Crop Phenology Estimation Using a Multitemporal Model and a Kalman Filtering Strategy

In this letter, a new approach for crop phenology estimation with remote sensing is presented. The proposed methodology is aimed to exploit tools from a dynamical system context. From a temporal sequence of images, a geometrical model is derived, which allows us to translate this temporal domain into the estimation problem. The evolution model in state space is obtained through dimensional reduction by a principal component analysis, defining the state variables, of the observations. Then, estimation is achieved by combining the generated model with actual samples in an optimal way using a Kalman filter. As a proof of concept, an example with results obtained with this approach over rice fields by exploiting stacks of TerraSAR-X dual polarization images is shown.

Estimation of Key Dates and Stages in Rice Crops Using Dual-Polarization SAR Time Series and a Particle Filtering Approach

Information of crop phenology is essential for evaluating crop productivity. In a previous work, we determined phenological stages with remote sensing data using a dynamic system framework and an extended Kalman filter (EKF) approach. In this paper, we demonstrate that the particle filter is a more reliable method to infer any phenological stage compared to the EKF. The improvements achieved with this approach are discussed. In addition, this methodology enables the estimation of key cultivation dates, thus providing a practical product for many applications. The dates of some important stages, as the sowing date and the day when the crop reaches the panicle initiation stage, have been chosen to show the potential of this technique.

Adaptive modeling and high quality spectral estimation for speech enhancement

In this work an adaptive modeling and spectral estimation scheme based on a dual Discrete Kalman Filtering (DKF) is proposed for speech enhancement. Both speech and noise signals are modeled by an autoregressive structure which provides an underlying time frame dependency and improves time-frequency resolution. The model parameters are arranged to obtain a combined state-space model and are also used to calculate instantaneous power spectral density estimates. The speech enhancement is performed by a dual discrete Kalman filter that simultaneously gives estimates for the models and the signals. This approach is particularly useful as a pre-processing module for parametric based speech recognition systems that rely on spectral time dependent models. The system performance has been evaluated by a set of human listeners and by spectral distances. In both cases the use of this pre-processing module has led to improved results.

Multiuser detection in a dynamic environment — Part II: Joint user identification and parameter estimation

The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknown continuous parameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We doso deriving Bayesian recursions that describe the evolution withtime of a posteriori densities of the unknown parameters and data.Unlike in the above cited paper, wherein one could evaluate theexact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximationsfor the receivers that are based on Sequential Monte Carlo (SMC)methods (“particle filtering”). Simulation results, referring to acode-divisin multiple-access (CDMA) system, are presented toillustrate the theory.

Multiple filtering devices for the estimation of cyclical DSGE models

We propose a method to estimate time invariant cyclical DSGE models using the informationprovided by a variety of filters. We treat data filtered with alternative procedures as contaminated proxies of the relevant model-based quantities and estimate structural and non-structuralparameters jointly using a signal extraction approach. We employ simulated data to illustratethe properties of the procedure and compare our conclusions with those obtained when just onefilter is used. We revisit the role of money in the transmission of monetary business cycles.

Minimum distance estimation of stationary and non-stationary ARFIMA processes

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator iseasy to compute and is consistent and asymptotically normally distributed for fractionallyintegrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Rigid body dynamics and Kalman filtering

X-ray computed log tomography has always been applied for qualitative reconstructions. In most cases, a series of consecutive slices of the timber are scanned to estimate the 3D image reconstruction of the entire log. However, the unexpected movement of the timber under study influences the quality of image reconstruction since the position and orientation of some scanned slices can be incorrectly estimated. In addition, the reconstruction time remains a significant challenge for practical applications. The present study investigates the possibility to employ modern physics engines for the problem of estimating the position of a moving rigid body and its scanned slices which are subject to X-ray computed tomography. The current work includes implementations of the extended Kalman filter and an algebraic reconstruction method for fan-bean computer tomography. In addition, modern techniques such as NVidia PhysX and CUDA are used in current study. As the result, it is numerically shown that it is possible to apply the extended Kalman filter together with a real-time physics engine, known as PhysX, in order to determine the position of a moving object. It is shown that the position of the rigid body can be determined based only on reconstructions of its slices. However, the simulation of the body movement sometimes is subject to an error during Kalman filter employment as PhysX is not always able to continue simulating the movement properly because of incorrect state estimation.

Model estimation of cerebral hemodynamics between blood flow and volume changes: A data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.

A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.

Simultaneous 3D object tracking and camera parameter estimation by Bayesian methods and transdimensional MCMC sampling

Multi-camera 3D tracking systems with overlapping cameras represent a powerful mean for scene analysis, as they potentially allow greater robustness than monocular systems and provide useful 3D information about object location and movement. However, their performance relies on accurately calibrated camera networks, which is not a realistic assumption in real surveillance environments. Here, we introduce a multi-camera system for tracking the 3D position of a varying number of objects and simultaneously refin-ing the calibration of the network of overlapping cameras. Therefore, we introduce a Bayesian framework that combines Particle Filtering for tracking with recursive Bayesian estimation methods by means of adapted transdimensional MCMC sampling. Addi-tionally, the system has been designed to work on simple motion detection masks, making it suitable for camera networks with low transmission capabilities. Tests show that our approach allows a successful performance even when starting from clearly inaccurate camera calibrations, which would ruin conventional approaches.

Spatio-temporal filtering with morphological operators for robust cell migration estimation in "in-vivo" images

The understanding of the embryogenesis in living systems requires reliable quantitative analysis of the cell migration throughout all the stages of development. This is a major challenge of the "in-toto" reconstruction based on different modalities of "in-vivo" imaging techniques -spatio-temporal resolution and image artifacts and noise. Several methods for cell tracking are available, but expensive manual interaction -time and human resources- is always required to enforce coherence. Because of this limitation it is necessary to restrict the experiments or assume an uncontrolled error rate. Is it possible to obtain automated reliable measurements of migration? can we provide a seed for biologists to complete cell lineages efficiently? We propose a filtering technique that considers trajectories as spatio-temporal connected structures that prunes out those that might introduce noise and false positives by using multi-dimensional morphological operators.

Tyre-force estimation by Kalman inverse filtering: applications to off-highway mining trucks

Kalman inverse filtering is used to develop a methodology for real-time estimation of forces acting at the interface between tyre and road on large off-highway mining trucks. The system model formulated is capable of estimating the three components of tyre-force at each wheel of the truck using a practical set of measurements and inputs. Good tracking is obtained by the estimated tyre-forces when compared with those simulated by an ADAMS virtual-truck model. A sensitivity analysis determines the susceptibility of the tyre-force estimates to uncertainties in the truck's parameters.

Scaphoid Fracture Nonunion: Correlation Of Radiographic Imaging, Proximal Fragment Histologic Viability Evaluation, And Estimation Of Viability At Surgery: Diagnosis Of Scaphoid Pseudarthrosis.

The purpose of this study was to correlate the pre-operative imaging, vascularity of the proximal pole, and histology of the proximal pole bone of established scaphoid fracture non-union. This was a prospective non-controlled experimental study. Patients were evaluated pre-operatively for necrosis of the proximal scaphoid fragment by radiography, computed tomography (CT) and magnetic resonance imaging (MRI). Vascular status of the proximal scaphoid was determined intra-operatively, demonstrating the presence or absence of puncate bone bleeding. Samples were harvested from the proximal scaphoid fragment and sent for pathological examination. We determined the association between the imaging and intra-operative examination and histological findings. We evaluated 19 male patients diagnosed with scaphoid nonunion. CT evaluation showed no correlation to scaphoid proximal fragment necrosis. MRI showed marked low signal intensity on T1-weighted images that confirmed the histological diagnosis of necrosis in the proximal scaphoid fragment in all patients. Intra-operative assessment showed that 90% of bones had absence of intra-operative puncate bone bleeding, which was confirmed necrosis by microscopic examination. In scaphoid nonunion MRI images with marked low signal intensity on T1-weighted images and the absence of intra-operative puncate bone bleeding are strong indicatives of osteonecrosis of the proximal fragment.