ABSTRACT
Many recent progresses in the field of sensors miniaturization have led to the design of small and cheap integrated navigation system hardware (complete IMU, GPS module, etc.), which have, for their part, contributed to boost significantly the market of mini-UAVs over the past few decades, making them more accessible to everyone. Nevertheless, this accessibility is frequently inconsistent with good measurement performances. For instance, the GPS modules used commonly in the Paparazzi autopilot (cf. Paparazzi project at: https://wiki.paparazziuav.org/) deliver a position with an average accuracy of 5 m, up to 10 m under certain flight conditions. Therefore, a need for multisensor data fusion arises, especially when the objective consists in developing robust advanced control strategies for mini-UAVs. To this aim, nonlinear estimation offers several well-proven algorithmic techniques that permit us to recover an acceptable level of accuracy on some key flight parameters (anemometric angles, orientation/attitude, linear and angular speeds, position, etc.) for mini-UAVs closed-loop handling qualities. An overview of nonlinear estimation methods can be found in the literature from many surveys or books (see, e.g., [1-3]). Figure 22.1 attempts to propose a classification of these latter and positions chapter 22 topic in it (white terms in gray boxes). As they
22.1 General Introduction ........................................................................................................... 391 22.1.1 Nonlinear Invariant State Estimation: A Brief Review ........................................ 391 22.1.2 Chapter Outline ..................................................................................................... 393 22.1.3 Mathematical Notations ........................................................................................ 394
22.2 Dynamical Systems Possessing Symmetries ...................................................................... 394 22.2.1 Theoretical Background ........................................................................................ 394 22.2.2 Notion of Invariant ................................................................................................ 397 22.2.3 Academic Example ............................................................................................... 398
22.3 Optimal Invariant Nonlinear State Estimation ...................................................................400 22.3.1 Invariant Observer ................................................................................................400 22.3.2 IUKF: Principles and Design ................................................................................402
