Backward Filter Research Articles

The development of a bio-inspired vibration source localization algorithm

Vibration source localization is an interdisciplinary topic that has applications in both engineering and biology. To develop bio-inspired technologies that can be applied in engineering, a vibration source localization algorithm is developed based on a spider dynamic model. The model includes: (i) a point source; (ii) a spider model with 8 legs resting on a non-dispersive substrate that introduces correlated leg inputs. The proposed algorithm first calculates the leg inputs using a backward filter forward smoother algorithm with given leg responses to the excitation from the vibration source; and then estimates the source angle, source distance, wave speed and decay rate through optimization. The optimization utilizes the time and amplitude relationships between the leg inputs and the leg-substrate contact locations. The effectiveness of the algorithm is validated by comparing the algorithm estimations with the actual parameters. Results show that the algorithm gives accurate estimation of the source angle and wave speed usually with errors within 3 deg and 1 m/s, respectively, but cannot estimate the source distance. Two spatially-separated spider-like models are needed for estimating the source distance. The algorithm works well even under low signal-to-noise ratio down to 11 dB.

Calibrated Eckhardt’s filter versus alternative baseflow separation methods: A silica-based approach in a Brazilian catchment

The Eckhardt’s filter, a recursive digital filter widely used in hydrology to separate baseflow, relies on two parameters: the recession constant (a) and the maximum allowable long-term ratio of baseflow to streamflow (BFImax). While a can be determined through regression analyses, BFImax is often assigned an arbitrary value because of limited catchment information for a more objective determination. This study aimed to assess and calibrate BFImax for a 1.2 km2 rural catchment in southern Brazil using dissolved silica data. Calibration involved minimizing differences between filter-generated baseflow hydrographs and those derived from dissolved silica measurements and mass balance across 13 monitored rainfall-runoff events. The calibrated model was compared to three established models: a modified graphical method based on local minima, a backward filter model, and a one-parameter filter. The results yielded an optimal BFImax of 0.653 with high model performance (PBias ≈ 0, NSE = 0.85, KGE = 0.74, and NRMSD = 13 %) against silica-derived baseflow. Applying the calibrated filter to a six-year streamflow dataset yielded a long-term baseflow index (BFI) value of 54 %, aligned with regional and global averages. Comparisons with other models showed that the backward filter model produced unrealistic baseflow values nearly identical to streamflow values; the local minima method overestimated baseflow by +19 % and failed to accurately represent the smoothness and peaks of the baseflow hydrographs; and the one-parameter filter represented the shape and timing of the baseflow hydrographs well, but underestimated magnitude by −19 %. These findings validate the effectiveness of the Eckhardt’s filter in generating accurate baseflow hydrographs and confirm the importance of calibrating BFImax for optimal performance. The research also endorses the use of dissolved silica measurements and the mass balance method as a reliable approach for calibrating BFImax for long-term assessment of baseflows.

A robust GNSS sensors in presence of signal blockage for USV application

Unmanned surface vehicle (USV) can navigate autonomously via the global navigation satellite system (GNSS). However, the traditional GNSS scalar tracking loop easily loses lock in low carrier-to-noise ratio (CNR) situations, such as signal occlusion and weak signals. Meanwhile, an increase in the carrier/code phase error leads to an increase in the measurement error of the navigation filter, which decreases the accuracy of the position estimation. To solve this problem, this paper proposes a carrier and code tracking structure based on a forward and backward Kalman filter to dynamically adjust the gain of the vector tracking loop. The carrier and code phase errors calculated by the loop discriminators were linearly transformed into pseudo-range rate and pseudo-range errors after filtering and smoothing, which were used as the measurements of the navigation filter. The signal CNR was used to adaptively adjust the measurement noise covariance matrix of the loop filters. The field tests used a commercial receiver’s navigation solution as the reference. In the stationary test, the proposed structure reduced the localization error by 44.3% compared with the traditional methods. In kinematic experiments, the proposed structure reduced the carrier and code phase errors in a harsh signal environment and improved the positioning accuracy at the source. The test results demonstrate that the proposed GNSS tracking method can provide a possible solution for the development of navigation systems for USV.

Kalman filter-based integration of GNSS and InSAR observations for local nonlinear strong deformations

The continuous monitoring of ground deformations can be provided by various methods, such as leveling, photogrammetry, laser scanning, satellite navigation systems, Synthetic Aperture Radar (SAR), and many others. However, ensuring sufficient spatiotemporal resolution of high-accuracy measurements can be challenging using only one of the mentioned methods. The main goal of this research is to develop an integration methodology, sensitive to the capabilities and limitations of Differential Interferometry SAR (DInSAR) and Global Navigation Satellite Systems (GNSS) monitoring techniques. The fusion procedure is optimized for local nonlinear strong deformations using the forward Kalman filter algorithm. Due to the impact of unexpected observations discontinuity, a backward Kalman filter was also introduced to refine estimates of the previous system’s states. The current work conducted experiments in the Upper Silesian coal mining region (southern Poland), with strong vertical deformations of up to 1 m over 2 years and relatively small and horizontally moving subsidence bowls (200 m). The overall root-mean-square (RMS) errors reached 13, 17, and 35 mm for Kalman forward and 13, 17, and 34 mm for Kalman backward in North, East, and Up directions, respectively, in combination with an external data source - GNSS campaign measurements. The Kalman filter integration outperformed standard approaches of 3-D GNSS estimation and 2-D InSAR decomposition.

Joint channel and impulse noise estimation based on compressed sensing and Kalman filter for OFDM system

Impulse noise (IN) widely exists in many communication systems, which seriously affects the performance of OFDM communication systems. A joint channel and IN estimation method based on all subcarriers is designed. This method uses a sparse Bayesian learning (SBL) algorithm incorporating forward–backward Kalman filter (FB-Kalman) to tackle the problem of joint channel and IN estimation and data detection for OFDM systems. Firstly, the channel impulse response and IN are regarded as unknown sparse vectors, and a SBL framework using all subcarriers is proposed to estimate the unknown vector. The SBL theory is used based on the prior distribution of variables, and then the forward–backward joint system is established, which applies the data detection simultaneously. We also propose the FB-Kalman implementation algorithm by using the expectation maximization updates. Explicit expressions of mean and covariance matrix of the posterior distribution are derived in the E-step. Simulation results show that the proposed algorithm improves the normalized mean square error and bit error rate performance of OFDM system in the presence of IN communication environment.

Methods to Detect Impact-Induced Orbit Perturbations Using Spacecraft Navigation Data

Debris strikes on operational spacecraft are becoming more common due to increasing numbers of space objects. Sample return missions indicate hundreds of minor strikes, but rigorous analysis is often only performed when a strike causes an anomaly in spacecraft performance. Developing techniques to identify and assess minor strikes that do not immediately cause anomalous behavior can help to validate models for debris populations and aid in the attribution of future anomalies. This study develops methods to detect subtle abrupt orbit perturbations indicative of minor debris strikes. An extended Kalman filter with dynamic model compensation is used to estimate a spacecraft’s orbit state based on simulated full-state (i.e., GPS) measurements. The filter is applied to the data forward and backward in time, and then a modified Fraser–Potter smoother is used to produce a fused state estimate. Various test statistics are developed and compared to identify abrupt unexpected changes in spacecraft velocity; techniques include McReynold’s filter-smoother consistency test and the Mahalanobis distance between forward and backward filter states. A trade study is performed to investigate the performance of test statistics as a function of filter parameters, and a Monte Carlo analysis illustrates the filter’s ability to detect and estimate strikes.

Selection principle of seed power in high-power narrow linewidth fiber amplifier seeded by a FBGs-based fiber oscillator.

Here, we have experimentally demonstrated the selection principle of the seed power in a narrow linewidth fiber amplifier seeded by fiber oscillator based on a pair of fiber Bragg gratings. During the study on the selection of seed power, the spectral instability of the amplifier is found when a low power seed with bad temporal characteristics is amplified. This phenomenon is thoroughly analyzed from seed itself and the influence of the amplifier. Increasing the seed power or isolating the backward light of amplifier could effectively eliminate the spectral instability. Based on this point, we optimize the seed power and utilize a band pass filter circulator to isolate the backward light and filter the Raman noise. Finally, a 4.2 kW narrow linewidth output power is achieved with signal to noise ratio of 35 dB, which has exceeded the value under the highest output power reported in this type of narrow linewidth fiber amplifiers. This work provides a solution for high power and high signal to noise ratio narrow-linewidth fiber amplifiers seeded by FBGs-based fiber oscillator.

Algorithms for Sparse Multichannel Blind Deconvolution

In this paper we present two algorithms for sparse multichannel blind deconvolution. The first algorithm is based on a cascade of a forward and a backward prediction error filter (C-PEF). The second consists in an alternating minimization algorithm for estimating both the reflectivity series and the seismic wavelet (AM-SMBD). We also compare the algorithms with other state-of-the-art sparse blind deconvolution algorithms. Simulation results with synthetic data for different SNR levels showed that the AM-SMBD was outperformed (in terms of the Pearson Correlation Coefficient and the Gini Correlation Coefficient) other estimation methods, like the reduced SMBD, the TS-sparseTLS (Toeplitz-structured sparse total least square) and the SMBD-SPG (Sparse multichannel blind deconvolution via spectral projected-gradient). For the same data, the C-PEF was able to provide better results (in terms of the Gini Correlation Coefficient, visual inspection and frequency gain) when compared with the F-SMBD (Fast sparse multichannel blind deconvolution). In a simulation considering reflectivities with different levels of sparsity, the C-PEF seems to be more robust for less sparse data when compared with AM-SMBD and SMBD-SPG (up to a certain degree of sparsity). Finally, simulations considering a real land acquisition show that both algorithms were able to greatly improve the resolution of the seismic data.

Detection and Interpretation of Change in Registered Satellite Image Time Series

Time series of satellite images are now massively available thanks to the existence of several constellations of recurrent satellites. We propose a method for detecting and measuring the duration of changes on such series. This approach is intended to be generic and independent of the type of satellite used, whether band limited or multispectral. It is based on a global analysis of the sequence. The statistical detection method is applied to a residual sequence computed from backward and forward novelty filters applied to all images in the series. Significant changes are computed with a guarantee on their number of false alarms (NFA). To establish the efficiency of the method, we have created an open database of 28 sequences of 20 images acquired by the Sentinel-2 satellite, in different regions of the world. We obtain satisfactory results, which are consistent with the visual observations.

Estimation of Three-Dimensional Thoracoabdominal Displacements During Respiration Using Inertial Measurement Units

This article presents a wearable inertial measurement unit based system that estimates three-dimensional respiratory displacements on the thoracoabdominal surface. Such estimates can be useful in the calculation of respiratory rate, tidal volume, and for monitoring synchrony of compartments of the thoracoabdominal wall for diagnosis and physiotherapy. Challenges in estimating displacements from inertial sensors include drift due to sensor bias, errors due to the measurement of a large gravity component by accelerometers, and the need to compensate for real-time tilt angles from natural bending of the subject during breathing. An algorithm that combines double integration, high-pass filters, tilt angle estimation, and a Kalman smoother to estimate real-time gravity components along the sensor axes is utilized. The algorithm is facilitated by a special formulation of the gravity vector's kinematic model about the sensor axes. Preliminary experimental results show that the three-axes displacements are estimated with 1 mm accuracy at normal breathing frequencies of 0.25 Hz or higher, but lose some accuracy at lower breathing rates. The Kalman smoother which uses a combination of forward and backward filters is shown to provide significantly superior performance compared to a traditional Kalman filter, which only uses forward propagation. Additionally, the developed system also provides very accurate estimates of breathing frequency.

Blocked electron transmission/reflection by coupled Rashba–Zeeman effects for forward and backward spin filtering

We present a theory for studying the quantum dynamics of both the transmission and reflection behavior of a two-dimensional electron gas across a planar potential step within a quantum well. In our model, we introduce the combined effect of the Rashba–Zeeman coupling on the conduction electrons. Our results demonstrate that as the energy of an incident or a transmitted electron stays within the Zeeman energy gap, both Klein reflection and Klein tunneling occur in this Rashba–Zeeman coupled electronic system, where the former corresponds to a backward spin filter while the latter to a forward spin filter. Meanwhile, our system also predicts a critical incident angle beyond which the electron tunneling will be fully suppressed. Such distinctive spin-filtering features are expected to give rise to a variety of applications in both spintronics and quantum-computation devices.

Bayesian Deep Learning for Aircraft Hard Landing Safety Assessment

Landing is generally cited as one of the riskiest phases of a flight, as indicated by the much higher accident rate than other flight phases. In this paper, we focus on the hard landing problem (which is defined as the touchdown vertical speed exceeding a predefined threshold), and build a probabilistic predictive model to forecast the aircraft’s vertical speed at touchdown, using DASHlink data. Previous work has treated hard landing as a classification problem, where the vertical speed is represented as a categorical variable based on a predefined threshold. In this paper, we build a machine learning model to numerically predict the touchdown vertical speed during aircraft landing. Probabilistic forecasting is used to quantify the uncertainty in model prediction, which in turn supports risk-informed decision-making. A Bayesian neural network approach is leveraged to construct the predictive model. The overall methodology consists of five steps. First, a clustering method based on the minimum separation between different airports is developed to identify flights in the dataset that landed at the same airport. Secondly, identifying the touchdown point itself is not straightforward; in this paper, it is determined by comparing the vertical speed distributions derived from different candidate touchdown indicators. Thirdly, a forward and backward filtering (filtfilt) approach is used to smooth the data without introducing phase lag. Next, a minimal-redundancy-maximal-relevance (mRMR) analysis is used to reduce the dimensionality of input variables. Finally, a Bayesian recurrent neural network is trained to predict the touchdown vertical speed and quantify the uncertainty in the prediction. The model is validated using several flights in the test dataset, and computational results demonstrate the satisfactory performance of the proposed approach.

Improved GNSS vector tracking loop to enhance the navigation performance of USV

The Global Navigation Satellite System (GNSS) is the most common source of location and heading information for unmanned surface vehicle (USV) in real time. However, in areas such as ports or bridges, the GNSS signal will be occluded or weakened. The carrier frequency and code frequency of scalar tracking (ST) in GNSS receiver fluctuates greatly, and even the tracking loop will lose lock. To enhance the navigation performance of USV's GNSS receiver, this paper proposes a framework that uses fixed-lag smoothing (FLS) to assist vector tracking (VT) and applies unscented Kalman filter in the navigation processor. The pseudo-range error and pseudo-range rate error are used as the measurements of navigation processor. FLS serves as a backward filter to enhance the tracking ability of the code loop. The field experiments show that the positioning error of the proposed method is reduced by 72.1% compared to the traditional VT method in the open-sky environments. When the signal is occluded, the positioning results of the traditional ST are dispersed, and also the traditional VT method displays a large error. Moreover, the proposed method is able to reduce the positioning error by 85.4%. The proposed GNSS loop tracking architecture and method can provide a possible solution for USV's navigation system development.

The Value of First-Order Features Based on the Apparent Diffusion Coefficient Map in Evaluating the Therapeutic Effect of Low-Intensity Pulsed Ultrasound for Acute Traumatic Brain Injury With a Rat Model.

PurposeIn order to evaluate the neuroprotective effect of low-intensity pulsed ultrasound (LIPUS) for acute traumatic brain injury (TBI), we studied the potential of apparent diffusion coefficient (ADC) values and ADC-derived first-order features regarding this problem.MethodsForty-five male Sprague Dawley rats (sham group: 15, TBI group: 15, LIPUS treated: 15) were enrolled and underwent magnetic resonance imaging. Scanning layers were acquired using a multi-shot readout segmentation of long variable echo trains (RESOLVE) to decrease distortion. The ultrasound transducer was applied to the designated region in the injured cortical areas using a conical collimator and was filled with an ultrasound coupling gel. Regions of interest were manually delineated in the center of the damaged cortex on the diffusion weighted images (b = 800 s/mm2) layer by layer for the TBI and LIPUS treated groups using the open-source software ITK-SNAP. Before analysis and modeling, the features were normalized using a z-score method, and a logistic regression model with a backward filtering method was employed to perform the modeling. The entire process was completed using the R language.ResultsDuring the observation time, the ADC values ipsilateral to the trauma in the TBI and LIPUS groups increased rapidly up to 24 h. After statistical analysis, the 10th percentile, 90th percentile, mean, skewness, and uniformity demonstrated a significant difference among three groups. The receiver operating characteristic curve (ROC) analysis shows that the combined LR model exhibited the highest area under the curve value (AUC: 0.96).ConclusionThe combined LR model of first-order features based on the ADC map can acquire a higher diagnostic performance than each feature only in evaluating the neuroprotective effect of LIPUS for TBI. Models based on first-order features may have potential value in predicting the therapeutic effect of LIPUS in clinical practice in the future.

Variable structure multiple model fixed-interval smoothing

This paper focuses on fixed-interval smoothing for stochastic hybrid systems. When the truth-mode mismatch is encountered, existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable. We develop a fixed-interval smoothing method based on forward- and backward-filtering in the Variable Structure Multiple Model (VSMM) framework in this paper. We propose to use the Simplified Equivalent model Interacting Multiple Model (SEIMM) in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters, and design a re-filtering procedure in the model-switching stage to enhance the estimation performance. To improve the computational efficiency, we make the basic model-set adaptive by the Likely-Model Set (LMS) algorithm. It turns out that the smoothing performance is further improved by the LMS due to less competition among models. Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.

Kernel learning backward SDE filter for data assimilation

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to propagate the state of the target dynamical model, and Bayesian inference is applied to incorporate the observational information. To characterize the dynamical model in the entire state space, we introduce a kernel learning method to learn a continuous global approximation for the conditional probability density function of the target state by using discrete approximated density values as training data. Numerical experiments demonstrate that the kernel learning backward SDE is highly effective.

상태변수 오차기반 스무더를 이용한 자율이동체 자세오차 보상

In this study, the navigation information of a guided missile was calculated using a smoothing algorithm and used for improving the attitude estimation accuracy of the guided missile. The state variables of the backward filter, designed in the fixed interval smoother, were set to attitude errors in the same way as the forward filter of the fixed interval smoother, which was implemented as a linearized Kalman filter algorithm. To verify the performance of the proposed algorithm, simple guided missile simulations were performed, which confirmed that the attitude error of the guided missile was reduced when the fixed interval smoother was applied.

Adaptive line enhancer for nonstationary harmonic noise reduction

In this paper, we propose a frequency-domain adaptive line enhancer (ALE) to reduce nonstationary harmonic noise, such as medical equipment beeps, from a noisy speech signal captured by a single microphone. The reduction of nonstationary noise is very challenging, with the tradeoff between noise reduction and speech distortion, often resulting with much noise residuals. The proposed ALE is a combination of the commonly-used forward adaptive linear filter and a non-causal backward adaptive linear filter used together with an indicator for the presence of transient noise. The proposed combined filter results in less noise residuals while preserving the speech components. We compare the proposed approach to conventional and recent methods, and show that it can outperform these methods, achieving lower distortion, more noise reduction, and overall better speech quality and intelligibility.

Flight Data-Based Wind Disturbance and Air Data Estimation

The instantaneous wind field and air data, including true airspeed, angle of attack, angle of sideslip, cannot be measured and recorded accurately in wind disturbance. A new air data and wind field estimation method is proposed based on flight data in this study. Since the wind field is the horizontal prevailing wind added by turbulence, the slowly time-varying prevailing wind and small-scale turbulence are described by the exponentially correlated stochastic wind model and von Karman turbulence model, respectively. The system update equation of air data is built based on inertial measurements instead of the complex aerodynamic and aero-engine model of aircraft. Benefitted by the post-analysis characteristics of flight data, a forward–backward filtering algorithm was designed to improve the estimation accuracy. Simulation results indicate that the forward–backward filter integrated with the von Karman turbulence model can reduce the estimation error and ensure filtering stability. A further test with actual flight data shows that the forward–backward filter is not only able to track the wide-range change in prevailing wind but also reduce the adverse effects of uncertain disturbance on estimation accuracy.

A New Triple Filtering Algorithm and Its Application for Aerial GNSS/INS‐Integrated Direct Georeferencing System

A global navigation satellite system and inertial navigation system‐ (GNSS/INS‐) integrated system is employed to provide direct georeferencing (DG) in aerial photogrammetry. However, GNSS/INS suffers from stochastic error, strong nonlinearity, and weak observability problems in high dynamic or less maneuver scenarios. In this paper, we proposed a new triple filtering algorithm for aerial GNSS/INS integration. The new algorithm implements filtering in the sequence of forward, backward, and forward directions. Each filter is initialized by a previous filter to get a quick convergence, and the final result is combination of the last two filtering to smooth error. The proposed triple filtering strategy avoids inaccuracy in the 1st forward filtering when the system has not reached convergence. Moreover, it facilitates engineering implementation because backward filtering can employ the same equations with forward filtering. To assess stochastic error of the inertial measurement unit, the Allan variance method is used and abbreviated stochastic model is built. A real aerial testing is conducted, and the result indicates that DG can achieve horizontal accuracy of 5 cm by the proposed algorithm, which has 63% improvement compared to standard extended Kalman filter.