Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

Abstract

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group SO (3) with the tracking error of the normalized Euclidean distance meeting predefined transient and steady-state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from lowcost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.

Nonlinear Stochastic Estimators on the Special Euclidean Group SE(3) Using Uncertain IMU and Vision Measurements

“…Let Assumption 1 hold. Suppose that T y is reconstructed based on the vector measurements in (16) and (14), and geared with the estimator in (40), (41), (42), (43), (44), and (45). Suppose that the design parameters are selected as follows:…”

“…The recent rise of micro-elector-mechanical systems (MEMS) allowed for development of IMU, which are relatively inexpensive, small in size, and light-weight. However, the output of the low-cost IMU is contaminated with noise resulting in unsatisfactory performance of Gaussian attitude filters [5,14,16]. Consequently, numerous nonlinear complementary estimators evolved directly on the Special Orthogonal Group SO (3) have been proposed, for example [12][13][14][15][16][17].…”

“…ConsiderV m = V + b V + ω V where the unknown constant bias b V = 0.1[2,5,1] and the random noise vector ω V has zero mean and STD = 0.15 (m/sec). Assume there is a landmark available for measurement v and its body-frame measurement is as(16). The associated bias is bB(L) 1 = 0.1 [0.3, 0.2, −0.2] and the noise vector ω B(L) 1 has zero mean and STD = 0.1 (m/sec).…”

Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping

“…The key objective of this subsection is to force e i = [e i,1 , e i,2 , e i,3 ] described in (11) to obey dynamically reducing transient boundaries and settle down within the narrow bounds adjusted by the user. A positive and time decreasing prescribed performance function (PPF) ξ i,k (t) with the map of ξ i,k : R + → R + [18,19] is employed to guide e i,k to initiate within a given large set ξ 0…”

“…I n refers to n-dimensional identity matrix, 0 n describes a zero column vector. For x ∈ R n the Euclidean norm is [19,20]. T ∈ R 4×4 describes the vehicle's pose in 3D space expressed as…”