Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Locally Efficient Estimation with Current Status Data and High Dimensional Covariates

In biostatistical applications, interest often focuses on the estimation of the distribution of time T between two consecutive events. If the initial event time is observed and the subsequent event time is only known to be larger or smaller than an observed monitoring time, then the data is described by the well known singly-censored current status model, also known as interval censored data, case I. We extend this current status model by allowing the presence of a time-dependent process, which is partly observed and allowing C to depend on T through the observed part of this time-dependent process. Because of the high dimension of the covariate process, no globally efficient estimators exist with a good practical performance at moderate sample sizes. We follow the approach of Robins and Rotnitzky (1992) by modeling the censoring variable, given the time-variable and the covariate-process, i.e., the missingness process, under the restriction that it satisfied coarsening at random. We propose a generalization of the simple current status estimator of the distribution of T and of smooth functionals of the distribution of T, which is based on an estimate of the missingness. In this estimator the covariates enter only through the estimate of the missingness process. Due to the coarsening at random assumption, the estimator has the interesting property that if we estimate the missingness process more nonparametrically, then we improve its efficiency. We show that by local estimation of an optimal model or optimal function of the covariates for the missingness process, the generalized current status estimator for smooth functionals become locally efficient; meaning it is efficient if the right model or covariate is consistently estimated and it is consistent and asymptotically normal in general. Estimation of the optimal model requires estimation of the conditional distribution of T, given the covariates. Any (prior) knowledge of this conditional distribution can be used at this stage without any risk of losing root-n consistency. We also propose locally efficient one step estimators. Finally, we show some simulation results.

Gauss-Seidel Estimation of Generalized Linear Mixed Models with Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases. This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM to subsetted versions of the data. Additional gains in efficiency are achieved for Poisson models, commonly used in disease mapping problems, because of their special collapsibility property which allows data reduction through summaries. Convergence of the proposed iterative procedure is guaranteed for canonical link functions. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. A simulation study demonstrates the algorithm's reliability in analyzing a data set with 12 million records for a (non-collapsible) logistic regression model.

Estimation of the normal boiling point of organic compounds via group contributions

The normal boiling point is a fundamental thermo-physical property, which is important in describing the transition between the vapor and liquid phases. Reliable method which can predict it is of great importance, especially for compounds where there are no experimental data available. In this work, an improved group contribution method, which is second order method, for determination of the normal boiling point of organic compounds based on the Joback functional first order groups with some changes and added some other functional groups was developed by using experimental data for 632 organic components. It could distinguish most of structural isomerism and stereoisomerism, which including the structural, cis- and trans- isomers of organic compounds. First and second order contributions for hydrocarbons and hydrocarbon derivatives containing carbon, hydrogen, oxygen, nitrogen, sulfur, fluorine, chlorine and bromine atoms, are given. The fminsearch mathematical approach from MATLAB software is used in this study to select an optimal collection of functional groups (65 functional groups) and subsequently to develop the model. This is a direct search method that uses the simplex search method of Lagarias et al. The results of the new method are compared to the several currently used methods and are shown to be far more accurate and reliable. The average absolute deviation of normal boiling point predictions for 632 organic compounds is 4.4350 K; and the average absolute relative deviation is 1.1047 %, which is of adequate accuracy for many practical applications.

Maximum likelihood estimation of new state space models for operational modal analysis

The modal analysis of a structural system consists on computing its vibrational modes. The experimental way to estimate these modes requires to excite the system with a measured or known input and then to measure the system output at different points using sensors. Finally, system inputs and outputs are used to compute the modes of vibration. When the system refers to large structures like buildings or bridges, the tests have to be performed in situ, so it is not possible to measure system inputs such as wind, traffic, . . .Even if a known input is applied, the procedure is usually difficult and expensive, and there are still uncontrolled disturbances acting at the time of the test. These facts led to the idea of computing the modes of vibration using only the measured vibrations and regardless of the inputs that originated them, whether they are ambient vibrations (wind, earthquakes, . . . ) or operational loads (traffic, human loading, . . . ). This procedure is usually called Operational Modal Analysis (OMA), and in general consists on to fit a mathematical model to the measured data assuming the unobserved excitations are realizations of a stationary stochastic process (usually white noise processes). Then, the modes of vibration are computed from the estimated model. The first issue investigated in this thesis is the performance of the Expectation- Maximization (EM) algorithm for the maximum likelihood estimation of the state space model in the field of OMA. The algorithm is described in detail and it is analysed how to apply it to vibration data. After that, it is compared to another well known method, the Stochastic Subspace Identification algorithm. The maximum likelihood estimate enjoys some optimal properties from a statistical point of view what makes it very attractive in practice, but the most remarkable property of the EM algorithm is that it can be used to address a wide range of situations in OMA. In this work, three additional state space models are proposed and estimated using the EM algorithm: • The first model is proposed to estimate the modes of vibration when several tests are performed in the same structural system. Instead of analyse record by record and then compute averages, the EM algorithm is extended for the joint estimation of the proposed state space model using all the available data. • The second state space model is used to estimate the modes of vibration when the number of available sensors is lower than the number of points to be tested. In these cases it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors). Here, the proposed state space model and the EM algorithm are used to estimate the modal parameters taking into account the data of all setups. • And last, a state space model is proposed to estimate the modes of vibration in the presence of unmeasured inputs that cannot be modelled as white noise processes. In these cases, the frequency components of the inputs cannot be separated from the eigenfrequencies of the system, and spurious modes are obtained in the identification process. The idea is to measure the response of the structure corresponding to different inputs; then, it is assumed that the parameters common to all the data correspond to the structure (modes of vibration), and the parameters found in a specific test correspond to the input in that test. The problem is solved using the proposed state space model and the EM algorithm. Resumen El análisis modal de un sistema estructural consiste en calcular sus modos de vibración. Para estimar estos modos experimentalmente es preciso excitar el sistema con entradas conocidas y registrar las salidas del sistema en diferentes puntos por medio de sensores. Finalmente, los modos de vibración se calculan utilizando las entradas y salidas registradas. Cuando el sistema es una gran estructura como un puente o un edificio, los experimentos tienen que realizarse in situ, por lo que no es posible registrar entradas al sistema tales como viento, tráfico, . . . Incluso si se aplica una entrada conocida, el procedimiento suele ser complicado y caro, y todavía están presentes perturbaciones no controladas que excitan el sistema durante el test. Estos hechos han llevado a la idea de calcular los modos de vibración utilizando sólo las vibraciones registradas en la estructura y sin tener en cuenta las cargas que las originan, ya sean cargas ambientales (viento, terremotos, . . . ) o cargas de explotación (tráfico, cargas humanas, . . . ). Este procedimiento se conoce en la literatura especializada como Análisis Modal Operacional, y en general consiste en ajustar un modelo matemático a los datos registrados adoptando la hipótesis de que las excitaciones no conocidas son realizaciones de un proceso estocástico estacionario (generalmente ruido blanco). Posteriormente, los modos de vibración se calculan a partir del modelo estimado. El primer problema que se ha investigado en esta tesis es la utilización de máxima verosimilitud y el algoritmo EM (Expectation-Maximization) para la estimación del modelo espacio de los estados en el ámbito del Análisis Modal Operacional. El algoritmo se describe en detalle y también se analiza como aplicarlo cuando se dispone de datos de vibraciones de una estructura. A continuación se compara con otro método muy conocido, el método de los Subespacios. Los estimadores máximo verosímiles presentan una serie de propiedades que los hacen óptimos desde un punto de vista estadístico, pero la propiedad más destacable del algoritmo EM es que puede utilizarse para resolver un amplio abanico de situaciones que se presentan en el Análisis Modal Operacional. En este trabajo se proponen y estiman tres modelos en el espacio de los estados: • El primer modelo se utiliza para estimar los modos de vibración cuando se dispone de datos correspondientes a varios experimentos realizados en la misma estructura. En lugar de analizar registro a registro y calcular promedios, se utiliza algoritmo EM para la estimación conjunta del modelo propuesto utilizando todos los datos disponibles. • El segundo modelo en el espacio de los estados propuesto se utiliza para estimar los modos de vibración cuando el número de sensores disponibles es menor que vi Resumen el número de puntos que se quieren analizar en la estructura. En estos casos es usual realizar varios ensayos cambiando la posición de los sensores de un ensayo a otro (múltiples configuraciones de sensores). En este trabajo se utiliza el algoritmo EM para estimar los parámetros modales teniendo en cuenta los datos de todas las configuraciones. • Por último, se propone otro modelo en el espacio de los estados para estimar los modos de vibración en la presencia de entradas al sistema que no pueden modelarse como procesos estocásticos de ruido blanco. En estos casos, las frecuencias de las entradas no se pueden separar de las frecuencias del sistema y se obtienen modos espurios en la fase de identificación. La idea es registrar la respuesta de la estructura correspondiente a diferentes entradas; entonces se adopta la hipótesis de que los parámetros comunes a todos los registros corresponden a la estructura (modos de vibración), y los parámetros encontrados en un registro específico corresponden a la entrada en dicho ensayo. El problema se resuelve utilizando el modelo propuesto y el algoritmo EM.

Phase noise tolerance study in coherent optical circular QAM transmissions with Viterbi- Viterbi carrier phase estimation

We present a performance evaluation of a non-conventional approach to implement phase noise tolerant optical systems with multilevel modulation formats. The performance of normalized Viterbi-Viterbi carrier phase estimation (V-V CPE) is investigated in detail for circular m-level quadrature amplitude modulation (C-mQAM) signals. The intrinsic property of C-mQAM constellation points with a uniform phase separation allows a straightforward employment of V-V CPE without the need to adapt constellation. Compared with conventional feed-forward CPE for square QAM signals, the simulated results show an enhanced tolerance of linewidth symbol duration product (ΔvTs) at a low sensitivity penalty by using feed-forward CPE structure with C-mQAM. This scheme can be easily upgraded to higher order modulations without inducing considerable complexity.

High performance shift invariant motion estimation and compensation in wavelet domain video compression

The contributions of this dissertation are in the development of two new interrelated approaches to video data compression: (1) A level-refined motion estimation and subband compensation method for the effective motion estimation and motion compensation. (2) A shift-invariant sub-decimation decomposition method in order to overcome the deficiency of the decimation process in estimating motion due to its shift-invariant property of wavelet transform. ^ The enormous data generated by digital videos call for an intense need of efficient video compression techniques to conserve storage space and minimize bandwidth utilization. The main idea of video compression is to reduce the interpixel redundancies inside and between the video frames by applying motion estimation and motion compensation (MEMO) in combination with spatial transform coding. To locate the global minimum of the matching criterion function reasonably, hierarchical motion estimation by coarse to fine resolution refinements using discrete wavelet transform is applied due to its intrinsic multiresolution and scalability natures. ^ Due to the fact that most of the energies are concentrated in the low resolution subbands while decreased in the high resolution subbands, a new approach called level-refined motion estimation and subband compensation (LRSC) method is proposed. It realizes the possible intrablocks in the subbands for lower entropy coding while keeping the low computational loads of motion estimation as the level-refined method, thus to achieve both temporal compression quality and computational simplicity. ^ Since circular convolution is applied in wavelet transform to obtain the decomposed subframes without coefficient expansion, symmetric-extended wavelet transform is designed on the finite length frame signals for more accurate motion estimation without discontinuous boundary distortions. ^ Although wavelet transformed coefficients still contain spatial domain information, motion estimation in wavelet domain is not as straightforward as in spatial domain due to the shift variance property of the decimation process of the wavelet transform. A new approach called sub-decimation decomposition method is proposed, which maintains the motion consistency between the original frame and the decomposed subframes, improving as a consequence the wavelet domain video compressions by shift invariant motion estimation and compensation. ^

Peak -to -average power ratio reduced parallel interference cancellation Multicarrier-Code Division Multiple Access system with anti -interference property

Orthogonal Frequency-Division Multiplexing (OFDM) has been proved to be a promising technology that enables the transmission of higher data rate. Multicarrier Code-Division Multiple Access (MC-CDMA) is a transmission technique which combines the advantages of both OFDM and Code-Division Multiplexing Access (CDMA), so as to allow high transmission rates over severe time-dispersive multi-path channels without the need of a complex receiver implementation. Also MC-CDMA exploits frequency diversity via the different subcarriers, and therefore allows the high code rates systems to achieve good Bit Error Rate (BER) performances. Furthermore, the spreading in the frequency domain makes the time synchronization requirement much lower than traditional direct sequence CDMA schemes. There are still some problems when we use MC-CDMA. One is the high Peak-to-Average Power Ratio (PAPR) of the transmit signal. High PAPR leads to nonlinear distortion of the amplifier and results in inter-carrier self-interference plus out-of-band radiation. On the other hand, suppressing the Multiple Access Interference (MAI) is another crucial problem in the MC-CDMA system. Imperfect cross-correlation characteristics of the spreading codes and the multipath fading destroy the orthogonality among the users, and then cause MAI, which produces serious BER degradation in the system. Moreover, in uplink system the received signals at a base station are always asynchronous. This also destroys the orthogonality among the users, and hence, generates MAI which degrades the system performance. Besides those two problems, the interference should always be considered seriously for any communication system. In this dissertation, we design a novel MC-CDMA system, which has low PAPR and mitigated MAI. The new Semi-blind channel estimation and multi-user data detection based on Parallel Interference Cancellation (PIC) have been applied in the system. The Low Density Parity Codes (LDPC) has also been introduced into the system to improve the performance. Different interference models are analyzed in multi-carrier communication systems and then the effective interference suppression for MC-CDMA systems is employed in this dissertation. The experimental results indicate that our system not only significantly reduces the PAPR and MAI but also effectively suppresses the outside interference with low complexity. Finally, we present a practical cognitive application of the proposed system over the software defined radio platform.

Peak-to-Average Power Ratio Reduced Parallel Interference Cancellation Multicarrier-Code Division Multiple Access System with Anti-Interference Property

Orthogonal Frequency-Division Multiplexing (OFDM) has been proved to be a promising technology that enables the transmission of higher data rate. Multicarrier Code-Division Multiple Access (MC-CDMA) is a transmission technique which combines the advantages of both OFDM and Code-Division Multiplexing Access (CDMA), so as to allow high transmission rates over severe time-dispersive multi-path channels without the need of a complex receiver implementation. Also MC-CDMA exploits frequency diversity via the different subcarriers, and therefore allows the high code rates systems to achieve good Bit Error Rate (BER) performances. Furthermore, the spreading in the frequency domain makes the time synchronization requirement much lower than traditional direct sequence CDMA schemes. There are still some problems when we use MC-CDMA. One is the high Peak-to-Average Power Ratio (PAPR) of the transmit signal. High PAPR leads to nonlinear distortion of the amplifier and results in inter-carrier self-interference plus out-of-band radiation. On the other hand, suppressing the Multiple Access Interference (MAI) is another crucial problem in the MC-CDMA system. Imperfect cross-correlation characteristics of the spreading codes and the multipath fading destroy the orthogonality among the users, and then cause MAI, which produces serious BER degradation in the system. Moreover, in uplink system the received signals at a base station are always asynchronous. This also destroys the orthogonality among the users, and hence, generates MAI which degrades the system performance. Besides those two problems, the interference should always be considered seriously for any communication system. In this dissertation, we design a novel MC-CDMA system, which has low PAPR and mitigated MAI. The new Semi-blind channel estimation and multi-user data detection based on Parallel Interference Cancellation (PIC) have been applied in the system. The Low Density Parity Codes (LDPC) has also been introduced into the system to improve the performance. Different interference models are analyzed in multi-carrier communication systems and then the effective interference suppression for MC-CDMA systems is employed in this dissertation. The experimental results indicate that our system not only significantly reduces the PAPR and MAI but also effectively suppresses the outside interference with low complexity. Finally, we present a practical cognitive application of the proposed system over the software defined radio platform.

Improving the estimation of psychometric functions in 2AFC discrimination tasks.

Ulrich and Vorberg (2009) presented a method that fits distinct functions for each order of presentation of standard and test stimuli in a two-alternative forced-choice (2AFC) discrimination task, which removes the contaminating influence of order effects from estimates of the difference limen. The two functions are fitted simultaneously under the constraint that their average evaluates to 0.5 when test and standard have the same magnitude, which was regarded as a general property of 2AFC tasks. This constraint implies that physical identity produces indistinguishability, which is valid when test and standard are identical except for magnitude along the dimension of comparison. However, indistinguishability does not occur at physical identity when test and standard differ on dimensions other than that along which they are compared (e.g., vertical and horizontal lines of the same length are not perceived to have the same length). In these cases, the method of Ulrich and Vorberg cannot be used. We propose a generalization of their method for use in such cases and illustrate it with data from a 2AFC experiment involving length discrimination of horizontal and vertical lines. The resultant data could be fitted with our generalization but not with the method of Ulrich and Vorberg. Further extensions of this method are discussed.

MIMU sensors for joint kinematic estimation: anatomical landmarking and frame correction

The ability to capture human motion allows researchers to evaluate an individual’s gait. Gait can be measured in different ways, from camera-based systems to Magnetic and Inertial Measurement Units (MIMU). The former uses cameras to track positional information of photo-reflective markers, while the latter uses accelerometers, gyroscopes, and magnetometers to measure segment orientation. Both systems can be used to measure joint kinematics, but the results vary because of their differences in anatomical calibrations. The objective of this thesis was to study potential solutions for reducing joint angle discrepancies between MIMU and camera-based systems. The first study worked to correct the anatomical frame differences between MIMU and camera-based systems via the joint angles of both systems. This study looked at full lower body correction versus correcting a single joint. Single joint correction showed slightly better alignment of both systems, but does not take into account that body segments are generally affected by more than one joint. The second study explores the possibility of anatomical landmarking using a single camera and a pointer apparatus. Results showed anatomical landmark position could be determined using a single camera, as the anatomical landmarks found from this study and a camera-based system showed similar results. This thesis worked on providing a novel way for obtaining anatomical landmarks with a single point-and-shoot camera, as well aligning anatomical frames between MIMUs and camera-based systems using joint angles.

Axis Mapping: The Estimation of Surface Orientations and its Applications in Vehicle Localization and Structural Geology

The map representation of an environment should be selected based on its intended application. For example, a geometrically accurate map describing the Euclidean space of an environment is not necessarily the best choice if only a small subset its features are required. One possible subset is the orientations of the flat surfaces in the environment, represented by a special parameterization of normal vectors called axes. Devoid of positional information, the entries of an axis map form a non-injective relationship with the flat surfaces in the environment, which results in physically distinct flat surfaces being represented by a single axis. This drastically reduces the complexity of the map, but retains important information about the environment that can be used in meaningful applications in both two and three dimensions. This thesis presents axis mapping, which is an algorithm that accurately and automatically estimates an axis map of an environment based on sensor measurements collected by a mobile platform. Furthermore, two major applications of axis maps are developed and implemented. First, the LiDAR compass is a heading estimation algorithm that compares measurements of axes with an axis map of the environment. Pairing the LiDAR compass with simple translation measurements forms the basis for an accurate two-dimensional localization algorithm. It is shown that this algorithm eliminates the growth of heading error in both indoor and outdoor environments, resulting in accurate localization over long distances. Second, in the context of geotechnical engineering, a three-dimensional axis map is called a stereonet, which is used as a tool to examine the strength and stability of a rock face. Axis mapping provides a novel approach to create accurate stereonets safely, rapidly, and inexpensively compared to established methods. The non-injective property of axis maps is leveraged to probabilistically describe the relationships between non-sequential measurements of the rock face. The automatic estimation of stereonets was tested in three separate outdoor environments. It is shown that axis mapping can accurately estimate stereonets while improving safety, requiring significantly less time and effort, and lowering costs compared to traditional and current state-of-the-art approaches.

A NOVEL MODELING AND STATE OF CHARGE ESTIMATION SCHEME FOR LITHIUM-ION BATTERIES

Lithium Ion (Li-Ion) batteries have got attention in recent decades because of their undisputable advantages over other types of batteries. They are used in so many our devices which we need in our daily life such as cell phones, lap top computers, cameras, and so many electronic devices. They also are being used in smart grids technology, stand-alone wind and solar systems, Hybrid Electric Vehicles (HEV), and Plug in Hybrid Electric Vehicles (PHEV). Despite the rapid increase in the use of Lit-ion batteries, the existence of limited battery models also inadequate and very complex models developed by chemists is the lack of useful models a significant matter. A battery management system (BMS) aims to optimize the use of the battery, making the whole system more reliable, durable and cost effective. Perhaps the most important function of the BMS is to provide an estimate of the State of Charge (SOC). SOC is the ratio of available ampere-hour (Ah) in the battery to the total Ah of a fully charged battery. The Open Circuit Voltage (OCV) of a fully relaxed battery has an approximate one-to-one relationship with the SOC. Therefore, if this voltage is known, the SOC can be found. However, the relaxed OCV can only be measured when the battery is relaxed and the internal battery chemistry has reached equilibrium. This thesis focuses on Li-ion battery cell modelling and SOC estimation. In particular, the thesis, introduces a simple but comprehensive model for the battery and a novel on-line, accurate and fast SOC estimation algorithm for the primary purpose of use in electric and hybrid-electric vehicles, and microgrid systems. The thesis aims to (i) form a baseline characterization for dynamic modeling; (ii) provide a tool for use in state-of-charge estimation. The proposed modelling and SOC estimation schemes are validated through comprehensive simulation and experimental results.

An Islanding Detection Method based on Impedance Estimation and Grid Identification for Grid-Tie Distributed Power Generation Systems

Power system policies are broadly on track to escalate the use of renewable energy resources in electric power generation. Integration of dispersed generation to the utility network not only intensifies the benefits of renewable generation but also introduces further advantages such as power quality enhancement and freedom of power generation for the consumers. However, issues arise from the integration of distributed generators to the existing utility grid are as significant as its benefits. The issues are aggravated as the number of grid-connected distributed generators increases. Therefore, power quality demands become stricter to ensure a safe and proper advancement towards the emerging smart grid. In this regard, system protection is the area that is highly affected as the grid-connected distributed generation share in electricity generation increases. Islanding detection, amongst all protection issues, is the most important concern for a power system with high penetration of distributed sources. Islanding occurs when a portion of the distribution network which includes one or more distributed generation units and local loads is disconnected from the remaining portion of the grid. Upon formation of a power island, it remains energized due to the presence of one or more distributed sources. This thesis introduces a new islanding detection technique based on an enhanced multi-layer scheme that shows superior performance over the existing techniques. It provides improved solutions for safety and protection of power systems and distributed sources that are capable of operating in grid-connected mode. The proposed active method offers negligible non-detection zone. It is applicable to micro-grids with a number of distributed generation sources without sacrificing the dynamic response of the system. In addition, the information obtained from the proposed scheme allows for smooth transition to stand-alone operation if required. The proposed technique paves the path towards a comprehensive protection solution for future power networks. The proposed method is converter-resident and all power conversion systems that are operating based on power electronics converters can benefit from this method. The theoretical analysis is presented, and extensive simulation results confirm the validity of the analytical work.