Formula used
Plate scale: Plate scale = 206265 × pixel pitch ÷ focal length.
Centroid angular error: σθ = σc × plate scale.
Multi-star accuracy: σmulti = σsingle ÷ √Neffective.
Motion smear: θsmear = angular rate × exposure time.
Total RSS error: σtotal = √(σcentroid² + σoptical² + σcatalog² + σcalibration² + σjitter² + σsmear²).
The calculator separates random terms from systematic terms. Random terms improve with frame averaging, while systematic errors normally remain. Roll accuracy receives an additional field geometry penalty because roll is usually less observable than cross-boresight motion.
How to use this calculator
- Select a preset close to your intended star tracker.
- Enter focal length, aperture, sensor resolution, pixel pitch, and spot size.
- Set the usable star count, star geometry, exposure, angular rate, and jitter.
- Open advanced options for noise, catalog, calibration, environment, and filtering inputs.
- Choose a calculation mode and target accuracy, then calculate.
- Review the pass or fail result, warnings, error budget, sensitivity charts, and required hardware values.
Example data
| Preset | Focal length | Pixel pitch | Stars used | Exposure | Typical purpose |
|---|---|---|---|---|---|
| CubeSat | 35–60 mm | 4–7 µm | 5–10 | 50–150 ms | Compact attitude knowledge |
| Wide-field acquisition | 20–40 mm | 5–10 µm | 8–20 | 20–80 ms | Fast lost-in-space recovery |
| Narrow-field precision | 100–250 mm | 3–6 µm | 3–8 | 100–500 ms | Fine pointing knowledge |
| High-accuracy spacecraft | 80–180 mm | 3–5 µm | 8–20 | 80–300 ms | Low-noise attitude estimation |
Understanding star tracker accuracy
A star tracker estimates spacecraft attitude by imaging known stars. Its achievable precision depends on optical scale, centroid quality, star geometry, motion, and calibration. A small plate scale converts subpixel centroid measurements into smaller angular errors.
Longer focal length usually improves angular sampling. However, it reduces field of view and may lower the number of visible stars. Designers must balance accuracy, acquisition reliability, package size, exposure time, and stray-light tolerance.
Centroid precision improves when the star image covers several pixels. Excessive blur spreads signal and lowers effective signal-to-noise ratio. Saturation can also bias a centroid even when the star appears bright.
Spacecraft motion during exposure creates image smear. The calculator converts angular rate into smear distance and an equivalent uncertainty term. Shorter exposures reduce smear but may weaken faint-star signals.
Multiple stars improve attitude accuracy through averaging. Their spatial distribution also matters because clustered stars provide weak roll observability. A broad, balanced pattern usually gives a stronger three-axis solution.
Calibration and installation errors often create an accuracy floor. Focal length, principal point, distortion, sensor alignment, and boresight offsets require careful characterization. Frame averaging cannot reliably remove fixed systematic biases.
Thermal change can alter focus and plate scale. Radiation, background illumination, and stray light can reduce signal quality over time. Environmental margins should therefore be included during early mission design.
The RSS result represents a statistical combination of independent terms. The worst-case result simply adds absolute contributions and is intentionally conservative. Real hardware should be verified with laboratory and on-orbit calibration data.
Frequently asked questions
What is star tracker accuracy?
It is the angular uncertainty of the estimated spacecraft attitude, normally expressed in arcseconds or microradians.
Why is roll accuracy often worse?
Roll depends strongly on star distribution across the field, making it less observable when stars are clustered.
How does focal length affect accuracy?
A longer focal length reduces angular size per pixel, but also narrows the field and may reduce detected stars.
What centroid accuracy is realistic?
Good systems may achieve a small fraction of one pixel, depending on spot shape, SNR, sampling, and calibration.
Does averaging frames always improve results?
Averaging reduces independent random noise, but fixed alignment, distortion, and boresight biases usually remain.
How many stars are needed?
Three non-collinear stars can support attitude determination, while additional well-distributed stars improve robustness and precision.
Why does motion smear matter?
Star energy spreads across pixels during exposure, increasing centroid uncertainty and potentially confusing identification.
What is a good plate scale?
The best value depends on target accuracy, optical blur, detector sampling, field of view, and expected star density.
Can this replace hardware qualification?
No. It supports preliminary design and trade studies, while final performance requires test data and validated calibration models.