A new method for evaluating the log-likelihood gradient, the Hessian, and the Fisher information matrix for linear dynamic systems

Segal, M.; Weinstein, E.

doi:10.1109/18.30995

Cited by 55 publications

(30 citation statements)

References 15 publications

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“…However, computing the gradient and Hessian of (6) is not straightforward. Possible approaches are discussed in [20], [21] for the case of linear models. In the case of nonlinear models, however, they only lead to approximate gradients, see e.g.…”

Section: A Optimization Algorithmmentioning

confidence: 99%

Magnetometer Calibration Using Inertial Sensors

2016

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Abstract-In this work we present a practical algorithm for calibrating a magnetometer for the presence of magnetic disturbances and for magnetometer sensor errors. To allow for combining the magnetometer measurements with inertial measurements for orientation estimation, the algorithm also corrects for misalignment between the magnetometer and the inertial sensor axes. The calibration algorithm is formulated as the solution to a maximum likelihood problem and the computations are performed offline. The algorithm is shown to give good results using data from two different commercially available sensor units. Using the calibrated magnetometer measurements in combination with the inertial sensors to determine the sensor's orientation is shown to lead to significantly improved heading estimates.

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Section: A Optimization Algorithmmentioning

confidence: 99%

Magnetometer Calibration Using Inertial Sensors

2016

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“…Its computation is hence more involved than in the case discussed in Section 3.2. In Åström (1980);Segal and Weinstein (1989), different approaches are discussed to determine analytical gradients of the objective function in (3.20). They, however, consider the case of a linear state-space model.…”

Section: Model Parameters In a State-space Modelmentioning

confidence: 99%

Probabilistic modeling for positioning applications using inertial sensors

Kok¹

2014

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In this thesis, we consider the problem of estimating position and orientation (6D pose) using inertial sensors (accelerometers and gyroscopes). Inertial sensors provide information about the change in position and orientation at high sampling rates. However, they suffer from integration drift and hence need to be supplemented with additional sensors. To combine information from the inertial sensors with information from other sensors we use probabilistic models, both for sensor fusion and for sensor calibration.Inertial sensors can be supplemented with magnetometers, which are typically used to provide heading information. This relies on the assumption that the measured magnetic field is equal to a constant local magnetic field and that the magnetometer is properly calibrated. However, the presence of metallic objects in the vicinity of the sensor will make the first assumption invalid. If the metallic object is rigidly attached to the sensor, the magnetometer can be calibrated for the presence of this magnetic disturbance. Afterwards, the measurements can be used for heading estimation as if the disturbance was not present. We present a practical magnetometer calibration algorithm that is experimentally shown to lead to improved heading estimates. An alternative approach is to exploit the presence of magnetic disturbances in indoor environments by using them as a source of position information. We show that in the vicinity of a magnetic coil it is possible to obtain accurate position estimates using inertial sensors, magnetometers and knowledge of the magnetic field induced by the coil.We also consider the problem of estimating a human body's 6D pose. For this, multiple inertial sensors are placed on the body. Information from the inertial sensors is combined using a biomechanical model which represents the human body as consisting of connected body segments. We solve this problem using an optimization-based approach and show that accurate 6D pose estimates are obtained. These estimates accurately represent the relative position and orientation of the human body, i.e. the shape of the body is accurately represented but the absolute position can not be determined.To estimate absolute position of the body, we consider the problem of indoor positioning using time of arrival measurements from an ultra-wideband (uwb) system in combination with inertial measurements. Our algorithm uses a tightlycoupled sensor fusion approach and is shown to lead to accurate position and orientation estimates. To be able to obtain position information from the uwb measurements, it is imperative that accurate estimates of the receivers' positions and clock offsets are known. Hence, we also present an easy-to-use algorithm to calibrate the uwb system. It is based on a maximum likelihood formulation and represents the uwb measurements assuming a heavy-tailed asymmetric noise distribution to account for measurement outliers.v Populärvetenskaplig sammanfattning I denna licentiatsavhandling betraktar vi problemet att skatta positio...

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“…This approximation requires the computation of the Kalman smoothing equations at closely spaced values of 0, a task that can be simplified by pre-computation of the smoothed error covariance matrices. Another approximation of the Hessian and the FIM, based on score computation, is presented in [14] .…”

Section: Gradient-based Algorithms and Performance Evaluationmentioning

confidence: 99%

Optimal source localization and tracking using arrays with uncertainties in sensor locations

Segal¹,

Weinstein²

1989

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We develop a computationally efficient iterative algorithm for source localization and tracking using active/passive arrays with uncertainties in sensor locations. We suppose that the available data consist of time delay, or differential time delay, measurements of the signal wavefront across the array. We consider a general senario in which the array uncertainties may be correlated in time and in space. The proposed algorithm is optimal in the sense that it converges montonically to the Maximum Likelihood (ML) estimate of the source trajectory parameters. In the case of multiple sources, the algorithm makes an essential use of the information available from all sources to reduce the array uncertainties (the so-called array callibration) and thus to improve the localization accuracy of each signal source. We also derive new expressions for the log-likelihood gradient, the Hessian, and the Fisher's information matrix, that may be used for efficient implementation of gradient based algorithms, and for assessing the mean square error of the resulting ML parameter estimates.

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A new method for evaluating the log-likelihood gradient, the Hessian, and the Fisher information matrix for linear dynamic systems

Cited by 55 publications

References 15 publications

Magnetometer Calibration Using Inertial Sensors

Magnetometer Calibration Using Inertial Sensors

Probabilistic modeling for positioning applications using inertial sensors

Optimal source localization and tracking using arrays with uncertainties in sensor locations

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