Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter

This paper corrects an unclear treatment of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren in Numerical aspects of different Kalman filter implementations, IEEE Trans. Automat. Contr., v. AC-31, no. 10, pp. 907-917, 1986. It is shown that habitual, incorrect implementation of the Kalman filter has been the major cause of its sensitivity to the so-called loss-of-symmetry phenomenon

The minimal residual QR-factorization algorithm for reliably solving subset regression problems

A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example

Round-off error propagation in four generally applicable, recursive, least-squares-estimation schemes

The numerical robustness of four generally applicable, recursive, least-squares-estimation schemes is analyzed by means of a theoretical round-off propagation study. This study highlights a number of practical, interesting insights of widely used recursive least-squares schemes. These insights have been confirmed in an experimental study as well

On the reliable and flexible solution of practical subset regression problems

A new algorithm for solving subset regression problems is described. The algorithm performs a QR decomposition with a new column-pivoting strategy, which permits subset selection directly from the originally defined regression parameters. This, in combination with a number of extensions of the new technique, makes the method a very flexible tool for analyzing subset regression problems in which the parameters have a physical meaning

Comparison of two numerical techniques for aerodynamic model identification

An algorithm, called the Minimal Residual QR algorithm, is presented to solve subset regression problems. It is shown that this scheme can be used as a numerically reliable implementation of the stepwise regression technique, which is widely used to identify an aerodynamic model from flight test data. This capability as well as the numerical superiority of this scheme over the stepwise regression technique is demonstrated in an experimental simulation study

The use of the QR factorization in the partial realization problem

The use of the QR factorization of the Hankel matrix in solving the partial realization problem is analyzed. Straightforward use of the QR factorization results in a realization scheme that possesses all of the computational advantages of Rissanen's realization scheme. These latter properties are computational efficiency, recursiveness, use of limited computer memory, and the realization of a system triplet having a condensed structure. Moreover, this scheme is robust when the order of the system corresponds to the rank of the Hankel matrix. When this latter condition is violated, an approximate realization could be determined via the QR factorization. In this second scheme, the given Hankel matrix is approximated by a low-rank non-Hankel matrix. Furthermore, it is demonstrated that column pivoting might be incorporated in this second scheme. The results presented are derived for a single input/single output system, but this does not seem to be a restriction

Linear phase retrieval for real-time adaptive optics

We developed a fast phase retrieval algorithm that is suitable for real-time applications such as adaptive optics. The phase retrieval model is developed by linearising the pupil function in the approximation of small aberrations and is valid for low-NA focused field. The linear model in conjunction with a particular choice for the position of the single out-of-focus measurement plane and an efficient control algorithm, significantly reduces the computation time for phase retrieval. The experimental results demonstrate the validity of the described approach for fast correction of aberrations

Accuracy of single progesterone test to predict early pregnancy outcome in women with pain or bleeding: Meta-analysis of cohort studies

Objective To determine the accuracy with which a single progesterone measurement in early pregnancy discriminates between viable and non-viable pregnancy. Design Systematic review and meta-analysis of diagnostic accuracy studies. Data sources Medline, Embase, CINAHL, Web of Science, ProQuest, Conference Proceedings Citation Index, and the Cochrane Library from inception until April 2012, plus reference lists of relevant studies. Study selection Studies were selected on the basis of participants (women with spontaneous pregnancy of less than 14 weeks of gestation); test (single serum progesterone measurement); outcome (viable intrauterine pregnancy, miscarriage, or ectopic pregnancy) diagnosed on the basis of combinations of pregnancy test, ultrasound scan, laparoscopy, and histological examination; design (cohort studies of test accuracy); and sufficient data being reported. Results 26 cohort studies, including 9436 pregnant women, were included, consisting of 7 studies in women with symptoms and inconclusive ultrasound assessment and 19 studies in women with symptoms alone. Among women with symptoms and inconclusive ultrasound assessments, the progesterone test (5 studies with 1998 participants and cut-off values from 3.2 to 6 ng/mL) predicted a non-viable pregnancy with pooled sensitivity of 74.6% (95% confidence interval 50.6% to 89.4%), specificity of 98.4% (90.9% to 99.7%), positive likelihood ratio of 45 (7.1 to 289), and negative likelihood ratio of 0.26 (0.12 to 0.57). The median prevalence of a non-viable pregnancy was 73.2%, and the probability of a non-viable pregnancy was raised to 99.2% if the progesterone was low. For women with symptoms alone, the progesterone test had a higher specificity when a threshold of 10 ng/mL was used (9 studies with 4689 participants) and predicted a non-viable pregnancy with pooled sensitivity of 66.5% (53.6% to 77.4%), specificity of 96.3% (91.1% to 98.5%), positive likelihood ratio of 18 (7.2 to 45), and negative likelihood ratio of 0.35 (0.24 to 0.50). The probability of a non-viable pregnancy was raised from 62.9% to 96.8%. Conclusion A single progesterone measurement for women in early pregnancy presenting with bleeding or pain and inconclusive ultrasound assessments can rule out a viable pregnancy.Jorine Verhaegen, Ioannis D Gallos, Norah M van Mello, Mohamed Abdel-Aziz, Yemisi Takwoingi, Hoda Harb, Jonathan J Deeks, Ben W J Mol, Arri Coomarasam