Pointing Error Analysis Tool |

The The Pointing Error Analysis Tool is a set of Matlab functions that are used to evaluate the Standard Pointing Error Metrics from time-domain and frequency-domain data. Other functions aid in evaluating the contribution of sensor noise on the pointing error metrics. The Pointing Error Analysis Tool has the following features and benefits - Quickly analyze time-domain, frequency-domain, and stochastic (random) pointing error.
- Determine the relative contribution of various disturbance sources.
- Determine which are the most offending disturbances in a pointing system.
- Evaluate the pointing error metrics for a variety of window times without having to recompute everything.
## Pointing Error Definitions
## Concepts from OpticsThe optical quality of an imaging system is limited partly by the quality of its optics. The point spread function (PSF) describes how a column of light is spread out after passing through the optics. The PSF is shown in the first figure below. The bright central region is called the Airy Disc. A cross section of the Airy Disc is shown in the second figure. This function can be approximated as a Gaussian G(x, σ
## Standard Pointing Error MetricsThe pointing error metrics are called the In the frequency domain, the pointing error metrics are given by the following expressions,
where S(ω) is the power spectral density of the attitude error, and T
The expressions for the pointing error metrics may appear to be difficult to evaluate, but a very simple computational method is described in the next section. In the case of a few sinusoidal disturbances, these metrics are particularly easy to evaluate. An example for the case of reaction wheel imbalance is given in the references (see the Further Reading page of this article). ## Computational Techniques for Evaluating the Pointing Error MetricsThe pointing error metrics are evaluated quickly and accurately from time-domain data by using fast computational algorithms that utilize the Discrete Fourier Transform to convert the time-domain data to the frequency domain. The frequency domain equations for the pointing error metrics are then evaluated by summing a weighted mean square response. A different weighting is used for each metric. Individual contributions to the pointing error metrics can be determined to determine the most offending disturbance sources and to determine sensitivities to disturbances. Frequency-domain data can also be obtained from the frequency response of a transfer function. It is particularly fast and easy to evaluate the pointing error metrics for reaction wheel or CMG disturbances. For stochastic (random) disturbances, one of two paths can be taken to evaluate the pointing error metrics. One path is to simulate random inputs in a time-domain simulation, and then evaluate the metrics using the time-domain response. The other path is to augment the frequency-domain plant model with weighting functions. These weighting functions are linear transfer functions that approximate the weighting functions in the pointing error metrics. The covariance (or variance) at the output of the transfer functions is then evaluated by using standard methods available in Matlab. This path is often the fastest. ## Why Not Use the Peak Stability or Other Metric?The peak stability matric and other metrics are very conservative, inconsistent, and they do not have any statistical meaning in connection with performance of an optical instrument. They also have no equivalence in the time domain and in the frequency domain. Furthermore, evaluation of the the peak stability metric and other metrics is computationally burdensome. See the discussion "What is the peak stability metric and why is it conservative?" in the FAQ for a detailed discussion. ## Pointing Error AnalysisThe figure below illustrates a flexible-body system with various inputs and outputs, including disturbances, actuator inputs, sensor outputs, and a payload line of sight. Particular nodes in the Nastran model correspond to the locations of the actuators, sensors, and payload. There can be other nodes of interest that define additional inputs and outputs, such as the locations of thrusters, accelerometers, the tip of a boom, or the end of a solar array. The reduced-order Nastran model shown in the figure is obtained from the Structural Model Reduction tool. The closed-loop response is evaluated by using the CSI Analysis tool, and the pointing errors are evaluated by the Pointing Error Analysis tool. ## Further ReadingThe development and application of the Standard Pointing Error Metrics can be found in the following documents and references therein. The Johns Hopkins University Applied Physics Laboratory, STEREO Guidance and Control System Specification, NASA Contract NAS5-97271, FSCM No. 88898, Drawing No. 7381-9310, February 2003. "Pointing Error Definitions, Metrics, and Algorithms", Paper No. AAS 03-559, AAS/AIAA Astrodynamics Specialists Conference, Big Sky, MT, 3–7 August 2003. In Advances in the Astronautical Sciences, Vol. 116, Part II, pp. 901–920, 2003. [CD, Book] "Definitions, Metrics, and Algorithms for Displacement, Jitter, and Stability", Flight Mechanics Symposium, NASA Goddard Space Flight Center, NASA/CP-2003-212246, 28–30 October 2003. [CD] |