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State Estimation
 

Control of spacecraft and other systems requires reliable real-time estimates of system state. Unfortunately, the complete state is not always observable. State Estimation takes all the telemetry seen so far and uses it to determine the underlying behavior of the system at any point in time. It includes fault detection and isolation and continuous system parameter estimation.

Benefit
The Exploration Vision includes many complex vehicles and systems that can benefit from this technology. This includes habitats, which require estimates of the state of their life-support and other systems, and reusable launch vehicles which can greatly benefit from state estimation techniques that can track gradual degradation of systems and components to not only enable intelligent control and detect faults, but also to predict future faults to make maintenance more efficient and reduce vehicle turnaround times.

Research Overview
There are two parts to state estimation: modeling and algorithms. The overall approach is to use a model to predict the behavior of the system in a particular state, and then compare that behavior with the actual telemetry from the system to determine which state or states is the most likely to produce the observed system behavior. Complex systems will benefit from state estimation.

Right: Complex systems will benefit from state estimation.

We use differential equations to model the system. A complex system can be thought of as having a number of discrete modes which consist of the possible control regimes the system could be in (for example, a thruster being on or off), plus various faults that could occur (for example, a valve being stuck open). Each of these discrete modes may have a different set of differential equations that govern the continuous behavior of the system (for example, the flow of propellant through a series of pipes and valves to a thruster). We call this a hybrid model.

To maintain an uncertain state estimate over the states of such a model, we use an approach known as Bayesian belief updating. At a high level, the idea is to maintain a probability distribution that represents our belief about the state of the system, given all the telemetry seen so far, and update that distribution whenever new telemetry arrives to reflect the new evidence. Because doing this exactly is intractable for the kinds of hybrid models we are interested in, we approximate it using particle filtering algorithms.

Particle filtering is a Monte Carlo approach to state estimation that is extensively used in signal processing, and more recently in robot localization algorithms such as SLAM. It works by representing the probability distribution over the states of the system as a set of samples, each of which represents a possible state of the complete system. When new telemetry arrives, each sample randomly predicts a possible future state, and is then compared with the observation. Samples which are inconsistent with the observation are discarded, and are replaced at the next step by samples that do predict the observation well.

Spacecraft typically have tightly constrained on-board processing capabilities which can make even approximate state estimation impractical. One attractive feature of particle filters is that they can easily be adapted to scarce computational resources by simply reducing the number of samples, although with a corresponding loss of accuracy in the state estimate. We have developed a number of innovative extensions to the basic particle filtering algorithm specifically to address this issue, including combining traditional approaches to diagnosis with hybrid state estimation to create algorithms that can produce state estimates with relatively low computational requirements when the system is operating nominally, but will use additional resources to refine the state estimate if it becomes particularly uncertain, or if a fault is likely to have occurred.

The technology has been demonstrated on the K-9 rover test bed and has been shown to accurately track the state of the system even in the presence of extremely noisy telemetry data, and can also reliably estimate continuous parameters of the system, even when those parameters are gradual system faults that cannot be directly observed.

Background
State Estimation is the problem of determining the current state of a complex system such as a spacecraft, given the stream of telemetry that has been seen from the system’s sensors so far. In the past, state estimation has mostly been seen as diagnosis—detecting and identifying faults when they occur—but safe and effective autonomous control of systems requires estimating all aspects of system state. In addition, estimating continuous system parameters such as battery charge has also become increasingly important.

State Estimation Caption: State estimation can provide prognostic information.

State estimation is critical for a number of reasons: Accurate state estimates make control much easier, and allow better control actions to be selected. In addition, state estimation is a superset of diagnosis, so faults and undesirable states can be detected to allow remedial actions to be taken. Finally, state estimation can provide prognostic information, identifying components or systems that are likely to fail soon and should be repaired or replaced.

A key aspect of state estimation is that it is rarely certain. There is inevitably some ambiguity in the sensor data received from a system, and it is of great use to have a state estimate that represents this uncertainty explicitly. This is for several reasons: First, a probability distribution representing the uncertainty can summarize all the telemetry received by the state estimator so far, making it easier to keep the state estimate up to date. Secondly, this probabilistic representation is of use in decision making by allowing the effects of planned future actions to be evaluated in states that have low probability but potentially catastrophic outcomes, rather than only in the most likely state. Finally, probabilistic information is of use for prognostics and maintenance, providing information about components that could have failed, or are degraded but not yet faulty.