A new method to reduce the noise of the miniaturized inertial sensors disposed in redundant linear configurations

Nomenclature A = n×n matrix with elements depending by) , 1 (2 n i i   variances A 1 = (n-1)×(n-1) matrix with elements depending by) , 1 (2 n i i   variances a = output acceleration (perturbed signal) a c = cross-axis acceleration a i = input acceleration B = n×1 matrix with all elements equal to 1 B 1 = (n-1)×1 matrix with all elements equal to 1 B = bias b i = sensors measurement biases) ˆ (x E = mean or expected value of x ˆ 4 1 ÷ E E   = vectors which describe the directions of the sensors' input axes K = scale factor k c = cross-axis sensitivity m = number of samples provided by each of the n sensors in a second N = misalignment of the sensitive axis n = number of collinear sensors in array W = n×1 matrix having as elements the weights) , 1 (n i w i  W 1 = (n-1)×1 matrix having as elements the weights) , 2 (n i w i  w i = weights of the) , 1 (n i x i  independent measures x = true value of the acceleration or angular speed applied to a sensors' array x i = estimates of the x quantity provided by the n sensors' independent measures x i (k) = k th measure from the i th sensor (corresponds to the k th data frame)) (k x i = arithmetic mean of the m samples acquired from the i th sensor in the k th data frame x ˆ = estimate of the x quantity characterised by a minimum variance 2 min  K  = scale factor calibration error  = sensor noise i  = terms reflecting the measurement noise from the n sensors 2  = variance of x ˆ 2 i  = variances of the) , 1 (n i x i  independent measures) (2 k i  = variance of the measure x i for the k th data frame, used in " data fusion " for the next data frame Abstract This paper presents a new adaptive algorithm for the statistical filtering of miniaturised inertial sensor noise. The algorithm uses the minimum variance method to perform a best estimate calculation of the accelerations or angular speeds on each of the three …