Dirichlet Process Mixtures for Density Estimation in Dynamic Nonlinear Modeling: Application to GPS Positioning in Urban Canyons

International audienceIn global positioning systems (GPS), classical localization algorithms assume, when the signal is received from the satellite in line-of-sight (LOS) environment, that the pseudorange error distribution is Gaussian. Such assumption is in some way very restrictive since a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments especially in urban canyons due to multipath/masking effects. In order to ensure high accuracy positioning, a good estimation of the observation error in these cases is required. To address this, an attractive flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Since the considered positioning problem involves elements of non-Gaussianity and nonlinearity and besides, it should be processed on-line, the suitability of the proposed modeling scheme in a joint state/parameter estimation problem is handled by an efficient Rao-Blackwellized particle filter (RBPF). Our approach is illustrated on a data analysis task dealing with joint estimation of vehicles positions and pseudorange errors in a global navigation satellite system (GNSS)-based localization context where the GPS information may be inaccurate because of hard reception conditions

Reception State Estimation of GNSS satellites in urban environment using particle filtering

International audienceThe reception state of a satellite is an unavailable information for Global Navigation Satellite System receivers. His knowledge or estimation can be used to evaluate the pseudorange. This article deals with the problem using three reception states: direct reception, alternate reception and blocked situation. This parameter, estimated using a Dirichlet distribution, is included in a particle filtering algorithm to improve the GNSS position in urban area. The algorithm takes into account two observation noise models depending on the reception of each satellite. Gaussian probability distribution is used with a direct path whereas a Gaussian mixture model is used in the alternate case

Robust GNSS Carrier Phase-based Position and Attitude Estimation Theory and Applications

Mención Internacional en el título de doctorNavigation information is an essential element for the functioning of robotic platforms and intelligent transportation systems. Among the existing technologies, Global Navigation Satellite Systems (GNSS) have established as the cornerstone for outdoor navigation, allowing for all-weather, all-time positioning and timing at a worldwide scale. GNSS is the generic term for referring to a constellation of satellites which transmit radio signals used primarily for ranging information. Therefore, the successful operation and deployment of prospective autonomous systems is subject to our capabilities to support GNSS in the provision of robust and precise navigational estimates. GNSS signals enable two types of ranging observations: –code pseudorange, which is a measure of the time difference between the signal’s emission and reception at the satellite and receiver, respectively, scaled by the speed of light; –carrier phase pseudorange, which measures the beat of the carrier signal and the number of accumulated full carrier cycles. While code pseudoranges provides an unambiguous measure of the distance between satellites and receiver, with a dm-level precision when disregarding atmospheric delays and clock offsets, carrier phase measurements present a much higher precision, at the cost of being ambiguous by an unknown number of integer cycles, commonly denoted as ambiguities. Thus, the maximum potential of GNSS, in terms of navigational precision, can be reach by the use of carrier phase observations which, in turn, lead to complicated estimation problems. This thesis deals with the estimation theory behind the provision of carrier phase-based precise navigation for vehicles traversing scenarios with harsh signal propagation conditions. Contributions to such a broad topic are made in three directions. First, the ultimate positioning performance is addressed, by proposing lower bounds on the signal processing realized at the receiver level and for the mixed real- and integer-valued problem related to carrier phase-based positioning. Second, multi-antenna configurations are considered for the computation of a vehicle’s orientation, introducing a new model for the joint position and attitude estimation problems and proposing new deterministic and recursive estimators based on Lie Theory. Finally, the framework of robust statistics is explored to propose new solutions to code- and carrier phase-based navigation, able to deal with outlying impulsive noises.La información de navegación es un elemental fundamental para el funcionamiento de sistemas de transporte inteligentes y plataformas robóticas. Entre las tecnologías existentes, los Sistemas Globales de Navegación por Satélite (GNSS) se han consolidado como la piedra angular para la navegación en exteriores, dando acceso a localización y sincronización temporal a una escala global, irrespectivamente de la condición meteorológica. GNSS es el término genérico que define una constelación de satélites que transmiten señales de radio, usadas primordinalmente para proporcionar información de distancia. Por lo tanto, la operatibilidad y funcionamiento de los futuros sistemas autónomos pende de nuestra capacidad para explotar GNSS y estimar soluciones de navegación robustas y precisas. Las señales GNSS permiten dos tipos de observaciones de alcance: –pseudorangos de código, que miden el tiempo transcurrido entre la emisión de las señales en los satélites y su acquisición en la tierra por parte de un receptor; –pseudorangos de fase de portadora, que miden la fase de la onda sinusoide que portan dichas señales y el número acumulado de ciclos completos. Los pseudorangos de código proporcionan una medida inequívoca de la distancia entre los satélites y el receptor, con una precisión de decímetros cuando no se tienen en cuenta los retrasos atmosféricos y los desfases del reloj. En contraposición, las observaciones de la portadora son super precisas, alcanzando el milímetro de exactidud, a expensas de ser ambiguas por un número entero y desconocido de ciclos. Por ende, el alcanzar la máxima precisión con GNSS queda condicionado al uso de las medidas de fase de la portadora, lo cual implica unos problemas de estimación de elevada complejidad. Esta tesis versa sobre la teoría de estimación relacionada con la provisión de navegación precisa basada en la fase de la portadora, especialmente para vehículos que transitan escenarios donde las señales no se propagan fácilmente, como es el caso de las ciudades. Para ello, primero se aborda la máxima efectividad del problema de localización, proponiendo cotas inferiores para el procesamiento de la señal en el receptor y para el problema de estimación mixto (es decir, cuando las incógnitas pertenecen al espacio de números reales y enteros). En segundo lugar, se consideran las configuraciones multiantena para el cálculo de la orientación de un vehículo, presentando un nuevo modelo para la estimación conjunta de posición y rumbo, y proponiendo estimadores deterministas y recursivos basados en la teoría de Lie. Por último, se explora el marco de la estadística robusta para proporcionar nuevas soluciones de navegación precisa, capaces de hacer frente a los ruidos atípicos.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidente: José Manuel Molina López.- Secretario: Giorgi Gabriele.- Vocal: Fabio Dovi

Robust GNSS Carrier Phase-based Position and Attitude Estimation

Navigation information is an essential element for the functioning of robotic platforms and intelligent transportation systems. Among the existing technologies, Global Navigation Satellite Systems (GNSS) have established as the cornerstone for outdoor navigation, allowing for all-weather, all-time positioning and timing at a worldwide scale. GNSS is the generic term for referring to a constellation of satellites which transmit radio signals used primarily for ranging information. Therefore, the successful operation and deployment of prospective autonomous systems is subject to our capabilities to support GNSS in the provision of robust and precise navigational estimates. GNSS signals enable two types of ranging observations: --code pseudorange, which is a measure of the time difference between the signal's emission and reception at the satellite and receiver, respectively, scaled by the speed of light; --carrier phase pseudorange, which measures the beat of the carrier signal and the number of accumulated full carrier cycles. While code pseudoranges provides an unambiguous measure of the distance between satellites and receiver, with a dm-level precision when disregarding atmospheric delays and clock offsets, carrier phase measurements present a much higher precision, at the cost of being ambiguous by an unknown number of integer cycles, commonly denoted as ambiguities. Thus, the maximum potential of GNSS, in terms of navigational precision, can be reach by the use of carrier phase observations which, in turn, lead to complicated estimation problems. This thesis deals with the estimation theory behind the provision of carrier phase-based precise navigation for vehicles traversing scenarios with harsh signal propagation conditions. Contributions to such a broad topic are made in three directions. First, the ultimate positioning performance is addressed, by proposing lower bounds on the signal processing realized at the receiver level and for the mixed real- and integer-valued problem related to carrier phase-based positioning. Second, multi-antenna configurations are considered for the computation of a vehicle's orientation, introducing a new model for the joint position and attitude estimation problems and proposing new deterministic and recursive estimators based on Lie Theory. Finally, the framework of robust statistics is explored to propose new solutions to code- and carrier phase-based navigation, able to deal with outlying impulsive noises

A moving fixed-interval filter/smoother for estimation of vehicle position using odometer and map-matched GPS

This paper presents some optimal real-time and post-processing estimators of vehicle position using odometer and map-matched GPS measurements. These estimators were based on a simple statistical error model of the odometer and the GPS which makes the model generalizable to other applications. Firstly, an asymptotically minimum variance unbiased estimator and two optimal moving fixed interval filters which are more flexibles are exposed. Then, the post-processing case leads to the construction of two moving fixed interval smoothers. These estimators are tested and compared with the classical Kalman filter with simulated and real data, and the results show a good accuracy of each of them

Optimized Filter Design for Non-Differential GPS/IMU Integrated Navigation

The endeavours in improving the performance of a conventional non-differential GPS/MEMS IMU tightly-coupled navigation system through filter design, involving nonlinear filtering methods, inertial sensors' stochastic error modelling and the carrier phase implementation, are described and introduced in this thesis. The main work is summarised as follows. Firstly, the performance evaluation of a recently developed nonlinear filtering method, the Cubature Kalman filter (CKF), is analysed based on the Taylor expansion. The theoretical analysis indicates that the nonlinear filtering method CKF shows its benefits only when implemented in a nonlinear system. Accordingly, a nonlinear attitude expression with direction cosine matrix (DCM) is introduced to tightly-coupled navigation system in order to describe the misalignment between the true and the estimated navigation frames. The simulation and experiment results show that the CKF performs better than the extended Kalman filter (EKF) in the unobservable, large misalignment and GPS outage cases when attitude errors accumulate quickly, rendering the psi-angle expression invalid and subsequently showing certain nonlinearity. Secondly, the use of shaping filter theory to model the inertial sensors' stochastic errors in a navigation Kalman filter is also introduced. The coefficients of the inertial sensors' noises are determined from the Allan variance plot. The shaping filter transfer function is deduced from the power spectral density (PSD) of the noises for both stationary and non-stationary processes. All the coloured noises are modelled together in the navigation Kalman filter according to equivalence theory. The coasting performance shows that the shaping filter based modelling method has a similar and even smaller maximum position drift than the conventional 1st-order Markovian process modelling method during GPS outages, thus indicating its effectiveness. Thirdly, according to the methods of dealing with carrier phase ambiguities, tightly-coupled navigation systems with time differenced carrier phase (TDCP) and total carrier phase (TCP) as Kalman filter measurements are deduced. The simulation and experiment results show that the TDCP can improve the velocity estimation accuracy and smooth trajectories, but position accuracy can only achieve the single point positioning (SPP) level if the TDCP is augmented with the pseudo-range, while the TCP based method's position accuracy can reach the sub-meter level. In order to further improve the position accuracy of the TDCP based method, a particle filter (PF) with modified TDCP observation is implemented in the TDCP/IMU tightly-coupled navigation system. The modified TDCP is defined as the carrier phase difference between the reference and observation epochs. The absolute position accuracy is determined by the reference position accuracy. If the reference position is taken from DGPS, the absolute position accuracy can reach the sub-meter level. For TCP/IMU tightly-coupled navigation systems, because the implementation of TCP in the navigation Kalman filter introduces additional states to the state vector, a hybrid CKF+EKF filtering method with the CKF estimating nonlinear states and the EKF estimating linear states, is proposed to maintain the CKF's benefits while reducing the computational load. The navigation results indicate the effectiveness of the method. After applying the improvements, the performance of a non-differential GPS/MEMS IMU tightly-coupled navigation system can be greatly improved

Estimation Algorithms for Non-Gaussian State-Space Models with Application to Positioning

State-space models (SSMs) are used to model systems with hidden time-varying state and observable measurement output. In statistical SSMs, the state dynamics is assumed known up to a random term referred to as the process noise, and the measurements contain random measurement noise. Kalman filter (KF) and Rauch– Tung–Striebel smoother (RTSS) are widely-applied closed-form algorithms that provide the parameters of the exact Bayesian filtering and smoothing distributions for discrete-time linear statistical SSMs where the process and measurement noises follow Gaussian distributions. However, when the SSM involves nonlinear functions and/or non-Gaussian noises, the Bayesian filtering and smoothing distributions cannot in general be solved using closed-form algorithms. This thesis addresses approximate Bayesian time-series inference for two positioning-related problems where the assumption of Gaussian noises cannot capture all useful knowledge of the considered system’s statistical properties: map-assisted indoor positioning and positioning using time-delay measurements.The motion constraints imposed by the indoor map are typically incorporated in the position estimate using the particle filter (PF) algorithm. The PF is a Monte Carlo algorithm especially suited for statistical SSMs where the Bayesian posterior distributions are too complicated to be adequately approximated using a well-known distribution family with a low-dimensional parameter space. In mapassisted indoor positioning, the trajectories that cross walls or floor levels get a low probability in the model. In this thesis, improvements to three different PF algorithms for map-assisted indoor positioning are proposed and compared. In the wall-collision PF, weighted random samples, also known as particles, are moved based on inertial sensor measurements, and the particles that collide with the walls are downweighted. When the inertial sensor measurements are very noisy, map information is used to guide the particles such that fewer particles collide with the walls, which implies that more particles contribute to the estimation. When no inertial sensor information is used, the particles are moved along the links of a graph that is dense enough to approximate the set of expected user paths.Time-delay based ranging measurements of e.g. ultra-wideband (UWB) and Global Navigation Satellite Systems (GNSSs) contain occasional positive measurement errors that are large relative to the majority of the errors due to multipath effects and denied line of sight. In this thesis, computationally efficient approximate Bayesian filters and smoothers are proposed for statistical SSMs where the measurement noise follows a skew t -distribution, and the algorithms are applied to positioning using time-delay based ranging measurements. The skew t -distribution is an extension of the Gaussian distribution, which has two additional parameters that affect the heavytailedness and skewness of the distribution. When the measurement noise model is heavy-tailed, the optimal Bayesian algorithm is robust to occasional large measurement errors, and when the model is positively (or negatively) skewed, the algorithms account for the fact that most large errors are known to be positive (or negative). Therefore, the skew t -distribution is more flexible than the Gaussian distribution and captures more statistical features of the error distributions of UWB and GNSS measurements. Furthermore, the skew t -distribution admits a conditionally Gaussian hierarchical form that enables approximating the filtering and smoothing posteriors with Gaussian distributions using variational Bayes (VB) algorithms. The proposed algorithms can thus be computationally efficient compared to Monte Carlo algorithms especially when the state is high-dimensional. It is shown in this thesis that the skew-t filter improves the accuracy of UWB based indoor positioning and GNSS based outdoor positioning in urban areas compared to the extended KF. The skew-t filter’s computational burden is higher than that of the extended KF but of the same magnitude.Tila-avaruusmalleilla mallinnetaan järjestelmiä, joilla on tuntema-ton ajassa muuttuva tila sekä mitatattava ulostulo. Tilastollisissa tila-avaruusmalleissa järjestelmän tilan muutos tunnetaan lukuunotta-matta prosessikohinaksi kutsuttua satunnaista termiä, ja mittauk-set sisältävät satunnaista mittauskohinaa. Kalmanin suodatin sekäRauchin Tungin ja Striebelin siloitin ovat yleisesti käytettyjä sulje-tun muodon estimointialgoritmeja, jotka tuottavat tarkat bayesiläi-set suodatus- ja siloitusjakaumat diskreettiaikaisille lineaarisille ti-lastollisille tila-avaruusmalleille, joissa prosessi- ja mittauskohinatnoudattavat gaussisia jakaumia. Jos käsiteltyyn tila-avaruusmalliinkuitenkin liittyy epälineaarisia funktioita tai epägaussisia kohinoita,bayesiläisiä suodatus- ja siloitusjakaumia ei yleensä voida ratkais-ta suljetun muodon algoritmeilla. Tässä väitöskirjassa tutkitaan ap-proksimatiivista bayesiläistä aikasarjapäättelyä ja sen soveltamistakahteen paikannusongelmaan, joissa gaussinen jakauma ei mallinnariittävän hyvin kaikkea hyödyllistä tietoa tutkitun järjestelmän tilas-tollisista ominaisuuksista: kartta-avusteinen sisätilapaikannus sekäsignaalin kulkuaikamittauksiin perustuva paikannus.Sisätilakartan tuottamat liikerajoitteet voidaan liittää paikkaestimaat-tiin käyttäen partikkelisuodattimeksi kutsuttua algoritmia. Partik-kelisuodatin on Monte Carlo -algoritmi, joka soveltuu erityisesti ti-lastollisille tila-avaruusmalleille, joissa bayesiläisen posteriorijakau-man tiheysfunktio on niin monimutkainen, että sen approksimointitunnetuilla matalan parametridimension jakaumilla ei ole mielekäs-tä. Kartta-avusteisessa sisätilapaikannuksessa reitit, jotka leikkaavatseiniä tai kerrostasoja, saavat muita pienemmät todennäköisyydet.Tässä väitöskirjassa esitetään parannuksia kolmeen eri partikkelisuo-datusalgoritmiin, joita sovelletaan kartta-avusteiseen sisätilapaikan-vnukseen. Seinätörmayssuodattimessa painolliset satunnaisnäytteeteli partikkelit liikkuvat inertiasensorimittausten mukaisesti, ja sei-nään törmäävät partikkelit saavat pienet painot. Kun inertiasensori-mittauksissa on paljon kohinaa, partikkeleita voidaan ohjata siten,että seinätörmäysten määrä vähenee, jolloin suurempi osa partikke-leista vaikuttaa estimaattiin. Kun inertiasensorimittauksia ei käytetälainkaan, sisätilakartta voidaan esittää graafina, jonka kaarilla partik-kelit liikkuvat ja joka on riittävän tiheä approksimoimaan odotetta-vissa olevien reittien joukkoa.Esimerkiksi laajan taajuuskaistan radioista (UWB, ultra-wideband)tai paikannussatelliiteista saatavat radiosignaalin kulkuaikaan pe-rustuvat etäisyysmittaukset taas voivat sisältää monipolkuheijastus-ten ja suoran reitin estymisen aiheuttamia positiivismerkkisiä vir-heitä, jotka ovat huomattavan suuria useimpiin mittausvirheisiinverrattuna. Tässä väitöskirjassa esitetään laskennallisesti tehokkaitabayesiläisen suodattimen ja siloittimen approksimaatioita tilastol-lisille tila-avaruusmalleille, joissa mittauskohina noudattaa vinoat -jakaumaa. Vino t -jakauma on gaussisen jakauman laajennos, jasillä on kaksi lisäparametria, jotka vaikuttavat jakauman paksuhän-täisyyteen ja vinouteen. Kun mittauskohinaa mallintava jakaumaoletetaan paksuhäntäiseksi, optimaalinen bayesiläinen algoritmi eiole herkkä yksittäisille suurille mittausvirheille, ja kun jakauma olete-taan positiivisesti (tai negatiivisesti) vinoksi, algoritmit hyödyntävättietoa, että suurin osa suurista virheistä on positiivisia (tai negatiivi-sia). Vino t -jakauma on siis gaussista jakaumaa joustavampi, ja sillävoidaan mallintaa kulkuaikaan perustuvien mittausten virhejakau-maa tarkemmin kuin gaussisella jakaumalla. Vinolla t -jakaumalla onmyös ehdollisesti gaussinen esitys, joka soveltuu suodatus- ja siloi-tusposteriorien approksimointiin variaatio-Bayes-algoritmilla. Näinollen esitetyt algoritmit voivat olla laskennallisesti tehokkaampiakuin Monte Carlo -algoritmit erityisesti tilan ollessa korkeaulotteinen.Tässä väitöskirjassa näytetään, että vino-t -virhejakauman käyttö pa-rantaa UWB-radioon perustuvan sisätilapaikannuksen tarkkuuttasekä satelliittipohjaisen ulkopaikannuksen tarkkuutta kaupunkiym-päristössä verrattuna laajennettuun Kalmanin suodattimeen. Vino-t -suodatuksen laskennallinen vaativuus on suurempi mutta samaakertaluokkaa kuin laajennetun Kalmanin suodattimen

Estimation Algorithms for Non-Gaussian State-Space Models with Application to Positioning

State-space models (SSMs) are used to model systems with hidden time-varying state and observable measurement output. In statistical SSMs, the state dynamics is assumed known up to a random term referred to as the process noise, and the measurements contain random measurement noise. Kalman filter (KF) and Rauch– Tung–Striebel smoother (RTSS) are widely-applied closed-form algorithms that provide the parameters of the exact Bayesian filtering and smoothing distributions for discrete-time linear statistical SSMs where the process and measurement noises follow Gaussian distributions. However, when the SSM involves nonlinear functions and/or non-Gaussian noises, the Bayesian filtering and smoothing distributions cannot in general be solved using closed-form algorithms. This thesis addresses approximate Bayesian time-series inference for two positioning-related problems where the assumption of Gaussian noises cannot capture all useful knowledge of the considered system’s statistical properties: map-assisted indoor positioning and positioning using time-delay measurements.The motion constraints imposed by the indoor map are typically incorporated in the position estimate using the particle filter (PF) algorithm. The PF is a Monte Carlo algorithm especially suited for statistical SSMs where the Bayesian posterior distributions are too complicated to be adequately approximated using a well-known distribution family with a low-dimensional parameter space. In mapassisted indoor positioning, the trajectories that cross walls or floor levels get a low probability in the model. In this thesis, improvements to three different PF algorithms for map-assisted indoor positioning are proposed and compared. In the wall-collision PF, weighted random samples, also known as particles, are moved based on inertial sensor measurements, and the particles that collide with the walls are downweighted. When the inertial sensor measurements are very noisy, map information is used to guide the particles such that fewer particles collide with the walls, which implies that more particles contribute to the estimation. When no inertial sensor information is used, the particles are moved along the links of a graph that is dense enough to approximate the set of expected user paths.Time-delay based ranging measurements of e.g. ultra-wideband (UWB) and Global Navigation Satellite Systems (GNSSs) contain occasional positive measurement errors that are large relative to the majority of the errors due to multipath effects and denied line of sight. In this thesis, computationally efficient approximate Bayesian filters and smoothers are proposed for statistical SSMs where the measurement noise follows a skew t -distribution, and the algorithms are applied to positioning using time-delay based ranging measurements. The skew t -distribution is an extension of the Gaussian distribution, which has two additional parameters that affect the heavytailedness and skewness of the distribution. When the measurement noise model is heavy-tailed, the optimal Bayesian algorithm is robust to occasional large measurement errors, and when the model is positively (or negatively) skewed, the algorithms account for the fact that most large errors are known to be positive (or negative). Therefore, the skew t -distribution is more flexible than the Gaussian distribution and captures more statistical features of the error distributions of UWB and GNSS measurements. Furthermore, the skew t -distribution admits a conditionally Gaussian hierarchical form that enables approximating the filtering and smoothing posteriors with Gaussian distributions using variational Bayes (VB) algorithms. The proposed algorithms can thus be computationally efficient compared to Monte Carlo algorithms especially when the state is high-dimensional. It is shown in this thesis that the skew-t filter improves the accuracy of UWB based indoor positioning and GNSS based outdoor positioning in urban areas compared to the extended KF. The skew-t filter’s computational burden is higher than that of the extended KF but of the same magnitude.Tila-avaruusmalleilla mallinnetaan järjestelmiä, joilla on tuntema-ton ajassa muuttuva tila sekä mitatattava ulostulo. Tilastollisissa tila-avaruusmalleissa järjestelmän tilan muutos tunnetaan lukuunotta-matta prosessikohinaksi kutsuttua satunnaista termiä, ja mittauk-set sisältävät satunnaista mittauskohinaa. Kalmanin suodatin sekäRauchin Tungin ja Striebelin siloitin ovat yleisesti käytettyjä sulje-tun muodon estimointialgoritmeja, jotka tuottavat tarkat bayesiläi-set suodatus- ja siloitusjakaumat diskreettiaikaisille lineaarisille ti-lastollisille tila-avaruusmalleille, joissa prosessi- ja mittauskohinatnoudattavat gaussisia jakaumia. Jos käsiteltyyn tila-avaruusmalliinkuitenkin liittyy epälineaarisia funktioita tai epägaussisia kohinoita,bayesiläisiä suodatus- ja siloitusjakaumia ei yleensä voida ratkais-ta suljetun muodon algoritmeilla. Tässä väitöskirjassa tutkitaan ap-proksimatiivista bayesiläistä aikasarjapäättelyä ja sen soveltamistakahteen paikannusongelmaan, joissa gaussinen jakauma ei mallinnariittävän hyvin kaikkea hyödyllistä tietoa tutkitun järjestelmän tilas-tollisista ominaisuuksista: kartta-avusteinen sisätilapaikannus sekäsignaalin kulkuaikamittauksiin perustuva paikannus.Sisätilakartan tuottamat liikerajoitteet voidaan liittää paikkaestimaat-tiin käyttäen partikkelisuodattimeksi kutsuttua algoritmia. Partik-kelisuodatin on Monte Carlo -algoritmi, joka soveltuu erityisesti ti-lastollisille tila-avaruusmalleille, joissa bayesiläisen posteriorijakau-man tiheysfunktio on niin monimutkainen, että sen approksimointitunnetuilla matalan parametridimension jakaumilla ei ole mielekäs-tä. Kartta-avusteisessa sisätilapaikannuksessa reitit, jotka leikkaavatseiniä tai kerrostasoja, saavat muita pienemmät todennäköisyydet.Tässä väitöskirjassa esitetään parannuksia kolmeen eri partikkelisuo-datusalgoritmiin, joita sovelletaan kartta-avusteiseen sisätilapaikan-vnukseen. Seinätörmayssuodattimessa painolliset satunnaisnäytteeteli partikkelit liikkuvat inertiasensorimittausten mukaisesti, ja sei-nään törmäävät partikkelit saavat pienet painot. Kun inertiasensori-mittauksissa on paljon kohinaa, partikkeleita voidaan ohjata siten,että seinätörmäysten määrä vähenee, jolloin suurempi osa partikke-leista vaikuttaa estimaattiin. Kun inertiasensorimittauksia ei käytetälainkaan, sisätilakartta voidaan esittää graafina, jonka kaarilla partik-kelit liikkuvat ja joka on riittävän tiheä approksimoimaan odotetta-vissa olevien reittien joukkoa.Esimerkiksi laajan taajuuskaistan radioista (UWB, ultra-wideband)tai paikannussatelliiteista saatavat radiosignaalin kulkuaikaan pe-rustuvat etäisyysmittaukset taas voivat sisältää monipolkuheijastus-ten ja suoran reitin estymisen aiheuttamia positiivismerkkisiä vir-heitä, jotka ovat huomattavan suuria useimpiin mittausvirheisiinverrattuna. Tässä väitöskirjassa esitetään laskennallisesti tehokkaitabayesiläisen suodattimen ja siloittimen approksimaatioita tilastol-lisille tila-avaruusmalleille, joissa mittauskohina noudattaa vinoat -jakaumaa. Vino t -jakauma on gaussisen jakauman laajennos, jasillä on kaksi lisäparametria, jotka vaikuttavat jakauman paksuhän-täisyyteen ja vinouteen. Kun mittauskohinaa mallintava jakaumaoletetaan paksuhäntäiseksi, optimaalinen bayesiläinen algoritmi eiole herkkä yksittäisille suurille mittausvirheille, ja kun jakauma olete-taan positiivisesti (tai negatiivisesti) vinoksi, algoritmit hyödyntävättietoa, että suurin osa suurista virheistä on positiivisia (tai negatiivi-sia). Vino t -jakauma on siis gaussista jakaumaa joustavampi, ja sillävoidaan mallintaa kulkuaikaan perustuvien mittausten virhejakau-maa tarkemmin kuin gaussisella jakaumalla. Vinolla t -jakaumalla onmyös ehdollisesti gaussinen esitys, joka soveltuu suodatus- ja siloi-tusposteriorien approksimointiin variaatio-Bayes-algoritmilla. Näinollen esitetyt algoritmit voivat olla laskennallisesti tehokkaampiakuin Monte Carlo -algoritmit erityisesti tilan ollessa korkeaulotteinen.Tässä väitöskirjassa näytetään, että vino-t -virhejakauman käyttö pa-rantaa UWB-radioon perustuvan sisätilapaikannuksen tarkkuuttasekä satelliittipohjaisen ulkopaikannuksen tarkkuutta kaupunkiym-päristössä verrattuna laajennettuun Kalmanin suodattimeen. Vino-t -suodatuksen laskennallinen vaativuus on suurempi mutta samaakertaluokkaa kuin laajennetun Kalmanin suodattimen

Intra- and Intersystem Interference in GNSS: Performance Models and Signal Design

The European Galileo, the American Global Positioning System (GPS), and other global navigation satellite systems (GNSSs) transmit direct-sequence spread spectrum (DSSS) signals from space, allowing receivers on Earth to compute their position, velocity, and time (PVT) based on the principle of pseudorange trilateration. However, as multiple satellites and systems transmit signals simultaneously within shared frequency bands, multiple access interference (MAI) in the form of intra- and intersystem interference can affect signal processing at the receiver. To compute a pseudorange, the receiver must estimate synchronization parameters of the respective signal with high resolution. This synchronization is performed in a two-step approach, consisting of signal acquisition (detection) and fine parameter estimation. Most GNSSs rely on asynchronous direct-sequence code-division multiple access (DS-CDMA), assigning different pseudorandom noise (PRN) code to each satellite. This multiple access scheme involves a controlled level of MAI degrading acquisition and parameter estimation performance, which needs to be carefully modeled before launching new signals or raising transmit power levels. The International Telecommunications Union (ITU) regulates that radio frequency compatibility (RFC) of systems, satellites and signals within the radionavigation frequency bands must be ensured, meaning that receiver performance must not be harmed significantly. Conventional receiver performance models are based on the spectral separation coefficient (SSC) between desired and interfering signal, and mostly rely on the idealization that GNSS signals are wide-sense stationary (WSS), circularly-symmetric Gaussian (CSG) random processes. In this work, we propose refined models for performance of coarse and fine estimation of synchronization parameters, taking into account the signals’ wide-sense cyclostationary (WSCS) property and their non-circularity. This is of particular interest in light of the recent signal design trend towards novel coarse/acquisition (C/A) signals with short PRN codes, which are especially vulnerable to MAI but very attractive for the group of mass-market GNSS-enabled electronic devices. Ultimately, our performance model enables the C/A signal designer to minimize the PRN code length while ensuring a given acquisition performance constraint. Moreover, with regard to RFC of an increasing number of navigation systems, satellites, and signals, our detailed models for interference effects on user equipment will allow to make more efficient use of the available radio frequency spectrum

Machine learning for modelling urban dynamics

We live in the age of cities. More than half of the world’s population live in cities and this urbanisation trend is only forecasted to continue. To understand cities now and in the foreseeable future, we need to take seriously the idea that it is not enough to study cities as sets of locations as we have done in the past. Instead, we need to switch our traditional focus from locations to interactions and in doing so, invoke novel approaches to modelling cities. Cities are becoming “smart” recording their daily interactions via various sensors and yielding up their secrets in large databases. We are faced with an unprecedented opportunity to reason about them directly from such secondary data. In this thesis, we propose model-based machine learning as a flexible framework for reasoning about cities at micro and macro scales. We use model-based machine learning to encode our knowledge about cities and then to automatically learn about them from urban tracking data. Driven by questions about urban dynamics, we develop novel Bayesian inference algorithms that improve our ability to learn from highly complex, temporal data feeds, such as tracks of vehicles in cities. Overall, the thesis proposes a novel machine learning toolkit, which, when applied to urban data, can challenge how we can think about cities now and about how to make them ”smarter”