The angular wheel speed of a vehicle is estimated by tracking the frequency of chassis vibrations measured with an accelerometer. A Bayesian filtering framework is proposed, allowing for straightforward incorporation of supporting information. The framework is evaluated on a large number of experimental test drives, showing comparable performance to the standard periodogram method. We then demonstrate the flexibility of the framework using accelerometer information in two ways, combining the high-frequency vibrations with low-frequency information about the vehicle acceleration. This is shown to improve robustness and resolve many cases where stand-alone frequency tracking fails.

Poor road conditions in underground mine tunnels can lead to decreased production efficiency and increased wear on production vehicles. A prototype system for road condition monitoring is presented in this paper to counteract this. The system consists of three components i.e. localization, road monitoring, and scheduling. The localization of vehicles is performed using a Rao-Blackwellized extended particle filter, combining vehicle mounted sensors with signal strengths of WiFi access points. Two methods for road monitoring are described: a Kalman filter used together with a model of the vehicle suspension system, and a relative condition measure based on the power spectral density. Lastly, a method for taking automatic action on an ill-conditioned road segment is proposed in the form of a rescheduling algorithm. The scheduling algorithm is based on the large neighborhood search and is used to integrate road service activities in the short-term production schedule while minimizing introduced production disturbances. The system is demonstrated on experimental data collected in a Swedish underground mine.

For robust Gaussian process regression problems where the measurements are contaminated by outliers, a likelihood/measurement noise model with heavy-tailed distributions should be used to improve the prediction performance. In this paper, we propose to use a G-confluent distribution as the measurement noise model and a coordinate ascent variational inference method to infer the overall statistical model. In contrast with the commonly used Students t distribution, the G-confluent distribution can also be written as a Gaussian scale mixture, but its inverse scale follows a Beta distribution rather than a Gamma distribution, and its main advantage is that it is more flexible for modeling outliers while being equally suitable for variational inference. Numerical simulations based on benchmark data show that the G-confluent distribution performs better than or as well as the Students t distribution. Copyright (C) 2020 The Authors.

Estimating the frequency of a periodic signal, or tracking the time-varying frequency of an almost periodic signal, is an important problem that is well studied in literature. This thesis focuses on two subproblems where contributions can be made to the existing theory: frequency tracking methods and measurements containing outliers.

Maximum-likelihood-based frequency estimation methods are studied, focusing on methods which can handle outliers in the measurements. Katkovnik’s frequency estimation method is generalized to real and harmonic signals, and a new method based on expectation-maximization is proposed. The methods are compared in a simulation study in which the measurements contain outliers. The proposed methods are compared with the standard periodogram method.

Recursive Bayesian methods for frequency tracking are studied, focusing on the Rao-Blackwellized point mass filter (RBPMF). Two reformulations of the RBPMF aiming to reduce computational costs are proposed. Furthermore, the technique of variational approximate Rao-Blackwellization is proposed, which allows usage of a Student’s t distributed measurement noise model. This enables recursive frequency tracking methods to handle outliers using heavy-tailed noise models in Rao-Blackwellized filters such as the RBPMF. A simulation study illustrates the performance of the methods when outliers occur in the measurement noise.

The framework above is applied to and studied in detail in two applications. The first application is on frequency tracking of engine sound. Microphone measurements are used to track the frequency of Doppler-shifted variants of the engine sound of a vehicle moving through an area. These estimates can be used to compute the speed of the vehicle. Periodogram-based methods and the RBPMF are evaluated on simulated and experimental data. The results indicate that the RBPMF has lower rmse than periodogram-based methods when tracking fast changes in the frequency.

The second application relates to frequency tracking of wheel vibrations, where a car has been equipped with an accelerometer. The accelerometer measurements are used to track the frequency of the wheel axle vibrations, which relates to the wheel rotational speed. The velocity of the vehicle can then be estimated without any other sensors and without requiring integration of the accelerometer measurements. In situations with high signal-to-noise ratio (SNR), the methods perform well. To remedy situations when the methods perform poorly, an accelerometer input is introduced to the formulation. This input is used to predict changes in the frequency for short time intervals.  

Periodiska signaler förekommer ofta i praktiken. I många tillämpningar är det intressant att försöka skatta frekvensen av dessa periodiska signaler, eller vibrationer, genom mätningar av dem. Detta kallas för frekvensskattning eller frekvensföljning beroende på om frekvensen är konstant eller varierar över tid. Två tillämpningar studeras i denna licentiatavhandling. Målet i båda tillämpningarna är att skatta hastigheten på fordon.

Den första tillämpningen handlar om att följa frekvensen av ett fordons motorljud, när fordonet kör genom ett område där mikrofoner har blivit utplacerade. Man kan skatta ett fordons hastighet från motorljudet, vars frekvens beror på Dopplereffekten. Denna avhandling undersöker förbättrad följning av denna frekvens, vilket förbättrar skattningen av hastigheten. Två olika sätt för frekvensföljning används. Ett sätt är att anta att frekvensen är konstant inom korta tidsintervall och räkna ut en skattning av frekvensen. Ett annat sätt är att använda en matematisk modell som tar hänsyn till att frekvensen varierar över tid, och försöka följa den. För detta syfte föreslås det Rao-Blackwelliserade punktmassefiltret. Det är en metod som utnyttjar strukturen i den matematiska modellen av problemet för att erhålla bra prestanda och lägre krav på beräkningskraft. Resultaten visar att den föreslagna metoden förbättrar träffsäkerheten på frekvensföljningen i vissa fall, vilket kan förbättra prestanda för hastighetsskattningen.

Den andra tillämpningen handlar om att skatta ett fordons hastighet med enbart en accelerometer (mätare av acceleration) fastsatt i chassit. Hjulvibrationer kan mätas av denna accelerometer. Frekvenserna av dessa vibrationer ges av hjulaxelns rotationshastighet. Om hjulradien är känd eller skattad så kan man räkna ut fordonets hastighet, så att man inte behöver använda externa mätningar som gps eller hjulhastighetsmätningar. Accelerationsmätningarna är brusiga och innehåller outliers, vilka är mätvärden som ibland slumpmässigt kraftigt skiljer sig från det förväntade. Därför studeras metoder som är konstruerade för att hantera dessa. Det föreslås en approximation till Rao-Blackwellisering för att kunna hantera dessa outliers. Det föreslås också en ny frekvensskattningsmetod baserad på expectation-maximization, vilket är ytterligare en metod som utnyttjar strukturer i matematiska modeller. En simuleringsstudie visar att metoderna har lägre genomsnittligt skattningsfel än standardmetoder. På insamlad experimentell data visas att metoderna ofta fungerar, men att de behöver kompletteras med en ytterligare komponent för död räkning (prognosvärden) med accelerometer för att öka antalet testfall där de erhåller godtagbar prestanda.

The speed of a wheeled vehicle is usually estimatedusing wheel speed sensors (WSS) or GPS. If these signals are unavailable, other methods must be used. We propose a novelapproach exploiting the fact that vibrations from rotating axles,with fundamental frequency proportional to vehicle speed, aretransmitted via the vehicle chassis. Using an accelerometer, these vibrations can be tracked to estimate vehicle speed whileother sources of vibrations act as disturbances. A state-space model for the dynamics of the harmonics is presented andformulated such that there is a conditional linear-Gaussiansubstructure, enabling efficient Rao-Blackwellized methods. Avariant of the Rao-Blackwellized point-mass filter is derived, significantly reducing computational complexity, and reducingthe memory requirements from quadratic to linear in thenumber of grid points. It is applied to experimental data from the sensor cluster of a car and validated using therotational frequency from WSS data. The proposed methodshows improved performance and robustness in comparisonto a Rao-Blackwellized particle filter implementation and afrequency spectrum maximization method.