Guidance Computer Noise Error Model

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Description

The Guidance Computer Noise Error Model introduces controlled noise perturbations into the navigation software modules hosted on a Guidance Computer. This model simulates the effects of sensor noise, quantisation errors, and other stochastic disturbances that affect real navigation systems. By injecting noise into the navigation solution, the model enables analysis of guidance and control system robustness, error budget allocation, and pointing performance under realistic conditions. The model supports both deterministic bias injection and randomised noise generation for Monte Carlo analysis.

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Example Use Cases

• Pointing Accuracy Analysis: Evaluate spacecraft pointing performance under various noise conditions to verify mission requirements.
• Monte Carlo Simulation: Inject randomized noise across multiple simulation runs to characterize statistical pointing error distributions.
• Control System Robustness: Test attitude control algorithm stability and performance margins in the presence of navigation noise.
• Error Budget Verification: Validate that the overall pointing error budget accounts for navigation system noise contributions.

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Module Implementation

The Guidance Computer Noise Error Model is a Universe Model that attaches to a Guidance Computer component. It discovers all Simple Navigation Software modules hosted on the parent computer and applies a configurable noise value to each at every simulation update.

Navigation Software Discovery

During initialization, the model queries the parent guidance computer for all attached Simple Navigation Software instances:

$$\mathcal{S}=\{s_i:s_i\in \text{behaviours}(\text{GuidanceComputer}),s_i\in \text{SimpleNavigationSoftware}\}$$

The discovered software modules are stored for noise injection during simulation updates.

Noise Generation

The model supports two noise generation modes controlled by the Randomize flag:

Deterministic Mode

When Randomize = false, the noise value is constant and equal to the configured noise factor:

$$n=N_f$$

where $N_f$ is the NoiseFactor parameter. This mode is useful for bias analysis and reproducible testing.

Randomised Mode

When Randomize = true, the noise value is drawn from a uniform distribution:

$$n\sim \mathcal{U}(-N_f,N_f)$$

The random value is computed as:

$$n=2N_f\cdot \xi -N_f$$

where $\xi \sim \mathcal{U}(0,1)$ is a uniformly distributed random number.

Noise Injection

At each simulation time step, the computed noise value is applied to all discovered navigation software modules:

$$\forall s_i\in \mathcal{S}:s_i.\text{NoiseAddition}=n$$

The NoiseAddition parameter in each navigation software module is used internally to perturb the navigation solution, typically affecting the attitude estimate or pointing direction.

Random Number Generator

The model maintains an internal random number generator (RNG) that can be seeded for reproducibility:

$$\text{RNG}=\text{Random}(\text{seed})$$

Setting a specific seed ensures identical noise sequences across simulation runs, which is essential for:

• Debugging and regression testing
• Reproducible Monte Carlo analysis
• Comparative studies between different configurations

Update Sequence

At each simulation time step, the model performs the following operations:

1. Generate Noise Value: Compute the noise based on the selected mode (deterministic or randomized).
2. Apply to Navigation Software: Iterate through all discovered navigation software modules and set their noise addition parameter.

Statistical Properties

For randomized mode, the noise has the following statistical properties:

Property	Value
Distribution	Uniform
Mean	$\mu =0$
Variance	${\sigma }^2=\frac{N_f^2}{3}$
Standard Deviation	$\sigma =\frac{N_f}{\sqrt{3}}$
Range	$[-N_f,N_f]$

The uniform distribution provides bounded noise, ensuring that extreme values do not exceed the configured noise factor. For applications requiring Gaussian noise characteristics, the noise factor can be scaled appropriately:

$$N_f=\sqrt{3}\cdot {\sigma }_{\text{desired}}$$

Effect on Navigation

The noise addition affects the navigation software’s attitude or pointing estimate. For a true attitude $\mathbf{\sigma }$ and noise $n$, the perturbed estimate becomes:

$${\mathbf{\sigma }}_{\text{est}}=\mathbf{\sigma }+n\cdot \hat{\mathbf{e}}$$

where $\hat{\mathbf{e}}$ represents the error direction determined by the specific navigation software implementation.

Configuration Parameters

Parameter	Units	Default	Description
NoiseFactor	-	0.001	Maximum magnitude of injected noise
Randomize	-	false	Enable randomised noise generation

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Assumptions/Limitations

• The model discovers navigation software modules only during initialization; software added after creation is not automatically included.
• All discovered navigation software modules receive the same noise value at each time step; independent noise per module is not supported.
• The noise distribution is uniform; Gaussian or other distributions require external implementation or post-processing.
• The noise value is scalar; vector-valued or attitude-specific noise injection is handled by the navigation software itself.
• The model does not account for time-correlated noise; each sample is independent (white noise assumption).
• In deterministic mode, the noise is constant over the entire simulation; time-varying bias requires randomized mode.
• The noise factor is unitless; its physical interpretation depends on the navigation software implementation.
• The random seed is not automatically varied between Monte Carlo runs; explicit seed management is required.
• The model does not validate that the noise factor is appropriate for the navigation accuracy being simulated.
• Power spectral density and bandwidth-limited noise are not directly modelled.