Estimation design of MEMS-based inertial navigation systems with noise coupling input saturation: Robust approach

There are, in practice, so many control systems possesses this kind of special feature, e.g., ballistic missile's maneuver couples with wind gusts, acceleration signal measured by accelerometers couples with the external and internal noises, and so on. Generally, the input signal u(k) is always assumed as an exactly known variable and never corrupted with noise; hence one is capable of dealing with these kinds of estimation problems by the well-known Kalman Filter that is widely used in the state estimation. Of course, it is no doubt that in the presence of unknown noise coupling input saturations, performance of Kalman Filter will be seriously degraded since the unknown input saturations coupling with input noises appear on a system model as extensive noises, and the constant processing noise variance will be not capable of covering it because of the time-variant character of these type signals. This investigation mainly focuses on the robust estimator design of MEMS-based inertial navigation systems that are coupling of the input noise and input saturation that come from the natural physical characters of accelerometers and gyroscopes, described by X (k +1) = FX (k) + G(sat(u(k)) + w(k)) where X (k) ∈ R ⁿ is the state vector, u(k)∈ R ^m is the input signal, and w(k) ∈ R ^P is the input noise. The saturation function sat of the input signal R ^m → R ^m is defined as sat(u(k))=[sat(u ₁(k)) sat(u ₂(k)) ... sat(u _m(k))] ^T with sat(u _i(k)) = sgn(u _i(k))min(ρ,|u _i(k)|).