Browsing by Author "Sarmavuori, Juha"

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Kaiunpoisto ja tandemkoodauksen esto
(2002) Sarmavuori, Juha
Helsinki University of Technology | Master's thesis
Hilbert Space Projection Methods for Numerical Integration and State Estimation
(2024) Sarmavuori, Juha
School of Electrical Engineering | Doctoral dissertation (article-based)
The aim of this thesis is to develop Hilbert space methods for approximation of integrals appearing in filtering and smoothing of nonlinear state-space models. State-space models have many applications in real-world problems and have been studied extensively for almost a century. In filtering, the state is estimated at a given time instant based on measurements up to the time instant. In smoothing, measurements after the given time instant are used as well. The used state-space models are stochastic and hence need to be estimated in probabilistic terms, which requires solving probability integrals. We consider two kinds of state-space models: discrete-time and continuous-discrete-time ones. In the latter case, the dynamics model is continuous time the measurements are obtained in discrete time instants. In linear state-space models with additive Gaussian noise, closed-form solutions are known for both filtering and smoothing problems. In a nonlinear case, we can use Gaussian approximations, which means that we approximate the probability distributions with Gaussian distributions. We study how to use Fourier–Hermite series for smoothing and filtering with Gaussian approximations. For computing terms of the Fourier–Hermite series, we develop a new method that uses partial differentials of a Weierstrass transform of a nonlinear function. Even with the simplifying Gaussian approximation, in general, we cannot solve the resulting Gaussian integrals in closed form, but we need numerical approximations instead. We develop a new numerical integration method based on an approximation of a multiplication operator with a finite matrix, and it is not only applicable to Gaussian integrals but can be used for more general numerical integration. This new numerical integration method generalises Gaussian quadrature and has many similar properties, which are analysed using the theory of linear operators in Hilbert space. Specifically, we prove convergence for a large class of functions. In the case of independent variables, it is possible to compute multidimensional integrals by product rule of unidimensional numerical integrals. With the new numerical integration method, we can generalise the product rule for non-independent variables. We apply this generalised product rule to filtering with arbitrary order moments.
Improving the process of debugging communication patterns in 5G Layer 1
(2019-10-21) Saarinen, Tommi
Perustieteiden korkeakoulu | Master's thesis
Debugging lower protocol layers in distributed mobile communication systems can be a complicated and a time-consuming task. Although software to inspect communication patterns between network endpoints exist, the process may require a lot of effort from software developers in the form of additional software installation and overall data processing to arrive into conclusions that can actually be used in solving reported faults in base station software and hardware. The primary goal of this thesis is to study the required fault debugging steps from 5G Layer 1 (L1) perspective. Previously, the typical workflow has consisted of acquiring a packet capture containing message exchange between endpoints, parsing it into a readable format and visually inspecting packet contents. Even though expert opinion is always needed in the final evaluation of a reported fault, the current process as a whole includes manual, repetitive and redundant phases that have potential for automation and improved tools. Thus, the priority for this thesis is to design and implement a framework automating these steps to speed up problem solving for L1 faults. Aside from the manual workflow, a lot of subtle faults can easily be missed by sheer human inspection. This thesis additionally discusses the use of graph-based modeling to automatically report discrepancies in communication sequences. This goal is realized in the form of a model checker, which is implemented to locate anomalies in message exchange with strict time constraints. The solution proposed in this thesis reduces the number of necessary debugging steps significantly. It implements relevant software components required to upload, dissect, index and store packet capture data and combines all the components into a software stack. To initiate the debugging sequence, also a clear user interface is included to require minimal effort from the user. The processed data in all its intermediate steps is included in the stack and made easily sharable, which can further reduce the total time spent if several people are included in the process.
On the convergence of numerical integration as a finite matrix approximation to multiplication operator
(2023-06) Sarmavuori, Juha; Särkkä, Simo
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We study the convergence of a family of numerical integration methods where the numerical integration is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, convergence has already been established using the theory of strong operator convergence. In this article, we consider unbounded functions and domains which pose several difficulties compared to the bounded case. A natural choice of method for this study is the theory of strong resolvent convergence which has previously been mostly applied to study the convergence of approximations of differential operators. The existing theory already includes convergence theorems that can be used as proofs as such for a limited class of functions and extended for a wider class of functions in terms of function growth or discontinuity. The extended results apply to all self-adjoint operators, not just multiplication operators. We also show how Jensen’s operator inequality can be used to analyse the convergence of an improper numerical integral of a function bounded by an operator convex function.