Parameter Estimation Error Research Articles

A time‐varying angle extraction method for refined proximity group targets tracking

AbstractIn order to improve the detection probability of weak targets, tracking radar using sum and difference beams often adopt the method of long‐time coherent integration. However, the multidimensional migration of time‐varying targets will lead to the decline of parameter estimation accuracy. To solve this problem, this article proposes a refined angle estimation method for time‐varying targets with the traditional sum and difference beam echo model, this method compensates and searches the angle parameters of the targets based on subarray rotation invariant and focus process. In addition, this article also studies the masking problem of highly dynamic proximity group targets detection, and proposes an adaptive weighted LMS‐CLEAN based on Least Mean Square criterion, which effectively reduces the influence of masking effect on the parameter estimation accuracy of weak targets. Firstly, the proposed algorithm performs angle search and phase compensation on the pulse compression echo of sum and difference channels based on subarray rotation invariant. Secondly, focus the search matrix, reconstruct the strong target echo, and stripe it from both channels by adaptive weighting. Lastly, repeat the above steps until parameters of all targets are achieved precisely. The proposed two algorithms maintain a very low computational effort while effectively reducing the parameter estimation error, and are highly promising for engineering applications. In order to verify the effectiveness of the proposed algorithm, this article also provides some numerical experiments to compares with two existing algorithms in error performance, anti‐noise performance, and computational complexity.

Lensing or luck? False alarm probabilities for gravitational lensing of gravitational waves

Strong gravitational lensing of gravitational waves (GWs) has been forecasted to become detectable in the upcoming LIGO/Virgo/KAGRA observing runs. However, definitively distinguishing pairs of lensed sources from random associations is a challenging problem. We investigate the degree to which unlensed events mimic lensed ones because of the overlap of parameters due to a combination of random coincidence and errors in parameter estimation. Lensed events are expected to have consistent masses and sky locations, and constrained relative phases, but may have differing apparent distances due to lensing magnification. We construct a mock catalog of lensed and unlensed events. We find that the probability of a false alarm based on coincidental overlaps of the chirp mass, sky location, and coalescence phase are approximately 9%, 1%, and 10% per pair, respectively. Combining all three parameters, we arrive at an overall false alarm probability per pair of $\ensuremath{\sim}{10}^{\ensuremath{-}4}$. We validate our results against the GWTC-2 data, finding that the catalog data is consistent with our simulations. As the number of events, $N$, in the GW catalogs increases, the number of random pairs of events increases as $\ensuremath{\sim}{N}^{2}$. Meanwhile, the number of lensed events will increase linearly with $N$, implying that, for sufficiently high $N$, the false alarms will always dominate over the true lensing events. This issue can be compensated for by placing higher thresholds on the lensing candidates (e.g., selecting a higher signal-to-noise ratio (SNR) threshold, ${\ensuremath{\rho}}_{\mathrm{thr}}$), which will lead to better parameter estimation and, thus, lower false alarm probabilities per pair---at the cost of dramatically decreasing the size of the lensing sample ($\ensuremath{\propto}{\ensuremath{\rho}}_{\mathrm{thr}}^{\ensuremath{-}3}$). We show that with our simple overlap criteria for current detectors at design sensitivity, the false alarms will dominate for realistic lensing rates ($\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$) even when selecting the highest SNR pairs. These results highlight the necessity to design alternative identification criteria beyond simple waveform and sky location overlap for conclusive detection of strong lensing. Future GW detectors such as Cosmic Explorer and Einstein Telescope may provide sufficient improvement in parameter estimation and a commensurate decrease in the incidence of coincidental overlap of parameters, allowing for the conclusive detection of strong lensing of GWs even without additional detection criteria.

A Modified Robust Adaptive Fault Compensation Design for Spacecraft with Guaranteed Transient Performance

A modified, robust adaptive fault compensation design is proposed for rigid spacecraft systems with uncertain actuator failures and unknown disturbances. The feedback linearization method is first introduced to linearize the nonlinear dynamics, and a model-reference adaptive controller is designed to suppress the unknown external disturbances and stabilize the linearized system. Then, a composite adaptive controller is developed by integrating multiple controllers designed for the corresponding actuator failure conditions, which can handle the essentially multiple uncertainties (failure time, values, type, and failure pattern) of actuator failures simultaneously. To further improve the transient performance problem in the failure compensation control, an H∞ compensator is introduced as an additional item in the basic controller to attenuate the adverse effects on tracking performance caused by parameter estimation errors. From the theoretical analysis and simulation results, it is obvious that the designed scheme can not only guarantee the stability of the closed-loop system is stable and asymptotical tracking properties for a given reference signal but also greatly improve the transient performance of the spacecraft system during the process of failure compensation.

Predictive Factors of Piperacillin Exposure and the Impact on Target Attainment after Continuous Infusion Administration to Critically Ill Patients

Critically ill patients undergo significant pathophysiological changes that affect antibiotic pharmacokinetics. Piperacillin/tazobactam administered by continuous infusion (CI) improves pharmacokinetic/pharmacodynamic (PK/PD) target attainment. This study aimed to characterize piperacillin PK after CI administration of piperacillin/tazobactam in critically ill adult patients with preserved renal function and to determine the empirical optimal dosing regimen. A total of 218 piperacillin concentrations from 106 patients were simultaneously analyzed through the population PK approach. A two-compartment linear model best described the data. Creatinine clearance (CLCR) estimated by CKD-EPI was the covariate, the most predictive factor of piperacillin clearance (CL) interindividual variability. The mean (relative standard error) parameter estimates for the final model were: CL: 12.0 L/h (6.03%); central and peripheral compartment distribution volumes: 20.7 L (8.94%) and 62.4 L (50.80%), respectively; intercompartmental clearance: 4.8 L/h (26.4%). For the PK/PD target of 100% fT>1×MIC, 12 g of piperacillin provide a probability of target attainment > 90% for MIC < 16 mg/L, regardless of CLCR, but higher doses are needed for MIC = 16 mg/L when CLCR > 100 mL/min. For 100% fT>4×MIC, the highest dose (24 g/24 h) was not sufficient to ensure adequate exposure, except for MICs of 1 and 4 mg/L. Our model can be used as a support tool for initial dose guidance and during therapeutic drug monitoring.

Neural Network-Based Adaptive Fractional-Order Backstepping Control of Uncertain Quadrotors with Unknown Input Delays

Adaptive control is essential and effective for reliable quadrotor operations in the presence of uncertain modeling parameters and unknown time-delayed inputs. This paper presents an original radial basis function neural network-based adaptive fractional-order backstepping controller (RBF-ADFOBC). The nonlinearity of the time-delayed inputs is eliminated by introducing an augmented state variable via Pade’s approximation method. For each subsystem in the quadrotor dynamics, a companioned second-order compensation system is developed. The candidate Lyapunov functions are then properly designed by incorporating the control errors, parameter uncertainties and estimation errors of the neural networks’ weight vectors. It is shown that the semi-globally uniformly ultimately boundedness of all the state variables and the estimation error of uncertain parameters can be guaranteed. In addition, the trajectory-tracking error of the state variables can be driven to an adjustable small neighborhood of origin by properly setting the selectable parameters. Numerical simulations reveal that the tracking performance of the proposed controller can be improved continuously as the fractional order increases to a specific positive value, and the controller with a negative order may demonstrate higher robustness to the modeling uncertainties. Favorably, the comparison to the other two previous controllers further reveals the superior tracking accuracy and robustness of the proposed RBF-ADFOBC controller.

Adaptive fault identification and reconfigurable fault‐tolerant control for unmanned surface vehicle with actuator magnitude and rate faults

AbstractThis study proposes a reconfigurable fault‐tolerant control method using an adaptive fault identification technique with application to an unmanned surface vehicle with consideration of environmental disturbances and system constraints, including both second‐order input operations (actuator magnitude and rate faults) and multi‐classification fault modeling features (lock‐in‐place or hard‐over, and loss of effectiveness). To begin with, unknown parameter compensator‐based observers with adaptive projection laws are designed for the respective double‐parameter and single‐parameter adaptive fault identification cases, and it is proved that the actual input estimation and fault parameter estimation errors are bounded. Then, double‐parameter and single‐parameter adaptive reconfigurable fault‐tolerant controllers are synthesized by combining the finite‐time baseline tracking control and terminal sliding‐mode mechanism to guarantee the second‐order dynamical tracking errors converge to the origin for the proper unmanned surface vehicle operation regardless of actuator magnitude and rate faults. Finally, simulation results and comparisons demonstrate the effectiveness and superiority of the proposed reconfigurable fault‐tolerant control algorithm.

Accumulating Errors in Tests of General Relativity with Gravitational Waves: Overlapping Signals and Inaccurate Waveforms

Observations of gravitational waves (GWs) from compact binary coalescences provide powerful tests of general relativity (GR), but systematic errors in data analysis could lead to incorrect scientific conclusions. This issue is especially serious in the third-generation GW detectors in which the signal-to-noise ratio (S/N) is high and the number of detections is large. In this work, we investigate the impacts of overlapping signals and inaccurate waveform models on tests of GR. We simulate mock catalogs for Einstein Telescope and Cosmic Explorer and perform parametric tests of GR using waveform models with different levels of inaccuracy. We find that the systematic error in non-GR parameter estimates could accumulate toward a false deviation from GR when combining results from multiple events, although a Bayesian model selection analysis may not favor a deviation. Waveform inaccuracies contribute most to the systematic errors, but multiple overlapping signals could magnify the effects of systematics owing to the incorrect removal of signals. We also point out that testing GR using selected “golden binaries” with high S/N is even more vulnerable to false deviations from GR. The problem of error accumulation is universal; we emphasize that it must be addressed to fully exploit the data from third-generation GW detectors and that further investigations, particularly in waveform accuracy, will be essential.

Анализ показателей качества устройства обнаружения и оценивания параметров протяженной по дальности коррелированной ответной шумовой помехи и в импульсно-доплеровских РЛС сопровождения

The device structure was designed for detecting and measuring the parameters of correlated cover-pulse jamming (CPJ) as a part of combined simulating and masking jamming (CIM jamming). It was made for pulse-Doppler tracking radar (PD radar). For the designed device the detection specification was calculated as well as the dependence of the estimation error of the CPJ parameters on the CPJ-to-noise ratio for various CPJ parameters.

Revisiting classical SIR modelling in light of the COVID-19 pandemic.

Classical infectious disease models during epidemics have widespread usage, from predicting the probability of new infections to developing vaccination plans for informing policy decisions and public health responses. However, it is important to correctly classify reported data and understand how this impacts estimation of model parameters. The COVID-19 pandemic has provided an abundant amount of data that allow for thorough testing of disease modelling assumptions, as well as how we think about classical infectious disease modelling paradigms. We aim to assess the appropriateness of model parameter estimates and prediction results in classical infectious disease compartmental modelling frameworks given available data types (infected, active, quarantined, and recovered cases) for situations where just one data type is available to fit the model. Our main focus is on how model prediction results are dependent on data being assigned to the right model compartment. We first use simulated data to explore parameter reliability and prediction capability with three formulations of the classical Susceptible-Infected-Removed (SIR) modelling framework. We then explore two applications with reported data to assess which data and models are sufficient for reliable model parameter estimation and prediction accuracy: a classical influenza outbreak in a boarding school in England and COVID-19 data from the fall of 2020 in Missoula County, Montana, USA. We demonstrated the magnitude of parameter estimation errors and subsequent prediction errors resulting from data misclassification to model compartments with simulated data. We showed that prediction accuracy in each formulation of the classical disease modelling framework was largely determined by correct data classification versus misclassification. Using a classical example of influenza epidemics in an England boarding school, we argue that the Susceptible-Infected-Quarantined-Recovered (SIQR) model is more appropriate than the commonly employed SIR model given the data collected (number of active cases). Similarly, we show in the COVID-19 disease model example that reported active cases could be used inappropriately in the SIR modelling framework if treated as infected. We demonstrate the role of misclassification of disease data and thus the importance of correctly classifying reported data to the proper compartment using both simulated and real data. For both a classical influenza data set and a COVID-19 case data set, we demonstrate the implications of using the "right" data in the "wrong" model. The importance of correctly classifying reported data will have downstream impacts on predictions of number of infections, as well as minimal vaccination requirements.

Distributed adaptive estimation without persistence of excitation: An online optimization perspective

SummaryThis work proposes a distributed adaptive estimation algorithm for multi‐agent system (MAS) architecture using online measurements in a continuous‐time setting. Classical adaptive parameter estimation algorithms demand to satisfy persistence of excitation (PE) or its distributed variant cooperative persistent of excitation (C‐PE) for parameter convergence. PE, C‐PE, are restrictive in nature since it requires excitation (richness of information content) over the entire time span of the signal/data, making it unrealistic in most real‐world applications, especially in robotics and cyber‐physical systems. Unlike past literature, the proposed work ensures parameter convergence under a slackened condition, coined as cooperative initial excitation (C‐IE), which demands information richness only in the initial time‐window (transient period) suitable for practical scenarios. A distributed differential parameter estimator algorithm is designed, which with the help of stable closed‐loop filter dynamics and strategic switching guarantees global exponential stability (GES) of the parameter estimation error dynamics in the sense of Lyapunov. The formulation is further augmented by providing an online optimization perspective. A novel cost function is constructed in such a way that the proposed distributed parameter estimator acts as a distributed continuous‐time gradient‐descent algorithm based on the cost function and the true uncertain parameter vector is the global minima of the cost function. Simulation results validate the efficacy of the proposed algorithm in contrast to the PE/C‐PE based methods.

Effects of Aging Uncertainty on the Estimation of Growth Functions of Major Tuna Species

Fishery stock assessment requires accurate specification of the growth function of target species, and aging uncertainty is an important factor that affects the estimation of growth parameters. In this study, we used simulations to study the effects of two types of aging uncertainty, aging error and sampled age range, on the parameter estimation of the Von Bertalanffy growth function, including asymptotic length (L∞), growth coefficient (k), and theoretical age in the year at zero length (t0) of five important tuna species. We found that the uncertainty of the estimated growth curves increased with increasing aging errors. When aging errors were fixed among ages, the effects of age range on estimation error of growth parameters were different among species and growth parameters. When the aging error increased with age, the estimation uncertainty of L∞ and k was the greatest when only young age groups were sampled, while the estimation uncertainty of t0 was the greatest when only old age groups were sampled. Therefore, reducing the aging error and sampling individuals with a wider age range are important for increasing the accuracy and decreasing the uncertainty of the estimated growth function, which will further reduce the uncertainty in fishery stock assessment.

An improved Hammerstein system identification method using Stein Variational Inference and sampling technology

This paper considers the identification of the Hammerstein system with immeasurable process noise. The complexity of the Hammerstein system makes it difficult to obtain accurate mathematical expressions of the parameters, or even impossible to obtain accurate mathematical expressions at all. In this contribution, we cast the Hammerstein system parameter identification problem as a posterior parameter estimation problem and take a sampling and Stein variational inference viewpoint to solve it. Improved Stein variational gradient descent(ISVGD)algorithm is proposed in posterior parameter calculation. Compared with other methods, not only the prior distribution of parameters but also the proposal distribution of parameters is considered. In other words, The posterior information is enriched and the parameter identification accuracy is improved. At the same time, ISVGD and reversible jump markov chain monte carlo (RJMCMC) algorithms are used (called ISVGD-RJMCMC algorithm) in the structure detection problem. In the algorithm, the correct basis function number k can be found in the parameter estimation. It tends to be accurate but is slow to converge. Three simulation examples were given to demonstrate the proposed algorithm’s effectiveness. Furthermore, the performances of these approaches were analyzed, including parameter estimation accuracy and error, system order estimation and parameter convergence analysis.

Time-domain source parameter estimation ofMw 3–7 earthquakes in Japan from a large database of moment-rate functions

SUMMARYTime-domain analyses of seismic waveforms have revealed diverse source complexity in large earthquakes (Mw &amp;gt; 7). However, source characteristics of small earthquakes have been studied by assuming a simple rupture pattern on the frequency domain. This study utilizes high-quality seismic network data from Japan to systematically address the source complexities and radiated energies of Mw 3–7 earthquakes on the time domain. We first determine the apparent moment-rate functions (AMRFs) of the earthquakes using the empirical Green's functions. Some of the AMRFs show multiple peaks, suggesting complex ruptures at multiple patches. We then estimate the radiated energies (ER) of 1736 events having more than ten reliable AMRFs. The scaled energy (eR = ER/M0) does not strongly depend on the seismic moment (M0), focal mechanisms, or depth. The median value of eR is 3.7 × 10−5, which is comparable to those of previous studies; however, eR varies by approximately one order of magnitude among earthquakes. We measure the source complexity based on the radiated energy enhancement factor (REEF). The values of REEF differ among earthquakes, implying diverse source complexity. The values of REEF do not show strong scale dependence for Mw 3–7 earthquakes, suggesting that the source diversity of smaller earthquakes is similar to that of larger earthquakes at their representative spatial scales. Applying a simple spectral model (e.g. the ω2-source model) to complex ruptures may produce substantial estimation errors in source parameters.

Detection of False Data Injection Attacks in Smart Grids Based on Expectation Maximization.

The secure operation of smart grids is closely linked to state estimates that accurately reflect the physical characteristics of the grid. However, well-designed false data injection attacks (FDIAs) can manipulate the process of state estimation by injecting malicious data into the measurement data while bypassing the detection of the security system, ultimately causing the results of state estimation to deviate from secure values. Since FDIAs tampering with the measurement data of some buses will lead to error offset, this paper proposes an attack-detection algorithm based on statistical learning according to the different characteristic parameters of measurement error before and after tampering. In order to detect and classify false data from the measurement data, in this paper, we report the model establishment and estimation of error parameters for the tampered measurement data by combining the the k-means++ algorithm with the expectation maximization (EM) algorithm. At the same time, we located and recorded the bus that the attacker attempted to tamper with. In order to verify the feasibility of the algorithm proposed in this paper, the IEEE 5-bus standard test system and the IEEE 14-bus standard test system were used for simulation analysis. Numerical examples demonstrate that the combined use of the two algorithms can decrease the detection time to less than 0.011883 s and correctly locate the false data with a probability of more than 95%.

Adaptive Bayesian inference of Markov transition rates

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our sequential Bayesian optimal design is updated with each observation and can be simply extended beyond two-state models to birth–death processes and multistate models. By iteratively finding the best time to obtain each sample, our adaptive algorithm maximally reduces variance, resulting in lower overall error in ground truth parameter estimates across a wide range of Markov chain parameterizations and conformations.

Iterative phase noise suppression for full-duplex communication systems

Oscillator phase noise is one of the bottlenecks that limits the self-interference (SI) cancellation capability of full-duplex systems. In this paper, we propose a method for the suppression of common phase error (CPE) and intercarrier interference (ICI) induced by the phase noise in full-duplex orthogonal frequency division multiplexing (OFDM) systems. First, we regard the effect of CPE as a portion of the SI channel and perform estimation, reconstruction and elimination in the time domain. Then, the ICI signal is estimated and suppressed in the frequency domain. Additionally, by analysing the performance of proposed algorithm, we further develop an iterative mechanism to reduce the parameter estimation error and improve SI cancellation capability. Simulation results show that the proposed method has a significant SI cancellation capability improvement over the traditional SI cancellation schemes.

Composite Learning Finite-Time Control of Robotic Systems With Output Constraints

In this article, for robotic systems with uncertain dynamics and time-varying asymmetric output constraints, we present a composite learning finite-time control scheme with salient features benefited from two design steps. In the first step, unlike existing composite adaptive/learning control algorithms, which result in either exponential convergence or finite-time convergence but exhibit a potential singularity issue, a modified nonsingular terminal sliding mode-based composite learning controller is adopted such that both tracking error and parameter estimation error converge to zero in finite time without singularity. The unknown parameter learning law is constructed by using online historical data and regressor extension, which gives a benefit of relaxing the typically required stringent persistent excitation with a much weaker excitation condition termed interval excitation. In the second step, a universal time-varying asymmetric barrier function (UTABF) is adopted to directly constrain the system output rather than the most commonly used barrier Lyapunov function, which indirectly converts the output constraints into the conservative tracking error constraints. Moreover, the UTABF can handle both constrained and unconstrained cases uniformly without the need for changing the control structure. Both theoretical analysis and experiments results on an industrial manipulator confirm the benefits and effectiveness of the proposed control scheme.

Extending time-series models for irregular observational gaps with a moving average structure for astronomical sequences

ABSTRACT In this study, we introduce a novel moving-average model for analyzing stationary time-series observed irregularly in time. The process is strictly stationary and ergodic under normality and weakly stationary when normality is not assumed. Maximum likelihood (ML) estimation can be efficiently carried out through a Kalman algorithm obtained from the state-space representation of the model. The Kalman algorithm has order O(n) (where n is the number of observations in the sequence), from which it is possible to efficiently generate parameter estimators, linear predictors, and their mean-squared errors. Two procedures were developed for assessing parameter estimation errors: one based on the Hessian of the likelihood function and another one based on the bootstrap method. The behaviour of these estimators was assessed through Monte Carlo experiments. Both methods give accurate estimation performance, even with relatively small number of observations. Moreover, it is shown that for non-Gaussian data, specifically for the Student's t and generalized error distributions, the parameters of the model can be estimated precisely by ML. The proposed model is compared to the continuous autoregressive moving average (MA) models, showing better performance when the MA parameter is negative or close to one. We illustrate the implementation of the proposed model with light curves of variable stars from the OGLE and HIPPARCOS surveys and stochastic objects from Zwicky Transient Facility. The results suggest that the irregular MA model is a suitable alternative for modelling astronomical light curves, particularly when they have negative autocorrelation.

Comparison of Spatial Weight Matrices in Spatial Autoregressive Model: Case Study of Intangible Cultural Heritage in Indonesia

Intangible Cultural Heritage (ICH) can effectively contribute to Sustainable Development Goals (SDGs) in all economic, social, and environmental dimensions, along with peace and security. Studying ICH in Indonesia cannot be separated from the spatial aspect of how an area's attributes are related to other areas located close to each other. Spatial regression modeling needs to be done by considering the selection of spatial weight matrix. Using the wrong spatial weight matrix will increase the standard error in parameter estimation. Therefore, this study aims to determine: the best spatial weight matrix to accommodate the spatial autocorrelation in analyzing the description of the spread of ICH in Indonesia; and the variables that are thought to influence the number of ICH determination in Indonesia. The spatial regression modeling used in this study is the Spatial Autoregressive (SAR) model and the spatial weight matrices compared in this study are queen contiguity and inverse distance. The best model is the SAR model used the queen contiguity spatial weight matrix because it has minimum values of AIC, BIC, RMSE and MAPE which are 310.397, 319.555, 18.857 and 57.169 respectively. Simultaneously, involved in performing arts, wearing traditional dress, knowing Indonesian folklore and the spatial lag contribute significantly to number of ICH determination in Indonesia. Partially, only knowing Indonesian folklore have a significant effect on number of ICH determination in Indonesia at significance level α=5%. Each additional 1% of population that knowing Indonesian folklore in an area increases number of ICH determination in that area by 0.6719 units .

Accurate parameter estimation for safety-critical systems with unmodeled dynamics

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. Much of feedback control design is parametric in nature and as such, accurate and fast estimation of the parameters in the modeled part of the dynamic system is a crucial property for designing risk-aware autonomous systems. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no deterministic unmodeled dynamics, the proposed approach can ensure a O˜(T) Regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.