Kalman Filter

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 Given an array of asteroid  positions with gaussian noise added and a motion model for an asteroid, find the actual position every asteroid (grey dots).  

A Kalman filter operates in two main steps: prediction and correction. In the prediction step, the system estimated the next state of the particle based on its previous state and assumed motion dynamics. In the correction step, the filter updated these estimates using new position measurements while accounting for noise and uncertainties. 

 By continuously refining the estimates, the Kalman filter was able to smooth out noisy observations. It successfully handled poor data, maintaining reasonable estimates. 

Given: Noisy distance moved and noisy heading direction; Distance to 

Find: Actual drone position

 The system used Simultaneous Localization and Mapping (SLAM), where the drone moved through a forested area, continuously measuring distances to trees. The Graph SLAM approach represented the environment as a graph, with nodes corresponding to drone poses and landmarks (trees), while edges encoded constraints based on sensor observations and motion estimates. 

As the drone moved, new position estimates were added to the graph, and loop closures were used to correct drift by recognizing previously visited locations. An optimization process refined the graph structure, minimizing errors in both drone trajectory and tree positions. 

Given: Robot start location; Target location; Boxes location 

Find: Optimal path for the robot to pick up and drop off all boxes at the target location

 The A* search process involves expanding nodes based on a cost function that combined the actual movement cost and a heuristic estimate of the remaining distance. The algorithm prioritizes paths with the lowest estimated total cost, ensuring an efficient and collision-free route. If an obstacle was encountered, the algorithm adjusted the plan, recalculating a new optimal path to reach the destination. 

Given a scalar value representing the gravity the satellite is experiencing, find the actual position of the satellite.

 This project used a Particle Filter to track an object moving counterclockwise in a 2D solar system with a central sun and occasional planets. The goal was to estimate its trajectory despite noisy observations and motion uncertainties.

The system simulated the object's orbit, influenced by gravity and planetary perturbations. The Particle Filter maintained a set of weighted particles representing possible states, evolving through prediction, update, and resampling.

Particles moved based on an orbital motion model, with weights adjusted using noisy position observations. Higher-likelihood particles were duplicated, while less likely ones were removed, ensuring accurate tracking. The filter adapted to sporadic measurements and disturbances, effectively handling non-linear motion and uncertainty better than traditional methods.