Section: Overall Objectives

Objectives

For engineers, a wide variety of information is not directly obtained through measurement. Some parameters (constants of an electrical actuator, delay in a transmission, etc) or internal variables (robot's posture, torques applied to a robot, localization of a mobile, etc) are unknown or are not measured. Similarly, more often than not, signals from sensors are distorted and tainted by measurement noises. In order to simulate, to control or to supervise processes, and to extract information conveyed by the signals, one has to estimate parameters or variables.

Estimation techniques are, under various guises, present in many parts of control, signal processing and applied mathematics. Such an important area gave rise to a huge international literature. However, from a general point of view, the performance of an estimation algorithm can be characterized by three indicators:

• The computation time. Here, we mean the time needed for obtaining the estimation. Indeed, estimation algorithms should have as small as possible computation time in order provide fast, real-time, online estimation for processes with fast dynamics (for example, a challenging problem is to make an Atomic Force Microspcope work at GHz rates).

• The algorithm complexity. Here, we mean the easiness of design and implementation. Estimation algorithms should have as low as possible algorithm complexity, in order to allow embedded real-time estimation (for example, in networked robotics, the embedded computation power is limited and can be even more limited for small sensors/actuators devices). Another question about complexity is: can the engineer appropriate and apply the algorithms? For instance, this is easier if the parameters have a physical meaning w.r.t. the process under study.

• The robustness. Estimation algorithms should exhibit as much as possible robustness with respect to a large class of measurement noises, to parameter uncertainties and to discretization and numerical implementation. A complementary point of view on robustness is to manage the compromise between existence of theoretical proofs versus universalism of the algorithm. In the first case, the performance is guaranteed in a particular case (a particular control designed for a particular model). In the second case, a same algorithm can be directly applied in “most of the cases", but may fail in few situations.