@spec chi2_inv(float(), pos_integer()) :: float()

Chi-square inverse CDF (quantile).

@spec fde(
  term(),
  [Sidereon.GNSS.Positioning.observation()],
  Sidereon.GNSS.Positioning.epoch(),
  keyword()
) ::
  {:ok,
   %{
     solution: Sidereon.GNSS.Positioning.Solution.t(),
     excluded: [{String.t(), :raim_excluded}],
     iterations: non_neg_integer()
   }}
  | {:error, {:fault_unresolved, float()}}
  | {:error, term()}

Fault detection and exclusion: solve, run RAIM, exclude the worst satellite, and repeat until the measurement set is self-consistent or the exclusion budget is exhausted.

Malformed FDE options are returned as tagged errors, including {:invalid_option, :p_fa}, {:invalid_option, :weights}, and {:invalid_option, :max_iterations}.

@spec pseudorange_variance(
  number(),
  keyword()
) :: float() | {:error, :invalid_elevation | :missing_cn0}

Pseudorange measurement variance (m^2) from satellite elevation.

Returns a float, {:error, :invalid_elevation} for elevations at or below the horizon, or {:error, :missing_cn0} when model: :elevation_cn0 is selected without :cn0.

@spec raim(
  Sidereon.GNSS.Positioning.Solution.t(),
  keyword()
) :: raim_result()

Residual-based RAIM: a chi-square goodness-of-fit test on a positioning solution.

@spec raim_fde_design(
  [map()],
  keyword()
) :: {:ok, map()} | {:error, term()}

Standalone range RAIM/FDE over a caller-supplied linearized measurement set, independent of any full positioning solve.

Each row of rows is a map describing one linearized range measurement:

• :id - stable measurement identifier (e.g. a satellite token "G01")
• :residual_m - observed-minus-computed range residual, metres
• :design_row - the measurement's row of the design matrix (a list of the partials of the predicted range with respect to each estimated state parameter); every row must carry the same length
• :weight - inverse-variance weight 1 / sigma^2, strictly positive

Options:

• :p_fa - false-alarm probability for the global chi-square test (default 0.001)
• :max_exclusions - maximum measurements the exclusion loop may remove (default: the row count)
• :min_redundancy - minimum redundancy an exclusion must leave behind (default 1)

Returns {:ok, result} where result carries the protected :state_correction, :state_covariance, the :global_test chi-square map, the :excluded ids, per-measurement :diagnostics, and the exclusion :iterations; or {:error, reason} for a malformed or rank-deficient input.

@spec robust_fde(
  term(),
  [Sidereon.GNSS.Positioning.observation()],
  Sidereon.GNSS.Positioning.epoch(),
  keyword()
) ::
  {:ok,
   %{
     solution: Sidereon.GNSS.Positioning.Solution.t(),
     excluded: [{String.t(), :raim_excluded}],
     iterations: non_neg_integer()
   }}
  | {:error, term()}

Core robust-reweighted SPP under the RAIM/FDE exclusion loop.

@spec sigmas(
  [weight_entry()],
  keyword()
) :: %{required(String.t()) => float()}

Build a satellite => sigma_m map for a list of weight entries.

@spec weight_vector(
  [weight_entry()],
  keyword()
) :: %{required(String.t()) => float()}

Build a satellite => inverse_variance_weight map for a list of weight entries.