Convergence of the auxiliary particle implementation of the PHD filter

Optimal Bayesian multi-target filtering is in general computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency was proposed by Whiteley et. al. Numerical examples were presented for two scenarios, including a challenging nonlinear observation model, to support the claim. This paper studies the theoretical properties of this auxiliary particle implementation. $\mathbb{L}_p$ error bounds are established from which almost sure convergence follows.

Auxiliary particle implementation of the probability hypothesis density filter

Optimal Bayesian multi-target filtering is, in general, computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), we present a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.

Heterogeneous reconfigurable system for adaptive particle filters in real-time applications

This paper presents a heterogeneous reconfigurable system for real-time applications applying particle filters. The system consists of an FPGA and a multi-threaded CPU. We propose a method to adapt the number of particles dynamically and utilise the run-time reconfigurability of the FPGA for reduced power and energy consumption. An application is developed which involves simultaneous mobile robot localisation and people tracking. It shows that the proposed adaptive particle filter can reduce up to 99% of computation time. Using run-time reconfiguration, we achieve 34% reduction in idle power and save 26-34% of system energy. Our proposed system is up to 7.39 times faster and 3.65 times more energy efficient than the Intel Xeon X5650 CPU with 12 threads, and 1.3 times faster and 2.13 times more energy efficient than an NVIDIA Tesla C2070 GPU. © 2013 Springer-Verlag.

Forecasting high-frequency futures returns using online langevin dynamics

Forecasting the returns of assets at high frequency is the key challenge for high-frequency algorithmic trading strategies. In this paper, we propose a jump-diffusion model for asset price movements that models price and its trend and allows a momentum strategy to be developed. Conditional on jump times, we derive closed-form transition densities for this model. We show how this allows us to extract a trend from high-frequency finance data by using a Rao-Blackwellized variable rate particle filter to filter incoming price data. Our results show that even in the presence of transaction costs our algorithm can achieve a Sharpe ratio above 1 when applied across a portfolio of 75 futures contracts at high frequency. © 2011 IEEE.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

An improved technique to measure axial variation in wall flow along the channels of a diesel particulate filter

A technique to measure wall flow variation in Diesel Particle Filters (DPFs) is described. In a recent paper, it was shown how the flow distribution in DPFs could be measured in a non-destructive manner. This involved measuring the progressive dilution of a tracer gas introduced at the "outlet" channel upstream end. In the present paper, a significant further improvement to this technique is described, in which only a single probe is required, rather than the two of the previous technique. The single, traversable, probe consists of a controllable flow sink, and slightly downstream, a tracer gas supply. By controlling the sink flow rate such that a very small concentration of tracer gas is aspirated into it, the total flow up to that location in the channel is determined. Typical results showing the axial variation in the wall flow for known wall blockage cases are presented. It is suggested that this technique could be used to interpret the soot loading in the filter channels in a non-intrusive way.

A backward-simulation based Rao-Blackwellized particle smoother for conditionally linear Gaussian models

In this article, we develop a new Rao-Blackwellized Monte Carlo smoothing algorithm for conditionally linear Gaussian models. The algorithm is based on the forward-filtering backward-simulation Monte Carlo smoother concept and performs the backward simulation directly in the marginal space of the non-Gaussian state component while treating the linear part analytically. Unlike the previously proposed backward-simulation based Rao-Blackwellized smoothing approaches, it does not require sampling of the Gaussian state component and is also able to overcome certain normalization problems of two-filter smoother based approaches. The performance of the algorithm is illustrated in a simulated application. © 2012 IFAC.