Patent ID: 8203482

Claim:
A GNSS-based positioning device comprising a receiver that computes a horizontal protection level (HPL) or a vertical protection level (VPL), that bound, up to a given confidence level 1−α, the horizontal and vertical components, respectively, of the position estimation error δ of a least squares-based GNSS navigation solution with a number m of estimated parameters, which navigation solution is based on n observations and an n×m observation matrix H and which navigation solution also provides a residuals vector r, and sets off or displays an alarm if said HPL or VPL exceeds an application-defined horizontal or vertical error tolerance threshold; and wherein the receiver computes the horizontal protection level HPL or the vertical protection level VPL according to one of the following expressions: HPL= k·∥r·a H , VPL= k·∥r∥·a v where: ∥r∥ is the Euclidean norm of the least squares estimation residuals vector r; a H ⁢ ⁢ is ⁢ ⁢ defined ⁢ ⁢ as ⁢ : ⁢ ⁢ a H = h EE + h NN 2 + ( h EE - h NN 2 ) 2 + ( h EN + h NE 2 ) 2 , and a V is defined as: a V =√{square root over (h UU )}, where h EE , h NN , h EN , h NE , h EU , h UE , h UU , h NU , h UN are the spatial components of the dilution of precision matrix DoP (H T ·H) −1 of the least squares estimation expressed in the local horizontal coordinate system of the estimated position, where subscripts E, N and U stand for East, North and Up components, respectively, and their combinations correspond to their correlations and cross-correlations: ( H T · H ) Space - 1 = [ h EE h EN h EU h NE h NN h NU h UE h UN h UU ] ; and where k is an isotropic confidence ratio computed by numerically solving the following expression Eq. 3 which links k with n, m and α: Γ ⁡ ( n 2 ) · ∫ z ∈ ℜ m , z 2 ≤ k 2 1 + k 2 ⁢ ( 1 - z 2 ) n - m - 2 2 · ⅆ z = Γ ⁡ ( n - m 2 ) · π m 2 · ( 1 - α ) [ Eq . ⁢ 3 ] where: Γ is Euler's Gamma function; and, m denotes a standard m-dimensional real vector space.