Variance Of Observation Noise Research Articles

A new algorithm for landslide dynamic monitoring with high temporal resolution by Kalman filter integration of multiplatform time-series InSAR processing

• Provide a new scheme for landslide dynamic monitoring and prediction. • Integrate multiplatform time-series InSAR processing by Kalman filter. • Compensate the deficiency of the space-borne InSAR in landslide temporal resolution. Free and open access to the earth observation synthetic aperture radar (SAR) satellite images has enabled the implementation of landslide time-series monitoring. However, with the restriction of the low revisit period of satellite, it is difficult to meet the requirements of landslide dynamic monitoring with high temporal resolution. Moreover, with the multiplication of SAR satellite platforms, a corresponding data integration algorithm is needed to obtain the complementary displacement information from every single observation orbit. In this work, an integrated algorithm for landslide multi-source displacement optimization estimation based on Kalman filter (KF) is proposed to improve the temporal resolution and realize the dynamic monitoring and prediction of landslide movement. Specifically, the landslide migration coordinate system is established firstly, and the interferometric SAR (InSAR) displacement results in line of sight (LOS) are projected to the downslope direction. Then, with the introduction of the acceleration variable into the process covariance matrix of prediction model and the observation noise variance weight determination, the downslope displacements of multiplatform InSAR observations are dynamically integrated into a unified time series by KF dynamic prediction and correction. So as to achieve the high temporal resolution monitoring of landslide. For validation purpose, the Baige landslide in Tibet, China is selected as the test area, and 55 Sentinel-1A ascending images, 42 Sentinel-1A descending images, and 10 ALOS-2 PALSAR-2 images collected over this area from May 2017 to April 2019 are used to estimate the high temporal time series. The temporal resolution of landslide monitoring is successfully improved from 12 days with a single orbit to the shortest 1 day and repeatedly 2–5 days with multiple platforms, and the prediction of subsequent displacement is also realized. Prospectively, with the continuous multiplication of the InSAR satellite platforms, this proposed algorithm can provide high temporal monitoring data for landslide and better assist relevant emergency response, which is necessary for the dynamic monitoring and early warning of landslide.

Enhanced Map-Aided GPS/3D RISS Combined Positioning Strategy in Urban Canyons

To realize the effective positioning in urban canyons, an enhanced map-aided Global Positioning System (GPS)/three-dimensional (3D) reduced inertial sensor system (RISS) tightly combined positioning strategy is proposed. First, the 3D RISS is only based on the built-in controller area network (CAN). CAN bus sensor without additional sensors is first constructed to lower the cost. Then, a simple but effective enhanced map is created to assist positioning. Based on the map, a Kalman filtering (KF) tightly coupled method is proposed to fuse the 3D RISS with GPS information and to achieve the preliminary positioning. In KF-based preliminary positioning method, a simply observation noise variance optimization algorithm based on 2D enhanced map is proposed to improve KF method. In this algorithm, the value of the observation noise variance matrix is determined only according to the building plane information which is contained in the enhanced map. Further, a multiweight map matching algorithm is proposed for optimizing the initial positioning results. In this algorithm, factors such as distance, direction, road network topology, and lane change are considered and applied to map matching to further increase the positioning performance and form the final positioning results. Finally, the effectiveness of the strategy is proved by field test. The results show that this method has better accuracy and reliability than the conventional method.

Grid Lifespan Enlargement for Assessment in Multihop Wireless Detector Facilities

In energy limited wireless sensor networks, both local quantization andmultihop transmission are essential to save transmission energy and thus prolong the network lifetime. The goal is to maximize the network lifetime, defined as the estimation task cycles accomplished before the network becomes nonfunctional.The network lifetime optimization problem includes three components: Optimizing source coding at each sensor node, optimizing source throughput at each sensor node.Optimizing multihop routing path. Source coding optimization can be decoupled from source throughput and multihop routing path optimization and is solved by introducing a concept of equivalent 1-bit Mean Square Error (MSE) function. Based on optimal source coding, multihop routing path optimization is formulated as a linear programming problem, which suggests a new notion of character based routing. It is also seen that optimal multihop routing improves the network lifetime bound significantly compared with single-hop routing for heterogeneous networks. Furthermore, the gain is more significant when the network is denser since there are more opportunities for multihop routing. Also the gain is more significant when the observation noise variances are more diverse.

Point cloud target detection and tracking algorithm based on K-means and Kalman

This paper is mainly about point cloud image and data processing, virtualization and visualization. An improved K-means iterative clustering algorithm is proposed. In addition, cloth simulation filtering algorithm is used to extract road surface information. On this basis, bilateral filtering and statistic filtering are used to smooth image denoising. Kalman filter is used to track and predict point cloud targets. Using the variance of innovation sequence, the noise variance and observation noise variance can be estimated and corrected gradually in the process of system calculation. The error is relatively small, and the accuracy and reliability are improved. For disordered, occluded, sparsity and noisy, complex terrain image, how to improve the denoising effect, the accuracy and effectiveness of target extraction and tracking is the focus of this paper.

Bandwidth constrained distributed estimation for wireless sensor networks

The focus of this paper is power constrained in wireless sensor networks. We purpose an adaptive transmit power levels based on sensors noise variance and channel conditions. We also investigate its impact on energy saving. First, the measurement results of the sensors are quantized into discrete messages. Second, the quantized data are transmitted to the fusion center where a final estimate is generated. The optimal transmit power levels for each sensor is determined by the sensor noise levels and channels conditions from sensor to the fusion center. The goal is minimized the total transmitting power, while ensuring a given Mean Squared Error (MSE) performance. The sensor will be active when the measurement results of the sensors have low noises variances and the condition of the channel between the sensor and the FC is good and if the conditions are otherwise the sensor is not active with the aim of saving power. For the remaining active sensors, their optimal transmit power levels are determined jointly by individual channels gain, local observation noise variance sensor and the targeted MSE performance. Numerical examples show that an adaptive power levels achieves significantly smaller MSE than uniform power levels for the same average power consumption.

A Novel Method of SOC Estimation for Electric Vehicle Based on Adaptive Particle Filter

Aimed at improving SOC estimation accuracy, speed and robust of battery on electric vehicle, SOC estimation method based on adaptive particle filter is proposed. 1-order RC and lag model, 2-order RC and lag model, 3-order RC and lag model are built. Particle Swarm algorithm is used to search optimal parameters. Considering calculation and model accuracy, 1-order lag model is chosen. Traditional particle filter principle is analyzed. State estimation is a substitute to observation equation, and observation estimation is gotten. Observation noise variance is adjusted adaptively through observation error. Verification by simulation, convergence speed and robust of adaptive particle filter are superior to traditional algorithm when SOC original error is large. Besides, SOC estimation accuracy and stability is superior to traditional algorithm obviously.

New estimation methods for autoregressive process in the presence of white observation noise

This paper presents four new methods for estimating the parameters of an autoregressive (AR) process based on observations corrupted by white noise. The first three methods are iterative, while the last one is non-iterative. One method is designed to achieve an unbiased estimation of the AR parameters by undermining the destructive impact of observation noise in terms of utilizing the null space of the AR parameter vector. Another one uses both low- and high-order Yule-Walker equations to construct a constrained least squares optimization problem, in which the variance of observation noise is estimated by alternating between two equations. One more method exploits an approximation which leads to reducing the problem of estimating the AR parameters with arbitrary order p to estimating just two parameters, while the last one estimates the variance of the observation noise using the minimum eigenvalue of the enlarged autocorrelation matrix. The performance of the proposed methods is evaluated in terms of various numerical examples, which demonstrate their superiority in terms of accuracy and robustness against the observation noise compared to state-of-the-art existing methods in most simulation examples. It makes the proposed methods a good fit for practical analysis of data contaminated by observation noise, when AR modeling is applicable, and gives a range of choices of methods for different data analysis situations.

Adaptive Least-Squares Collocation Algorithm Considering Distance Scale Factor for GPS Crustal Velocity Field Fitting and Estimation

High-precision, high-reliability, and high-density GPS crustal velocity are extremely important requirements for geodynamic analysis. The least-squares collocation algorithm (LSC) has unique advantages over crustal movement models to overcome observation errors in GPS data and the sparseness and poor geometric distribution in GPS observations. However, traditional LSC algorithms often encounter negative covariance statistics, and thus, calculating statistical Gaussian covariance function based on the selected distance interval leads to inaccurate estimation of the correlation between the random signals. An unreliable Gaussian statistical covariance function also leads to inconsistency in observation noise and signal variance. In this study, we present an improved LSC algorithm that takes into account the combination of distance scale factor and adaptive adjustment to overcome these problems. The rationality and practicability of the new algorithm was verified by using GPS observations. Results show that the new algorithm introduces the distance scale factor, which effectively weakens the influence of systematic errors by improving the function model. The new algorithm can better reflect the characteristics of GPS crustal movement, which can provide valuable basic data for use in the analysis of regional tectonic dynamics using GPS observations.

Bayesian forecasting approach for structure response prediction and load effect separation of a revolving auditorium

A Bayesian dynamic linear model (BDLM) is presented for a data-driven analysis for response prediction and load effect separation of a revolving auditorium structure, where the main loads are self-weight and dead loads, temperature load, and audience load. Analyses are carried out based on the long-term monitoring data for static strains on several key members of the structure. Three improvements are introduced to the ordinary regression BDLM, which are a classificatory regression term to address the temporary audience load effect, improved inference for the variance of observation noise to be updated continuously, and component discount factors for effective load effect separation. The effects of those improvements are evaluated regarding the root mean square errors, standard deviations, and 95% confidence intervals of the predictions. Bayes factors are used for evaluating the probability distributions of the predictions, which are essential to structural condition assessments, such as outlier identification and reliability analysis. The performance of the present BDLM has been successfully verified based on the simulated data and the real data obtained from the structural health monitoring system installed on the revolving structure.

Optimal deployment of vehicles with circular formation for bearings-only multi-target localization

This paper focuses on the optimal deployment problem of multiple mobile vehicles with circular formation for multi-target localization using bearings-only sensors. Initially, a general closed-form formula of geometric dilution of precision (GDOP) is derived based on the Cramer–Rao lower bound (CRLB) for bearings-only localization. By this generalized formula, the analytical formula of GDOP for multiple vehicles containing the same observation noise variance with circular formation is then deduced directly. Next, the necessary and sufficient condition for sensor placement optimality with the minimization of GDOP is presented, which guarantees what are the best positions where the vehicles should be in the desired observation circumference with the given radius centered at the target. The optimal deployment positions as well as the global minimum of GDOP are then proposed with analytical expressions. Furthermore, an efficient optimal deployment algorithm is developed to deploy the vehicles to approach the best positions as precisely as possible for practical multi-target localization. Finally, an illustrative example is used to demonstrate the effectiveness of the proposed approach.

Empirical Bayes matrix completion

We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris. Since the EB algorithm is derived as the Expectation–Maximization algorithm applied to a simple model, it does not require heuristic parameter tuning other than tolerance. Also, it can account for the heterogeneity in variance of observation noise. Numerical results demonstrate that the EB algorithm attains at least comparable accuracy to existing algorithms for matrices not close to square and that it works particularly well when the rank is relatively large or the proportion of observed entries is small. Application to real data also shows the practical utility of the EB algorithm.

SVRPF: An Improved Particle Filter for a Nonlinear/Non-Gaussian Environment

The performance of a particle filter (PF) in nonlinear and non-Gaussian environments is often affected by particle degeneracy and impoverishment problems. In this paper, these two problems are re-assessed using the concepts of importance region (IR) selection and particle density (PD), where IR describes the distribution region of particles, and PD describes the density of particles in IR. Based on these two factors, a support vector regression PF (SVRPF) is proposed to overcome the problems from nonlinear and non-Gaussian environments, especially in regard to narrow observation noise. Furthermore, the consistency of the SVRPF and Bayes' filtering is demonstrated. A numerical simulation shows that the performance of the SVRPF is more stable than other filter algorithms. Provided that other conditions are the same, when the observation noise variance is 0.1 and 5, the root-mean-square errors of the SVRPF decrease by 0.5 and 0.03, respectively, compared with that of a general PF.

Inference for ergodic diffusions plus noise

AbstractWe research an adaptive maximum‐likelihood–type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation noise, the diffusion parameter, and the drift one of the latent diffusion process. Moreover, it can lessen the computational burden compared to simultaneous maximum likelihood–type estimation. In addition to adaptive estimation, we propose a test to see if noise exists or not and analyze real data as the example such that the data contain observation noise with statistical significance.

A fast temperature rise identification method based on an adaptive particle filter

A fast temperature rise identification method for motorized spindle is presented based on an adaptive particle filter (APF). The advantage of this method is the ability to predict the entire temperature change in a short time. For example, to obtain the whole temperature variation curve of the measured points, it will take about 390 min. However, if APF method is used, the data of the first 24 min can be used to predict the entire temperature change. Temperature signals with multiple variables, long time delay, and nonlinear coupling characteristics as well as the uncertainty of actual measurement of noise in the process making measured temperature fluctuate widely. However, sampled data contain a lot of noise; hence, finding the real temperature range and predicting the future temperature changes using only few data are quite challenging tasks. For this reason, particle filter (PF) method was utilized to get the identification result. Then, the adaptive factor was introduced by adjusting state equations and observation noise variance. Results showed that APF can achieve better identification of temperature rise. Finally, the temperature rise test was verified on the motorized spindle, which utilized PF method and the APF method. Experimental results showed that APF can reduce the recognition time to about 24 min, while the PF takes about 38 min. The effectiveness of the method was verified by using experimental data, and the approach to obtain the minimal recognition time was also explained. In 390 min of measuring time, the root mean square error (RMSE) between estimated and measured temperature is 0.415 °C, and the error between the estimated and measured steady-state temperature is 0.01 °C. The results proved that this method can be used to identify motorized spindle temperature, with high speed and high accuracy.

An Enhanced Non-Coherent Pre-Filter Design for Tracking Error Estimation in GNSS Receivers.

Tracking error estimation is of great importance in global navigation satellite system (GNSS) receivers. Any inaccurate estimation for tracking error will decrease the signal tracking ability of signal tracking loops and the accuracies of position fixing, velocity determination, and timing. Tracking error estimation can be done by traditional discriminator, or Kalman filter-based pre-filter. The pre-filter can be divided into two categories: coherent and non-coherent. This paper focuses on the performance improvements of non-coherent pre-filter. Firstly, the signal characteristics of coherent and non-coherent integration—which are the basis of tracking error estimation—are analyzed in detail. After that, the probability distribution of estimation noise of four-quadrant arctangent (ATAN2) discriminator is derived according to the mathematical model of coherent integration. Secondly, the statistical property of observation noise of non-coherent pre-filter is studied through Monte Carlo simulation to set the observation noise variance matrix correctly. Thirdly, a simple fault detection and exclusion (FDE) structure is introduced to the non-coherent pre-filter design, and thus its effective working range for carrier phase error estimation extends from (−0.25 cycle, 0.25 cycle) to (−0.5 cycle, 0.5 cycle). Finally, the estimation accuracies of discriminator, coherent pre-filter, and the enhanced non-coherent pre-filter are evaluated comprehensively through the carefully designed experiment scenario. The pre-filter outperforms traditional discriminator in estimation accuracy. In a highly dynamic scenario, the enhanced non-coherent pre-filter provides accuracy improvements of 41.6%, 46.4%, and 50.36% for carrier phase error, carrier frequency error, and code phase error estimation, respectively, when compared with coherent pre-filter. The enhanced non-coherent pre-filter outperforms the coherent pre-filter in code phase error estimation when carrier-to-noise density ratio is less than 28.8 dB-Hz, in carrier frequency error estimation when carrier-to-noise density ratio is less than 20 dB-Hz, and in carrier phase error estimation when carrier-to-noise density belongs to (15, 23) dB-Hz (26, 50) dB-Hz.

Scaling limits in computational Bayesian inversion

Computational Bayesian inversion of operator equations with distributed uncertain input parameters is based on an infinite-dimensional version of Bayes' formula established in (31) and its nu- merical realization in (27,28). Based on the sparsity of the posterior density shown in (29), dimension- adaptive Smolyak quadratures afford higher convergence rates than MCMC in terms of the number M of solutions of the forward (parametric operator) equation (27,28). The error bounds and convergence rates obtained in (27,28) are independent of the parameter dimension (in particular free from the curse of dimensionality) but depend on the (co)variance G > 0 of the additive, Gaussian observation noise as exp(bG −1 ) for some constant b > 0. It is proved that the Bayesian estimates admit asymptotic ex- pansions as G ↓ 0. Sufficient (nondegeneracy) conditions for the existence of finite limits as G ↓ 0 are presented. For Gaussian priors, these limits are related to MAP estimators obtained from Tikhonov regularized least-squares functionals. Non-intrusive identification of concentration points and curva- ture information of the posterior density at these points by Quasi-Newton (QN) minimization of the Bayesian potential with SR1 updates from (7,14) is proposed. Two Bayesian estimation algorithms with robust in G performance are developed: first, dimension-adaptive Smolyak quadrature from (27, 28) combined with a novel, curvature-based reparametrization of the parametric Bayesian posterior den- sity near the (assumed unique) global maximum of the posterior density and, second, extrapolation to the limit of vanishing observation noise variance. For either approach, we prove convergence with rates independent of the number of parameters as well as of the observation noise variance G. The generalized Richardson extrapolation to the limit G ↓ 0 due to A. Sidi (30) is justified by establishing asymptotic expansions wr. to G ↓ 0 of the Bayesian estimates. Numerical experiments are presented which indicate a performance independent of G on the curvature-rescaled, adaptive Smolyak algorithm.

Novel parameter estimation of autoregressive signals in the presence of noise

This paper proposes a new method for estimating the parameters of an autoregressive (AR) signal from observations corrupted by white noise. The feature of the new method is that the observation noise variance estimate is converted into the only solution of a nonlinear equation to yield unbiased estimate of the AR parameters. Moreover, a convergent Newton iterative algorithm with a deterministic initial point is presented for efficient implementation of the proposed new estimation method. As a result, the proposed new method can minimize the error of estimating the variance of the observation noise. Since more accurate estimates of this observation noise variance can be attained at earlier stages, the proposed method can achieve a good performance in estimating the AR signal parameters. Numerical results demonstrate that the proposed new algorithm is more effective in terms of accuracy and robustness against noise than conventional algorithms.

Using frequency analysis to improve the precision of human body posture algorithms based on Kalman filters

With the advent of miniaturized inertial sensors many systems have been developed within the last decade to study and analyze human motion and posture, specially in the medical field. Data measured by the sensors are usually processed by algorithms based on Kalman Filters in order to estimate the orientation of the body parts under study. These filters traditionally include fixed parameters, such as the process and observation noise variances, whose value has large influence in the overall performance. It has been demonstrated that the optimal value of these parameters differs considerably for different motion intensities. Therefore, in this work, we show that, by applying frequency analysis to determine motion intensity, and varying the formerly fixed parameters accordingly, the overall precision of orientation estimation algorithms can be improved, therefore providing physicians with reliable objective data they can use in their daily practice.

Secret Key Generation Via Localization and Mobility

We consider secret key generation by a pair of mobile nodes utilizing observations of their relative locations in the presence of a mobile eavesdropper. In our proposed algorithm, the legitimate node pair makes noisy observations of the relative locations of each other. Based on these observations, the nodes generate secret key bits via information reconciliation, data compression, and privacy amplification. We characterize a theoretically achievable secret key bit rate in terms of the observation noise variance at the legitimate nodes and the eavesdropper and show that the performance of our algorithm is comparable to the theoretical bounds. We also test our algorithm in a vehicular setting based on observations made using wireless beacon exchange between the legitimate nodes. To achieve this, we used TelosB wireless radios mounted on the sides of the vehicles on local roads and freeways. Note that our approach relies solely on distance reciprocity, and thus, it is not restricted to the use of wireless radios and can be used with other localization systems (e.g., infrared and ultrasound systems) as well. Overall, this study proves, via both information theoretic and practical analysis, that localization information provides a significant additional resource for secret key generation in mobile networks.

Scaling Limits in Computational Bayesian Inversion

Computational Bayesian inversion of operator equations with distributed uncertain input parameters is based on an infinite-dimensional version of Bayes' formula established in (31) and its nu- merical realization in (27,28). Based on the sparsity of the posterior density shown in (29), dimension- adaptive Smolyak quadratures afford higher convergence rates than MCMC in terms of the number M of solutions of the forward (parametric operator) equation (27,28). The error bounds and convergence rates obtained in (27,28) are independent of the parameter dimension (in particular free from the curse of dimensionality) but depend on the (co)variance G > 0 of the additive, Gaussian observation noise as exp(bG −1 ) for some constant b > 0. It is proved that the Bayesian estimates admit asymptotic ex- pansions as G ↓ 0. Sufficient (nondegeneracy) conditions for the existence of finite limits as G ↓ 0 are presented. For Gaussian priors, these limits are related to MAP estimators obtained from Tikhonov regularized least-squares functionals. Non-intrusive identification of concentration points and curva- ture information of the posterior density at these points by Quasi-Newton (QN) minimization of the Bayesian potential with SR1 updates from (7,14) is proposed. Two Bayesian estimation algorithms with robust in G performance are developed: first, dimension-adaptive Smolyak quadrature from (27, 28) combined with a novel, curvature-based reparametrization of the parametric Bayesian posterior den- sity near the (assumed unique) global maximum of the posterior density and, second, extrapolation to the limit of vanishing observation noise variance. For either approach, we prove convergence with rates independent of the number of parameters as well as of the observation noise variance G. The generalized Richardson extrapolation to the limit G ↓ 0 due to A. Sidi (30) is justified by establishing asymptotic expansions wr. to G ↓ 0 of the Bayesian estimates. Numerical experiments are presented which indicate a performance independent of G on the curvature-rescaled, adaptive Smolyak algorithm.