## Hybrid Estimation

The problem of hybrid estimation involves estimating both continuous state and discrete state of a hybrid system. This problem proves to be challenging: if we do not know the discrete state transition history, the evolution of a hybrid system involves exponentially increasing computational complexity, which is often referred to as a growing hypothesis tree. This fact makes "optimal estimation" of the hybrid system computationally prohibitive. Therefore, a primary issue that most hybrid estimation algorithms are faced with is how to reduce the number of the hypotheses to an acceptable amount.

There are two commonly used techniques to manage the growing number of the hypotheses: merging and pruning. In the merging approach, the hypothesis tree is approximated repeatedly by a simpler tree with each new branch lumps together similar branches of the original tree. The representative algorithms are the Generalized Pseudo Bayesian algorithm of order n (GBPn), the Interacting Multiple Model (IMM) algorithm and their variants, which treat the model of the discrete state transitions as a homogeneous Markov process with constant discrete state transition probabilities. The pruning technique reduces the number of hypotheses by eliminating the branches of the hypothesis tree with low probabilities.

### State-Dependent-Transition Hybrid Estimation (SDTHE) Algorithm

Based on the IMM approach, we develop a hybrid estimation called the **State-Dependent-Transition Hybrid Estimation (SDTHE)** algorithm. Because the SDTHE algorithm utilizes the special structure of the SLHS (namely, the linear Gaussian continuous state dynamics within each mode, and the mode transitions described by polytopic guards), it is more computationally efficient than other hybrid estimation algorithms, such as the particle filters. read more

### Aircraft Tracking in Air Traffic Control

Air Traffic Control (ATC) is responsible for managing the flow of aircraft operating within the National Airspace System (NAS). The Federal Aviation Agency (FAA) has projected that demands at the nation''s major airports may soon exceed capacity. Hence, the flow of traffic around airports is a major bottleneck to air traffic. Various researchers have investigated several concepts to enhance future Air Traffic Management. These include conflict detection and resolution, pilot intent inference, accurate aircraft trajectory predictions, and aircraft time-of-arrival predictions. A key requirement for implementation of the above concepts is an accurate knowledge of aircraft positions, velocities and flight modes. Furthermore, an accurate modeling of aircraft flight mode transitions is required for conformance monitoring under future ATM operations, such as Airborne spacing, trajectory based operations, and super density operations, under the Next Generation Air Transportation System (NextGen). read more

### Conformance Monitoring in Air Traffic Control

Conformance monitoring in Air Traffic control is an approach that is used to monitor and detect any deviations of an aircraft's flight path from the assigned flight plan, that might compromise safety or efficiency. Currently, the task of conformance monitoring is performed by air traffic controllers based on comparisons between observed aircraft positions from radar surveillance and the expected aircraft positions based on clearances or flight plans. If the differences between the observed and expected positions exceeds some allowable deviations, non-conformance can be determined. Due to limited resources available to the air traffic controllers, this method does not give good performance. The conformance monitoring task would be even more difficult in future ATC operations. Under the NextGen, a larger number of aircraft are expected to operate with reduced separation thresholds between aircraft within a given airspace. The new concept of operation also allows aircraft the flexibility of changing flight routes (or flight plans) in response to changing conditions. Furthermore, different aircraft would have very different navigation capabilities due to different levels of equipping. Under such complex scenarios in future ATC operations, it would be important to have a conformance monitoring tool for monitoring the aircraft movements. read more

### Unknown Fault Input Hybrid Estimation (UFIHE)

For the purpose of Fault Detection and Isolation (FDI), we propose a robust hybrid estimation algorithm for a class of hybrid system with unknown fault input. The algorithm is named as the **Unknown Fault Input Hybrid Estimation (UFIHE)** algorithm. Normally, an estimation algorithm for a hybrid system with unknown fault inputs typically has more discrete states than the nominal system, because the resulting hybrid system has extra discrete states representing individual faults. read more

### Intent Inference Algorithm

We are developing robust **intent inference algorithms** based on hybrid system modeling and estimation. In many inference algorithms, it is necessary to consider all past measurement history to carry out the intent inference. As a result, the computational cost of the inference algorithms often grows exponentially with time. Our intent inference is based on the hybrid estimation algorithm which uses the past measurements *recursively*. read more

### Fault Detection and Isolation (FDI)

Apart from ATC operations and Air Traffic Management systems, many practical systems, such as embedded systems, multi-agent systems, and cooperative systems, are also best described by hybrid systems. The continuous dynamics of the hybrid systems could model the physical system dynamics and the discrete dynamics could represent the logical decision components. To enhance the reliability or safety of these systems, fault detection methods have been used to determine the occurrences of failures so that appropriate remedy actions can be taken. read more

### Event Triggered Filtering

Most of the existing state estimation problems have been formulated based on time-based sampling methods, where measurements are taken at synchronous or asynchronous time intervals. Another way of sampling is "event"-based sampling in which measurements are generated only when pre-defined events happen. read more

### Estimated Time of Arrival (ETA) Prediction

As the National Airspace System (NAS) has been facing the pressure of steadily increasing air travel demand, air traffic congestion and flight delays around airports have become major issues in air traffic management. To mitigate such issues, a new framework known as the Next Generation Air Transportation System (NextGen) has been proposed. Under NextGen, a key requirement for safe and efficient air traffic flow management in terminal airspace is accurate knowledge of the aircraft’s states (e.g., position, velocity, and flight mode) and accurate prediction of the aircraft’s estimated time of arrival (ETA). Using the accurate state information of the aircraft, more efficient airborne spacing with reduced separation thresholds can be achieved, and thereby, air traffic flow near an airport can be effectively managed within its capacity. In addition, the accurate prediction of ETA can play an important role in enhancing the efficiency of airport surface operations, since it can reduce unnecessary delays in taxi times caused by inaccurate ETA of arrival aircraft. read more

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