Brett Ninness

This paper addresses the problem of computing fixed-interval smoothed state estimates of a linear time varying Gaussian stochastic system. There already exist many algorithms that perform this computation, but all of them impose certain restrictions on system matrices in order for them to be applicable, and the restrictions vary considerably between the various existing algorithms. This paper establishes a new sufficient condition for the fixed-interval smoothing density to exist in a Gaussian form that can be completely characterised by associated means and covariances. It then develops an algorithm to compute these means and covariances with no further assumptions required. This results in an algorithm more generally applicable than any one of the multitude of existing algorithms available to date.

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulated and real examples focusing on the robustness to parameter initialisation; additionally, favourable comparisons are performed against state-of-the-art alternatives.

This letter considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modeled by a nonlinear state-space model, but where the model parameters, state and future disturbances are not known and are treated as random variables. Central to our formulation is that the joint distribution of these unknown objects is conditioned on the observed data. Crucially, as new measurements become available, this joint distribution continues to evolve so that control decisions are made accounting for uncertainty as evidenced in the data. The resulting problem is intractable which we obviate by providing approximations that result in finite dimensional deterministic optimization problems. The proposed approach is demonstrated in simulation on a nonlinear system.

Glitches introduce impulse-like disturbances which are not be readily attenuated by low-pass filtering. This article presents a model that describes the behaviour of glitches, and a method for mitigation based on a large-amplitude dither signal. Analytical and experimental results demonstrate that a dither signal with sufficient amplitude can mitigate the effect of glitches, when used in conjunction with a low-pass filter. The dither signal in conjunction with low-pass filtering essentially converts a glitch from a high-frequency to low-frequency disturbance.

We present a general and computationally tractable method for the operation of a Backwards Information Filter on a linear Gaussian Mixture Model system, which can be used to generate the smoothed density. Unlike other methods, the algorithm proposed here does not make unimodal approximations, and is exact with the exception of the mode reduction strategy.

Pseudo-marginal Metropolis-Hastings (pmMH) is a versatile algorithm for sampling from target distributions which are not easy to evaluate point-wise. However, pmMH requires good proposal distributions to sample efficiently from the target, which can be problematic to construct in practice. This is especially a problem for high-dimensional targets when the standard random-walk proposal is inefficient. We extend pmMH to allow for constructing the proposal based on information from multiple past iterations. As a consequence, quasi-Newton (qN) methods can be employed to form proposals which utilize gradient information to guide the Markov chain to areas of high probability and to construct approximations of the local curvature to scale step sizes. The proposed method is demonstrated on several problems which indicate that qN proposals can perform better than other common Hessian-based proposals.

This paper is concerned with the problem of distributed Kalman filtering in a network of several interconnected subsystems. We consider networks, which can be either homogeneous or heterogeneous, of linear time-invariant subsystems, given in state-space form. We propose a distributed Kalman filtering scheme for this setup. The proposed scheme provides estimates based only on locally available measurements. We compare its outcomes with those of a centralized Kalman filter, which offers the best minimum error variance estimate, using all measurements available all over the network. We show that the estimate produced by the proposed method asymptotically approaches to that of the centralized Kalman filter, i.e., the optimal one with global knowledge of all network parameters, and we are able to bound the convergence rate. Moreover, if the initial states of all subsystems are mutually uncorrelated, the estimates of these two schemes are identical at each time step.