A nongyroscopic inertial measurement unit

Abstract

This paper describes a concept of a low-cost gyroless inertial measurement unit. By means of an orthogonal triad of rotating or vibrating accelerometers, angular rates are measured along with specific forces. The precise separation of the two signals from the accelerometer readings is described. Apart from its simplicity, the special features of the separation method are that signal bandwidth is not sacrified, inertial angular rate measurements are essentially drift-free, and dynamical errors due to angular rate and specific force derivatives are reduced to negligible values. A detailed statistical analysis of the error sources, due to dynamical effects, sampling, nonlinearities, and vibration is given. The residual angular rate offset is due to the electronic processor which, with modern CMOS components, is shown to provide a performance level in the 1 n.mi./h class. The possibility of dispensing with the costly gyroscopes, which are essential in conventional designs, indicates a substantial saving in cost. Nomenclaturea = vector of accelerometer outputs a = bandwidth of random process b = index of body axes c = index of coherent terms F = vector of specific forces applied to vehicle g = gravity vector h (t) = impulse response / = index of coordinates x,y, z I = distance vector m = ratio of frequencies n = vector of measurement noise o = index of orthogonal terms p, q, r -components of angular rate R E -radius of Earth R = position error / = time T = period of cycle u = normalized distance function V = vibration amplitude X, Y, Z = rectangular coordinate system a = bandwidth normalized to Schuler frequency co 5 f = normalized time f=co 5 / \L = beat frequency v = vibration frequency T = time difference p = radius of rotation or amplitude of vibration a = standard deviation </>(•) = autocorrelation function $ (•)= power density spectrum $* (*) = power density spectrum of sampled signal co = frequency of revolution co 5 = Schuler frequency ft = angular rate vector of body axis system Q,.= component of angular rate error

Angular Rate Esimtation Using an Array of Fixed and Vibrating Triaxial Acceleration Measurements

“…The problem of determining the algebraic sign of angular rates can be avoided by using acceleration sensors that are fixed to the body along with acceleration sensors that vibrate in a known manner with respect to the body. Merhav [7] developed a method to estimate body angular rates using 3 single axis, fixed and vibrating acceleration measurements. This technique requires integration over a single vibration period to compute body angular rates.…”

“…The technique developed by Merhav [7] utilizes a set of three fixed and three vibrating single axis acceleration measurements. Referring to Figure 1, sensors 1 2 3 1 2 , , , , F F F V V and 3…”

Analytic Error Assessment of Gyro-Free INS

“…Another possibility to implement an IMU architecture, is to use six or more distributed accelerometers to form a system capable of obtaining three accelerations and three angular accelerations, thereby capable of functioning as an IMU; this system is termed a Gyro-Free (GF) IMU or all-accelerometer IMU. This concept of GF navigation was proposed over 45 years ago, but apparently has not matured into practical technologies [12,14,15]. Recently, there is a growing in-*Corresponding Author: Itzik Klein: Technion, Israel Institute of Technology, Haifa, Israel, E-mail: iklein@technion.ac.il terest in GF based navigation [5,16] because of the emergence of low cost MEMS accelerometers with rapidly increasing performance [11] and expectations for a new technology (e.g.…”

Magnetometer based high operating range angular rate measurement system

“…Ayrıca yüksek çalışma aralıklı dönüölçerlerin kullanımı, ihraç lisansı ve maliyet problemleri nedeniyle kısıtlıdır. Bu nedenlerden dolayı dönüölçer kullanılmadan ivmeölçerler ile açısal hızın ölçülmesi ile ilgili çalışmalar yapılmıştır [2][3][4][5][6]. Bu çalışmalarda açısal hız merkez-kaç kuvvetine dayanılarak ölçülmeye çalışıldığı için kuvvet kolunun kısa olması yapılan hesapları önemli derecede etkilemektedir.…”