Self-Calibration of Inertial Sensor Arrays

Quantifying the Uncertainty of the Relative Geometry in Inertial Sensors Arrays

“…The optimal step length for the MH algorithm using a Gaussian random walk as the proposal distribution is obtained when the acceptance probability is approximately 23% [42], which can be empirically estimated by running the chain with different values of σ q . Furthermore, the amount of correlation in a Markov chain produced by the PmMH algorithm also depends on the variance of the likelihood estimator in (26). If the variance is too high, an accepted state θ (m) may yield a high value for p N (y 1:T |θ (m) ) by chance.…”

“…To simulate field conditions, we generate a random motion sequence η 1:T so that it emulates the dynamics of twisting the array with a hand. Specifically, ω,ω, and s are assumed to be zero-mean normally distributed with a standard deviation of 1000°/s, 35 000°/s 2 , and 20 m/s 2 , respectively [26]. We set the true values of the accelerometer positions equal to the center of the IMU packages shown in Fig.…”

“…We evaluated Algorithm 1 for three different lengths of measurement sequences y 1:T , that is, T ∈ {5, 50, 500}. For each realization of the measurement sequence y 1:T , we tuned the number of Monte Carlo samples N for the likelihood estimator in (26) and the step length σ q for the Gaussian random walk according to Section III-C. Fig.…”

“…For high dynamic motions, the posterior distribution of the angular velocity given the gyroscope measurements, p(ω t |y (g) t ), may yield a distribution that is not sufficiently centered around the true angular velocity. This inaccurate localization of the distribution becomes a problem when numerically marginalizing the angular velocity in (26), since the drawn samples are from low probability regions. We mitigate this problem by replacing the estimated covariance during stationary conditions with the sample covariance during a single time sample.…”

“…The alternative to using dedicated external equipment is to jointly estimate the unknown motion and the calibration parameters. Such joint estimation has been done before using maximum likelihood methods for accelerometer position errors [24]- [26], accelerometer offset, scale factor, and misalignment errors [27] and magnetometers [28]. The drawback of the maximum likelihood method is, however, the difficulty to directly quantify the estimation uncertainty given specific measurements.…”