A Comparison Between Numerical Differentiation and Kalman Filtering for a Leo Satellite Velocity Determination

Sharifi, Mohammad Ali; Seif, Mohammad Reza; Hadi, Musadaq A.

doi:10.2478/arsa-2013-0009

Cited by 11 publications

(7 citation statements)

References 13 publications

(11 reference statements)

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“…The presence of an undefined input

does not allow the use the standard Kalman linear correction [ 1 ]. In order to suppress disturbances in systems (12), (13), one can select discontinuous corrective actions [ 11 ].…”

Section: Problem Definitionmentioning

confidence: 99%

“…Note that, when estimating, it is fundamentally impossible to separate the useful signal from the noise in the case when they operate in the same frequency band. Under certain conditions, the Kalman filter can be optimally tuned according to the criterion of minimum mean square estimation error [ 1 ]. The implementation of the Kalman filter requires exact knowledge of the parameters of the plant model, or their adequate identification, which is not always possible.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Smoothing, Filtering and Differentiation of Signals Defining the Path of the UAV

Antipov

Kokunko

Krasnova

et al. 2022

Sensors

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On the example of a control system for an unmanned aerial vehicle, we consider the problems of filtering, smoothing and restoring derivatives of reference action signals. These signals determine the desired spatial path of the plant at the first approximation. As a rule, researchers have considered these problems separately and have used different methods to solve each of them. The paper aims to develop a unified approach that provides a comprehensive solution to mentioned problems. We propose a dynamic admissible path generator. It is constructed as a copy of the canonical control plant model with smooth and bounded sigmoid corrective actions. For the deterministic case, a synthesis procedure has been developed, which ensures that the output variables of the generator track a non-smooth reference signal. Moreover, it considers the constraints on the velocity and acceleration of the plant. As a result, the generator variables produce a naturally smoothed spatial curve and its derivatives, which are realizable reference actions for the plant. The construction of the generator does not require exact knowledge of the plant parameters. Its dynamic order is less than that of the standard differentiators. We confirm the effectiveness of the approach by the results of numerical simulation.

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“…The presence of an undefined input

does not allow the use the standard Kalman linear correction [ 1 ]. In order to suppress disturbances in systems (12), (13), one can select discontinuous corrective actions [ 11 ].…”

Section: Problem Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Smoothing, Filtering and Differentiation of Signals Defining the Path of the UAV

Antipov

Kokunko

Krasnova

et al. 2022

Sensors

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show abstract

“…Since there are no mature mathematical models for above mentioned errors and their influences are much smaller than the clock errors (see Table . 2), we adopt a general error model which contains systematic b Satellite's position errors are assumed as 10 mm (Kang et al, 2006), velocity errors are assumed as 0.1mm/s (Sharifi et al, 2013).…”

Section: "Observed" Valuesmentioning

confidence: 99%

Unification of global vertical height system using precise frequency signal links

Shen¹,

Shen²,

Zhang³

2020

Preprint

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<p>The realization of International Height Reference System (IHRS) is one of the major tasks of the International Association of Geodesy (IAG). Here we formulate a framework for connecting two local VHSs using ultra-precise frequency signal transmission links between satellites and ground stations, which is referred to as satellite frequency signal transmission (SFST) approach. The SFST approach can directly determine the geopotential difference between two ground datum stations without location restrictions, and consequently determine the height difference of the two VHSs. Simulation results show that the China&#8217;s VHS and the US&#8217;s VHS can be unified at the accuracy of several centimeters, provided that the stability of atomic clocks used on board the satellite and on ground datum stations reach the highest level of current technology, about 4.8&#215;10<sup>-18</sup> in 100 s. The SFST approach is promising to unify the global vertical height datum in centimeter level in future, providing a new way for the IHRS realization. This study is supported by NSFCs (grant Nos. 41721003, 41631072, 41874023, 41804012, 41429401, 41574007) and Natural Science Foundation of Hubei Province of China (grant No. 2019CFB611).</p>

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“…df vepo is the position and velocity errors of ground station and satellite. The position error in the precise ephemeris of a GPS satellite is about 10 À2 m (Kang et al 2006;Guo et al 2015), and the velocity error can be reduced to below 10 À5 m/s (Sharifi et al 2013).…”

Section: Gravitational Potential Difference Determination Between a Smentioning

confidence: 99%

Determination of Gravitational Potential at Ground Using Optical-Atomic Clocks on Board Satellites and on Ground Stations and Relevant Simulation Experiments

Shen

Zhang

2017

Surv Geophys

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The general relativity theory provides a potential way to directly determine the gravitational potential (GP) difference by comparing the running rate or vibration frequencies of two optical-atomic clocks located at two stations. Recently we proposed an approach referred to as satellite frequency signal transmission based on the Doppler canceling technique or tri-frequency combination technique to determine the GP difference between a satellite and a ground site via exchanging microwave signals. Here, as an extension of our previous study, we aim to formulate determination of GP at ground stations and establish simulation experiments in different cases, including determining the GP at a ground station via one or more satellites and determining the GP difference between two ground stations via one or more satellites. Concerning each case we made simulating experiments, and results show that the precision of the GP at a ground station and that of the GP difference between two stations, determined via one satellite, are, respectively, about 0.383 and 0.454 m 2 /s 2 , assuming the clocks with inaccuracy of about 1 Â 10 À18 (s/s) level are available. If more satellites equipped with ultra-high-precise clocks are available, the precision of the determined GP (difference) at ground stations can be further improved.

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A Comparison Between Numerical Differentiation and Kalman Filtering for a Leo Satellite Velocity Determination

Cited by 11 publications

References 13 publications

Dynamic Smoothing, Filtering and Differentiation of Signals Defining the Path of the UAV

Dynamic Smoothing, Filtering and Differentiation of Signals Defining the Path of the UAV

Unification of global vertical height system using precise frequency signal links

Determination of Gravitational Potential at Ground Using Optical-Atomic Clocks on Board Satellites and on Ground Stations and Relevant Simulation Experiments

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