Table 2 - uploaded by Jason J Ford
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Failure Operating Environment Performance
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Context 1
... 1 shows the separation distance achieved (during normal communication network operation) by the original centralised separation management and a pure decentralised separation management approach. Table 2 shows the separation distances achieved (during communication network failure) by the new proposed approach with/without inter-aircraft communication (separation is deemed to have been maintained if separation distance is kept greater than 1500m). The results given in Table 1 show that the decentralized separation management system achieved separation distances significantly larger than required minimum separation distances, corresponding to large heading deviations from original trajectory (these large deviations are undesirable). ...
Context 2
... results given in Table 2 suggest that, in two aircraft scenario, the aircraft will be able to resolve potential conflicts even during communication network failure with the help of decentralized separation management on the basis of propagated traffic information (without the need for new information), as long as only one aircraft changes their course after network failure. However if both aircraft change their course during the period of communication blackout then it is possible for conflict to occur if no additional information is obtained from inter-aircraft communication. ...
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Citations
... It is also possible to propose an on-line version of the EM algorithm. This was originally proposed for finite state-space and linear Gaussian models in [36], [44]; see [13] for a detailed presentation in the finite state-space case. Assume that p θ (x 0:n , y 0:n ) is in the exponential family. ...
Nonlinear non-Gaussian state-space models are ubiquitous in statistics,
econometrics, information engineering and signal processing. Particle methods,
also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical
approximations to the associated state inference problems. However, in most
applications, the state-space model of interest also depends on unknown static
parameters that need to be estimated from the data. In this context, standard
particle methods fail and it is necessary to rely on more sophisticated
algorithms. The aim of this paper is to present a comprehensive review of
particle methods that have been proposed to perform static parameter estimation
in state-space models. We discuss the advantages and limitations of these
methods and illustrate their performance on simple models.
... Likewise, the EM algorithm can also be implemented offline or online. The online EM algorithm, assuming all calculations can be performed exactly, is presented in[25],[22],[23],[33]and[9]. For a general SSM for which the quantities required by the online EM cannot be calculated exactly, an SMC implementation is possible[8], [28, Section 3.2.]; ...
... As there is no backward pass, there is no need to store the particle approximations of {p θ (dx k |y 0:k )} k=0,...,n , which can result in a significant memory saving for large data sets. In the online implementation, running averages of the sufficient statistics are computed instead[8],[22],[23],[25], [28, Section 3.2.],[33]. Let {θ k } 0≤k≤n be the sequence of parameter estimates of the online EM algorithm computed sequentially based on y 0:n. ...
... The authors are also grateful to Rong Chen for pointing out the link between the forward smoothing recursion and dynamic programming. Finally, we are thankful to Robert Elliott to have pointed out to us references[22],[23]and[25]. ...
Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an online or forward-only implementation of a forward filtering backward smoothing SMC algorithm proposed in Doucet .et .al (2000). Compared to the standard path space SMC estimator whose asymptotic variance increases quadratically with time even under favourable mixing assumptions, the asymptotic variance of the proposed SMC estimator only increases linearly with time. This forward smoothing procedure allows us to implement on-line maximum likelihood parameter estimation algorithms which do not suffer from the particle path degeneracy problem.
Considers adaptive estimation of noisy finite impulse response linear systems driven by stationary inputs from a discrete set. An algorithm based on an equivalent hidden Markov model representation is presented. The algorithm presented is globally convergent while previous approaches have only been locally convergent
