Jump Detection Algorithm Research Articles

Optimal Fitting and Debiasing for Detectors Read Out Up-the-Ramp

This paper derives the optimal fit to a pixel’s count rate in the case of an ideal detector read out nondestructively in the presence of both read and photon noise. The approach is general for any readout scheme, provides closed-form expressions for all quantities, and has a computational cost that is linear in the number of resultants (groups of reads). I also derive the bias of the fit from estimating the covariance matrix and show how to remove it to first order. The ramp-fitting algorithm I describe provides the χ 2 value of the fit of a line to the accumulated counts, which can be interpreted as a goodness-of-fit metric. I provide and describe a pure Python implementation of these algorithms that can process a 10-resultant ramp on a 4096 × 4096 detector in ≈8 s with bias removal on a single core of a 2020 Macbook Air. This Python implementation, together with tests and a tutorial notebook, are available at https://github.com/t-brandt/fitramp. A companion paper describes a jump detection algorithm based on hypothesis testing of ramp fits and demonstrates all algorithms on data from JWST.

Development of a simple algorithm to detect big air jumps and jumps during skiing.

Jumping is an important task in skiing, snowboarding, ski jumping, figure skating, volleyball and many other sports. In these examples, jumping tasks are a performance criterion, and therefore detailed insight into them is important for athletes and coaches. Therefore, this paper aims to introduce a simple and easy-to-implement jump detection algorithm for skiing using acceleration data from inertial measurement units attached to ski boots. The algorithm uses the average of the absolute vertical accelerations of the two boots. We provide results for different parameter settings of the algorithm and two types of jumps: Big Air jumps and jumps during skiing. The latter are divided into small (time of flight < 500 ms) and medium (time of flight ≥ 500 ms) jumps. The algorithm detects 100% of Big Air, 94% of medium and 44% of small jumps. In addition, the settings with the highest detection rates also have the highest number of overdetected jumps. To resolve this conflict, a penalty-adjusted score that considers the number of overdetected jumps in the final performance analysis is proposed.

Distributed debiased estimation of high-dimensional partially linear models with jumps

In this paper, we focus on the estimations of both parameter vector and nonparametric component in a high-dimensional partially linear model with jumps within the framework of divide and conquer strategy. We find that a three-stage estimation procedure works well in this setting. Applying the lasso penalty and projected spline approximation, first a profiled estimator for the linear part and a projected spline estimator for the nonparametric part are obtained on each local machine. In the second stage, an efficient jump detection algorithm is developed to obtain the new knot sequence, and then based on this, the estimate of the nonparametric function is obtained and averaged after plugging in the linear part estimate on each local machine. The aggregated estimate of the nonparametric function is then computed by pooling these local estimates. In the third stage, a debiased lasso estimator is averaged to obtain a distributed debiased estimator of the linear part after plugging in the aggregated estimate of nonparametric function. Asymptotic properties of resultant estimators are established under some mild assumptions. Some simulations are conducted to illustrate the empirical performances of our proposed method.

Automatic jump detection in skiing/snowboarding using head-mounted MEMS inertial and pressure sensors

With advancing technology in the miniature microelectromechanical systems (MEMS) sensors, wearable devices are becoming increasingly popular, facilitating convenient activity detection. One particular application is in sports performance monitoring. This article presents a novel real-time jump detection algorithm in skiing and snowboarding using a microelectromechanical systems–based inertial measurement unit, which is integrated with a barometric pressure sensor. The key performance variables of the jump can be extracted and evaluated for training and/or entertainment purposes. In contrast to the existing jump detection algorithms based on acceleration signals, the proposed algorithm uses vertical velocity and air time in addition to acceleration in the vertical direction. The experimental results show that by incorporating the velocity and air time into the detection algorithm, the sensitivity and specificity increase dramatically to 92% and 93%, respectively.

A modeling approach to financial time series based on market microstructure model with jumps

A continuous-time generalized market microstructure (GMMS) model and its discretized model are proposed for characterizing a class of financial time series. The GMMS model is a kind of jump-diffusion model that may describe the dynamic behaviors of measurable market price, immeasurable market excess demand and market liquidity, as well as the interaction among the three variates in a market. The model includes a jump component that is used to capture the large abnormal variations of financial assets, which may occur when a market is affected by some special events happened suddenly, such as release of important financial information. On the basis of the discrete-time GMMS model, an online recursive jump detection algorithm is proposed, which is developed in accordance with the Markov property of financial time series and the Bayes theorem. Simulations and case studies demonstrate the feasibility and effectiveness of the model and its estimation approach presented in this paper.

Reliable jump detection for snow sports with low-cost MEMS inertial sensors

Body-mounted devices, incorporating low-cost micro-electromechanical systems (MEMS) Inertial Measurement Units (IMUs), for real-time sports performance feedback are commercially available. In sports such as skiing, snowboarding, and mountain biking, aerial jumps can be detected with these devices and performance variables including air time and jump drop can be calculated real-time. However, the performance of currently used real-time athletic jump detection algorithms using MEMS IMUs is unsatisfactory in terms of accuracy, power efficiency, and reliability. In this paper, a novel algorithm for jump detection with a head-mounted MEMS IMU is proposed. Two novel methods used in this algorithm, namely Windowed Mean Canceled Multiplication and Preceding and Following Acceleration Difference, are introduced. Field experiments are conducted and the results of the proposed algorithm are compared with those of algorithms used in two state-of-the-art sport performance measurement devices. Results demonstrate that the proposed jump detection algorithm comprehensively outperforms these commercial algorithms.

Algorithms for frequency jump detection

The detection of jumps in a frequency record is a challenging problem by either visual or mathematical means. The former takes considerable experience and judgment, and is therefore quite subjective, but has the advantage of providing insight into device behaviour. The latter is more impartial and consistent, and can be automated. In combination, mathematical jump detection can be applied for automatic clock testing and monitoring. If a jump is detected, the record can then be inspected visually before deciding on the action required. This paper describes frequency jump detection algorithms that are included in a program for frequency stability analysis.

Novel Adaptive Generalized Likelihood Ratio Detector with Application to Maneuvering Target Tracking

A novel adaptive jump-detection algorithm is introduced for scenarios involving abrupt changes in the inputs to linear systems, such as those that might occur in tracking maneuvering targets. Improving upon the standard generalized likelihood ratio (GLR) detector, presented over two decades ago, the new algorithm is characterized by increased robustness with respect to uncertainties in the system input, which frequently arise in the context of target tracking applications. The performance of the new algorithm is demonstrated in an endgame scenario involving an interceptor missile and a maneuerable tactical ballistic missile. An extensive Monte Carlo simulation study is used to demonstrate the superiority of the method over the conventional GLR method in terms of its much smaller observed false alarm probability, which actually agrees with the theoretical value. The new algorithm also facilitates a correct isolation of the abrupt change, is consistent in the usual statistical sense, and generally proves more reliable.

A Local Polynomial Jump-Detection Algorithm in Nonparametric Regression

We suggest a one-dimensional jump-detection algorithm based on local polynomial fitting for jumps in regression functions (zero-order jumps) or jumps in derivatives (first-order or higherorder jumps). If jumps exist in the mth-order derivative of the underlying regression function, then an (m + 1). Order polynomial is fitted in a neighborhood of each design point. We then characterize the jump information in the coefficients of the highest-order terms of the fitted polynomials and suggest an algorithm for jump detection. This method is introduced briefly for the general setup and then presented in detail for zero-order and first-order jumps. Several simulation examples are discussed. We apply this method to the Bombay (India) sea-level pressure data.

Local Polynomial Jump-Detection Algorithm in Nonparametric Regression

We suggest a one-dimensional jump-detection algorithm based on local polynomial fitting for jumps in regression functions (zero-order jumps) or jumps in derivatives (first-order or higherorder jumps). If jumps exist in the mth-order derivative of the underlying regression function, then an (m + 1). Order polynomial is fitted in a neighborhood of each design point. We then characterize the jump information in the coefficients of the highest-order terms of the fitted polynomials and suggest an algorithm for jump detection. This method is introduced briefly for the general setup and then presented in detail for zero-order and first-order jumps. Several simulation examples are discussed. We apply this method to the Bombay (India) sea-level pressure data.

Jump Detection in Regression Surfaces

We consider the problem of locating jumps in regression surfaces. A jump detection algorithm is suggested based on local least squares estimation. This method requires O(Nk) computations, where N is the sample size and k is the window width of the neighborhood. This property makes it possible to handle large data sets. The conditions imposed on the jump location curves, the jump surfaces, and the noise are mild. We demonstrate this method in detail with some numerical examples.

Identification of a Biological System: Transitions Between Molecular Conformations of a Single Transmembrane Channel Protein

Patch-clamp measurements allow to investigate the kinetics of single transport proteins conducting ions across biological membranes. The complex pattern of open and closed intervals is described by a discrete-state continuous-time Markov model. This article shows how to identify the rate constants, the transition probabilities from one conformation to another: A jump detection algorithm reconstructs the noise-free time series of the electrical current through the channel and creates dwell-time histograms. By means of a novel equation for missed-events correction, the rate constants are determined from the time constants found in the dwell-time histograms.

A nonlinear filter algorithm for the detection of jumps in patch-clamp data.

This paper presents a new algorithm for the detection of channel openings and closures from noisy current signals, especially for the correct generation and interpretation of open-time and closed-time histograms. The Hinkley detector is a nonlinear off-line jump detection algorithm from the field of fault detection. Here, an improved version, the higher-order Hinkley detector H.O.H.D., is developed. A general description of the sensitivity of a detector is introduced by the time resolution tres. This allows a comparison of the nonlinear detectors with the standard threshold detectors preceded by a low-pass filter for noise suppression. By means of application to simulated and real data, the performance of the detection algorithms is investigated. The higher-order Hinkley detector gave the best results with respect to correct reconstruction of the event length, to a small amount of missed brief events as well as to the ability to achieve short time resolution without pretending false events, especially in the presence of colored noise.

Desgin and comparative study of some sequential jump detection algorithms for digital signals

The purpose of this paper is to analyze the behavior of several jump detection algorithms when applied to the same real data (geophysical signals) and to compare these algorithms from different points of view: complexity, efficiency, robustness, and ability to characterize the detected jumps. Three types of algorithms are investigated: "filtered derivatives" detectors, cumulative sum (cusum) tests, and Willsky's generalized likelihood ratio (GLR) algorithm. A modified version of this last test is elaborated, and a new detector, mixing GLR and cusum tests, is presented.