Approximate Inference in State-Space Models With Heavy-Tailed Noise

Agamennoni, Gabriel; Nieto, Juan; Nebot, E.

doi:10.1109/tsp.2012.2208106

Cited by 220 publications

(136 citation statements)

References 53 publications

(89 reference statements)

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“…The three other algorithms were an EKF, a VB robust lter called the outlier robust Kalman lter (ORKF) [9,15], and an EKF that uses robust statistics to reduce the impact of measurement outliers. In the experimental results, the last lter will be referred to as the robust Kalman lter (RKF) and is similar to algorithms presented by Masreliez and Martin [4] and Schick and Mitter [6].…”

Section: Resultsmentioning

confidence: 99%

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Robust State Estimation with Sparse Outliers

Graham

How

Gustafson

2015

Journal of Guidance, Control, and Dynamics

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One of the major challenges for state estimation algorithms, such as the Kalman lter, is the impact of outliers that do not match the assumed Gaussian process and measurement noise. When these errors occur they can induce large state estimate errors and even lter divergence. This paper presents a robust recursive ltering algorithm, the l 1 -norm lter, that can provide reliable state estimates in the presence of both measurement and state propagation outliers. The algorithm consists of a convex optimization to detect the outliers followed by a state update step based on the results of the error detection. Monte Carlo simulation results are presented to demonstrate the robustness of the l 1 -norm lter estimates to both state prediction and measurement outliers. Finally, vision-aided navigation experimental results are presented that demonstrate that the proposed algorithm can provide improved state estimation performance over existing robust ltering approaches.

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Section: Resultsmentioning

confidence: 99%

“…with the information state,d k+1|k given by (9). After calculating the information matrix and state, they can be updated as follows [11] d k+1|k+1 =d k+1|k +H…”

Section: State and Error Estimationmentioning

confidence: 99%

Robust State Estimation with Sparse Outliers

Graham

How

Gustafson

2015

Journal of Guidance, Control, and Dynamics

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“…The idea of using a variational mean-field approximation to consider Student's t noise in a filter is similar to Agamennoni et al (2012), but in this method, all recursions are conditional on x n k . The primary contribution is to use the evidence lower bound L as an approximation (4.18) which is then used to compute point mass weights w j k|k in the point mass filter component as w j k|k ∝ p(y k |x n,j k , Y k−1 )w j k|k−1 .…”

Section: Student's T Measurement Noise Models With Variational Approxmentioning

confidence: 99%

Frequency Tracking for Speed Estimation

Lindfors¹

2018

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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.v Populärvetenskaplig sammanfattningPeriodiska 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...

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“…2. Robustness to outliers is achieved using "uncertainty about uncertainty" approach [1]. The sequence of measurement noise covariance is modelled as stochastic process over the set of symmetric positive-definite matrices in which prior is given as inverse Wishart distribution; 3.…”

Section: Literature Review and Contributions Of The Papermentioning

confidence: 99%

“…Outliers are defined as observations that significantly differ from the rest of the data [1], [2]. In engineering applications on-line processing of data is essential [2,3,4,5,6,7,8,9,10,11] and failing to recognize, identify and process outliers may seriously jeopardize system's performance and eventually cause failure.…”

Section: Introductionmentioning

confidence: 99%