Aerospace Control Systems

Spacecraft GNC Systems Engineering




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What are the Standard Pointing Error Metrics? PDF Print E-mail

A fundamental problem in the design of a spacecraft is demonstrating to the customer or principal investigator that the pointing accuracy (either attitude control accuracy or pointing knowledge accuracy) is within requirements. Equally important is correctly and unambiguously specifying the requirements for pointing accuracy. Both the pointing error requirements and the means for verification have been a source of contention on many spacecraft projects. The "peak stability metric" is quite often used, but is known to be very conservative, ambiguous, and difficult to evaluate. (See the FAQ "What is the peak stability metric and why is it conservative?".)

The Standard Pointing Error Metrics are called the accuracy metric, displacement metric, jitter metric, stability metric, and the windowed stability metric. These metrics are based on unambiguous mathematical models involving the point spread function of optical instruments, and therefore relate the pointing error directly to instrument performance.

The mean-square pointing error is expressed by exactly equivalent mathematical expressions in the time domain and in the frequency domain. For computational efficiency, the time-domain data is converted to the frequency domain by using the Fast Fourier Transform (FFT). The Standard Pointing Error Metrics are then easily evaluated. The sample rate of the time-domain data has to be only high enough to contain the highest frequency component of attitude error with significant amplitude, which is a natural consequence of a valid time-domain simulation. It is not necessary that the time-domain samples align with the window times associated with the metrics. The Standard Pointing Error Metrics are readily evaluated when the control system is evaluated in the frequency domain.

Further Reading

More detailed information is provided in the section on the Pointing Error Analysis Tool and in the references below.

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]
See the Errata sheet.

"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]
See the Errata sheet.