Probability hypothesis density filter with adaptive parameter estimation for tracking multiple maneuvering targets

AbstractThe probability hypothesis density (PHD) filter has been recognized as a promising technique for tracking an unknown number of targets. The performance of the PHD filter, however, is sensitive to the available knowledge on model parameters such as the measurement noise variance and those associated with the changes in the maneuvering target trajectories. If these parameters are unknown in advance, the tracking performance may degrade greatly. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation (APE) method in the PHD filter so that the model parameters, which may be static and/or time-varying, can be estimated jointly with target states. The resulting APE-PHD algorithm is implemented using the particle filter (PF), which leads to the PF-APE-PHD filter. Simulations show that the newly proposed algorithm can correctly identify the unknown measurement noise variances, and it is capable of tracking multiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Inference for reaction networks using the Linear Noise Approximation

We consider inference for the reaction rates in discretely observed networks such as those found in models for systems biology, population ecology and epidemics. Most such networks are neither slow enough nor small enough for inference via the true state-dependent Markov jump process to be feasible. Typically, inference is conducted by approximating the dynamics through an ordinary differential equation (ODE), or a stochastic differential equation (SDE). The former ignores the stochasticity in the true model, and can lead to inaccurate inferences. The latter is more accurate but is harder to implement as the transition density of the SDE model is generally unknown. The Linear Noise Approximation (LNA) is a first order Taylor expansion of the approximating SDE about a deterministic solution and can be viewed as a compromise between the ODE and SDE models. It is a stochastic model, but discrete time transition probabilities for the LNA are available through the solution of a series of ordinary differential equations. We describe how a restarting LNA can be efficiently used to perform inference for a general class of reaction networks; evaluate the accuracy of such an approach; and show how and when this approach is either statistically or computationally more efficient than ODE or SDE methods. We apply the LNA to analyse Google Flu Trends data from the North and South Islands of New Zealand, and are able to obtain more accurate short-term forecasts of new flu cases than another recently proposed method, although at a greater computational cost

A Survey of Recent Advances in Particle Filters and Remaining Challenges for Multitarget Tracking

[EN]We review some advances of the particle filtering (PF) algorithm that have been achieved in the last decade in the context of target tracking, with regard to either a single target or multiple targets in the presence of false or missing data. The first part of our review is on remarkable achievements that have been made for the single-target PF from several aspects including importance proposal, computing efficiency, particle degeneracy/impoverishment and constrained/multi-modal systems. The second part of our review is on analyzing the intractable challenges raised within the general multitarget (multi-sensor) tracking due to random target birth and termination, false alarm, misdetection, measurement-to-track (M2T) uncertainty and track uncertainty. The mainstream multitarget PF approaches consist of two main classes, one based on M2T association approaches and the other not such as the finite set statistics-based PF. In either case, significant challenges remain due to unknown tracking scenarios and integrated tracking management

Sequential Modelling and Inference of High-frequency Limit Order Book with State-space Models and Monte Carlo Algorithms

The high-frequency limit order book (LOB) market has recently attracted increasing research attention from both the industry and the academia as a result of expanding algorithmic trading. However, the massive data throughput and the inherent complexity of high-frequency market dynamics also present challenges to some classic statistical modelling approaches. By adopting powerful state-space models from the field of signal processing as well as a number of Bayesian inference algorithms such as particle filtering, Markov chain Monte Carlo and variational inference algorithms, this thesis presents my extensive research into the high-frequency limit order book covering a wide scope of topics. Chapter 2 presents a novel construction of the non-homogeneous Poisson process to allow online intensity inference of limit order transactions arriving at a central exchange as point data. Chapter 3 extends a baseline jump diffusion model for market fair-price process to include three additional model features taken from real-world market intuitions. In Chapter 4, another price model is developed to account for both long-term and short-term diffusion behaviours of the price process. This is achieved by incorporating multiple jump-diffusion processes each exhibiting a unique characteristic. Chapter 5 observes the multi-regime nature of price diffusion processes as well as the non-Markovian switching behaviour between regimes. As such, a novel model is proposed which combines the continuous-time state-space model, the hidden semi-Markov switching model and the non-parametric Dirichlet process model. Additionally, building upon the general structure of the particle Markov chain Monte Carlo algorithm, I further propose an algorithm which achieves sequential state inference, regime identification and regime parameters learning requiring minimal prior assumptions. Chapter 6 focuses on the development of efficient parameter-learning algorithms for state-space models and presents three algorithms each demonstrating promising results in comparison to some well-established methods. The models and algorithms proposed in this thesis not only are practical tools for analysing high-frequency LOB markets, but can also be applied in various areas and disciplines beyond finance

Joint Modelling of Gas and Electricity spot prices

The recent liberalization of the electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. In this paper, we modelize jointly gas and electricity spot prices using a mean-reverting model which fits the correlations structures for the two commodities. The dynamics are based on Ornstein processes with parameterized diffusion coefficients. Moreover, using the empirical distributions of the spot prices, we derive a class of such parameterized diffusions which captures the most salient statistical properties: stationarity, spikes and heavy-tailed distributions. The associated calibration procedure is based on standard and efficient statistical tools. We calibrate the model on French market for electricity and on UK market for gas, and then simulate some trajectories which reproduce well the observed prices behavior. Finally, we illustrate the importance of the correlation structure and of the presence of spikes by measuring the risk on a power plant portfolio