Dietmar Bauer

Inferring land use from mobile phone activity

Understanding the spatiotemporal distribution of people within a city is crucial to many planning applications. Obtaining data to create required knowledge, currently involves costly survey methods. At the same time ubiquitous mobile sensors from personal GPS devices to mobile phones are collecting massive amounts of data on urban systems. The locations, communications, and activities of millions of people are recorded and stored by new information technologies. This work utilizes novel dynamic data, generated by mobile phone users, to measure spatiotemporal changes in population. In the process, we identify the relationship between land use and dynamic population over the course of a typical week. A machine learning classification algorithm is used to identify clusters of locations with similar zoned uses and mobile phone activity patterns. It is shown that the mobile phone data is capable of delivering useful information on actual land use that supplements zoning regulations.

Analysis of the asymptotic properties of the MOESP type of subspace algorithms

The MOESP type of subspace algorithms are used for the identification of linear, discrete time, finite-dimensional state-space systems. They are based on the geometric structure of covariance matrices and exploit the properties of the state vector extensively. In this paper the asymptotic properties of the algorithms are examined. The main results include consistency and asymptotic normality for the estimates of the system matrices, under suitable assumptions on the noise sequence, the input process and the underlying true system.

Asymptotic properties of subspace estimators

Since the proposal of subspace methods in the 1980s and early 1990s substantial efforts have been made in the analysis of the statistical properties of the algorithms. This paper surveys the literature on the asymptotic properties of particular subspace methods used for linear, dynamic, time invariant, discrete time systems. The goals of this paper are threefold: First this survey tries to present the most relevant results on the asymptotic properties of estimators obtained using subspace methods. Secondly the main methods and tools that have been used in the derivation of these results are presented to make the literature more accessible. Thirdly main unsolved questions and rewarding research topics are identified some of which can be attacked using the toolbox discussed in the paper.

Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs

Asymptotic normality for a class of subspace algorithms, which estimate the state in a first step, is derived. Expressions for the asymptotic variance are given. Linear systems with unobserved white noise inputs are considered. A class of subspace estimates for the system matrices obtained by estimating the state in the first step is analyzed. The main result presented here states asymptotic normality of subspace estimates. In addition, a consistency result for the system matrix estimates is given. An algorithm to compute the asymptotic variances of the estimates is presented. In a final section the implications of the result are discussed.

Some facts about the choice of the weighting matrices in Larimore type of subspace algorithms

In this paper the effect of some weighting matrices on the asymptotic variance of the estimates of linear discrete time state space systems estimated using subspace methods is investigated. The analysis deals with systems with white or without observed inputs and refers to the Larimore type of subspace procedures. The main result expresses the asymptotic variance of the system matrix estimates in canonical form as a function of some of the user choices, clarifying the question on how to choose them optimally. It is shown, that the CCA weighting scheme leads to optimal accuracy. The expressions for the asymptotic variance can be implemented more efficiently as compared to the ones previously published.

Order estimation for subspace methods

Three different order estimation criteria in the context of subspace algorithms are introduced and sufficient conditions for strong consistency are derived. A simulation study points to open questions.

Estimating cointegrated systems using subspace algorithms

The properties of the so-called subspace algorithms, up to now used almost only for stationary processes, are investigated in the context of cointegrated processes of order 1. It is shown for one of these algorithms that it can be adapted to deliver consistent estimates of all system parameters in the case of general I(1) VARMA models and mild conditions on the underlying noise. Estimates of the cointegrating space are derived and several test procedures for the cointegrating rank are proposed. Consistent estimation of the system order is also discussed. A simulation study shows the usefulness of subspace algorithms for estimation of and testing in cointegrated systems.

ESTIMATING LINEAR DYNAMICAL SYSTEMS USING SUBSPACE METHODS

This paper provides a survey on a class of so-called subspace methods whose main proponent is CCA proposed by Larimore (1983, Proceedings of the 1983 American Control Conference 2). Because they are based on regressions these methods for the estimation of ARMAX systems are attractive as a result of their conceptual simplicity and their numerical advantages as compared to traditional estimators based on criterion optimization. Under the assumption of correct specification the methods provide consistent and asymptotically normal estimates for stationary ARMAX processes where the innovations may be conditionally heteroskedastic and the exogenous inputs are strictly stationary of sufficiently short memory. For stationary autoregressive moving average (ARMA) processes with independent and identically distributed (i.i.d.) Gaussian innovations the estimates are even asymptotically efficient. For I(1) ARMA processes the estimates of both the long-run and the short-run dynamics are consistent without using the knowledge that the data are integrated in the algorithm. Additionally the algorithms provide easily accessible information on the appropriateness of the chosen model complexity. The algorithms include a number of design parameters that have to be set by the user. These include the order of the estimated system. This paper collects up-to-date knowledge on the effects of these design parameters, leading to a number of suggested automated choices to obtain a fully automated estimation procedure.

Asymptotic properties of least-squares estimates of Hammerstein-Wiener models

This paper investigates the asymptotic properties of least squares estimates of Hammerstein-Wiener model structures, and in doing so establishes consistency and asymptotic normality under fairly mild conditions on the additive noise process, the inputs and the static non-linearities. In relation to the asymptotic distributional results, a consistent procedure for the estimation of the asymptotic variance of the parameter estimates is provided. A key theme of this paper is to demonstrate how recent results from the econometrics literature may be employed in an engineering setting. In this respect the Hammerstein-Wiener model structure serves as a demonstration example. A simulation study complements the theoretical findings.

Estimating Pedestrian Movement Characteristics for Crowd Control at Public Transport Facilities

Capacities of doors, staircases and other bottle-necks are a key aspect in the design of infrastructures for public transport. Especially major events like soccer games and concerts may lead to large crowds which need to be accommodated, while at the same time potential safety hazards like overcrowding must be avoided. The bottleneck capacities limit the capacities of the whole system and control the potential of high crowd densities on critical elements such as the platforms. We present an approach to estimate the maximum and effective capacity of key bottleneck elements based on controlled experiments and real world data sets of pedestrian movements for a subway station next to the main soccer stadium in Vienna. The focus is the fundamental diagram revealing both the maximal capacity as well as the effective capacity in terms of pedestrian flow rates. We present two controlled experiments and results based on real world data obtained during the European Soccer Championship (UEFA EURO 2008trade).