Clock modelling techniques for an enhanced GNSS orbit determination

Author(s):  
Pedro Roldan ◽  
Pierre Guerin ◽  
Julie Anton ◽  
Marco Laurenti ◽  
Sebastien Trilles

<p>The determination of GNSS orbits is generally based on the processing of pseudorange and carrier phase measurements from a station network, with an Orbit Determination and Time Synchronization (ODTS) process. This process involves the satellite and ground station clocks as part of the GNSS measurement reconstruction. The clocks are generally estimated as a snapshot parameter, without assuming any correlation between epochs. However, the stability of satellite and some station clocks, based on technologies of hydrogen, cesium or rubidium, allows for a significant predictability. Taking advantage of this predictability the ODTS process can be improved, especially in those cases where the station network is limited or does not provide a good coverage for certain areas.</p><p>The clock modelling can be directly done by estimating additional parameters in the filter. A quadratic model is generally estimated for each clock, keeping a small snapshot contribution to account for the stochastic part and for potential deviations with respect to the theoretical behavior of the clock. The detection of this kind of deviations in the satellite and station clocks becomes a major factor for achieving a good performance with these techniques. In case the clock experiences feared events like phase or frequency jumps, the estimated clock model stops being valid and the estimation of model parameters needs to be reset.</p><p>In case a composite clock algorithm is used to provide the reference timescale for the ODTS, the estimation of clock models can rely on this algorithm. Algorithms of composite clock are generally based on a Kalman filter that estimates as part of the state vector the differences between each contributing clock and the composite timescale. These differences can be used not only to define the reference timescale of the ODTS, but also to remove the deterministic part of the clocks in the measurement reconstruction. As for the case of clock modelling, for algorithms of composite clock the detection and correction of anomalies in the contributing clocks becomes a critical point.</p><p>In this work, the integration of orbit determination, clock modelling and composite clock algorithms will be described. The impact of clock modeling techniques on the GNSS orbit determination accuracy will be presented, both considering a direct estimation of clock models in the ODTS and the estimation provided by the composite clock algorithm. These analyses will be based on NEODIS, the orbit determination software developed by Thales Alenia Space, which integrates with a Kalman filter approach GNSS orbit determination and composite clock algorithms.</p><p> </p>

2009 ◽  
Vol 6 (4) ◽  
pp. 8279-8309 ◽  
Author(s):  
W. Ju ◽  
S. Wang ◽  
G. Yu ◽  
Y. Zhou ◽  
H. Wang

Abstract. Soil and atmospheric water deficits have significant influences on CO2 and energy exchanges between the atmosphere and terrestrial ecosystems. Model parameterization significantly affects the ability of a model to simulate carbon, water, and energy fluxes. In this study, an ensemble Kalman filter (EnKF) and observations of gross primary productivity (GPP) and latent heat (LE) fluxes were used to optimize model parameters significantly affecting the calculation of these fluxes for a subtropical coniferous plantation in southeastern China. The optimized parameters include the maximum carboxylation rate (Vcmax), the Ball-Berry coefficient (m) and the coefficient determining the sensitivity of stomatal conductance to atmospheric water vapor deficit D0). Optimized Vcmax and m showed larger seasonal and interannual variations than D0. Seasonal variations of Vcmax and m are more pronounced than the interannual variations. Vcmax and m are associated with soil water content (SWC). During dry periods, SWC at the 20 cm depth can explain 61% and 64% of variations of Vcmax and m, respectively. EnKF parameter optimization improves the simulations of GPP, LE and sensible heat (SH), mainly during dry periods. After parameter optimization using EnKF, the variations of GPP, LE and SH explained by the model increased by 1% to 4% at half-hourly steps and by 3% to 5% at daily time steps. Efforts are needed to develop algorithms that can properly describe the variations of these parameters under different environmental conditions.


Author(s):  
Kamalanand Krishnamurthy

Parameter estimation is a central issue in mathematical modelling of biomedical systems and for the development of patient specific models. The technique of estimating parameters helps in obtaining diagnostic information from computational models of biological systems. However, in most of the biomedical systems, the estimation of model parameters is a challenging task due to the nonlinearity of mathematical models. In this chapter, the method of estimation of nonlinear model parameters from measurements of state variables, using the extended Kalman filter, is extensively explained using an example of the three-dimensional model of the HIV/AIDS system.


2010 ◽  
Vol 7 (3) ◽  
pp. 845-857 ◽  
Author(s):  
W. Ju ◽  
S. Wang ◽  
G. Yu ◽  
Y. Zhou ◽  
H. Wang

Abstract. Soil and atmospheric water deficits have significant influences on CO2 and energy exchanges between the atmosphere and terrestrial ecosystems. Model parameterization significantly affects the ability of a model to simulate carbon, water, and energy fluxes. In this study, an ensemble Kalman filter (EnKF) and observations of gross primary productivity (GPP) and latent heat (LE) fluxes were used to optimize model parameters significantly affecting the calculation of these fluxes for a subtropical coniferous plantation in southeastern China. The optimized parameters include the maximum carboxylation rate (Vcmax), the slope in the modified Ball-Berry model (M) and the coefficient determining the sensitivity of stomatal conductance to atmospheric water vapor deficit (D0). Optimized Vcmax and M showed larger variations than D0. Seasonal variations of Vcmax and M were more pronounced than the variations between the two years. Vcmax and M were associated with soil water content (SWC). During dry periods, SWC at the 20 cm depth explained 61% and 64% of variations of Vcmax and M, respectively. EnKF parameter optimization improved the simulations of GPP, LE and SH, mainly during dry periods. After parameter optimization using EnKF, the variations of GPP, LE and SH explained by the model increased by 1% to 4% at half-hourly steps and by 3% to 5% at daily time steps. Further efforts are needed to differentiate the real causes of parameter variations and improve the ability of models to describe the change of stomatal conductance with net photosynthesis rate and the sensitivity of photosynthesis capacity to soil water stress under different environmental conditions.


2018 ◽  
pp. 690-713
Author(s):  
Kamalanand Krishnamurthy

Parameter estimation is a central issue in mathematical modelling of biomedical systems and for the development of patient specific models. The technique of estimating parameters helps in obtaining diagnostic information from computational models of biological systems. However, in most of the biomedical systems, the estimation of model parameters is a challenging task due to the nonlinearity of mathematical models. In this chapter, the method of estimation of nonlinear model parameters from measurements of state variables, using the extended Kalman filter, is extensively explained using an example of the three-dimensional model of the HIV/AIDS system.


2017 ◽  
Vol 20 (06) ◽  
pp. 1750037 ◽  
Author(s):  
TIM LEUNG ◽  
HYUNGBIN PARK

This paper studies the long-term growth rate of expected utility or expected return from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. We develop a martingale extraction approach to tackle the path-dependence in the expectation and determine the long-term growth rate through the eigenpair associated with the infinitesimal generator of a time-homogeneous Markovian diffusion. The long-term growth rates are derived explicitly under a number of models for the reference asset, including the geometric Brownian motion model, GARCH model, inverse GARCH model, extended CIR model, 3/2 model, quadratic model, as well as the Heston and [Formula: see text] stochastic volatility models. We also investigate the impact of stochastic interest rate such as the Vasicek model and the inverse GARCH short rate model. Additionally, we determine the optimal leverage ratio that maximizes the long-term growth rate, and examine the effects of model parameters.


Author(s):  
S. M. Borodachev

The influence of both the absolute values of the dollar/ruble exchange rate (rate) and its changes per day on the balance of the Bank of Russia operations for ruble liquidity provision and absorption (saldo) was investigated. Daily data were used from January 2015 to April 2018. It was found that the change in the rate 6 days ago is the cause (according to Granger) of the saldo value. For the saldo dynamics, an oscillatory model with an external force - a change in the rate - is proposed. Using the Kalman filter, the model parameters were estimated and saldo forecasted. Found period of self-oscillation is 4.218 days and attenuation of the amplitude for a day in 2.179 times. The rate growth of 1 RUB, after 6 days, causes saldo increase of approximately 20 billion rubles. In fact, the changes in rate cause the variability of the saldo not more than for found coefficient of determination (26.7%), but the "change in the rate-liquidity saldo" system during the crisis-free period has a high "Q-factor," and changes in the rate, repeated with a period close to self-one, can cause large-amplitude fluctuations in saldo.


Author(s):  
REHAB A. EL KHARBOUTLY ◽  
SWAPNA S. GOKHALE ◽  
REDA A. AMMAR

With the growing complexity of software applications and increasing reliance on the services provided by these applications, architecture-based reliability analysis has become the focus of several recent research efforts. Most of the prevalent research in this area does not consider simultaneous or concurrent execution of application components. Concurrency, however, may be common in modern software applications. Thus, reliability analysis considering concurrent component execution within the context of the application architecture is necessary for contemporary software applications. This paper presents an architecture-based reliability analysis methodology for concurrent software applications. Central to the methodology is a state space approach, based on discrete time Markov chains (DTMCs), to represent the application architecture taking into consideration simultaneous component execution. A closed form, analytical expression for the expected application reliability based on the average execution times, constant failure rates, and the average number of visits to the components is derived. The average number of visits to application components are obtained from the solution of the DTMC model representing the application architecture. The potential of the methodology to facilitate sensitivity analysis, identification of reliability bottlenecks, and an assessment of the impact of workload and component changes, in addition to providing a reliability estimate, is discussed. To enable the application of the methodology in practice, estimation of model parameters from different software artifacts is described. The methodology is illustrated with a case study. Finally, strategies to alleviate the state space explosion issue for an efficient application of the methodology are proposed.


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