Fusing Loop and GPS Probe Measurements to Estimate Freeway Density

In an age of ever-increasing penetration of GPS-enabled mobile devices, the potential of real-time "probe" location information for estimating the state of transportation networks is receiving increasing attention. Much work has been done on using probe data to estimate the current speed of vehicle traffic (or equivalently, trip travel time). While travel times are useful to individual drivers, the state variable for a large class of traffic models and control algorithms is vehicle density. Our goal is to use probe data to supplement traditional, fixed-location loop detector data for density estimation. To this end, we derive a method based on Rao-Blackwellized particle filters, a sequential Monte Carlo scheme. We present a simulation where we obtain a 30\% reduction in density mean absolute percentage error from fusing loop and probe data, vs. using loop data alone. We also present results using real data from a 19-mile freeway section in Los Angeles, California, where we obtain a 31\% reduction. In addition, our method's estimate when using only the real-world probe data, and no loop data, outperformed the estimate produced when only loop data were used (an 18\% reduction). These results demonstrate that probe data can be used for traffic density estimation

Rao-Blackwellized Particle Filters with Out-of-Sequence Measurement Processing

This paper addresses the out-of-sequence measurement (OOSM) problem for mixed linear/nonlinear state-space models, which is a class of nonlinear models with a tractable, conditionally linear substructure. We develop two novel algorithms that utilize the linear substructure. The first algorithm effectively employs the Rao-Blackwellized particle filtering framework for updating with the OOSMs, and is based on storing only a subset of the particles and their weights over an arbitrary, predefined interval. The second algorithm adapts a backward simulation approach to update with the delayed (out-of-sequence) measurements, resulting in superior tracking performance. Extensive simulation studies show the efficacy of our approaches in terms of computation time and tracking performance. Both algorithms yield estimation improvements when compared with recent particle filter algorithms for OOSM processing; in the considered examples they achieve up to 10% enhancements in estimation accuracy. In some cases the proposed algorithms even deliver accuracy that is similar to the lower performance bounds. Because the considered setup is common in various estimation scenarios, the developed algorithms enable improvements in different types of filtering applications

Rao-Blackwellized Out-of-Sequence Processing for Mixed Linear/Nonlinear State-Space Models

We investigate the out-of-sequence measurements particle filtering problem for a set of conditionally linear Gaussian state-space models, known as mixed linear/nonlinear state-space models. Two different algorithms are proposed, which both exploit the conditionally linear substructure. The first approach is based on storing only a subset of the particles and their weights, which implies low memory and computation requirements. The second approach is based on a recently reported Rao-Blackwellized forward filter/backward simulator, adapted to the out-of-sequence filtering task with computational considerations for enabling online implementations. Simulation studies on two examples show that both approaches outperform recently reported particle filters, with the second approach being superior in terms of tracking performance

Multiple Model Rao-Blackwellized Particle Filter for Manoeuvring Target Tracking

Particle filters can become quite inefficient when applied to a high-dimensional state space since a prohibitively large number of samples may be required to approximate the underlying density functions with desired accuracy. In this paper, a novel multiple model Rao-Blackwellized particle filter (MMRBPF)-based algorithm has been proposed for manoeuvring target tracking in a cluttered environment. The advantage of the proposed approach is that the Rao-Blackwellization allows the algorithm to be partitioned into target tracking and model selection sub-problems, where the target tracking can be solved by the probabilistic data association filter, and the model selection by sequential importance sampling. The analytical relationship between target state and model is exploited to improve the efficiency and accuracy of the proposed algorithm. Moreover, to reduce the particle-degeneracy problem, the resampling approach is selectively carried out. Finally, experiment results, show that the proposed algorithm, has advantages over the conventional IMM-PDAF algorithm in terms of robust and  efficiency.Defence Science Journal, 2009, 59(3), pp.197-204, DOI:http://dx.doi.org/10.14429/dsj.59.151

Dirichlet Process Mixtures for Density Estimation in Dynamic Nonlinear Modeling: Application to GPS Positioning in Urban Canyons

International audienceIn global positioning systems (GPS), classical localization algorithms assume, when the signal is received from the satellite in line-of-sight (LOS) environment, that the pseudorange error distribution is Gaussian. Such assumption is in some way very restrictive since a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments especially in urban canyons due to multipath/masking effects. In order to ensure high accuracy positioning, a good estimation of the observation error in these cases is required. To address this, an attractive flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Since the considered positioning problem involves elements of non-Gaussianity and nonlinearity and besides, it should be processed on-line, the suitability of the proposed modeling scheme in a joint state/parameter estimation problem is handled by an efficient Rao-Blackwellized particle filter (RBPF). Our approach is illustrated on a data analysis task dealing with joint estimation of vehicles positions and pseudorange errors in a global navigation satellite system (GNSS)-based localization context where the GPS information may be inaccurate because of hard reception conditions