Hybrid precoder and combiner designs are conceived for decentralized parameter estimation in millimeter wave (mmWave) multiple-input multiple-output (MIMO) wireless sensor networks (WSNs). More explicitly, efficient pre- and post-processing of the sensor observations and received signal are proposed for the minimum mean square error (MMSE) estimation of a parameter vector. The proposed techniques exploit the limited scattering nature of the mmWave MIMO channel for formulating the hybrid transceiver design framework as a multiple measurement vectors (MMV)-based sparse signal recovery problem. This is then solved using the iterative appealingly low-complexity simultaneous orthogonal matching pursuit (SOMP). Tailor-made designs are presented for WSNs operating under both total and per-sensor power constraints, while considering ideal noiseless as well as realistic noisy sensors. Furthermore, both the Bayesian Cramer-Rao lower bound and the centralized MMSE bound are derived for benchmarking the proposed decentralized estimation schemes. Our simulation results demonstrate the efficiency of the designs advocated and verify the analytical findings.
The accurate predictions and principled uncertainty measures provided by GP regression incur O(n^3) cost which is prohibitive for modern-day large-scale applications. This has motivated extensive work on computationally efficient approximations. We introduce a new perspective by exploring robustness properties and limiting behaviour of GP nearest-neighbour (GPnn) prediction. We demonstrate through theory and simulation that as the data-size n increases, accuracy of estimated parameters and GP model assumptions become increasingly irrelevant to GPnn predictive accuracy. Consequently, it is sufficient to spend small amounts of work on parameter estimation in order to achieve high MSE accuracy, even in the presence of gross misspecification. In contrast, as n tends to infinity, uncertainty calibration and NLL are shown to remain sensitive to just one parameter, the additive noise-variance; but we show that this source of inaccuracy can be corrected for, thereby achieving both well-calibrated uncertainty measures and accurate predictions at remarkably low computational cost. We exhibit a very simple GPnn regression algorithm with stand-out performance compared to other state-of-the-art GP approximations as measured on large UCI datasets. It operates at a small fraction of those other methods' training costs, for example on a basic laptop taking about 30 seconds to train on a dataset of size n = 1.6 x 10^6.
Synthetic Aperture Radar (SAR) image understanding is crucial in remote sensing applications, but it is hindered by its intrinsic noise contamination, called speckle. Sophisticated statistical models, such as the $\mathcal{G}^0$ family of distributions, have been employed to SAR data and many of the current advancements in processing this imagery have been accomplished through extracting information from these models. In this paper, we propose improvements to parameter estimation in $\mathcal{G}^0$ distributions using the Method of Log-Cumulants. First, using Bayesian modeling, we construct that regularly produce reliable roughness estimates under both $\mathcal{G}^0_A$ and $\mathcal{G}^0_I$ models. Second, we make use of an approximation of the Trigamma function to compute the estimated roughness in constant time, making it considerably faster than the existing method for this task. Finally, we show how we can use this method to achieve fast and reliable SAR image understanding based on roughness information.
This paper introduces a new linear parameterization to the problem of visual inertial simultaneous localization and mapping (VI-SLAM) -- without any approximation -- for the case only using information from a single monocular camera and an inertial measurement unit. In this problem set, the system state evolves on the nonlinear manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully to generate invariant foliations, such that the problem can be reformulated into online \emph{constant parameter} identification, then interestingly with linear regression models obtained. It demonstrates that VI-SLAM can be translated into a linear least squares problem, in the deterministic sense, \emph{globally} and \emph{exactly}. Based on this observation, we propose a novel SLAM observer, following the recently established parameter estimation-based observer (PEBO) methodology. A notable merit is that the proposed observer enjoys almost global asymptotic stability, requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with provable stability but can hardly be assured in many practical scenarios.
Objective: COVID-19 has spread worldwide and made a huge influence across the world. Modeling the infectious spread situation of COVID-19 is essential to understand the current condition and to formulate intervention measurements. Epidemiological equations based on the SEIR model simulate disease development. The traditional parameter estimation method to solve SEIR equations could not precisely fit real-world data due to different situations, such as social distancing policies and intervention strategies. Additionally, learning-based models achieve outstanding fitting performance, but cannot visualize mechanisms. Methods: Thus, we propose a deep dynamic epidemiological (DDE) method that combines epidemiological equations and deep-learning advantages to obtain high accuracy and visualization. The DDE contains deep networks to fit the effect function to simulate the ever-changing situations based on the neural ODE method in solving variants' equations, ensuring the fitting performance of multi-level areas. Results: We introduce four SEIR variants to fit different situations in different countries and regions. We compare our DDE method with traditional parameter estimation methods (Nelder-Mead, BFGS, Powell, Truncated Newton Conjugate-Gradient, Neural ODE) in fitting the real-world data in the cases of countries (the USA, Columbia, South Africa) and regions (Wuhan in China, Piedmont in Italy). Our DDE method achieves the best Mean Square Error and Pearson coefficient in all five areas. Further, compared with the state-of-art learning-based approaches, the DDE outperforms all techniques, including LSTM, RNN, GRU, Random Forest, Extremely Random Trees, and Decision Tree. Conclusion: DDE presents outstanding predictive ability and visualized display of the changes in infection rates in different regions and countries.
By multiplexing information symbols in the delay-Doppler (DD) domain, orthogonal time frequency space (OTFS) is a promising candidate for future wireless communication in high-mobility scenarios. In addition to the superior communication performance, OTFS is also a natural choice for radar sensing since the primary parameters (range and velocity of targets) in radar signal processing can be inferred directly from the delay and Doppler shifts. Though there are several works on OTFS radar sensing, most of them consider the integer parameter estimation only, while the delay and Doppler shifts are usually fractional in the real world. In this paper, we propose a two-step method to estimate the fractional delay and Doppler shifts. We first perform the two-dimensional (2D) correlation between the received and transmitted DD domain symbols to obtain the integer parts of the parameters. Then a difference-based method is implemented to estimate the fractional parts of delay and Doppler indices. Meanwhile, we implement a target detection method based on a generalized likelihood ratio test since the number of potential targets in the sensing scenario is usually unknown. The simulation results show that the proposed method can obtain the delay and Doppler shifts accurately and get the number of sensing targets with a high detection probability.
MCMC algorithms offer empirically efficient tools for sampling from a target distribution $\pi(x) \propto \exp(-V(x))$. However, on the theory side, MCMC algorithms suffer from slow mixing rate when $\pi(x)$ is non-log-concave. Our work examines this gap and shows that when Poincar\'e-style inequality holds on a subset $\mathcal{X}$ of the state space, the conditional distribution of MCMC iterates over $\mathcal{X}$ mixes fast to the true conditional distribution. This fast mixing guarantee can hold in cases when global mixing is provably slow. We formalize the statement and quantify the conditional mixing rate. We further show that conditional mixing can have interesting implications for sampling from mixtures of Gaussians, parameter estimation for Gaussian mixture models and Gibbs-sampling with well-connected local minima.
We present a novel approach to system identification (SI) using deep learning techniques. Focusing on parametric system identification (PSI), we use a supervised learning approach for estimating the parameters of discrete and continuous-time dynamical systems, irrespective of chaos. To accomplish this, we transform collections of state-space trajectory observations into image-like data to retain the state-space topology of trajectories from dynamical systems and train convolutional neural networks to estimate the parameters of dynamical systems from these images. We demonstrate that our approach can learn parameter estimation functions for various dynamical systems, and by using training-time data augmentation, we are able to learn estimation functions whose parameter estimates are robust to changes in the sample fidelity of their inputs. Once trained, these estimation models return parameter estimations for new systems with negligible time and computation costs.
Phase-modulated continuous-wave (PMCW) multiple-input multiple-output (MIMO) radar systems are known to possess excellent mutual interference mitigation capabilities, but require costly and power-hungry high sampling rate and high-precision analog-to-digital converters (ADC's). To reduce cost and power consumption, we consider a mixed-ADC architecture, in which most receive antenna outputs are sampled by one-bit ADC's, and only one or a few outputs by high-precision ADC's. We first derive the Cram{\'e}r-Rao bound (CRB) for the mixed-ADC based PMCW MIMO radar to characterize the best achievable performance of an unbiased target parameter estimator. The CRB analysis demonstrates that the mixed-ADC architecture with a relatively small number of high-precision ADC's and a large number of one-bit ADC's allows us to drastically reduce the hardware cost and power consumption while still maintain a high dynamic range needed for autonomous driving applications. We also introduce a two-step estimator to realize the computationally efficient maximum likelihood (ML) estimation of the target parameters. We formulate the angle-Doppler imaging problem as a sparse parameter estimation problem, and a computationally efficient majorization-minimization (MM) based estimator of sparse parameters, referred to as mLIKES, is devised for accurate angle-Doppler imaging. This is followed by using a relaxation-based approach to cyclically refine the results of mLIKES for accurate off-grid target parameter estimation. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithms for angle-Doppler imaging using mixed-ADC based PMCW MIMO radar.
We consider code optimization and angle-Doppler imaging for slow-time code division multiplexing (ST-CDM) linear frequency-modulated continuous-wave (LFMCW) multiple-input multiple-output (MIMO) radar systems. We optimize the slow-time code via the minimization of a Cram{\'e}r-Rao Bound (CRB)-based metric to enhance the parameter estimation performance. Then, a computationally efficient RELAX-based algorithm is presented to obtain the maximum likelihood (ML) estimates of the target angle-Doppler parameters. Numerical examples show that the proposed approaches can be used to improve the performance of parameter estimation and angle-Doppler imaging of ST-CDM LFMCW MIMO radar systems.
Learned visual dynamics models have proven effective for robotic manipulation tasks. Yet, it remains unclear how best to represent scenes involving multi-object interactions. Current methods decompose a scene into discrete objects, but they struggle with precise modeling and manipulation amid challenging lighting conditions as they only encode appearance tied with specific illuminations. In this work, we propose using object-centric neural scattering functions (OSFs) as object representations in a model-predictive control framework. OSFs model per-object light transport, enabling compositional scene re-rendering under object rearrangement and varying lighting conditions. By combining this approach with inverse parameter estimation and graph-based neural dynamics models, we demonstrate improved model-predictive control performance and generalization in compositional multi-object environments, even in previously unseen scenarios and harsh lighting conditions.
This doctoral thesis develops new methods for set-based state estimation and active fault diagnosis (AFD) of (i) nonlinear discrete-time systems, (ii) discrete-time nonlinear systems whose trajectories satisfy nonlinear equality constraints (called invariants), (iii) linear descriptor systems, and (iv) joint state and parameter estimation of nonlinear descriptor systems. Set-based estimation aims to compute tight enclosures of the possible system states in each time step subject to unknown-but-bounded uncertainties. To address this issue, the present doctoral thesis proposes new methods for efficiently propagating constrained zonotopes (CZs) through nonlinear mappings. Besides, this thesis improves the standard prediction-update framework for systems with invariants using new algorithms for refining CZs based on nonlinear constraints. In addition, this thesis introduces a new approach for set-based AFD of a class of nonlinear discrete-time systems. An affine parametrization of the reachable sets is obtained for the design of an optimal input for set-based AFD. In addition, this thesis presents new methods based on CZs for set-valued state estimation and AFD of linear descriptor systems. Linear static constraints on the state variables can be directly incorporated into CZs. Moreover, this thesis proposes a new representation for unbounded sets based on zonotopes, which allows to develop methods for state estimation and AFD also of unstable linear descriptor systems, without the knowledge of an enclosure of all the trajectories of the system. This thesis also develops a new method for set-based joint state and parameter estimation of nonlinear descriptor systems using CZs in a unified framework. Lastly, this manuscript applies the proposed set-based state estimation and AFD methods using CZs to unmanned aerial vehicles, water distribution networks, and a lithium-ion cell.
Bayesian state and parameter estimation have been automated effectively in a variety of probabilistic programming languages. The process of model comparison on the other hand, which still requires error-prone and time-consuming manual derivations, is often overlooked despite its importance. This paper efficiently automates Bayesian model averaging, selection, and combination by message passing on a Forney-style factor graph with a custom mixture node. Parameter and state inference, and model comparison can then be executed simultaneously using message passing with scale factors. This approach shortens the model design cycle and allows for the straightforward extension to hierarchical and temporal model priors to accommodate for modeling complicated time-varying processes.
Cardiac digital twins provide a physics and physiology informed framework to deliver predictive and personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs and the high number of model evaluations needed for patient-specific personalization. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. In this work, we use Latent Neural Ordinary Differential Equations (LNODEs) to learn the temporal pressure-volume dynamics of a heart failure patient. Our surrogate model based on LNODEs is trained from 400 3D-0D whole-heart closed-loop electromechanical simulations while accounting for 43 model parameters, describing single cell through to whole organ and cardiovascular hemodynamics. The trained LNODEs provides a compact and efficient representation of the 3D-0D model in a latent space by means of a feedforward fully-connected Artificial Neural Network that retains 3 hidden layers with 13 neurons per layer and allows for 300x real-time numerical simulations of the cardiac function on a single processor of a standard laptop. This surrogate model is employed to perform global sensitivity analysis and robust parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor. We match pressure and volume time traces unseen by the LNODEs during the training phase and we calibrate 4 to 11 model parameters while also providing their posterior distribution. This paper introduces the most advanced surrogate model of cardiac function available in the literature and opens new important venues for parameter calibration in cardiac digital twins.
This article introduces a novel probability distribution model, namely Complex Isotropic {\alpha}-Stable-Rician (CI{\alpha}SR), for characterizing the data histogram of synthetic aperture radar (SAR) images. Having its foundation situated on the L\'evy {\alpha}-stable distribution suggested by a generalized Central Limit Theorem, the model promises great potential in accurately capturing SAR image features of extreme heterogeneity. A novel parameter estimation method based on the generalization of method of moments to expectations of Bessel functions is devised to resolve the model in a relatively compact and computationally efficient manner. Experimental results based on both synthetic and empirical SAR data exhibit the CI{\alpha}SR model's superior capacity in modelling scenes of a wide range of heterogeneity when compared to other state-of-the-art models as quantified by various performance metrics. Additional experiments are conducted utilizing large-swath SAR images which encompass mixtures of several scenes to help interpret the CI{\alpha}SR model parameters, and to demonstrate the model's potential application in classification and target detection.
DCE-MRI provides information about vascular permeability and tissue perfusion through the acquisition of pharmacokinetic parameters. However, traditional methods for estimating these pharmacokinetic parameters involve fitting tracer kinetic models, which often suffer from computational complexity and low accuracy due to noisy arterial input function (AIF) measurements. Although some deep learning approaches have been proposed to tackle these challenges, most existing methods rely on supervised learning that requires paired input DCE-MRI and labeled pharmacokinetic parameter maps. This dependency on labeled data introduces significant time and resource constraints, as well as potential noise in the labels, making supervised learning methods often impractical. To address these limitations, here we present a novel unpaired deep learning method for estimating both pharmacokinetic parameters and the AIF using a physics-driven CycleGAN approach. Our proposed CycleGAN framework is designed based on the underlying physics model, resulting in a simpler architecture with a single generator and discriminator pair. Crucially, our experimental results indicate that our method, which does not necessitate separate AIF measurements, produces more reliable pharmacokinetic parameters than other techniques.
This paper presents novel methods for parameter identification in electrical grids with small numbers of spatially distributed measuring devices, which is an issue for distribution system operators managing aged and not properly mapped underground Low Voltage (LV) grids, especially in Germany. For this purpose, the total impedance of individual branches of the overall system is estimated by measuring currents and voltages at a subset of all system nodes over time. It is shown that, under common assumptions for electrical distsribution systems, an estimate of the total impedance can be made using readily computable proxies. Different regression methods are then used and compared to estimate the total impedance of the respective branches, with varying weights of the input data. The results on realistic LV feeders with different branch lengths and number of unmeasured segments are discussed and multiple influencing factors are investigated through simulations. It is shown that estimates of the total impedances can be obtained with acceptable quality under realistic assumptions.
In this paper, we study the problem of parameter estimation in a sensor network, where the measurements and updates of some sensors might be arbitrarily manipulated by adversaries. Despite the presence of such misbehaviors, normally behaving sensors make successive observations of an unknown $d$-dimensional vector parameter and aim to infer its true value by cooperating with their neighbors over a directed communication graph. To this end, by leveraging the so-called dynamic regressor extension and mixing procedure, we transform the problem of estimating the vector parameter to that of estimating $d$ scalar ones. For each of the scalar problem, we propose a resilient combine-then-adapt diffusion algorithm, where each normal sensor performs a resilient combination to discard the suspicious estimates in its neighborhood and to fuse the remaining values, alongside an adaptation step to process its streaming observations. With a low computational cost, this estimator guarantees that each normal sensor exponentially infers the true parameter even if some of them are not sufficiently excited.
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we construct a physics-informed prior probability measure on the function space of system responses so that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems.
Advanced experimental measurements are crucial for driving theoretical developments and unveiling novel phenomena in condensed matter and material physics, which often suffer from the scarcity of facility resources and increasing complexities. To address the limitations, we introduce a methodology that combines machine learning with Bayesian optimal experimental design (BOED), exemplified with x-ray photon fluctuation spectroscopy (XPFS) measurements for spin fluctuations. Our method employs a neural network model for large-scale spin dynamics simulations for precise distribution and utility calculations in BOED. The capability of automatic differentiation from the neural network model is further leveraged for more robust and accurate parameter estimation. Our numerical benchmarks demonstrate the superior performance of our method in guiding XPFS experiments, predicting model parameters, and yielding more informative measurements within limited experimental time. Although focusing on XPFS and spin fluctuations, our method can be adapted to other experiments, facilitating more efficient data collection and accelerating scientific discoveries.