State Estimation for a Class of Linear Systems with Quadratic Output

TL;DR

This paper introduces a novel observer design for linear systems with quadratic outputs, transforming the system into a state-affine form and employing a Kalman-type observer under persistence of excitation conditions.

Contribution

It presents an immersion-based approach that converts quadratic output systems into state-affine systems, enabling global state estimation with a Kalman-type observer.

Findings

Successful application to vehicle position and velocity estimation

Effective observer design under persistence of excitation

Numerical example demonstrating practical applicability

Abstract

This paper deals with the problem of state estimation for a class of linear time-invariant systems with quadratic output measurements. An immersion-type approach is presented that transforms the system into a state-affine system by adding a finite number of states to the original system. Under suitable persistence of excitation conditions on the input and its higher derivatives, global state estimation is exhibited by means of a Kalman-type observer. A numerical example is provided to illustrate the applicability of the proposed observer design for the problem of position and velocity estimation for a vehicle navigating in the $n-$dimensional Euclidean space using a single position range measurement.