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What is Least Squares? Least squares is a mathematical (specifically statistical) method to identify a curve through data as an average of error through datapoints. It serves as a general basis for linear optimization problems. History Least squares began to surface as a result of a mathematical competition to describe the orbital patterns between Saturn…

Model Predictive Control (MPC) is an optimal control architecture rooted in optimization. Most often, formulations of MPC are quadratic programs (QP’s) and result in powerful predictive models across some time horizon in the near future. Where other trajectory planning methods like Sequential Quadratic Programming (SQP) might predict the entire trajectory, MPC stays local to the…

Idea In general, I think most people have an intuitive idea of what “optimization” and “optimal” mean: to find the solution that minimizes all constraints (cost, time, materials, labor, energy, etc.). But mathematically in the generalized nonlinear case, it is extremely difficult to find a true global minimum on a function’s surface with iterative methods.…

Idea State estimation is the art of making confident analyses from noisy data. There are several techniques to achieve this. Some more simple, some more complex. The current industry standard is a variation of Kalman filtering, but other options like least squares, MSE, and particle filtering are also options. State estimation plays a key role…