This thesis proposes a novel nonlinear estimator to estimate the state of a class of systems with linear dynamics and noisy quadratic measurements. It is shown that the error dynamics is described by a nonlinear Verhulst logistic equation. This observation unveils a link between population dynamics and state estimation for this class of systems. The stationary distribution of the estimation error converges to a zero-mean Gaussian with adjustable variance.
This estimator is used to estimate the physical state variables in energy harvesters by using the measurement of electrical energy. Furthermore, the problem of estimating the position of a quadrotor in waypoint navigation using noisy range measurements can be formulated in a way in which it can be solved by the proposed estimator. This application emphasizes the practical use of the estimator, which guides the quadrotor through various pipeline configurations. The quadrotor’s input is designed to maintain the piecewise affine trajectory within the thickness of the pipeline for the inspection task. The simulation results illustrate a stable estimation error that consistently converges to an area around zero with different initial conditions. In addition to evaluating the performance of the proposed estimator, a comparison is made with the Kalman filter for the augmented linearized system.