Applications of KLF (Research Papers)

1.An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series

In this paper, the extended Kalman filter (EKF) algorithm is applied to model the gene regulatory network from gene time series data. The gene regulatory network is considered as a nonlinear dynamic stochastic model that consists of the gene measurement equation and the gene regulation equation. After specifying the model structure, the EKF algorithm is applied for identifying both the model parameters and the actual value of gene expression levels. It is shown that the EKF algorithm is an online estimation algorithm that can identify a large number of parameters (including parameters of nonlinear functions) through iterative procedure by using a small number of observations. Four real-world gene expression data sets are employed to demonstrate the effectiveness of the EKF algorithm, and the obtained models are evaluated from the viewpoint of bioinformatics.

2.Relaxed parametric design with probabilistic constraints

Parametric design is an important modelling paradigm in computer-aided design. Relationships (constraints) are specified between the degrees of freedom (DOFs) of the model, instead of the DOFs themselves, resulting in efficient design modifications and variations. Current parametric modellers require an exact specification of all the constraints involved, which causes overwork for the designer during design iterations. The relaxed-parametric-design modelling paradigm is described, in which decisions which needlessly limit the freedom of design in later stages are avoided. The designer usesb soft constraints, and specifies the level of exactness with which they are to be met. As a specific scheme for implementing relaxed parametric design, probabilistic constraints are presented, where a parametric model is viewed as a stochastic process. The softness of a constraint is represented as the covariance of a suitably distributed random variable. A novel method is described of expressing the DOFs and the model as a system of probabilistic equations, which is then solved using the Kalman filter, a powerful estimation tool for stochastic systems. An a priori covariance matrix associated with a DOF can be used as a guideline for the solver to select a particular solution from multiple solutions.

3.An alternative Kalman innovation filter approach for receiver position estimation based on GPS measurements

This article presents an alternative Kalman innovation filter approach for receiver position estimation, based on pseudorange measurements of the global positioning system. First, a dynamic pseudorange model is represented as an ARMAX model and a pseudorange state-space innovation model suitable for both parameter identification and state estimation. The Kalman gain in the pseudorange coordinates is directly calculated from the identified parameters without prior knowledge of the noise properties and the receiver parameters. Then, the pseudorange state-space innovation model is transformed into the receiver state-space innovation model for optimal estimation of the receiver position. Hence, the proposed approach overcomes the drawbacks of the classical Kalman filter approach since it does not require prior knowledge of the noise properties, and the receiver's dynamic model to calculate the Kalman gain. In addition, due to its simplicity, it can be easily implemented in any receiver. To demonstrate the effectiveness of the approach, it is utilized to estimate the position of a stationary receiver and its performance is compared against two versions of the classical Kalman filter approach. The results show that the proposed approach yields consistently good estimation of the receiver position and outperforms the other methods.

4 Parallel computation of the modified extended kalman filter

In this paper, certain techniques for mapping the modified extended Kalman filter (MEKF) onto systolic array processors are described. First, a square-root algorithm based on the singular value decomposition (SVD) for the Kalman filteris introduced. Then, VLSI architecture of the systolic array type for its implementation is developed. Compared with other existing square-root Kalman filtering algorithms, this new design is numerically more stable and has nicer parallel and pipelining characteristics when it is applied to the MEKF. Moreover, it achieves higher efficiency. For n-dimensional state vector estimations, the proposed architecture consists of O(3/2n²) processing elements and completes an iteration in time O((s + 8)n), in contrast to the time complexity of O((s + 3)n³) for a sequential implementation, where s ≈ log n.