Abrupt Changes In Signals Research Articles

Estimation of Biases in Gyro Drifts by Means of l1-norm Approximation.

A strapdown inertial navigation system at bench tests is under consideration. Because of jump variations of gyro drifts, the estimates of the drifts obtained by standard quadratic methods are not sufficiently accurate. We investigate the application of l1-norm approximation to estimation of gyro drifts. Such approach is robust to abrupt changes in signals. An additional calculation of non-optimality levels for the current iterations of numerical algorithm makes the computational procedure more efficient.

State Estimation via l1-norm Approximation: Application to Inertial Navigation

AbstractThe problem of the detection of jumps in the biases of the sensors of a strapdown inertial navigation system at bench tests is considered. This problem is set as a state estimation problem for a dynamic system under the presence of outliers in object disturbances. The estimation method is based on l1-norm approximation and is robust to abrupt changes in signals.

Oscillations in Monotone Systems with a Negative Feedback

We study a finite-dimensional monotone system coupled to a slowly evolving scalar differential equation which provides a negative feedback to the monotone system. We use a theory of multivalued characteristics to show that this system admits a relaxation periodic orbit if a simple model system in $\mathbf{R}^2$ does. Our construction can be used to prove the existence of periodic orbits in slow-fast systems of arbitrary dimension. We apply our theory to a model of a cell cycle in Xenopus embryos. Abrupt changes in signals upon entry to mitosis suggests that the cell cycle is generated by a relaxation oscillation. Our results show that the cell cycle orbit is not a relaxation oscillator. However, we construct a closely related system that exhibits relaxation oscillations and that approximates the cell cycle oscillator for an intermediate range of negative feedback strengths. We show that the cell cycle oscillation disappears if the negative feedback is too weak or too strong.

Theory and applications of a new methodology for the random sequential probability ratio test

Wald’s [A. Wald, Sequential Analysis, Wiley, New York, 1947] sequential probability ratio test (SPRT) and group sequential probability ratio test (GSPRT) remain relevant in addressing a wide range of practical problems. The area of clinical trials owes a great debt to the theory and methodologies of SPRT and GSPRT. In recent years, there has been a surge of practical applications of these methodologies in many areas including low frequency sonar detection, tracking of signals, early detection of abrupt changes in signals, computer simulations, agricultural sciences, pest management, educational testing, economics, and finance. But, obviously, there are circumstances where sampling one observation at a time may not be practical. In contexts of monitoring “inventory” or “queues”, observations may appear sequentially but in groups where the group sizes may be ideally treated as random variables themselves. For example, one may sequentially record the number of stopped cars ( M i ) and the number of cars ( ∑ j = 1 M i X i j ) without “working brake lights” when a traffic signal changes from green to red, i = 1 , 2 , … . This can be easily accomplished since every “working brake light” must glow bright red when a driver applies brakes. In this example, one notes that (i) it may be reasonable to model M i ’s as random, but (ii) it would appear impossible to record data sequentially on the status of brake lights (that is, X i j = 0 or 1) individually for car #1, and then for car #2, and so on when a group of cars rush to stop at an intersection! In order to address these kinds of situations, we start with an analog of the concept of a best “fixed-sample-size” test based on data { M i , X i 1 , … , X i M i , i = 1 , … , k } . Then, a random sequential probability ratio test (RSPRT) is developed for deciding between a simple null hypothesis and a simple alternative hypothesis with preassigned Type I and II errors α , β . The RSPRT and the best “fixed-sample-size” test with k ≡ k min associated with the same errors α , β are compared. Illustrations of RSPRT include a one-parameter exponential family followed by substantive computer simulations that lead to a broad set of guidelines. Two real applications and data analysis are highlighted.

The wavelet response as a multiscale characterization of scattering processes at granular interfaces

We perform a multiscale analysis of the backscattering properties of a complex interface between water and a layer of randomly arranged glass beads with diameter D=1mm. An acoustical experiment is done to record the wavelet response of the interface in a large frequency range from λ/D=0.3 to λ/D=15. The wavelet response is a physical analog of the mathematical wavelet transform which possesses nice properties to detect and characterize abrupt changes in signals. The experimental wavelet response allows to identify five frequency domains corresponding to different backscattering properties of the complex interface. This puts quantitative limits to the validity domains of the models used to represent the interface and which are flat elastic, flat visco-elastic, rough random half-space with multiple scattering, and rough elastic from long to short wavelengths respectively. A physical explanation based on Mie scattering theory is proposed to explain the origin of the five frequency domains identified in the wavelet response.

Efficient recursive algorithms for detection of abrupt changes in signals and control systems

This paper addresses a number of open problems concerning the generalized likelihood ratio (GLR) rules for online detection of faults and parameter changes in control systems. It is shown that with an appropriate choice of the threshold and window size, these GLR rules are asymptotically optimal. The rules are also extended to non-likelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing Gaussian approximations to these statistics when the window size is chosen suitably. Recursive algorithms are developed for practical implementation of the procedure, and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate.

Book Review: Lecture Notes in Control and Information Sciences: Detection of Abrupt Changes in Signals and Dynamical Systems

Book Review: Lecture Notes in Control and Information Sciences: Detection of Abrupt Changes in Signals and Dynamical Systems

Book reviews - Detection of abrupt changes in signals and dynamical systems

Book reviews - Detection of abrupt changes in signals and dynamical systems