Stochastic Processes: Simulation and Tracking of a fish school through statistical processes

Stochastic Processes: Tracking of a fish school, Sep 2018 – Jan 2019

Tasks: In the context of the Stochastic Process course. We implement a simulation of tracking a fish school when confronted to a predator.

Problem solving strategy:

Part1: Fishes motion statistical characterisation

• Setting the problem: N empirical observation, speed as random variable, known parametric data model
• Mathematical development for the Maximum likelyhood estimator and the method of moment
• Python simulations for deciding the best estimator compared to data.

Fig.1 - Comparison of the average on 500 test evaluation of Ŝ on the left and K̂ on the right with its real value. In red the MLE evaluation and in blue the Moment method

Fig.2 - Standard deviation of determined Ŝ on the left and K̂ on the right. In red the MLE evaluation and in blue the Moment method

Part2: Fish tracking through time

• Reformulation of the problem as a stochastic process
• Implementation of a Monte Carlo filter
• Matlab simulations.

Fig.3 - On the left figure , the evolution of the MLE when the number of particle increases for a determined σ²obs=0.5 and a time step=0.05s. On the right one, evolution of the MLE when the time step increases with the same σ²obs=0.5 and for 500 particles.

Report in English available on Github.