This chapter reviews standard parameter-estimation techniques and presents a novel gradient-, ensemble-, adjoint-free data-driven parameter estimation technique in the DDDAS framework. This technique, called retrospective cost parameter estimation (RCPE), is motivated by large-scale complex estimation models characterized by high-dimensional nonlinear dynamics, nonlinear parameterizations, and representational models. RCPE is illustrated by estimating unknown parameters in three examples. In the first example, salient features of RCPE are investigated by considering parameter estimation problem in a low-order nonlinear system. In the second example, RCPE is used to estimate the convective coefficient and the viscosity in the generalized Burgers equation by using a scalar measurement. In the final example, RCPE is used to estimate thermal conductivity coefficients that relate temporal temperature variation with the vertical gradient of the temperature in the atmosphere.
This paper examines model parameter estimation in dynamic power systems whose governing electro-mechanical equations are ill-conditioned or singular. This ill-conditioning is because of converter-interfaced power systems generators' zero or small inertia contribution. Consequently, the overall system inertia decreases, resulting in low-inertia power systems. We show that the standard state-space model based on least squares or subspace estimators fails to exist for these models. We overcome this challenge by considering a least-squares estimator directly on the coupled swing-equation model but not on its transformed first-order state-space form. We specifically focus on estimating inertia (mechanical and virtual) and damping constants, although our method is general enough for estimating other parameters. Our theoretical analysis highlights the role of network topology on the parameter estimates of an individual generator. For generators with greater connectivity, estimation of the associated parameters is more susceptible to variations in other generator states. Furthermore, we numerically show that estimating the parameters by ignoring their ill-conditioning aspects yields highly unreliable results.
Monocular camera sensors are vital to intelligent vehicle operation and automated driving assistance and are also heavily employed in traffic control infrastructure. Calibrating the monocular camera, though, is time-consuming and often requires significant manual intervention. In this work, we present an extrinsic camera calibration approach that automatizes the parameter estimation by utilizing semantic segmentation information from images and point clouds. Our approach relies on a coarse initial measurement of the camera pose and builds on lidar sensors mounted on a vehicle with high-precision localization to capture a point cloud of the camera environment. Afterward, a mapping between the camera and world coordinate spaces is obtained by performing a lidar-to-camera registration of the semantically segmented sensor data. We evaluate our method on simulated and real-world data to demonstrate low error measurements in the calibration results. Our approach is suitable for infrastructure sensors as well as vehicle sensors, while it does not require motion of the camera platform.
Purpose: For quantitative susceptibility mapping (QSM), the lack of ground-truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with built-in parameter estimation, and incorporate the nonlinear formulation of the dipole inversion to achieve a robust recovery of the susceptibility maps. Theory: From a Bayesian perspective, the image wavelet coefficients are approximately sparse and modelled by the Laplace distribution. The measurement noise is modelled by a Gaussian-mixture distribution with two components, where the second component is used to model the noise outliers. Through probabilistic inference, the susceptibility map and distribution parameters can be jointly recovered using approximate message passing (AMP). Methods: We compare our proposed AMP with built-in parameter estimation (AMP-PE) to the state-of-the-art L1-QSM, FANSI and MEDI approaches on the simulated and in vivo datasets, and perform experiments to explore the optimal settings of AMP-PE. Reproducible code is available at https://github.com/EmoryCN2L/QSM_AMP_PE Results: On the simulated Sim2Snr1 dataset, AMP-PE achieved the lowest NRMSE, DFCM and the highest SSIM, while MEDI achieved the lowest HFEN. On the in vivo datasets, AMP-PE is robust and successfully recovers the susceptibility maps using the estimated parameters, whereas L1-QSM, FANSI and MEDI typically require additional visual fine-tuning to select or double-check working parameters. Conclusion: AMP-PE provides automatic and adaptive parameter estimation for QSM and avoids the subjectivity from the visual fine-tuning step, making it an excellent choice for the clinical setting.
Given a set of images of a scene, the re-rendering of this scene from novel views and lighting conditions is an important and challenging problem in Computer Vision and Graphics. On the one hand, most existing works in Computer Vision usually impose many assumptions regarding the image formation process, e.g. direct illumination and predefined materials, to make scene parameter estimation tractable. On the other hand, mature Computer Graphics tools allow modeling of complex photo-realistic light transport given all the scene parameters. Combining these approaches, we propose a method for scene relighting under novel views by learning a neural precomputed radiance transfer function, which implicitly handles global illumination effects using novel environment maps. Our method can be solely supervised on a set of real images of the scene under a single unknown lighting condition. To disambiguate the task during training, we tightly integrate a differentiable path tracer in the training process and propose a combination of a synthesized OLAT and a real image loss. Results show that the recovered disentanglement of scene parameters improves significantly over the current state of the art and, thus, also our re-rendering results are more realistic and accurate.
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to incomplete data. Second, it utilizes time-to-failure (TTF) to supervise the extraction of low-dimensional features which makes the extracted features more effective for the subsequent prognostic. Besides, an optimization algorithm is proposed for parameter estimation and closed-form solutions are derived under certain distributions.
Multiband fusion enhances WiFi sensing by jointly utilizing signals from multiple non-contiguous frequency bands. However, in the multi-band WiFi sensing signal model, there are many local optimums in the associated likelihood function due to the existence of high frequency component and phase distortion factors, posing challenges for high-accuracy parameter estimation. To address this, we propose a two-stage scheme equipped with different signal models derived from the original model, where the first-stage coarse estimation is performed using a weighted root MUSIC algorithm to narrow down the search range for the subsequent stage, and the second-stage refined estimation utilizes a Bayesian approach to avoid convergence to bad suboptimal solutions. Specifically, we apply the block stochastic successive convex approximation (SSCA) approach to derive a novel stochastic particle-based variational Bayesian inference (SPVBI) algorithm in the refined stage. Unlike conventional particle-based VBI (PVBI) that optimizes only particle probability and incurs exponential per-iteration complexity with particle count, our more flexible SPVBI algorithm optimizes both the position and probability of each particle. Additionally, it utilizes block SSCA to significantly improve sampling efficiency by averaging over iterations, making it suitable for high-dimensional problems. Extensive simulations demonstrate the superiority of our proposed algorithm over various baseline methods.
Trajectory prediction has been widely pursued in many fields, and many model-based and model-free methods have been explored. The former include rule-based, geometric or optimization-based models, and the latter are mainly comprised of deep learning approaches. In this paper, we propose a new method combining both methodologies based on a new Neural Differential Equation model. Our new model (Neural Social Physics or NSP) is a deep neural network within which we use an explicit physics model with learnable parameters. The explicit physics model serves as a strong inductive bias in modeling pedestrian behaviors, while the rest of the network provides a strong data-fitting capability in terms of system parameter estimation and dynamics stochasticity modeling. We compare NSP with 15 recent deep learning methods on 6 datasets and improve the state-of-the-art performance by 5.56%-70%. Besides, we show that NSP has better generalizability in predicting plausible trajectories in drastically different scenarios where the density is 2-5 times as high as the testing data. Finally, we show that the physics model in NSP can provide plausible explanations for pedestrian behaviors, as opposed to black-box deep learning. Code is available: https://github.com/realcrane/Human-Trajectory-Prediction-via-Neural-Social-Physics.
The surprisingly mercurial Covid-19 pandemic has highlighted the need to not only accelerate research on infectious disease, but to also study them using novel techniques and perspectives. A major contributor to the difficulty of containing the current pandemic is due to the highly asymptomatic nature of the disease. In this investigation, we develop a modeling framework to study the spatio-temporal evolution of diseases with high rates of asymptomatic transmission, and we apply this framework to a hypothetical country with mathematically tractable geography; namely, square counties uniformly organized into a rectangle. We first derive a model for the temporal dynamics of susceptible, infected, and recovered populations, which is applied at the county level. Next we use likelihood-based parameter estimation to derive temporally varying disease transmission parameters on the state-wide level. While these two methods give us some spatial structure and show the effects of behavioral and policy changes, they miss the evolution of hot zones that have caused significant difficulties in resource allocation during the current pandemic. It is evident that the distribution of cases will not be stagnantly based on the population density, as with many other diseases, but will continuously evolve. We model this as a diffusive process where the diffusivity is spatially varying based on the population distribution, and temporally varying based on the current number of simulated asymptomatic cases. With this final addition coupled to the SIR model with temporally varying transmission parameters, we capture the evolution of "hot zones" in our hypothetical setup.
We describe a method for signal parameter estimation using the signed cumulative distribution transform (SCDT), a recently introduced signal representation tool based on optimal transport theory. The method builds upon signal estimation using the cumulative distribution transform (CDT) originally introduced for positive distributions. Specifically, we show that Wasserstein-type distance minimization can be performed simply using linear least squares techniques in SCDT space for arbitrary signal classes, thus providing a global minimizer for the estimation problem even when the underlying signal is a nonlinear function of the unknown parameters. Comparisons to current signal estimation methods using $L_p$ minimization shows the advantage of the method.
Understanding factors affecting social interactions among animals is important for applied animal behavior research. Thus, there is a need to elicit statistical models to analyze data collected from pairwise behavioral interactions. In this study, we propose treating social interaction data as dyadic observations and propose a statistical model for their analysis. We performed posterior predictive checks of the model through different validation strategies: stratified 5-fold random cross-validation, block-by-social-group cross-validation, and block-by-focal-animals validation. The proposed model was applied to a pig behavior dataset collected from 797 growing pigs freshly remixed into 59 social groups that resulted in 10,032 records of directional dyadic interactions. The response variable was the duration in seconds that each animal spent delivering attacks on another group mate. Generalized linear mixed models were fitted. Fixed effects included sex, individual weight, prior nursery mate experience, and prior littermate experience of the two pigs in the dyad. Random effects included aggression giver, aggression receiver, dyad, and social group. A Bayesian framework was utilized for parameter estimation and posterior predictive model checking. Prior nursery mate experience was the only significant fixed effect. In addition, a weak but significant correlation between the random giver effect and the random receiver effect was obtained when analyzing the attacking duration. The predictive performance of the model varied depending on the validation strategy, with substantially lower performance from the block-by-social-group strategy than other validation strategies. Collectively, this paper demonstrates a statistical model to analyze interactive animal behaviors, particularly dyadic interactions.
Motivated by automotive applications, we consider joint radar sensing and data communication for a system operating at millimeter wave (mmWave) frequency bands, where a Base Station (BS) is equipped with a co-located radar receiver and sends data using the Orthogonal Time Frequency Space (OTFS) modulation format. We consider two distinct modes of operation. In Discovery mode, a single common data stream is broadcast over a wide angular sector. The radar receiver must detect the presence of not yet acquired targets and perform coarse estimation of their parameters (angle of arrival, range, and velocity). In Tracking mode, the BS transmits multiple individual data streams to already acquired users via beamforming, while the radar receiver performs accurate estimation of the aforementioned parameters. Due to hardware complexity and power consumption constraints, we consider a hybrid digital-analog architecture where the number of RF chains and A/D converters is significantly smaller than the number of antenna array elements. In this case, a direct application of the conventional MIMO radar approach is not possible. Consequently, we advocate a beam-space approach where the vector observation at the radar receiver is obtained through a RF-domain beamforming matrix operating the dimensionality reduction from antennas to RF chains. Under this setup, we propose a likelihood function-based scheme to perform joint target detection and parameter estimation in Discovery, and high-resolution parameter estimation in Tracking mode, respectively. Our numerical results demonstrate that the proposed approach is able to reliably detect multiple targets while closely approaching the Cramer-Rao Lower Bound (CRLB) of the corresponding parameter estimation problem.
Mobile robotic applications need precise information about the geometric position of the individual sensors on the platform. This information is given by the extrinsic calibration parameters which define how the sensor is rotated and translated with respect to a fixed reference coordinate system. Erroneous calibration parameters have a negative impact on typical robotic estimation tasks, e.g. SLAM. In this work we propose a new method for a continuous estimation of the calibration parameters during operation of the robot. The parameter estimation is based on the matching of point clouds which are acquired by the sensors from multiple static viewpoints. Consequently, our method does not need any special calibration targets and is applicable to any sensor whose measurements can be converted to point clouds. We demonstrate the suitability of our method by calibrating a multi-sensor system composed by 2 lidar sensors, 3 cameras, and an imaging radar sensor.
Recent years have seen substantial advances in the development of biofunctional materials using synthetic polymers. The growing problem of elusive sequence-functionality relations for most biomaterials has driven researchers to seek more effective tools and analysis methods. In this study, statistical models are used to study sequence features of the recently reported random heteropolymers (RHP), which transport protons across lipid bilayers selectively and rapidly like natural proton channels. We utilized the probabilistic graphical model framework and developed a generalized hidden semi-Markov model (GHSMM-RHP) to extract the function-determining sequence features, including the transmembrane segments within a chain and the sequence heterogeneity among different chains. We developed stochastic variational methods for efficient inference on parameter estimation and predictions, and empirically studied their computational performance from a comparative perspective on Bayesian (i.e., stochastic variational Bayes) versus frequentist (i.e., stochastic variational expectation-maximization) frameworks that have been studied separately before. The real data results agree well with the laboratory experiments, and suggest GHSMM-RHP's potential in predicting protein-like behavior at the polymer-chain level.
A hybrid model for biomedical time series comprising a continuous second-order linear time-invariant system driven by an input sequence of positively weighted Dirac delta-functions is considered. The problem of the joint estimation of the input sequence and the continuous system parameters from output measurements is investigated. A solution that builds upon and refines a previously published least-squares formulation is proposed. Based on a thorough analysis of the properties of the least-squares solution, improvements in terms of accuracy and ease of use are achieved on synthetic data, compared to the original algorithm.
This paper demonstrates spherical convolutional neural networks (S-CNN) offer distinct advantages over conventional fully-connected networks (FCN) at estimating scalar parameters of tissue microstructure from diffusion MRI (dMRI). Such microstructure parameters are valuable for identifying pathology and quantifying its extent. However, current clinical practice commonly acquires dMRI data consisting of only 6 diffusion weighted images (DWIs), limiting the accuracy and precision of estimated microstructure indices. Machine learning (ML) has been proposed to address this challenge. However, existing ML-based methods are not robust to differing dMRI gradient sampling schemes, nor are they rotation equivariant. Lack of robustness to sampling schemes requires a new network to be trained for each scheme, complicating the analysis of data from multiple sources. A possible consequence of the lack of rotational equivariance is that the training dataset must contain a diverse range of microstucture orientations. Here, we show spherical CNNs represent a compelling alternative that is robust to new sampling schemes as well as offering rotational equivariance. We show the latter can be leveraged to decrease the number of training datapoints required.
The time of arrival (TOA)-based localization techniques, which need to estimate the delay of the line-of-sight (LoS) path, have been widely employed in location-aware networks. To achieve a high-accuracy delay estimation, a number of multiband-based algorithms have been proposed recently, which exploit the channel state information (CSI) measurements over multiple non-contiguous frequency bands. However, to the best of our knowledge, there still lacks an efficient scheme that fully exploits the multiband gains when the phase distortion factors caused by hardware imperfections are considered, due to that the associated multi-parameter estimation problem contains many local optimums and the existing algorithms can easily get stuck in a "bad" local optimum. To address these issues, we propose a novel two-stage global estimation (TSGE) scheme for multiband delay estimation. In the coarse stage, we exploit the group sparsity structure of the multiband channel and propose a Turbo Bayesian inference (Turbo-BI) algorithm to achieve a good initial delay estimation based on a coarse signal model, which is transformed from the original multiband signal model by absorbing the carrier frequency terms. The estimation problem derived from the coarse signal model contains less local optimums and thus a more stable estimation can be achieved than directly using the original signal model. Then in the refined stage, with the help of coarse estimation results to narrow down the search range, we perform a global delay estimation using a particle swarm optimization-least square (PSO-LS) algorithm based on a refined multiband signal model to exploit the multiband gains to further improve the estimation accuracy. Simulation results show that the proposed TSGE significantly outperforms the benchmarks with comparative computational complexity.
In this study, we introduce new estimation methods for the required rate of return of the stochastic dividend discount model (DDM) and the private company valuation model, which will appear below. To estimate the required rate of return, we use the maximum likelihood method, the Bayesian method, and the Kalman filtering. We apply the model to a set of firms from the S\&P 500 index using historical dividend and price data over a 32--year period. Overall, suggested methods can be used to estimate the required rate of return.
A comprehensive methodology for inference in vector autoregressions (VARs) using sign and other structural restrictions is developed. The reduced-form VAR disturbances are driven by a few common factors and structural identification restrictions can be incorporated in their loadings in the form of parametric restrictions. A Gibbs sampler is derived that allows for reduced-form parameters and structural restrictions to be sampled efficiently in one step. A key benefit of the proposed approach is that it allows for treating parameter estimation and structural inference as a joint problem. An additional benefit is that the methodology can scale to large VARs with multiple shocks, and it can be extended to accommodate non-linearities, asymmetries, and numerous other interesting empirical features. The excellent properties of the new algorithm for inference are explored using synthetic data experiments, and by revisiting the role of financial factors in economic fluctuations using identification based on sign restrictions.
This work presents a solution to the adaptive tracking control of Euler Lagrange systems with guaranteed tracking and parameter estimation error convergence. Specifically a concurrent learning based update rule fused by the filtered version of the desired system dynamics in conjunction with a desired state based regression matrix has been utilized to ensure that both the position tracking error and parameter estimation error terms converge to origin exponentially. As the regression matrix used in proposed controller makes use of the desired versions of the system states, an initial, sufficiently exciting memory stack can be formed from the knowledge of the desired system trajectory a priori, thus removing the initial excitation condition required for the previously proposed concurrent learning based controllers in the literature. The output feedback versions of the proposed method where only the position measurements are available for the controller design, (for both gradient and composite type adaptions) are also presented in order to illustrate the modularity of the proposed method. The stability and boundedness of the closed loop signals for all the proposed controllers are ensured via Lyapunov based analysis. %Trajectory tracking control of a class of fully actuated Euler Lagrange systems is considered in this work. System dynamics is considered to be subject to parametric uncertainties and on--line identification uncertain model parameters is also aimed. When compared with the relevant past research, via a novel approach, desired states are proposed to be used in forming the regression matrix and a desired compensation based concurrent learning type adaptive update rule is designed. Via utilizing novel Lyapunov analysis, semi--global exponential convergence of both tracking and parameter identification error to the origin is ensured.