These notes explain how to use a hidden Markov model (HMM) approach for analysing possibly highly nonlinear time series data in a state-space formulation. The text introduces the general state-space model and gives an overview of other methods for filtering and smoothing ranging from the simple linear and Gaussian case to the fully general case. A discretization of the state-space is instrument...

State Space Models (SSM) is a MATLAB toolbox for time series analysis by state space methods. The software features fully interactive construction and combination of models, with support for univariate and multivariate models, complex time-varying (dynamic) models, non-Gaussian models, and various standard models such as ARIMA and structural time-series models. The software includes standard fu...

We propose a novel tracking method that allows to switch between different state representations as, e.g., image coordinates in different views or image and ground plane coordinates. During the tracking process, our method adaptively switches between these representations. We demonstrate the applicability of our method for dynamic cameras tracking dynamic objects: Using the image based represen...

In this paper we develop and validate a procedure for testing against a shift in mean in the observa-tions and hidden state sequence of state space models with Gaussian noise. State space models are popular for modelling stochastic networks as they allow to take into account that observations of the true state of a sys-tem may be corrupted by measurement noise (usually, a Gaussian noise process...

The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior of the latent state given the model. However, the key challenge in GPSSMs has not been satisfactorily addressed yet: system identification, i.e...

The quantitative analysis of the dependability attributes of computer systems using stochastic modelling is a process that requires ability and experience. Building the model of a system needs the introduction of assumptions, simplifications and abstractions, whose impact on the final results can not be estimated a priori. Also, slight variations in the value of a crucial parameter might cause ...

Although the state space approach for estimating multilevel regression models has been well established for decades in the time series literature, it does not receive much attention from educational and psychological researchers. In this article, we (a) introduce the state space approach for estimating multilevel regression models and (b) extend the state space approach for estimating multileve...

If a dynamic system has active constraints on the state vector and they are known, then taking them into account during modeling is often advantageous. Unfortunately, in constrained discrete-time state-space estimation, equality constraint defined for parameter matrix not as commonly found regression problems. To address this problem, firstly, we show how to rewrite matrices be estimated. Then,...