11 research outputs found

    Stability analysis and near optimal gain tuning of an attitude estimator on the special orthogonal group

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    Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs

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    This paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown constant bias. The key contribution of the paper is to study the combined state and input bias estimation problem in the general setting of Lie groups, a question for which only case studies of specific Lie groups are currently available. We show that any candidate observer (with the same state space dimension as the observed system) results in non-autonomous error dynamics, except in the trivial case where the Lie-group is Abelian. This precludes the application of the standard non-linear observer design methodologies available in the literature and leads us to propose a new design methodology based on employing invariant cost functions and general gain mappings. We provide a rigorous and general stability analysis for the case where the underlying Lie group allows a faithful matrix representation. We demonstrate our theory in the example of rigid body pose estimation and show that the proposed approach unifies two competing pose observers published in prior literature.Comment: 11 page

    State Estimation for Systems on Lie Groups with Nonideal Measurements

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    This thesis considers the state estimation problem for invariant systems on Lie groups with inputs in its associated Lie algebra and outputs in homogeneous spaces of the Lie group. A particular focus of this thesis is the development of state estimation methodologies for systems with nonideal measurements, especially systems with additive input measurement bias, output measurement delay, and sampled outputs. The main contribution of the thesis is to effectively employ the symmetries of the system dynamics and to benefit from the Lie group structure of the underlying state space in order to design robust state estimators that are computationally simple and are ideal for embedded applications in robotic systems. We address the input measurement bias problem by proposing a novel nonlinear observer to adaptively eliminate the input measurement bias. Despite the nonlinear and non-autonomous nature of the resulting error dynamics and the complexity of the underlying state space, the proposed observer exhibits asymptotic/exponential convergence of the state and bias estimation errors to zero. To tackle the output measurement delay problem, we propose novel dynamic predictors used in an observer-predictor arrangement. The observer provides estimates of the delayed state using the delayed output measurements and the predictor takes those estimates, compensates for the delay, and provides predictions of the current state. Separately, we propose output predictors employed in a predictor-observer arrangement to address the problem of sampled output measurements. The output predictors take the sampled measurements and provide continuous predictions of the current outputs. Feeding the predicted outputs into the observer yields estimates of the current state. Both methods rely on the invariance of the underlying system dynamics to recursively provide predictions with low computation requirements. We demonstrate applications of the theory with examples of attitude, velocity, and position estimation on SO(3) and SE(3). A key contribution of this thesis is the development of C++ libraries in an embedded implementation as well as experimental verification of the developed theory with real flight tests using model UAVs

    State estimation for nonlinear systems with delayed output measurements

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    In this paper, we consider the problem of state estimation for nonlinear systems when the output measurements are delayed. We assume an observer is available that takes the delayed outputs and estimates the delayed states of the system. We propose a novel predictor that takes the delayed estimates from the observer and fuses them with the current input measurements of the system to compensate for the delay. We provide a rigorous stability analysis for globally Lipschitz systems demonstrating that the prediction of the system state converges (asymptotically/exponentially) to the current system trajectory if the observer state converges (asymptotically/exponentially) to the delayed system state. The predictor is omputationally simple as it is recursively implementable with a set of delay differential equations. We demonstrate the performance of the proposed predictor via simulation studies

    Recursive attitude estimation in the presence of multi-rate and multi-delay vector measurements

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    International audienceThis paper proposes an attitude estimation methodology for the case where attitude sensors provide discrete-time samples of vector measurements at different sample rates and with time delays. The proposed methodology is based on a cascade combination of an output predictor and an attitude observer or filter. The predictor compensates for the effect of sampling and delays in vector measurements and provides continuous-time predictions of outputs. These predictions are then used in an observer or filter to estimate the current attitude. The primary contribution of the paper is to exploit the underlying symmetry of the attitude kinematics to design a recursive predictor that is computationally simple and generic, in the sense that it can be combined with any asymptotically stable observer or filter. We prove that the predictor is able to reproduce the continuous time delay-free vector measurements. In a simulation example, we demonstrate good performance of the combined predictor-observer even in presence of measurement noise and delay uncertainties

    Analysis of physical changes in Fars province water zones related to climatic parameters using remote sensing, Bakhtegan, Tashk, Iran

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    In recent decades, severe climate change, decreased precipitation, temperature rise, and increased evapotranspiration (ET) have significantly reduced waterbodies. Furthermore, governments have prioritized the study of water level fluctuations of lakes to protect them from degradation nationally and regionally. The present study investigated the physical changes in lakes Bakhtegan and Tashk due to climatic parameters. To this end, Landsat satellite imagery and the NDWI were employed to calculate the area of the waterbodies from 1986 to 2018. The results showed that the area had decreased during the study period-- since 2009, Lake Bakhtegan had dried up completely. In 2008 and 2010, the lowest precipitation was 127.82 and 107.7 mm, respectively. During the study period (1986 to 2018), the average temperature was 19.44 °C, with an increase of 0.6 °C. Among the climatic parameters, precipitation, with a correlation coefficient of 0.55, and potential evapotranspiration (PET), with a correlation coefficient of about −0.68, were more strongly correlated with changes in the area of the waterbodies. To predict temperature and precipitation in the study area in the coming decades (2020–2050), the HadCM2 model of the CORDEX Project -WAS (South Asia) was used under two scenarios: RCP4.5 and RCP8.5. These scenarios revealed the decrease in precipitation and increase in temperature trends. As a result, the waterbodies’ areas were estimated using the projected precipitation and PET for the period 2050–2020, indicating a decrease in the areas of the waterbodies

    Velocity aided attitude estimation on SO(3) with sensor delay

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    This paper provides a nonlinear attitude estimation method for vehicles performing high acceleration maneuvers when measurements of linear velocity and the ambient magnetic field are delayed. Linear velocity is measured using the Global Positioning System (GPS) and the delays of GPS and magnetometer measurements are assumed to be known constants. Our proposed method consists of a delayed observer coupled with a dynamic predictor. The delayed observer uses delayed measurements and provides estimates of delayed attitude and velocity states that are in turn used in the predictor to generate estimates of the current attitude and velocity. A key contribution of the paper is effective use of the underlying symmetries of the system in order to design a generic predictor that can be coupled to different observers. We prove exponential convergence of the predicted attitude and velocity for a specific observer choice drawn from the literature

    Herbal medicines in the treatment of coronavirus disease 2019 (COVID-19)

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    Coronavirus disease 2019 (COVID-19), caused by a novel coronavirus, started in livestock within the markets of Wuhan, China and was consequently spread around the world. The virus has been rapidly spread worldwide due to the outbreak. COVID-19 is the third serious coronavirus outbreak in less than 20 years after Severe Acute Respiratory Syndrome (SARS) in 2003 and Middle East Respiratory Syndrome (MERS) in 2012. The novel virus has a nucleotide identity closer to that of the SARS coronavirus than that of the MERS coronavirus. Since there is still no vaccine, the main ways to improve personal immunity against this disease are prophylactic care and self-resistance including an increased personal hygiene, a healthy lifestyle, an adequate nutritional intake, a sufficient rest, and wearing medical masks and increasing time spent in well ventilated areas. There is a need for novel antivirals that are highly efficient and economical for the management and control of viral infections when vaccines and standard therapies are absent. Herbal medicines and purified natural products have the potential to offer some measure of resistance as the development of novel antiviral drugs continues. In this review, we evaluated 41 articles related to herbal products which seemed to be effective in the prevention or treatment of COVID-19
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