Abstract
In this paper, we introduce a modified cellular particle filter (CPF) which we mapped on a graphics processing unit (GPU) architecture. We developed this filter adaptation using a state-of-the art CPF technique. Mapping this filter realization on a highly parallel architecture entailed a shift in the logical representation of the particles. In this process, the original two-dimensional organization is reordered as a one-dimensional ring topology. We proposed a proof-of-concept measurement on two models with an NVIDIA Fermi architecture GPU. This design achieved a 411- μ s kernel time per state and a 77-ms global running time for all states for 16,384 particles with a 256 neighbourhood size on a sequence of 24 states for a bearing-only tracking model. For a commonly used benchmark model at the same configuration, we achieved a 266- μ s kernel time per state and a 124-ms global running time for all 100 states. Kernel time includes random number generation on the GPU with curand. These results attest to the effective and fast use of the particle filter in high-dimensional, real-time applications.
Highlights
In applications in the field of image processing [1,2], navigation [3], and financial mathematics [4,5] we deal with non-linear state-space models subject to additive noise which is not restricted to Gaussian noise
We focus on a particle filter (PF) [8] which is both part of the sequential Monte Carlo methods (SMCM) algorithm family and can be considered an extension of a Kalman filter
While there are many alternations, we focus on a particle filter with sequential importance resampling [23]
Summary
In applications in the field of image processing [1,2], navigation [3], and financial mathematics [4,5] we deal with non-linear state-space models subject to additive noise which is not restricted to Gaussian noise. Even if each state only depends on the previous state (i.e. the sequence follows the Markov dynamics [6]), a Kalman filter [7] is suboptimal for the state estimation due to non-linearity and non-Gaussian noise. . ., depending only on the current hidden state plus an additive noise which is not limited to Gaussian: yt = ψ(xt) + e2(t) (2) These notable extensions transfer the resolution beyond the Kalman filter [7] to the scope of particle filtering. A particle filter is a tool for estimating the hidden states based on the observation. It is not an analytical calculation but the use of a set of particles at each time step that follows the model dynamics. The algorithm is built up from three main steps in each time t (i.e. state)
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