A Reconstruction Filter for Saturated Accelerometer Signals Due to Insufficient FSR in Foot-mounted Inertial Navigation System

In pedestrian inertial navigation, one possible placement of Inertial Measurement Units (IMUs) is on a footwear. This placement allows to limit the accumulation of navigation errors due to the bias drift of inertial sensors and is generally a preferable placement of sensors to achieve the highest precision of pedestrian inertial navigation. However, inertial sensors mounted on footwear experience significantly higher accelerations and angular velocities during regular pedestrian activities than during more conventional navigation tasks, which could exceed Full Scale Range (FSR) of many commercial-off-the-shelf IMUs, therefore degrading accuracy of pedestrian navigation systems. This paper proposes a reconstruction filter to mitigate localization error in pedestrian navigation due to insufficient FSR of inertial sensors. The proposed reconstruction filter approximates immeasurable accelerometer's signals with a triangular function and estimates the size of the triangles using a Gaussian Process regression. To evaluate performance of the proposed reconstruction filter, we conducted two series of indoor pedestrian navigation experiments with a VectorNav VN-200 IMU and an Analog Device ADIS16497-3 IMU. In the first series of experiments, forces experienced by the IMUs did not exceed the FSRs of the sensors, while in the second series, the forces surpassed the FSR of the VN-200 IMU and saturated the accelerometer's readings. The saturated readings reduced the accuracy of estimated positions using the VN-200 by 1.34× and 3.37× along horizontal and vertical directions. When applying our proposed reconstruction filter to the saturated measurements, the navigation accuracy was increased by 5% horizontally and 50% vertically, as compared to using unreconstructed signals.

A Reconstruction Filter for Saturated Accelerometer Signals Due to Insufficient FSR in Foot-mounted Inertial Navigation System

In pedestrian inertial navigation, one possible placement of Inertial Measurement Units (IMUs) is on a footwear. This placement allows to limit the accumulation of navigation errors due to the bias drift of inertial sensors and is generally a preferable placement of sensors to achieve the highest precision of pedestrian inertial navigation. However, inertial sensors mounted on footwear experience significantly higher accelerations and angular velocities during regular pedestrian activities than during more conventional navigation tasks, which could exceed Full Scale Range (FSR) of many commercial-off-the-shelf IMUs, therefore degrading accuracy of pedestrian navigation systems. This paper proposes a reconstruction filter to mitigate localization error in pedestrian navigation due to insufficient FSR of inertial sensors. The proposed reconstruction filter approximates immeasurable accelerometer's signals with a triangular function and estimates the size of the triangles using a Gaussian Process regression. To evaluate performance of the proposed reconstruction filter, we conducted two series of indoor pedestrian navigation experiments with a VectorNav VN-200 IMU and an Analog Device ADIS16497-3 IMU. In the first series of experiments, forces experienced by the IMUs did not exceed the FSRs of the sensors, while in the second series, the forces surpassed the FSR of the VN-200 IMU and saturated the accelerometer's readings. The saturated readings reduced the accuracy of estimated positions using the VN-200 by 1.34× and 3.37× along horizontal and vertical directions. When applying our proposed reconstruction filter to the saturated measurements, the navigation accuracy was increased by 5% horizontally and 50% vertically, as compared to using unreconstructed signals.

New Channel Errors Estimation Method for Multichannel SAR Based on Virtual Calibration Source

The multichannel synthetic aperture radar (SAR) system can effectively overcome the fundamental limitation between high-resolution and wide-swath. However, the unavoidable channel errors will result in a mismatch of the reconstruction filter and false targets in pairs. To address this issue, a novel channel errors calibration method is proposed based on the idea of minimizing the mean square error (MMSE) between the signal subspace and the space spanned by the practical steering vectors. The practical steering matrix of each Doppler bin can be constructed according to the Doppler spectrum. Compared with the time-domain correlation method, the proposed method no longer depends on the accuracy of the Doppler centroid estimation. Besides, compared with the orthogonal subspace method, the proposed method has the advantage of robustness under the condition of large samples by using the diagonal loading technique. To evaluate the performance, the results of simulation data and the real data acquired by the GF-3 dual-channel SAR system demonstrate that the proposed method has higher accuracy and more robustness than the conventional methods, especially in the case of low SNRs and high non-uniformity.

Combination of HP and LP filters for narrow band antialiasing filter

The discrete time signal processing requires an anti-aliasing filter at the input and a reconstruction filter at output. Some filters of biquads structure are characterized by a decreasing of the attenuation at high frequencies, caused by the final value of the output resistance of the operational amplifier. In this paper we discuss a design of combined BP filter without mentioned decrease. The proposed filter structure was verified by SPICE simulation.

Sampling and Reconstruction of Continuous-Time Signals

This chapter presents the theory for transferring a continuous-time signal into its discrete-time form by sampling, and then converting the obtained samples to a digital signal suitable for processing in a processing machine, using the procedure of sample quantizing and coding. Then, the procedure of converting a digitally processed signal into discrete signal samples and the reconstruction of the initial continuous-time signal via a lowpass reconstruction filter is presented. The theory provides the mathematical base for both analogue-to-digital and digital-to-analogue conversions, which are extensively used for processing signals in discrete communication systems. The chapter goes on to show that the Nyquist criterion must be fulfilled to eliminate signal aliasing in the frequency domain. Finally, the mathematical model for transferring a continuous-time signal into its discrete-time form, and vice versa, is presented and demonstrated for a sinusoidal signal.

Frame multiresolution analysis of continuous piecewise linear functions

The Franklin wavelet is constructed using the multiresolution analysis (MRA) generated from a scaling function [Formula: see text] that is continuous on [Formula: see text], linear on [Formula: see text] and [Formula: see text] for every [Formula: see text]. For [Formula: see text] and [Formula: see text], it is shown that if a function [Formula: see text] is continuous on [Formula: see text], linear on [Formula: see text] and [Formula: see text], for [Formula: see text], and generates MRA with dilation factor [Formula: see text], then [Formula: see text]. Conversely, for [Formula: see text], it is shown that there exists a [Formula: see text], as satisfying the above conditions, that generates MRA with dilation factor [Formula: see text]. The frame MRA (FMRA) is useful in signal processing, since the perfect reconstruction filter banks associated with FMRA can be narrow-band. So it is natural to ask, whether the above results can be extended for the case of FMRA. In this paper, for [Formula: see text], we prove that if [Formula: see text] generates FMRA with dilation factor [Formula: see text], then [Formula: see text]. For [Formula: see text], we prove similar results when [Formula: see text]. In addition, for [Formula: see text] we prove that there exists a function [Formula: see text] as satisfying the above conditions, that generates FMRA. Also, we construct tight wavelet frame and wavelet frame for such scaling functions.

Early Weak Fault Diagnosis of Rolling Bearing Based on Multilayer Reconstruction Filter

The early weak fault characteristics of rolling bearings are extremely weak and are easily overwhelmed by other noises. In order to effectively extract the characteristics of the early weak faults of the rolling bearings and draw on the multilayer wavelet decomposition idea, a method for diagnosing the early weak faults of the rolling bearing based on the multilayer reconstruction filter is proposed. As we all know, empirical wavelet transform (EWT) makes full use of wavelet filter bank, and variational mode decomposition (VMD) uses Wiener filter bank. This paper fully combines the advantages of the above two methods, adaptively determines the number of modes through empirical wavelet decomposition and divides the original signal, extracts the frequency band that contains the fault characteristic information, and effectively eliminates noise interference. These steps are repeated until the optimal component of the condition is obtained. In the output layer, the weak fault impact components are further separated by the strong filtering and signal decomposition capability of VMD. The advantages of the proposed method are proved by the experiment of weak fault of rolling bearing and the accelerated failure experiment of full life. The proposed method has the advantages of reducing noise influence and adaptive estimation of decomposed modes, which can be applied more efficiently in practice.

Correction of the skull density ratio for transcranial MRI-guided focused ultrasound thalamotomy: clinical significance of predicting therapeutic temperature

OBJECTIVE In transcranial magnetic resonance imaging–guided focused ultrasound (TcMRgFUS), a high skull density ratio (SDR) is advantageous to achieve a sufficiently high temperature at the target. However, it is not easy to estimate the temperature rise because the SDR shows different values depending on the reconstruction filter used. The resolution characteristic of a computed tomography (CT) image depends on a modulation transfer function (MTF) defined by the reconstruction filter. Differences in MTF induce unstable SDRs. The purpose of this study was both to standardize SDR by developing a method to correct the MTF and to enable effective patient screening prior to TcMRgFUS treatment and more accurate predictions of focal temperature. METHODS CT images of a skull phantom and five subjects were obtained using eight different reconstruction filters. A frequency filter (FF) was calculated using the MTF of each reconstruction filter, and the validity of SDR standardization was evaluated by comparing the variation in SDR before and after FF correction. Subsequently, FF processing was similarly performed using the CT images of 18 patients who had undergone TcMRgFUS, and statistical analyses were performed comparing the relationship between the SDRs before and after correction and the maximum temperature in the target during TcMRgFUS treatment. RESULTS The FF was calculated for each reconstruction filter based on one manufacturer's BONE filter. In the CT images of the skull phantom, the SDR before FF correction with five of the other seven reconstruction filters was significantly smaller than that with the BONE filter (p < 0.01). After FF correction, however, a significant difference was recognized under only one condition. In the CT images of the five subjects, variation of the SDR due to imaging conditions was significantly improved after the FF correction. In 18 cases treated with TcMRgFUS, there was no correlation between SDR before FF correction and maximum temperature (rs = 0.31, p > 0.05); however, a strong positive correlation was observed after FF correction (rs = 0.71, p < 0.01). CONCLUSIONS After FF correction, the difference in SDR due to the reconstruction filter used is smaller, and the correlation with temperature is stronger. Therefore, the SDR can be standardized by applying the FF, and the maximum temperature during treatment may be predicted more accurately.