Title:

State estimation and trajectory planning using box particle kernels

State estimation and trajectory planning are two crucial functions for autonomous systems, and in particular for aerospace systems. Particle filters and samplebased trajectory planning approaches have been widely considered to tackle nonlinear models and nonGaussian noises. However, these approaches may produce erratic results due to the sampled approximation of the state density. In addition, they have a high computational cost which limits their practical interest. This thesis investigates the use of box kernel mixtures to describe multimodal probability density functions. A box kernel mixture is a weighted sum of basic functions (e.g. uniform kernels) that integrate to unity, and whose supports are bounded by boxes, i.e. vectors of intervals. This modelling approach yields a more extensive description of the state density function while requiring a lower computational load. New algorithms are developed, based on a derivation of the Box Particle Filter (BPF) for state estimation, and of a particle based Chance Constrained optimisation (equivalently, failure probability constraint) for trajectory planning under uncertainty. In order to tackle ambiguous state estimation problems, a Box Regularised Particle Filter (BRPF) is introduced. The BRPF consists of an improved BPF with a guaranteed resampling step, and a smoothing strategy based on kernel regularisation. The proposed strategy is theoretically proved to outperform the original BPF in terms of Mean Integrated Square Error (MISE), and empirically shown to reduce the Root Mean Square Error (RMSE) of estimation. For Terrain Aided Navigation (TAN) BRPF reduces computation load by 75% (4fold reduction) compared to BPF, and by 97% (33fold) compared to Particle Filter for a similar performance budget. BRPF is shown to be robust to measurement ambiguity and unknownbutbounded measurement densities. BRPF is also integrated to federated and distributed architectures to demonstrate its efficiency in multisensor and multiagent systems. In order to tackle constrained trajectory planning under nonGaussian uncertainty, a Box Particle Control (BPC) is introduced. BPC relies on an interval bounded kernel mixture state density description, and consists of propagating the state density along a state trajectory at a given horizon. It yields a more accurate description of the state uncertainty than previous particle based algorithms. A chance constrained optimisation is performed, which consists of finding the sequence of future control inputs that minimises a cost function, while ensuring that the probability of constraint violation (failure probability) remains below a given threshold. For similar performance, BPC yields a computation load reduction of 30% (1.4fold reduction) with respect to Particle Control. The use of box kernel mixtures in estimation algorithms (e.g. BRPF) and state control methods (e.g. BPC), makes it possible to run complex estimation and control operations in real time on computationally limited devices. The results are quite general and apply where (a) measurement is ambiguous, uncertain but bounded, (b) computational load is constrained, (c) either state estimation (BRPF) or control (BPC) are needed. These characteristics are of particular interest in the aerospace field.
