Integrating features for man-made target tracking from FLIR image sequence using particle filter

A new man-made target tracking algorithm integrating features from (Forward Looking InfraRed) image sequence is presented based on particle filter. Firstly, a multiscale fractal feature is used to enhance targets in FLIR images. Secondly, the gray space feature is defined by Bhattacharyya distance between intensity histograms of the reference target and a sample target from MFF (Multi-scale Fractal Feature) image. Thirdly, the motion feature is obtained by differencing between two MFF images. Fourthly, a fusion coefficient can be automatically obtained by online feature selection method for features integrating based on fuzzy logic. Finally, a particle filtering framework is developed to fulfill the target tracking. Experimental results have shown that the proposed algorithm can accurately track weak or small man-made target in FLIR images with complicated background. The algorithm is effective, robust and satisfied to real time tracking.

State estimation using the particle filter with mode tracking

A particle filter is a data assimilation scheme that employs a fully nonlinear, non-Gaussian analysis step. Unfortunately as the size of the state grows the number of ensemble members required for the particle filter to converge to the true solution increases exponentially. To overcome this Vaswani [Vaswani N. 2008. IEEE Trans Signal Process 56:4583–97] proposed a new method known as mode tracking to improve the efficiency of the particle filter. When mode tracking, the state is split into two subspaces. One subspace is forecast using the particle filter, the other is treated so that its values are set equal to the mode of the marginal pdf. There are many ways to split the state. One hypothesis is that the best results should be obtained from the particle filter with mode tracking when we mode track the maximum number of unimodal dimensions. The aim of this paper is to test this hypothesis using the three dimensional stochastic Lorenz equations with direct observations. It is found that mode tracking the maximum number of unimodal dimensions does not always provide the best result. The best choice of states to mode track depends on the number of particles used and the accuracy and frequency of the observations.

An exploration of the equivalent weights particle filter

Particle filters are fully non-linear data assimilation techniques that aim to represent the probability distribution of the model state given the observations (the posterior) by a number of particles. In high-dimensional geophysical applications the number of particles required by the sequential importance resampling (SIR) particle filter in order to capture the high probability region of the posterior, is too large to make them usable. However particle filters can be formulated using proposal densities, which gives greater freedom in how particles are sampled and allows for a much smaller number of particles. Here a particle filter is presented which uses the proposal density to ensure that all particles end up in the high probability region of the posterior probability density function. This gives rise to the possibility of non-linear data assimilation in large dimensional systems. The particle filter formulation is compared to the optimal proposal density particle filter and the implicit particle filter, both of which also utilise a proposal density. We show that when observations are available every time step, both schemes will be degenerate when the number of independent observations is large, unlike the new scheme. The sensitivity of the new scheme to its parameter values is explored theoretically and demonstrated using the Lorenz (1963) model.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

Implicit equal-weights particle filter

Filter degeneracy is the main obstacle for the implementation of particle filter in non-linear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced. In this scheme samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1,000-dimensional simple linear model, and the 1,000-dimensional non-linear Lorenz96 model, and compare the performance of the scheme to a Local Ensemble Kalman Filter. The experiments show that the new scheme can easily be implemented in high-dimensional systems and is never degenerate, with good convergence properties in both systems.

Particle filtering in geophysical systems

The application of particle filters in geophysical systems is reviewed. Some background on Bayesian filtering is provided, and the existing methods are discussed. The emphasis is on the methodology, and not so much on the applications themselves. It is shown that direct application of the basic particle filter (i.e., importance sampling using the prior as the importance density) does not work in high-dimensional systems, but several variants are shown to have potential. Approximations to the full problem that try to keep some aspects of the particle filter beyond the Gaussian approximation are also presented and discussed.

Towards the automatic reconstruction of dendritic trees using particle filters

The 3D reconstruction of a Golgi-stained dendritic tree from a serial stack of images captured with a transmitted light bright-field microscope is investigated. Modifications to the bootstrap filter are discussed such that the tree structure may be estimated recursively as a series of connected segments. The tracking performance of the bootstrap particle filter is compared against Differential Evolution, an evolutionary global optimisation method, both in terms of robustness and accuracy. It is found that the particle filtering approach is significantly more robust and accurate for the data considered.

Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

Efficient non-linear data assimilation in geophysical fluid dynamics

New ways of combining observations with numerical models are discussed in which the size of the state space can be very large, and the model can be highly nonlinear. Also the observations of the system can be related to the model variables in highly nonlinear ways, making this data-assimilation (or inverse) problem highly nonlinear. First we discuss the connection between data assimilation and inverse problems, including regularization. We explore the choice of proposal density in a Particle Filter and show how the ’curse of dimensionality’ might be beaten. In the standard Particle Filter ensembles of model runs are propagated forward in time until observations are encountered, rendering it a pure Monte-Carlo method. In large-dimensional systems this is very inefficient and very large numbers of model runs are needed to solve the data-assimilation problem realistically. In our approach we steer all model runs towards the observations resulting in a much more efficient method. By further ’ensuring almost equal weight’ we avoid performing model runs that are useless in the end. Results are shown for the 40 and 1000 dimensional Lorenz 1995 model.

Measures of observation impact in non-Gaussian data assimilation

ABSTRACT Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz ’63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

Efficient fully nonlinear data assimilation for geophysical fluid dynamics

A potential problem with Ensemble Kalman Filter is the implicit Gaussian assumption at analysis times. Here we explore the performance of a recently proposed fully nonlinear particle filter on a high-dimensional but simplified ocean model, in which the Gaussian assumption is not made. The model simulates the evolution of the vorticity field in time, described by the barotropic vorticity equation, in a highly nonlinear flow regime. While common knowledge is that particle filters are inefficient and need large numbers of model runs to avoid degeneracy, the newly developed particle filter needs only of the order of 10-100 particles on large scale problems. The crucial new ingredient is that the proposal density cannot only be used to ensure all particles end up in high-probability regions of state space as defined by the observations, but also to ensure that most of the particles have similar weights. Using identical twin experiments we found that the ensemble mean follows the truth reliably, and the difference from the truth is captured by the ensemble spread. A rank histogram is used to show that the truth run is indistinguishable from any of the particles, showing statistical consistency of the method.