Kalman Filtering

This paper presents a non-intrusive system that gives the illusion of a 3D immersive and interactive environment with 2D projectors. The user does not need to wear glasses, nor to watch a (limited) screen. The virtual world is all around him, drawn on the floor. As the user is himself immersed in the virtual world, there is no need for a proxy like an avatar; he can move inside the virtual environment freely. Moreover, the I-see-3D system allows a user to manipulate virtual objects with his own body, making interactions with the virtual world very intuitive. Giving the illusion of 3D requires to render images in such a way that the deformation of the image projected on the floor is taken into account, as well as the position of the user’s “eye” in its virtual world. The resulting projection is neither perspective nor orthographic. Nevertheless, we describe how this can be implemented with the standard OpenGL pipeline, without any shader. Our experiments demonstrate that our system i...

— The goal of object tracking is segmenting a region of interest from a video scene and keeping track of its motion, positioning and occlusion. The object detection and object classification are preceding steps for tracking an object in sequence of images. Mean shift algorithm is recently widely used in tracking clustering, etc. First phase of the system is to detect the moving objects in the video. Second phase of the system will track the detected object. In this paper, detection of the moving object has been done using simple background subtraction and tracking of single moving object has been done using modified mean shift method and Kalman filter. Further result of both algorithm is compared on basis on time and accuracy. Index Terms— object tracking; kalman filter; mean shift method..

In this paper, a comprehensive comparison of two robust estimation techniques namely, compensated closed-loop Kalman filtering and open-loop Kalman filtering is presented. A common problem of data loss in a real-time control system is investigated through these two schemes. The open-loop scheme, dealing with the data-loss, suffers from several shortcomings. These shortcomings are overcome using compensated scheme, where an accommodating observation signal is obtained through linear prediction technique-a closed-loop setting and is adopted at a posteriori update step. The calculation and employment of accommodating observation signal causes computational complexity. For simulation purpose, a linear time invariant spacecraft model is however, obtained from the nonlinear spacecraft attitude dynamics through linearization at nonzero equilibrium points-achieved off-line through Levenberg-Marguardt iterative scheme. Attempt has been made to analyze the selected example from most of the perspectives in order to display the performance of the two techniques.

As a new type of energy storage device, supercapacitors are widely applied in various fields owing to their irreplaceable extraordinary characteristics. The remaining useful life represents the safe service range of a supercapacitor. Precise monitoring of its value can ensure timely replacement before reaching the service limit. An accurate state-of-charge estimation can ensure that the supercapacitor works in a safe area. Superior precision ensures that the safe area is more explicit. Thus, the supercapacitor can exercise maximum effectiveness without damaging the device. Hence, this paper reviews the above sections. The remaining useful life prediction and state-of-charge estimation of supercapacitors are reviewed based on the model and data. The methods of different innovation points are enumerated, the disparate evaluation frameworks are compared, and their merits and demerits are generalized and reviewed. In the research field, while studying the remaining useful life of supercapacitors based on data, the application of artificial neural networks is emphasized. Hence, this study focuses on reviewing the relevant content for this approach. Finally, the challenges and prospects for the prediction of the above studies are briefly described.

A methodology to create statistical arbitrage in stock Index S&P500 is presented. A synthetic asset based on the cointegration relationship of the stocks with Index was constructed. In order to capture the dynamic of the market time adaptive algorithms have been developed and discussed. The pair trading strategy was applied in different periods between S&P500 and synthetic asset and the results were evaluated. Different metrics have shown that the Multvariate Kalman Algorithm creates statistical arbitrage in index with much lower Maximum Drawdown and higher profit. The algorithm is neutral as the beta is close to zero and the Sharp Ratio remains high in all cases.

The nonlinearity and the chaotic fluctuations in the wind speed pattern are the reasons of inaccurate wind speed forecasting results using a linear autoregressive integrated moving average (ARIMA) model. The inaccurate forecasting of ARIMA model is a problem that reflects the uncertainty of modelling process. This study aims to improve the accuracy of wind speed forecasting by suggesting more appropriate approaches. An artificial neural network (ANN) and Kalman filter (KF) will be used to handle nonlinearity and uncertainty problems. Once ARIMA model was used only for determining the inputs structures of KF and ANN approaches, using an autoregressive (AR) Instead of ARIMA may be resulted in more simplicity and more accurate forecasting. ANN and KF based on the AR model are called hybrid AR-ANN model and hybrid AR-KF model, respectively. In this study, hybrid AR-ANN and hybrid AR-KF models are proposed to improve the wind speed forecasting. The performance of ARIMA, hybrid AR-ANN, an...

Scientists, engineers and the like are a strange lot. Unperturbed by societal norms, they direct their energies to finding better alternatives to existing theories and concocting solutions to unsolved problems. Driven by an insatiable curiosity, they record their observations and crunch the numbers. This tome is about the science of crunching. It’s about digging out something of value from the detritus that others tend to leave behind. The described approaches involve constructing models to process the available data. Smoothing entails revisiting historical records in an endeavour to understand something of the past. Filtering refers to estimating what is happening currently, whereas prediction is concerned with hazarding a guess about what might happen next.
This book describes the classical smoothing, filtering and prediction techniques together with some more recently developed embellishments for improving performance within applications. It aims to present the subject in an accessible way, so that it can serve as a practical guide for undergraduates and newcomers to the field. The material is organised as an eleven-lecture course. The foundations are laid in Chapters 1 and 2, which explain minimum-mean-square-error solution construction and asymptotic behaviour. Chapters 3 and 4 introduce continuous-time and discrete-time minimum-variance filtering. Generalisations for missing data, deterministic inputs, correlated noises, direct feedthrough terms, output estimation and equalisation are described. Chapter 5 simplifies the minimum-variance filtering results for steady-state problems. Observability, Riccati equation solution convergence, asymptotic stability and Wiener filter equivalence are discussed. Chapters 6 and 7 cover the subject of continuous-time and discrete-time smoothing. The main fixed-lag, fixed-point and fixed-interval smoother results are derived. It is shown that the minimum-variance fixed-interval smoother attains the best performance. Chapter 8 attends to parameter estimation. As the above-mentioned approaches all rely on knowledge of the underlying model parameters, maximum-likelihood techniques within expectation-maximisation algorithms for joint state and parameter estimation are described. Chapter 9 is concerned with robust techniques that accommodate uncertainties within problem specifications. An extra term within Riccati equations enables designers to trade-off average error and peak error performance. Chapter 10 applies the afore-mentioned linear techniques to nonlinear estimation problems. It is demonstrated that step-wise linearisations can be used within predictors, filters and smoothers, albeit by forsaking optimal performance guarantees. Chapter 11 rounds off the course by exploiting knowledge about transition probabilities. HMM and minimum-variance-HMM filters and smoothers are derived. The improved performance offered by these techniques needs to be reconciled against the significantly higher calculation overheads.

The performance of a tracking filter can be evaluated in terms of the filterpsilas optimality conditions. Testing for optimality is necessary because the estimation error covariance as provided by the filter is not a reliable indicator of performance, which is known to be ldquooptimisticrdquo (inconsistent) particularly when there are model mismatches and target maneuvers. The conventional root-mean square (RMS) error value and its variants are widely used for performance evaluation in simulation and testing but it is not feasible for real-time operations where the ground truth is hardly available. One approach for real-time reliability assessment is optimality self online monitoring (OSOM) investigated in this paper. Statistical tests for optimality conditions are formulated. Simulation examples are presented to illustrate their possible use in evaluation and adaptation.

Modern Unmanned Aircraft Systems (UAS) employ a variety of sensors and multi-sensor data fusion techniques to provide advanced operational capabilities and trusted autonomy (i.e., required levels of safety, integrity, security and interoperability), when sharing the airspace with other manned and unmanned platforms. Low-cost and high-performance Navigation and Guidance Systems (NGS) for UAS have been developed at RMIT University by employing a combination of compact and lightweight sensors to satisfy the Required Navigation Performance (RNP) in all flight phases. Additionally, recent research at RMIT has focused on the development of a unified approach to separation assurance and collision avoidance suitable for UAS cooperative/non-cooperative sensor architectures and allowing for an extended range of operations both in mission-essential and safety-critical tasks. The Sense-and-Avoid Unified Method (SUM) developed at RMIT provides an innovative analytical framework to combine real-time measurements (and associated uncertainties) of navigation states, platform dynamics and tracking observables to produce high-fidelity dynamic geo-fences suitable for integration in future avionics, Air Traffic Management (ATM) and defense decision support tools.

This report covers the important topic of stochastic volatility modelling with an emphasis on linear state models. The approach taken focuses on comparing models based on their ability to flt the data and their forecasting performance. To this end several parsimonious stochastic volatility models are estimated using realised volatility, a volatility proxy from high frequency stock price data. The

Two multisensor system architectures for navigation and guidance of small Unmanned Aircraft (UA) are presented and compared. The main objective of our research is to design a compact, light and relatively inexpensive system capable of providing the required navigation performance in all phases of flight of small UA, with a special focus on precision approach and landing, where Vision Based Navigation (VBN) techniques can be fully exploited in a multisensor integrated architecture. Various existing techniques for VBN are compared and the Appearance-Based Navigation (ABN) approach is selected for implementation. Feature extraction and optical flow techniques are employed to estimate flight parameters such as roll angle, pitch angle, deviation from the runway centreline and body rates. Additionally, we address the possible synergies of VBN, Global Navigation Satellite System (GNSS) and MEMS-IMU (Micro-Electromechanical System Inertial Measurement Unit) sensors, and the use of Aircraft Dynamics Model (ADM) to provide additional information suitable to compensate for the shortcomings of VBN and MEMS-IMU sensors in high-dynamics attitude determination tasks. An Extended Kalman Filter (EKF) is developed to fuse the information provided by the different sensors and to provide estimates of position, velocity and attitude of the UA platform in real-time. The key mathematical models describing the two architectures i.e., VBN-IMU-GNSS (VIG) system and VIGADM
(VIGA) system are introduced. The first architecture uses VBN and GNSS to augment the MEMS-IMU. The second mode also includes the ADM to provide augmentation of the attitude channel.  Simulation of these two modes is carried out and the performances of the two schemes are compared in a small UA integration scheme (i.e.,
AEROSONDE UA platform) exploring a representative cross-section
of this UA operational flight envelope, including high dynamics manoeuvres and CAT-I to CAT-III precision approach tasks.  Simulation of the first system architecture (i.e., VIG system) shows that the integrated system can reach position, velocity and attitude accuracies compatible with the Required Navigation Performance (RNP) requirements. Simulation of the VIGA system also show promising results since the achieved attitude accuracy is higher using the VBN-IMU-ADM than using VBN-IMU only. A comparison of VIG and VIGA system is also performed and it shows that the position and attitude accuracy of the proposed VIG and VIGA systems are both compatible with the RNP specified in the various UA flight phases, including precision approach down to CAT-II.

This paper describes an algorithm for distributed acoustic navigation for Autonomous Underwater Vehicles (AUVs). Whereas typical AUV navigation systems utilize pre-calibrated arrays of static transponders, our work seeks to create a fully mobile network of AUVs that perform acoustic ranging and data exchange with one another to achieve cooperative positioning for extended duration missions over large areas. The algorithm enumerates possible solutions for the AUV trajectory based on dead-reckoning and range-only measurements provided by acoustic modems that are mounted on each vehicle, and chooses the trajectory via minimization of a cost function based on these constraints. The resulting algorithm is computationally efficient, meets the strict bandwidth requirements of available AUV modems, and has potential to scale well to networks of large numbers of vehicles. The method has undergone extensive experimentation, and results from three different scenarios are reported in this paper...

This paper investigates the cubature Kalman filtering (CKF) for nonlinear dynamic systems. This third-degree rule based filter employs a spherical-radial cubature rule to numerically compute the integrals encountered in nonlinear filtering problems, thereby removing the requirements of explicitly computing the Jacobians. The cubature rule, however, requires computing the intractable integrals over a high-dimensional spherical region for multidimensional applications. Moreover, the cubature formula that has been used to construct the spherical cubature formula has some demerits, most notably its inconvenient properties in computation and low estimation accuracy. Aimed at these issues, a general class of CKFs that uses only cubature rules is derived in this paper. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes higher-degree CKFs, especially two representative types of the fifth-degree CKFs. Performance of the proposed algorithms is demonstrated via two target tracking problems. The experimental results, presented herein, illustrate the superior performance of higher-degree CKFs to conventional nonlinear filters.

This paper presents a novel approach for angular positioning of a robotic elbow movement and reducing the error response using kalman filter. In recent years, there is an increasing trend of research in robotics application to be place in terrain, sky, and ocean. Robotic elbow movement is introduced in this paper for mimicking human arm to help doing functions such as welding, painting, manufacturing and production assembly, welding, screwing, etc. Simulation study is carried out to verify the effectiveness of the proposed method. The system developed in this work was done with ISIS. A random noise is introduced in the system making the angular positioning movement of the DC motor unstable. Kalman filter is applied and is able to correct itself. The desirable response is met and the error response of the angular positioning of a DC motor was smoothened. In conclusion, the application of kalman filter improves the accuracy and response of angular position of the robotic elbow.

This chapter presents the minimum-variance filtering results simplified for the case when the model parameters are time-invariant and the noise processes are stationary. The filtering objective remains the same, namely, the task is to estimate a signal in such as way to minimise the filter error covariance.A somewhat naïve approach is to apply the standard filter recursions using the time-invariant problem parameters. Although this approach is valid, it involves recalculating the Riccati difference equation solution and filter gain at each time-step, which is computationally expensive. A lower implementation cost can be realised by recognising that the Riccati difference equation solution asymptotically approaches the solution of an algebraic Riccati equation. In this case, the algebraic Riccati equation solution and hence the filter gain can be calculated before running the filter.
The steady-state discrete-time Kalman filtering literature is vast and some of the more accessible accounts [1] – [14] are canvassed here. The filtering problem and the application of the standard time-varying filter recursions are described in Section 5.2. An important criterion for checking whether the states can be uniquely reconstructed from the measurements is observability. For example, sometimes states may be internal or sensor measurements might not be available, which can result in the system having hidden modes. Section 5.3 describes two common tests for observability, namely, checking that an observability matrix or an observability gramian are of full rank. The subject of Riccati equation monotonicity and convergence has been studied extensively by Chan [4], De Souza [5], [6], Bitmead [7], [8], Wimmer  [9] and Wonham [10], which is discussed in Section 5.4. Chan, et al [4] also showed that if the underlying system is stable and observable then the minimum-variance filter is stable. Section 6 describes a discrete-time version of the Kalman-Yakubovich-Popov Lemma, which states for time-invariant systems that solving a Riccati equation is equivalent to spectral factorisation. In this case, the Wiener and Kalman filters are the same.
Since the optimal filter is model-based, any unknown model parameters need to be estimated (as explained in Chapter 7) prior to implementation. The estimated parameters can be inexact which leads to degraded filter performance. An iterative frequency weighting procedure is described in Section 5.5 for mitigating the performance degradation.

Structural health monitoring of civil engineer-ing infrastructure involves uncertainties for damage detection, damage identification, damage classification, sensor optimization, safety, durability, reliability, service-ability, performance based engineering, life-cycle perfor-mance, risk management, decision making and so on. For incorporating such uncertainties, several filtering tech-niques accounting for stochasticity can be implemented utilizing collected data from the structures. In this paper, an iterated square root unscented Kalman filter method is proposed for the estimation of the nonlinear state variables of nonlinear structural systems. Various conventional and state-of-the-art state estimation methods are compared for the estimation performance, namely the unscented Kalman filter (UKF), the square-root unscented Kalman filter (SRUKF), the iterated unscented Kalman filter (IUKF) and the iterated square root unscented Kalman filter (ISRUKF), in two comparative studies. In the first study, UKF, IUKF, SRUKF and ISRUKF methods are utilized at a simple non-linear second order LTI system with the aim to predict a two state variables, and to estimate two model parameters. In the second study, UKF, IUKF, SRUKF and ISRUKF techniques are utilized to a complex three degree of free-dom spring-mass-dashpot system to predict the displace-ments and the velocities state variables. They are also used to estimate the model’s hysteretic parameters. Furthermore, the effect of practical challenges (e.g., measurement noise, number of states and parameters to be estimated) on the performances of UKF, IUKF, SRUKF and ISRUKF were investigated. The results of both comparative studies reveal that the ISRUKF method provides a better estimation accuracy than the IUKF method; while both methods provide improved accuracy over the UKF and SRUKF methods. The benefit of the ISRUKF method lies in its ability to provide accuracy related advantages over other estimation methods since it re-linearizes the measurement equation by iterating an approximate maximum a posteriori (MAP) estimate around the updated state, instead of relying on the predicted state. The results of the comparative studies show also that, for all the techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The ISRUKF, however, still provides advan-tages over other methods in terms of the estimation accu-racy and convergence.

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

This paper presents a tutorial on Kalman filtering that is designed for instruction to undergraduate students. The idea behind this work is that undergraduate students do not have much of the statistical and theoretical background necessary to fully understand the existing research papers and textbooks on this topic. Instead, this work offers an introductory experience for students which takes a more practical usage perspective on the topic, rather than the statistical derivation. Students reading this paper should be able to understand how to apply Kalman filtering tools to mathematical problems without requiring a deep theoretical understanding of statistical theory.

We consider the problem of using Levi's expected epistemic decision theory for classification when the hypotheses are of different informational values, conditioned on convex sets obtained from a set-valued Kalman filter. The background of epistemic utility ...

Bevezetés: Kálmán szűrő hét lépésből áll, melyet folyamatosan végrehajt, mintavételezésenként. 1. Állapot becslése dinamikai modell alapján. Nagyon fontos a Kálmán szűrőnél a modell, mert ez tartja majd helyesen az eredményeket, miközben a gyorsulásérzékelő, illetve a giroszkóp értelmetlen adatokkal is megtölti majd a szűrőt. Például a mérési zajokat, illetve, hogy a gyorsulásérzékelőnél a z tengelynél adott időben esetleg nem lefelé mutat a vektor más gyorsulás miatt ami nem a gravitáció, ami zavarja a mérést, hibát visz az eredmények közé. A modell feladata, hogy előre jelezze a rendszer állapotát a jelenlegi helyzeten alapulva és egy plusz megfelelő bemenet segítségével: jelen esetben a giroszkóp Állapot vektor esetemben két elemet tartalmaz (csak egy irányban dől, 1D modell kezdetben): ez pedig a szög és a szögsebesség eltérülését (giroszkóp driftelése).. Használva az állapotot leíró lineáris differencia egyenletet:. Ezzel tehető egy jó becslés illetve előrejelzés, hogy mi lesz a rendszer állapot az adott mintavételezésben. Vagyis mi lesz a szög, illetve a szögsebesség driftelése az adott mintavételezésben. Az előrejelzés az előző mintavételezésen alapszik, ahol már számoltunk (előre jeleztünk) egy szöget (szintén az előző mintavételezés alapján) és volt egy bemeneti adatunk, jelen esetben a giroszkóptól. Felhasználva a rendszert leíró differencia egyenlet előre tudok jelezni, hogy mi lesz a rendszer állapot a következő mintavételezésnél. Két mintavételezési idő között vagyok tehát és ott számolok. És a következő mintavételezéshez tudok egy szöget előre jelezni. Itt az F és a B mátrix a következők:. . De a modell csak egy közelítése a valóságnak. Mondhatjuk, hogy hát persze a harmadik negyedik lépésben nem pont ott lesz ahol a modell alapján lennie kellene. Itt jön be a modell zaj. Hozzá teszünk egy 0 középértékű Gauss eloszlást minden számolt állapothoz ezzel jelezzük azokat a változásokat, melyeket nem ír le a modell. Matematikailag:

Bad weather, consisting of thunderstorms, normally causes the presence of strong winds and heavy rain that may develop into a storm over a certain area. Radar has been the most potential and powerful instrument used to detect and monitor the development of thunderstorms over a large area; however, it also has certain weaknesses. Weather radar can be affected by different sources of errors, which have to be well considered and quantified for a proper interpretation of the collected data. We design a method that combines the Kalman Filter with a multivariate analysis technique. The implementation of this technique is for the purpose of developing a formulation that may help to reduce error. These studies involved parameters such as temperature, humidity, point of gauge rainfall, and weather radar reflectivity. The approach of using the Kalman Filter combined with multivariate analysis is still a new way to improve radar rainfall estimates by prediction (time update) and correction (measurement update). This particular research was developed purposefully to reduce radar rainfall bias due to the uncertain sources of error seen in the weather radar, and many studies have been developed, but still did not achieve suitable values between radar readings with rain gauge returns. Copyright © 2012 IEEE.

http://ieeexplore.ieee.org/ielx5/6416135/6422834/06422906.pdf?tp=&arnumber=6422906&isnumber=6422834

The nonlinearity and the chaotic fluctuations in the wind speed pattern are the reasons of inaccurate wind speed forecasting results using a linear autoregressive integrated moving average (ARIMA) model. The inaccurate forecasting of ARIMA model is a problem that reflects the uncertainty of modelling process. This study aims to improve the accuracy of wind speed forecasting by suggesting more appropriate approaches. An artificial neural network (ANN) and Kalman filter (KF) will be used to handle nonlinearity and uncertainty problems. Once ARIMA model was used only for determining the inputs structures of KF and ANN approaches, using an autoregressive (AR) Instead of ARIMA may be resulted in more simplicity and more accurate forecasting. ANN and KF based on the AR model are called hybrid AR-ANN model and hybrid AR-KF model, respectively. In this study, hybrid AR-ANN and hybrid AR-KF models are proposed to improve the wind speed forecasting. The performance of ARIMA, hybrid ARANN, and hybrid AR-KF models will be compared to determine which had the most accurate forecasts. A case study will be carried out that used daily wind speed data from Iraq and Malaysia. Hybrid AR-ANN and AR-KF models performed better than ARIMA model while the hybrid AR-KF model was the most adequate and provided the most accurate forecasts. In conclusion, the hybrid AR-KF model will result in better wind speed forecasting accuracy than other approaches, while the performances of both hybrid models will be provided acceptable forecasts compared to ARIMA model that will provide ineffectual wind speed forecasts.

One of the most successful applications of Bayesian inference is the Kalman filter. Even if very simple, Kalman filtering may constitute a very powerful tool on a trading desk. Here we briefly discuss some of the issues concerning volatility filtering and then we apply a Kalman filter to estimate recursively a multi asset GARCH(1,1) model on realized credit volatility. We test the model both from a static “descriptive” point of view and from a dynamic “predictive” point of view. The fitted Kalman filter works very well for both applications. The procedure can be easily extended to more asset classes or to allow for more complex GARCH specifications.

This paper proposes an approach for infinite-horizon control of partially-observed Boolean dynamical systems (POBDS) with uncertain continuous control input and infinite observation space. To cope with the partial observability of states, the proposed method first maps the POBDS to an unnormalized belief space. The nonlinear dynamics in this continuous belief space are linearized over a nominal trajectory. Then, the optimal feedback controller is derived, based on the well-known linear quadratic regulator (LQR), to push the system to follow the nominal trajectory. This nominal trajectory is computed in a planning stage before starting execution, and updated efficiently during execution, whenever the system is found to deviate from the nominal trajectory. We prove that, under mild regularization conditions, the proposed controller approaches the cost of the nominal trajectory as the linearization error approaches zero. The performance of the proposed controller is demonstrated by numerical experiments with a Melanoma gene regulatory network observed through noisy gene expression measurements.

This paper introduces a new digital signal processing algorithm for frequency and amplitude estimation based on Unscented Kalman Filter (UKF). The results of computer simulated and realistic synthetic data tests are presented. The initial parameters used during the tests were chosen carefully using an established parameter estimation method, the Self Tuning Least Square (STLS). It is concluded that the proposed algorithm is simple, efficient and has low computational demands compare to STLS which makes the UKF a very promising method in next generation of power quality monitoring devices.