiological model, consisting of susceptible, infected, and removed compartments. This novel methodology is used to estimate the basic reproduction ratio of recent outbreaks, including the ongoing COVID-19 epidemic.
We discuss the parameter estimation of the probability of default (PD), the correlation between the obligors, and a phase transition. In our previous work, we studied the problem using the beta-binomial distribution. A non-equilibrium phase transition with an order parameter occurs when the temporal correlation decays by power law. In this article, we adopt the Merton model, which uses an asset correlation as the default correlation, and find that a phase transition occurs when the temporal correlation decays by power law. When the power index is less than one, the PD estimator converges slowly. Thus, it is difficult to estimate PD with limited historical data. Conversely, when the power index is greater than one, the convergence speed is inversely proportional to the number of samples. We investigate the empirical default data history of several rating agencies. The estimated power index is in the slow convergence range when we use long history data. This suggests that PD could have a long memory and that it is difficult to estimate parameters due to slow convergence.
Motivated by future automotive applications, we study the joint target detection and parameter estimation problem using orthogonal time frequency space (OTFS), a digital modulation format robust to time-frequency selective channels. Assuming the transmitter is equipped with a mono-static MIMO radar, we propose an efficient maximum likelihood based approach to detect targets and estimate the corresponding delay, Doppler, and angle-of-arrival parameters. In order to reduce the computational complexity associated to the high-dimensional search, our scheme proceeds in two steps, i.e., target detection and coarse parameter estimation followed by refined parameter estimation. Interestingly, our numerical results demonstrate that the proposed scheme is able to identify multiple targets if they are separated in at least one domain out of three (delay, Doppler, and angle), while achieving the Cram\'er-Rao lower bound for the parameter estimation.
For the description of a pandemic mathematical models could be interesting. Both for physicians and politicians as a base for decisions to treat the disease. The responsible estimation of parameters is a main issue of mathematical pandemic models. Especially a good choice of $\beta$ as the number of others that one infected person encounters per unit time (per day) influences the adequateness of the results of the model. For the actual COVID-19 pandemic some aspects of the parameter choice will be discussed. Because of the incompatibility of the data of the Johns-Hopkins-University to the data of the German Robert-Koch-Institut we use the COVID-19 data of the European Centre for Disease Prevention and Control (ECDC) as a base for the parameter estimation. Two different mathematical methods for the data analysis will be discussed in this paper and possible sources of trouble will be shown. As example of the parameter choice serve the data of the USA and the UK. The resulting parameters will be used estimated and used in W.\,O. Kermack and A.\,G. McKendrick's SIR model. Strategies for the commencing and ending of social and economic shutdown measures are discussed. The numerical solution of the ordinary differential equation system of the modified SIR model is being done with a Runge-Kutta integration method of fourth order. At the end the applicability of the SIR model could be shown essentially. Suggestions about appropriate points in time at which to commence with lockdown measures based on the acceleration rate of infections conclude the paper.
Estimating downlink (DL) channel state information (CSI) in frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems generally requires downlink pilots and feedback overheads. Accordingly, this paper investigates the feasibility of zero-feedback FDD massive MIMO systems based on channel extrapolation. We use the high-resolution parameter estimation (HRPE), specifically the space-alternating generalized expectation-maximization (SAGE) algorithm, to extrapolate the DL CSI based on the extracted parameters of multipath components in the uplink channel. We apply the HRPE to two different channel models: the vector spatial signature (VSS) model and the direction of arrival (DOA) model. We verify these methods through real-world channel data acquired from channel measurement campaigns with two different types of channel sounders: a) a switched array-based, real-time, time-domain, outdoors setup at 3.5 GHz, and b) a virtual array-based, high-accuracy, frequency-domain, indoors setup at 2.4 and 5-7 GHz. The performance metrics of the extrapolated channels that we evaluate include the mean squared error, beamforming efficiency, and spectral efficiency in multiuser MIMO scenarios. The results show that the HRPE-based channel extrapolation performs best under the simple VSS model, which does not require array calibration, and if the BS is in an open outdoor environment having line-of-sight (LOS) paths to well-separated users.
This paper studies cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our paper. Distributed adaptive observers are designed for all follower nodes, simultaneously estimate the state and parameters of the leader node. The observer design does not rely on the frequency knowledge of the leader node, and the estimation errors are shown to converge to zero exponentially. Moreover, the results are applied to general directed graphs, where the symmetry of Laplacian matrix does not hold. This is due to two newly developed Lyapunov equations, which solely depend on communication network topologies. Interestingly, using these Lyapunov equations, many results of multi-agent systems over undirected graphs can be extended to general directed graphs. Finally, this paper also advances the knowledge base of adaptive control systems by providing a main tool in the analysis of parameter convergence for adaptive observers.
Electromagnetic inverse scattering problems (ISPs) aim to retrieve permittivities of dielectric scatterers from the scattering measurement. It is often highly nonlinear, caus-ing the problem to be very difficult to solve. To alleviate the issue, this letter exploits a linear model-based network (LMN) learning strategy, which benefits from both model complexity and data learning. By introducing a linear model for ISPs, a new model with network-driven regular-izer is proposed. For attaining efficient end-to-end learning, the network architecture and hyper-parameter estimation are presented. Experimental results validate its superiority to some state-of-the-arts.
This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and limit-cycle oscillations, we prove consistency of the parameter estimation procedure under output feedback. Hence, this paper provides a rigorous framework for the application of conventional nonlinear system identification methods to discrete-time stochastic neuronal systems. The main result exploits the elementary property that conductance-based models of neurons have an exponentially contracting inverse dynamics. This property is implied by the voltage-clamp experiment, which has been the fundamental modeling experiment of neurons ever since the pioneering work of Hodgkin and Huxley.
This paper presents a Bayesian parameter estimation approach and identifiability analysis for a lithium-ion battery model, to determine the uniqueness, evaluate the sensitivity and quantify the uncertainty of a subset of the model parameters. The analysis was based on the single particle model with electrolyte dynamics, rigorously derived from the Doyle-Fuller-Newman model using asymptotic analysis including electrode-average terms. The Bayesian approach allows complex target distributions to be estimated, which enables a global analysis of the parameter space. The analysis focuses on the identification problem (i) locally, under a set of discrete quasi-steady states of charge, and in comparison (ii) globally with a continuous excursion of state of charge. The performance of the methodology was evaluated using synthetic data from multiple numerical simulations under diverse types of current excitation. We show that various diffusivities as well as the transference number may be estimated with small variances in the global case, but with much larger uncertainty in the local estimation case. This also has significant implications for estimation where parameters might vary as a function of state of charge or other latent variables.
Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are then post-processed to reveal details about the motion. In this work, we develop an algorithm for jointly estimating both particle trajectory and motion model parameters from the data. Our approach uses Expectation Maximization (EM) combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), allowing us to use an accurate, nonlinear model of the observations acquired by the camera. Due to the shot noise characteristics of the photon generation process, this model uses a Poisson distribution to capture the measurement noise inherent in imaging. In order to apply a UKF, we first must transform the measurements into a model with additive Gaussian noise. We consider two approaches, one based on variance stabilizing transformations (where we compare the Anscombe and Freeman-Tukey transforms) and one on a Gaussian approximation to the Poisson distribution. Through simulations, we demonstrate efficacy of the approach and explore the differences among these measurement transformations.
The extent of vibrations experienced by a vehicle driving over natural terrain defines its ride quality. Generally, surface irregularities, ranging from single discontinuities to random variations of the elevation profile, act as a major source of excitation that induces vibrations in the vehicle body through the tire-soil interaction and suspension system. Therefore, the ride response of off-road vehicles is tightly connected with the ground properties. The objective of this research is to develop a model-based observer that estimates automatically terrain parameters using available onboard sensors. Two acceleration signals, one coming from the vehicle body and one from the wheel suspension, are fed into a dynamic vehicle model that takes into account tire/terrain interaction to estimate ground properties. To solve the resulting nonlinear simultaneous state and parameter estimation problem, the cubature Kalman filter is used, which is shown to outperform the standard extended Kalman filter in terms of accuracy and stability. An extensive set of simulation tests is presented to assess the performance of the proposed estimator under various surface roughness and deformability conditions. Results show the potential of the proposed observer to estimate automatically terrain properties during operations that could be implemented onboard of a general family of intelligent vehicles, ranging from off-road high-speed passenger cars to lightweight and low-speed planetary rovers.
The integration of renewables into electrical grids calls for the development of tailored control schemes which in turn require reliable grid models. In many cases, the grid topology is known but the actual parameters are not exactly known. This paper proposes a new approach for online parameter estimation in power systems based on optimal experimental design using multiple measurement snapshots. In contrast to conventional methods, our method computes optimal excitations extracting the maximum information in each estimation step to accelerate convergence. The performance of the proposed method is illustrated on a case study.
The advent of single molecule microscopy has revolutionized biological investigations by providing a powerful tool for the study of intercellular and intracellular trafficking processes of protein molecules which was not available before through conventional microscopy. In practice, pixelated detectors are used to acquire the images of fluorescently labeled objects moving in cellular environments. Then, the acquired fluorescence microscopy images contain the numbers of the photons detected in each pixel, during an exposure time interval. Moreover, instead of having the exact locations of detection of the photons, we only know the pixel areas in which the photons impact the detector. These challenges make the analysis of single molecule trajectories, from pixelated images, a complex problem. Here, we investigate the effect of pixelation on the parameter estimation of single molecule trajectories. In particular, we develop a stochastic framework to calculate the maximum likelihood estimates of the parameters of a stochastic differential equation that describes the motion of the molecule in living cells. We also calculate the Fisher information matrix for this parameter estimation problem. The analytical results are complicated through the fact that the observation process in a microscope prohibits the use of standard Kalman filter type approaches. The analytical framework presented here is illustrated with examples of low photon count scenarios for which we rely on Monte Carlo methods to compute the associated probability distributions.
We construct a data-driven statistical indicator for quantifying the tail risk perceived by the EURGBP option market surrounding Brexit-related events. We show that under lognormal SABR dynamics this tail risk is closely related to the so-called martingale defect and provide a closed-form expression for this defect which can be computed by solving an inverse calibration problem. In order to cope with the the uncertainty which is inherent to this inverse problem, we adopt a Bayesian statistical parameter estimation perspective. We probe the resulting posterior densities with a combination of optimization and adaptive Markov chain Monte Carlo methods, thus providing a careful uncertainty estimation for all of the underlying parameters and the martingale defect indicator. Finally, to support the feasibility of the proposed method, we provide a Brexit "fever curve" for the year 2019.
Target parameter estimation in active sensing, and particularly radar signal processing, is a long-standing problem that has been studied extensively. In this paper, we propose a novel approach for target parameter estimation in cases where one-bit analog-to-digital-converters (ADCs), also known as signal comparators with time-varying thresholds, are employed to sample the received radar signal instead of high-resolution ADCs. The considered problem has potential applications in the design of inexpensive radar and sensing devices in civilian applications, and can likely pave the way for future radar systems employing low-resolution ADCs for faster sampling and high-resolution target determination. We formulate the target estimation as a multivariate weighted-least-squares optimization problem that can be solved in a cyclic manner. Numerical results are provided to exhibit the effectiveness of the proposed algorithms.
In this paper, we build a new, simple, and interpretable mathematical model to estimate and forecast physiology related to the human glucose-insulin system, constrained by available data. By constructing a simple yet flexible model class with interpretable parameters, this general model can be specialized to work in different settings, such as type 2 diabetes mellitus (T2DM) and intensive care unit (ICU); different choices of appropriate model functions describing uptake of nutrition and removal of glucose differentiate between the models. In both cases, the available data is sparse and collected in clinical settings, major factors that have constrained our model choice to the simple form adopted. The model has the form of a linear stochastic differential equation (SDE) to describe the evolution of the BG level. The model includes a term quantifying glucose removal from the bloodstream through the regulation system of the human body and two other terms representing the effect of nutrition and externally delivered insulin. The stochastic fluctuations encapsulate model error necessitated by the simple model form and enable flexible incorporation of data. The model parameters must be learned in a patient-specific fashion, leading to personalized models. We present experimental results on patient-specific parameter estimation and future BG level forecasting in T2DM and ICU settings. The resulting model leads to the prediction of the BG level as an expected value accompanied by a band around this value which accounts for uncertainties in the prediction. Such predictions, then, have the potential for use as part of control systems that are robust to model imperfections and noisy data. Finally, the model's predictive capability is compared with two different models built explicitly for T2DM and ICU contexts.
Mathematical modeling and real-time dynamics identification of the mean arterial blood pressure (MAP) response of a patient to vasoactive drug infusion can provide a reliable tool for automated drug administration and therefore, reduce the emergency costs and significantly benefit the patient's MAP regulation in an intensive care unit. To this end, a dynamic first-order linear parameter-varying (LPV) model with varying parameters and varying input delay is considered to capture the MAP response dynamics. Such a model effectively addresses the complexity and the intra- and inter-patient variability of the physiological response. We discretize the model and augment the state vector with model parameters as unknown states of the system and a Bayesian-based multiple-model square root cubature Kalman filtering (MMSRCKF) approach is utilized to estimate the model time-varying parameters. Since, unlike the other model parameters, the input delay cannot be captured by a random-walk process, a multiple-model module with a posterior probability estimation is implemented to provide the delay identification. Validation results confirm the effectiveness of the proposed identification algorithm both in simulation scenarios and also using animal experiment data.
Accurate estimation of the distance between the transmitter (TX) and the receiver (RX) in molecular communication (MC) systems can provide faster and more reliable communication. Existing theoretical models in the literature are not suitable for distance estimation in a practical scenario. Furthermore, deriving an analytical model is not easy due to effects such as boundary conditions in the diffusion process, the initial velocity of the molecules and unsteady flows. Therefore, five different practical methods comprising three novel data analysis based methods and two supervised machine learning (ML) methods, Multivariate Linear Regression (MLR) and Neural Network Regression (NNR), are proposed for distance estimation at the RX side. In order to apply the ML methods, a macroscale practical MC system, which consists of an electric sprayer without a fan, alcohol molecules, an alcohol sensor and a microcontroller, is established, and the received signals are recorded. A feature extraction algorithm is proposed to utilize the measured signals as the inputs in ML methods. The numerical results show that the ML methods outperform the data analysis based methods in the root mean square error sense with the cost of complexity. Moreover, the peak time based estimation, which is one of the proposed data analysis based methods, yields better results with respect to the other proposed four methods, as the distance increases. Given the experimental data and fluid dynamics theory, a possible trajectory of the molecules between the TX and RX is given. Our findings show that distance estimation performance is jointly affected by unsteady flows and the non-linearity of the sensor. According to our findings based on fluid dynamics, it is evaluated that fluid dynamics should be taken into account for more accurate parameter estimation in practical macroscale MC systems.
Demystifying effective connectivity among neuronal populations has become the trend to understand the brain mechanisms of Parkinson's disease, schizophrenia, mild traumatic brain injury, and many other unlisted neurological diseases. Dynamic modeling is a state-of-the-art approach to explore various connectivities among neuronal populations corresponding to different electrophysiological responses. Through estimating the parameters in the dynamic models, including the strengths and propagation delays of the electrophysiological signals, the discovery of the underlying connectivities can lead to the elucidation of functional brain mechanisms. In this report, we survey six dynamic models that describe the intrinsic function of a single neuronal/subneuronal population and three effective network estimation methods that can trace the connections among the neuronal/subneuronal populations. The six dynamic models are event related potential, local field potential, conductance-based neural mass model, mean field model, neural field model, and canonical micro-circuits; the three effective network estimation approaches are dynamic causal modeling, structural causal model, and vector autoregression. Subsequently, we discuss dynamic parameter estimation methods including variational Bayesian, particle filtering, Metropolis-Hastings algorithm, Gauss-Newton algorithm, collocation method, and constrained optimization. We summarize the merits and drawbacks of each model, network estimation approach, and parameter estimation method. In addition, we demonstrate an exemplary effective network estimation problem statement. Last, we identify possible future work and challenges to develop an elevated package.
We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include: (i) a unified treatment of the continuous and the discrete-time cases; (ii) the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and (iii) an alternative estimator ensuring parameter estimation in finite-time that retains its alertness to track time-varying parameters. Simulations that illustrate our results are also presented.