Holger M. Jaenisch

Chaos and Fractal Algorithms Applied to Signal Processing and Analysis

Modern signal processing methods strive to maximize signal to noise ratios, even in the presence of severe noise. Frequently, real world data is degraded by under sampling of intrinsic periodicities, or by sampling with unevenly spaced intervals. This results in dropout or missing data, and such data sets are particularly difficul to process using conventional methods. In many cases, one must still extract as much information as possible from a given data set, although the available discrete data is sparse or very noisy. In such cases, we have found the algorithms derived from Chaos and fractal theory to represent a viable alternative to traditional spectral analysis. The data analysis techniques discussed in this work include phase space reconstruction, Poincare projections radius of gyration exponent, artificial insymmetration patterns (AIP), Liapunov spectra, correlation techniques, R/S analysis, K-factor, fractal statistics, maximum entropy method, and wavelets.

Data modeling for predictive behavior hypothesis formation and testing

This paper presents a novel hypothesis analysis tool building on QUEST and DANCER. Unique is the ability to convert cause/effect relationships into analytical equation transfer functions for exploitation. In this the third phase of our work, we derive Data Models for each unique word and its ontological associated unique words. We form a classical control theory transfer function using the associated words as the input vector and the assigned unique word as the output vector. Each transfer function model can be tested against new evidence to yield new output. Additionally, conjectured output can be passed through the inverse model to predict the requisite case observations required to yield the conjectured output. Hypotheses are tested using circumstantial evidence, notional similarity, evidential strength, and plausibility to determine if they are supported or rejected. Examples of solving for evidence links are provided from tool execution.

Image resolution and performance analysis of webcams for ground-based astronomy

We present here a novel concept for achieving real-time super-resolution ground-based imagery for small aperture telescopes. We explore the combination of existing stacking and registration software in conjunction with real-time equation based Data Models. Our research indicates that for anisoplanatic imagery, a real-time video/software enhanced analog to conventional speckle imaging is possible. This paper highlights the technique and theory for creating such a system.

Data modeling for virtual observatory data mining

< 869.47 -3.27 41.37 602.25 10053.48 620.0042> We propose a novel approach for index-tagging Virtual Observatory data files with descriptive statistics enabling rapid data mining and mathematical modeling. This is achieved by calculating at data collection time 6 standard moments as descriptive file tags. Data Change Detection Models are derived from these tags and used to filter databases for similar or dissimilar information such as stellar spectra, photometric data, images, and text. Currently, no consistent or reliable method for searching, collating, and comparing 2-D imagery exists. Traditionally, methods used to address these data problems are disparate and unrelated to text data mining and extraction. We explore the use of mathematical Data Models as a unifying tool set for enabling data mining across all data class domains.

Spatial voting with data modeling for behavior based tracking and discrimination of human from fauna from GMTI radar tracks

We introduce a novel method of using ground track indicators in conjunction with our Spatial Voting (SV) algorithm and data fusing Data Models to distinguish target types from motion signatures alone. We simulate 3 different types of behaviors: rabbit, coyote, and human. We then apply SV to combine individual position reports obtained via radar track indicators into object tracks that are then characterized using the methods shown in this paper. The features obtained from this characterization are then used as input into a Data Model equation classifier or a look-up table classifier to label the track behavior as either rabbit, coyote, or human. Our results and methods show promise and are presented here.

Data models as a general fast framework for converting simulations at all scales into fast real-time approximations

Data Modeling is a process that can convert non-real-time algorithms into functional approximations that can be executed in near real-time as platform independent mathematical equations or information transfer functions. These functional approximations are converted into a form amenable for streaming real-time execution by being converted into pre-calculated look-up table (LUT) form. We present the technique and relevant theory and demonstrate how this method can be applied to high level interactions, system level modeling and component modeling using a common framework. An important benefit of our technique is the ability to predict anomalous parameters from our models.

Human behavior digitization and intent recognition using data modeling

Autonomous and network centric smart cameras for use in homeland security and other human activities monitoring applications require a multi-layer approach for real time image processing. We propose a novel method to achieve behavior digitization and preemptive course of action (COA) analysis by converting temporal and spatial pixel subframes into a form that can be encoded into equation based Data Models. Output from these Data Models is fused with evidence and sensor data in the COA decision cascade, which recommends COAs that yield evidence. Evidence from the decision cascade continues to be amassed until the hypothesized threat forms a strong enough conviction to initiate alert responses and external intercepting events. This paper outlines our proposed methodology and approach.

Enabling unattended data logging and publication by data model change detection and environmental awareness

This paper presents a novel self-initializing algorithm using Change Detection to achieve self-awareness of unusual conditions without a prior modeling assumptions. Deviations from baseline nominal conditions yield a tip-off and the variation off baseline indicates a novelty to be logged for publication. Incremental processing of the data log enables common transients to be ignored and viewed as nominal. In this framework, only second pass novelties invoke enough interest for publication. The mathematical methods for enabling this exploit both classical control theory transfer functions to model the environment and O(3n) Volterra series type polynomials as an innovative change detection method without explicit modeling.

Insect vision based collision avoidance system for Remotely Piloted Aircraft

Remotely Piloted Aircraft (RPA) are designed to operate in many of the same areas as manned aircraft; however, the limited instantaneous field of regard (FOR) that RPA pilots have limits their ability to react quickly to nearby objects. This increases the danger of mid-air collisions and limits the ability of RPAs to operate in environments such as terminals or other high-traffic environments. We present an approach based on insect vision that increases awareness while keeping size, weight, and power consumption at a minimum. Insect eyes are not designed to gather the same level of information that human eyes do. We present a novel Data Model and dynamically updated look-up-table approach to interpret non-imaging direction sensing only detectors observing a higher resolution video image of the aerial field of regard. Our technique is a composite hybrid method combining a small cluster of low resolution cameras multiplexed into a single composite air picture which is re-imaged by an insect eye to provide real-time scene understanding and collision avoidance cues. We provide smart camera application examples from parachute deployment testing and micro unmanned aerial vehicle (UAV) full motion video (FMV).

How to convert Bayesian causal networks into equivalent equation based data models

We present a simple approach for deriving ensembles of training data from notional belief networks. This is accomplished by specifying the belief variable interactions in the form of Bayes expert system or directed graph, where the node conditional and prior probabilities are specified heuristically from data or from subject matter expert (SME) heuristics. The resulting network is then sampled across parameter space and the associated input/output pairs retained for deriving a principal component Data Model using regression techniques. The method is general and the details of the algorithm are presented.