Binomial Gaussian mixture filter
نویسندگان
چکیده
In this work, we present a novel method for approximating a normal distribution with a weighted sum of normal distributions. The approximation is used for splitting normally distributed components in a Gaussian mixture filter, such that components have smaller covariances and cause smaller linearization errors when nonlinear measurements are used for the state update. Our splitting method uses weights from the binomial distribution as component weights. The method preserves the mean and covariance of the original normal distribution, and in addition, the resulting probability density and cumulative distribution functions converge to the original normal distribution when the number of components is increased. Furthermore, an algorithm is presented to do the splitting such as to keep the linearization error below a given threshold with a minimum number of components. The accuracy of the estimate provided by the proposed method is evaluated in four simulated single-update cases and one time series tracking case. In these tests, it is found that the proposed method is more accurate than other Gaussian mixture filters found in the literature when the same number of components is used and that the proposed method is faster and more accurate than particle filters.
منابع مشابه
Improved Bearings-Only Multi-Target Tracking with GM-PHD Filtering
In this paper, an improved nonlinear Gaussian mixture probability hypothesis density (GM-PHD) filter is proposed to address bearings-only measurements in multi-target tracking. The proposed method, called the Gaussian mixture measurements-probability hypothesis density (GMM-PHD) filter, not only approximates the posterior intensity using a Gaussian mixture, but also models the likelihood functi...
متن کاملOn the Convergence of the Gaussian Mixture Filter
This paper presents convergence results for the Box Gaussian Mixture Filter (BGMF). BGMF is a Gaussian Mixture Filter (GMF) that is based on a bank of Extended Kalman Filters. The critical part of GMF is the approximation of probability density function (pdf) as pdf of Gaussian mixture such that its components have small enough covariance matrices. Because GMF approximates prior and posterior a...
متن کاملSpeech Enhancement Using Gaussian Mixture Models, Explicit Bayesian Estimation and Wiener Filtering
Gaussian Mixture Models (GMMs) of power spectral densities of speech and noise are used with explicit Bayesian estimations in Wiener filtering of noisy speech. No assumption is made on the nature or stationarity of the noise. No voice activity detection (VAD) or any other means is employed to estimate the input SNR. The GMM mean vectors are used to form sets of over-determined system of equatio...
متن کاملBinomial filters
Binomial filters are simple and efficient structures based on the binomial coefficients for implementing Gaussian filtering. They do not require multipliers and can therefore be implemented efficiently in programmable hardware. There are many possible variations of the basic binomial filter structure, and they provide a wide range of space-time trade-offs; a number of these designs have been ca...
متن کاملGaussian Mixture Approximation by Another Gaussian Mixture for 'Blob' Filter Re-Sampling
A new method has been developed to approximate one Gaussian mixture by another in a process that generalizes the idea of importance re-sampling in a particle filter. This algorithm is being developed as part of an effort to generalize the concept of a particle filter. In a traditional particle filter, the underlying probability density function is described by particles: Dirac delta functions w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- EURASIP J. Adv. Sig. Proc.
دوره 2015 شماره
صفحات -
تاریخ انتشار 2015