Digital synthesis of non-linear filters

Bucy, R. S.; Senne, Kenneth D.

doi:10.1016/0005-1098(71)90121-x

Cited by 294 publications

(143 citation statements)

References 2 publications

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“…The unnormalized weights are then chosen as w j ∝ p(θ j , Y ) (Bucy and Senne, 1971), where the common proportionality constant is chosen to ensure N S j=1 w j = 1. The value θ j can also be sampled.…”

Section: Discretization Of Bayesian Posteriorsmentioning

confidence: 99%

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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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Section: Discretization Of Bayesian Posteriorsmentioning

confidence: 99%

“…The point mass filter (pmf) or discrete grid filter (Bucy and Senne, 1971;Sorenson, 1974) evaluates the Bayesian filtering recursions (2.57) using a deterministic discretization (x j k ) N S j=1 over the state space of x k , as discussed in Section 2.4.2. The method is given in Algorithm 2.6.…”

Section: Point Mass Filtermentioning

confidence: 99%

Frequency Tracking for Speed Estimation

Lindfors¹

2018

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“…The tracker in the clutter environment (sea and rain etc.) proposed in this paper was based on the Bayes optimal estimation theory [3,4], which recursively finds the conditional probability density function (conditioned on the entire measurement history) of the position and velocity of the target. With multiple detects at each sampling time, the obtained conditional probability density functions would initially have several Gaussian-shaped peaks at the locations of the clutter points as well as at the target.…”

Section: Pulse Typementioning

confidence: 99%

Maritime radar display unit based on PC for safe ship navigation

Bae¹,

Lee²,

Hwang³

2011

International Journal of Ocean System Engineering

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A prototype radar display unit was implemented using inexpensive off-the-shelf components, including a nonlinear estimation algorithm for the target tracking in a clutter environment. Two custom designed boards; an analog signal processing board and a DSP board, can be plugged into an expansion slot of a personal computer (PC) to form a maritime radar display unit. Our system provided all the functionality specified in the International Maritime Organization (IMO) resolution A422(XI). The analog signal processing board was used for A/D conversion as well as rain and sea clutter suppression. The main functions of the DSP board were scan conversion and video overlay operations. A host PC was used to run the tracking algorithm of targets in clutter, using the discrete-time Bayes optimal (nonlinear, and non-Gaussian) estimation method, and the graphic user interface (GUI) software for Automatic Radar Plotting Aid (ARPA). The proposed tracking method recursively found the entire probability density function of the target position and velocity by converting into linear convolution operations.

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“…We use a point-mass representation for the distributions [27] and approximate the integrals in the filtering equations by replacing continuous integrals with Riemann sums over finite regions. The distributions are modeled as piecewise constant over these regions.…”

Section: Tree-based Filtering Frameworkmentioning

confidence: 99%

Human-computer interaction

Butler

Jacob

John

1999

CHI '99 Extended Abstracts on Human Factors in Computing Systems - CHI '99

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SUMMARYThis paper presents a method for markerless human motion capture using a single camera. It uses tree-based filtering to efficiently propagate a probability distribution over poses of a 3D body model. The pose vectors and associated shapes are arranged in a tree, which is constructed by hierarchical pairwise clustering, in order to efficiently evaluate the likelihood in each frame. A new likelihood function based on silhouette matching is proposed that improves the pose estimation of thinner body parts, i.e. the limbs. The dynamic model takes self-occlusion into account by increasing the variance of occluded body-parts, thus allowing for recovery when the body part reappears. We present two applications of our method that work in real-time on a Cell Broadband Engine TM : a computer game and a virtual clothing application. key words: video motion capture, tree-based filtering, silhouette matching, Cell Broadband Engine TM

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Digital synthesis of non-linear filters

Cited by 294 publications

References 2 publications

Frequency Tracking for Speed Estimation

Frequency Tracking for Speed Estimation

Maritime radar display unit based on PC for safe ship navigation

Human-computer interaction

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