Sparse sensor placement, with various design objectives, has successfully been employed in diverse application areas, particularly for enhanced parameter estimation and receiver performance. The sparse array design criteria are generally categorized into environment-independent and environment-dependent performance metrics. The former are largely benign to the underlying environment and, in principle, seek to maximize the spatial degrees of freedom by extending the coarray aperture. Environment-dependent objectives, on the other hand, consider the operating conditions characterized by emitters and targets in the array field of view, in addition to receiver noise. In this regard, applying such objectives renders the array configuration as well as the array weights time-varying in response to dynamic and changing environment. This work is geared towards designing environment-dependent sparse array beamformer to improve the output signal-to-interference and noise ratio using both narrowband and wideband signal platforms. One key challenge in implementing the data-dependent approaches is the lack of knowledge of exact or estimated values of the data autocorrelation function across the full sparse array aperture. At the core of this work is to address the aforementioned issues by devising innovative solutions using convex optimization and machine learning tools, structured sparsity concepts, low rank matrix completion schemes and fusing the environment-dependent and environment-independent deigns by developing a hybrid approach.
We propose a novel three-stage delay-Doppler-angle estimation algorithm for a MIMO-OFDM radar in the presence of inter-carrier interference (ICI). First, leveraging the observation that spatial covariance matrix is independent of target delays and Dopplers, we perform angle estimation via the MUSIC algorithm. For each estimated angle, we next formulate the radar delay-Doppler estimation as a joint carrier frequency offset (CFO) and channel estimation problem via an APES (amplitude and phase estimation) spatial filtering approach by transforming the delay-Doppler parameterized radar channel into an unstructured form. In the final stage, delay and Doppler of each target can be recovered from target-specific channel estimates over time and frequency. Simulation results illustrate the superior performance of the proposed algorithm in high-mobility scenarios.
Cellular-connected unmanned aerial vehicles (UAVs) have recently attracted a surge of interest in both academia and industry. Understanding the air-to-ground (A2G) propagation channels is essential to enable reliable and/or high-throughput communications for UAVs and protect the ground user equipments (UEs). In this contribution, a recently conducted measurement campaign for the A2G channels is introduced. A uniform circular array (UCA) with 16 antenna elements was employed to collect the downlink signals of two different Long Term Evolution (LTE) networks, at the heights of 0-40m in three different, namely rural, urban and industrial scenarios. The channel impulse responses (CIRs) have been extracted from the received data, and the spatial/angular parameters of the multipath components in individual channels were estimated according to a high-resolution-parameter estimation (HRPE) principle. Based on the HRPE results, clusters of multipath components were further identified. Finally, comprehensive spatial channel characteristics were investigated in the composite and cluster levels at different heights in the three scenarios.
This paper investigates the theoretical Cramer-Rao bounds on estimation accuracy of longitudinal vehicle dynamics parameters. This analysis is motivated by the value of parameter estimation in various applications, including chassis model validation and active safety. Relevant literature addresses this demand through algorithms capable of estimating chassis parameters for diverse conditions. While the implementation of such algorithms has been studied, the question of fundamental limits on their accuracy remains largely unexplored. We address this question by presenting two contributions. First, this paper presents theoretical findings which reveal the prevailing effects underpinning vehicle chassis parameter identifiability. We then validate these findings with data from on-road experiments. Our results demonstrate, among a variety of effects, the strong relevance of road grade variability in determining parameter identifiability from a drive cycle. These findings can motivate improved experimental designs in the future.
System identification poses a significant bottleneck to characterizing and controlling complex systems. This challenge is greatest when both the system states and parameters are not directly accessible leading to a dual-estimation problem. Current approaches to such problems are limited in their ability to scale with many-parameter systems as often occurs in networks. In the current work, we present a new, computationally efficient approach to treat large dual-estimation problems. Our approach consists of directly integrating pseudo-optimal state estimation (the Extended Kalman Filter) into a dual-optimization objective, leaving a differentiable cost/error function of only in terms of the unknown system parameters which we solve using numerical gradient/Hessian methods. Intuitively, our approach consists of solving for the parameters that generate the most accurate state estimator (Extended Kalman Filter). We demonstrate that our approach is at least as accurate in state and parameter estimation as joint Kalman Filters (Extended/Unscented), despite lower complexity. We demonstrate the utility of our approach by inverting anatomically-detailed individualized brain models from human magnetoencephalography (MEG) data.
One of the most critical tasks in tractor operation is the accurate steering during field operations, e.g., accurate trajectory following during mechanical weeding or spraying, to avoid damaging the crop or planting when there is no crop yet. To automate the trajectory following problem of an autonomous tractor-trailer system and also increase its steering accuracy, a nonlinear model predictive control approach has been proposed in this paper. For the state and parameter estimation, moving horizon estimation has been chosen since it considers the state and the parameter estimation within the same problem and also constraints both on inputs and states can be incorporated. The experimental results show the accuracy and the efficiency of the proposed control scheme in which the mean values of the Euclidean error for the tractor and the trailer, respectively, are 6.44 and 3.61 cm for a straight line trajectory and 49.78 and 41.52 cm for a curved line trajectory.
We consider the problem of range-Doppler imaging using one-bit automotive LFMCW1 or PMCW radar that utilizes one-bit ADC sampling with time-varying thresholds at the receiver. The one-bit sampling technique can significantly reduce the cost as well as the power consumption of automotive radar systems. We formulate the one-bit LFMCW/PMCW radar rangeDoppler imaging problem as one-bit sparse parameter estimation. The recently proposed hyperparameter-free (and hence user friendly) weighted SPICE algorithms, including SPICE, LIKES, SLIM and IAA, achieve excellent parameter estimation performance for data sampled with high precision. However, these algorithms cannot be used directly for one-bit data. In this paper we first present a regularized minimization algorithm, referred to as 1bSLIM, for accurate range-Doppler imaging using onebit radar systems. Then, we describe how to extend the SPICE, LIKES and IAA algorithms to the one-bit data case, and refer to these extensions as 1bSPICE, 1bLIKES and 1bIAA. These onebit hyperparameter-free algorithms are unified within the one-bit weighted SPICE framework. Moreover, efficient implementations of the aforementioned algorithms are investigated that rely heavily on the use of FFTs. Finally, both simulated and experimental examples are provided to demonstrate the effectiveness of the proposed algorithms for range-Doppler imaging using one-bit automotive radar systems.
We propose two algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation (PE) condition, another for constant parameters under no PE condition. For the first algorithm, we show that in the presence of time-varying unknown parameters, the parameter estimation error converges uniformly to a compact set under conditions of persistent excitation, with the size of the compact set proportional to the time-variation of unknown parameters. Leveraging a projection operator, the second algorithm is shown to result in boundedness guarantees when the plant has constant unknown parameters. Simulations show better convergence results compared to recursive least squares (RLS) and comparable results to RLS with forgetting factor.
In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton-Jacobi-Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability of the HJB solutions and stable growth rates for the optimal portfolios. To gauge how these optimal portfolios behave in practice, we perform backtests on historical stock prices of the S&P 500 constituents from year 2000 through year 2021. These backtests suggest three key conclusions: that the proposed co-integrated model with eigenportfolios being factors can generate a large number of co-integrated stocks over a long time horizon, that the optimal portfolios are sensitive to parameter estimation, and that the statistical arbitrage strategies are more profitable in periods when overall market volatilities are high.
The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic (PK) processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Although each single process has been systematically investigated, a quantitative understanding on their interaction remains limited and hence identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against different clinical datasets. Without any parameter estimation based on individual study data, the developed model simultaneously predicted (1) lung retention profiles of inhaled insoluble particles, (2) particle size-dependent PK of inhaled monodisperse particles, (3) PK differences between inhaled fluticasone propionate and budesonide, and (4) PK differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, we investigated the impact of input parameters on both pulmonary and systemic exposure. Solubility of the inhaled drug did not have any relevant impact on local and systemic PK. Instead, pulmonary dissolution rate, particle size, tissue affinity, and systemic clearance were impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool to identify optimal drug and formulation characteristics.
Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. in 2015 for modeling immunotherapy against melanoma skin cancer. First, we estimate the parameters of the deterministic limit of the model based on biological data of tumor growth in mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic Approximation Expectation Maximization algorithm. With the estimated parameters, we head back to the stochastic model and calculate the probability that the T cells all get exhausted during the treatment. We show that for some relevant parameter values, an early relapse is due to stochastic fluctuations (complete T cells exhaustion) with a non negligible probability. Then, focusing on the relapse related to the T cell exhaustion, we propose to optimize the treatment plan (treatment doses and restimulation times) by minimizing the T cell exhaustion probability in the parameter estimation ranges.
The paper was suggested by a brief note of the second author about the application of the Hubbert curve to predict decay of resource exploitation. A further suggestion came from the interpretation of the Hubbert curve in terms of a specific Lotka Volterra (LV) equation. The link with population dynamics was obvious as logistic function and LV equation were proposed within the demography science field. Mathematical population dynamics has a history of about two centuries. The first principle and model of population dynamics can be regarded the exponential law of Malthus. In the XIX century, the Malthusian demographic model was first refined to include mortality rate by Gompertz. In the early XIX century the model was further refined by Verhulst by introducing the standard logistic function. The previous models only concern the population of a single species. In the early XX century, the American demographer Lotka and the Italian mathematician Volterra proposed a pair of state equations which describe the population dynamics of two competing species, the predator and the prey. This paper is concerned with the single and two-species fundamental equations: the logistic and LV equation. The paper starts with the generalized logistic equation whose free response is derived together with equilibrium points and stability properties. The parameter estimation of the logistic function is applied to the raw data of the US crude oil production. The paper proceeds with the Lotka Volterra equation of the competition between two species, with the goal of applying it to resource exploitation. At the end, a limiting version of the LV equation is studied since it describes a competition model between the production rate of exploited resources and the relevant capital stock employed in the exploitation.
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in their environments allows for an increased understanding of animal cognition. 2. Here we describe a model that accounts for the memory of seasonal or ephemeral qualities of an animal's environment. The model captures multiple behaviors at once by allowing for resource selection in the present time as well as long-distance navigations to previously visited locations within an animal's home range. 3. We performed a set of analyses on simulated data to test our model, determining that it can provide informative results from as little as one year of discrete-time location data. We also show that the accuracy of model selection and parameter estimation increases with more location data. 4. This model has potential to identify a specific mechanism in which animals use memory to optimize their foraging, by revisiting temporally and predictably variable resources at consistent time lags.
We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact observation of some of the species in continuous time. The conditional probability distribution of the unobserved states is shown to satisfy a system of differential equations with jumps. We provide a method of simulating a process that is a proxy for the vector copy number of the unobserved species along with a weight. The resulting weighted Monte Carlo simulation is then used to compute the conditional probability distribution of the unobserved species. We also show how our algorithm can be adapted for a Bayesian estimation of parameters and for the estimation of a past state value based on observations up to a future time.
We found evidence of dynamic scaling in the spreading of MDCK monolayer, which can be characterized by the Hurst exponent ${\alpha} = 0.86$ and the growth exponent ${\beta} = 0.73$, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. During the spreading of the monolayer, it is known that so-called "leader cells" generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading, and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation revealed that the model could reproduce the different scaling law from ${\alpha} = 0.5, {\beta} = 0.25$ to ${\alpha} = 0.9, {\beta} = 0.75$, and the exponents ${\alpha}, {\beta}$ were determined by the two indices: $\rho t$ and $c$. Based on the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law ${\alpha} = 0.74, {\beta} = 0.68$, suggesting that cell motility increased by 9 folds. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and proposed a new mechanism that exhibits the dynamic scaling property.
We consider the problem of sinusoidal parameter estimation using signed observations obtained via one-bit sampling with fixed as well as time-varying thresholds. In a previous paper, a relaxation-based algorithm, referred to as 1bRELAX, has been proposed to iteratively maximize the likelihood function. However, the exhaustive search procedure used in each iteration of 1bRELAX is time-consuming. In this paper, we present a majorization-minimization (MM) based 1bRELAX algorithm, referred to as 1bMMRELAX, to enhance the computational efficiency of 1bRELAX. Using the MM technique, 1bMMRELAX maximizes the likelihood function iteratively using simple FFT operations instead of the more computationally intensive search used by 1bRELAX. Both simulated and experimental results are presented to show that 1bMMRELAX can significantly reduce the computational cost of 1bRELAX while maintaining its excellent estimation accuracy.
We consider the derivation of data-dependent simultaneous bandwidths for double kernel heteroskedasticity and autocorrelation consistent (DK-HAC) estimators. In addition to the usual smoothing over lagged autocovariances for classical HAC estimators, the DK-HAC estimator also applies smoothing over the time direction. We obtain the optimal bandwidths that jointly minimize the global asymptotic MSE criterion and discuss the trade-off between bias and variance with respect to smoothing over lagged autocovariances and over time. Unlike the MSE results of Andrews (1991), we establish how nonstationarity affects the bias-variance trade-o?. We use the plug-in approach to construct data-dependent bandwidths for the DK-HAC estimators and compare them with the DK-HAC estimators from Casini (2021) that use data-dependent bandwidths obtained from a sequential MSE criterion. The former performs better in terms of size control, especially with stationary and close to stationary data. Finally, we consider long-run variance estimation under the assumption that the series is a function of a nonparametric estimator rather than of a semiparametric estimator that enjoys the usual T^(1/2) rate of convergence. Thus, we also establish the validity of consistent long-run variance estimation in nonparametric parameter estimation settings.
We propose a novel structural estimation framework in which we train a surrogate of an economic model with deep neural networks. Our methodology alleviates the curse of dimensionality and speeds up the evaluation and parameter estimation by orders of magnitudes, which significantly enhances one's ability to conduct analyses that require frequent parameter re-estimation. As an empirical application, we compare two popular option pricing models (the Heston and the Bates model with double-exponential jumps) against a non-parametric random forest model. We document that: a) the Bates model produces better out-of-sample pricing on average, but both structural models fail to outperform random forest for large areas of the volatility surface; b) random forest is more competitive at short horizons (e.g., 1-day), for short-dated options (with less than 7 days to maturity), and on days with poor liquidity; c) both structural models outperform random forest in out-of-sample delta hedging; d) the Heston model's relative performance has deteriorated significantly after the 2008 financial crisis.
We present an epidemiological compartment model, SAIR(S), that explicitly captures the dynamics of asymptomatic infected individuals in an epidemic spread process. We first present a group model and then discuss networked versions. We provide an investigation of equilibria and stability properties for these models, and present simulation results illustrating the effects of asymptomatic-infected individuals on the spread of the disease. We also discuss local isolation effects on the epidemic dynamics in terms of the networked models. Finally, we provide initial parameter estimation results based on simple least-squares approaches and local test-site data.\par Keywords: Epidemic dynamics, networks, data-informed modeling, stability analysis, parameter estimation
This paper presents an efficient in-field calibration method tailored for low-cost triaxial MEMS gyroscopes often used in healthcare applications. Traditional calibration techniques are challenging to implement in clinical settings due to the unavailability of high-precision equipment. Unlike the auto-calibration approaches used for triaxial MEMS accelerometers, which rely on local gravity, gyroscopes lack a reliable reference since the Earth's self-rotation speed is insufficient for accurate calibration. To address this limitation, we propose a novel method that uses manual rotation of the MEMS gyroscope to a specific angle (360{\deg}) as the calibration reference. This approach iteratively estimates the sensor's attitude without requiring any external equipment. Numerical simulations and empirical tests validate that the calibration error is low and that parameter estimation is unbiased. The method can be implemented in real-time on a low-energy microcontroller and completed in under 30 seconds. Comparative results demonstrate that the proposed technique outperforms existing state-of-the-art methods, achieving scale factor and bias errors of less than $2.5\times10^{-2}$ for LSM9DS1 and less than $1\times10^{-2}$ for ICM20948.