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docs: align markdown tables
Apply markdown-table-formatter's layout to the tables this tier adds or edits, as suggested by MegaLinter. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Q53m7MZDmHwocmKbhhd2o5
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‎README.md‎

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## Documentation
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| Category | Description |
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|--------------------------------------------------------------------|----------------------------------------------------------------------|
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| [Analysis](doc/analysis/README.md) | FFT, Real-Input FFT (RFFT), Power Spectral Density, DCT, Discrete Wavelet Transform (Haar/Daubechies), Window Functions, Signal Detectors, Convolution & Correlation, Goertzel Algorithm, Decibels, Hilbert Transform / Analytic Signal, Mel Filterbank / MFCC |
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| [Control Analysis](doc/control_analysis/README.md) | Frequency Response, Root Locus, Controllability/Observability Matrices & Gramians, Continuous-to-Discrete, Transfer Function ↔ State Space |
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| [Controllers](doc/controllers/README.md) | Bang-Bang/Hysteresis, Deadbeat Control, PID, LQR, LQI (Integral/Servo State Feedback), MPC, Saturation, Rate Limiter, Slew-Limited Saturation, Feedforward/2-DOF, Gain-Scheduled Controller, Lead-Lag Compensator, Luenberger Observer, Friction Compensation (Coulomb + Viscous + Stribeck) |
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| [Estimators](doc/estimators/README.md) | Linear Regression, Polynomial Fitting, Total Least Squares, Yule-Walker (offline), Recursive Least Squares, Recursive Instrumental Variables, LMS / NLMS Adaptive Filter (online), Consistency Metrics / NEES / NIS, Incremental QR Least Squares (rank-revealing) |
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| [Filters](doc/filters/README.md) | Kalman, Extended Kalman, Unscented Kalman, Square-Root Kalman, Alpha-Beta/Alpha-Beta-Gamma, FIR, IIR, Exponential Moving Average, Moving Average, Complementary, Median Filter, CIC (Cascaded Integrator-Comb), Notch/Comb Filter, Savitzky-Golay Filter, Biquad/Second-Order-Section Cascade, IIR Filter Design (Butterworth/Chebyshev-I + Bilinear Transform), Madgwick/Mahony AHRS |
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| [Optimization](doc/optimization/README.md) | Gradient Descent, SGD / Adam Step Optimisers |
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| [Regularization](doc/regularization/README.md) | L1 (Lasso), L2 (Ridge) |
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| [Math](doc/math/README.md) | CORDIC, Quaternion, MatrixNorms, Step Response Metrics, MatrixExponential, Angle Utilities, Tridiagonal (Thomas) Solver, Cubic Spline Interpolation, SE(3) Transform (Twists, Wrenches, Exp/Log) |
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| [Motion Profiles](doc/motion_profiles/README.md) | Polynomial (Cubic/Quintic) Point-to-Point Profile, Trapezoidal (LSPB) Profile, S-Curve (Jerk-Limited) Profile |
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| Category | Description |
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|--------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
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| [Analysis](doc/analysis/README.md) | FFT, Real-Input FFT (RFFT), Power Spectral Density, DCT, Discrete Wavelet Transform (Haar/Daubechies), Window Functions, Signal Detectors, Convolution & Correlation, Goertzel Algorithm, Decibels, Hilbert Transform / Analytic Signal, Mel Filterbank / MFCC |
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| [Control Analysis](doc/control_analysis/README.md) | Frequency Response, Root Locus, Controllability/Observability Matrices & Gramians, Continuous-to-Discrete, Transfer Function ↔ State Space |
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| [Controllers](doc/controllers/README.md) | Bang-Bang/Hysteresis, Deadbeat Control, PID, LQR, LQI (Integral/Servo State Feedback), MPC, Saturation, Rate Limiter, Slew-Limited Saturation, Feedforward/2-DOF, Gain-Scheduled Controller, Lead-Lag Compensator, Luenberger Observer, Friction Compensation (Coulomb + Viscous + Stribeck) |
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| [Estimators](doc/estimators/README.md) | Linear Regression, Polynomial Fitting, Total Least Squares, Yule-Walker (offline), Recursive Least Squares, Recursive Instrumental Variables, LMS / NLMS Adaptive Filter (online), Consistency Metrics / NEES / NIS, Incremental QR Least Squares (rank-revealing) |
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| [Filters](doc/filters/README.md) | Kalman, Extended Kalman, Unscented Kalman, Square-Root Kalman, Alpha-Beta/Alpha-Beta-Gamma, FIR, IIR, Exponential Moving Average, Moving Average, Complementary, Median Filter, CIC (Cascaded Integrator-Comb), Notch/Comb Filter, Savitzky-Golay Filter, Biquad/Second-Order-Section Cascade, IIR Filter Design (Butterworth/Chebyshev-I + Bilinear Transform), Madgwick/Mahony AHRS |
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| [Optimization](doc/optimization/README.md) | Gradient Descent, SGD / Adam Step Optimisers |
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| [Regularization](doc/regularization/README.md) | L1 (Lasso), L2 (Ridge) |
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| [Math](doc/math/README.md) | CORDIC, Quaternion, MatrixNorms, Step Response Metrics, MatrixExponential, Angle Utilities, Tridiagonal (Thomas) Solver, Cubic Spline Interpolation, SE(3) Transform (Twists, Wrenches, Exp/Log) |
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| [Motion Profiles](doc/motion_profiles/README.md) | Polynomial (Cubic/Quintic) Point-to-Point Profile, Trapezoidal (LSPB) Profile, S-Curve (Jerk-Limited) Profile |
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| [Solvers](doc/solvers/README.md) | Gaussian Elimination, Levinson-Durbin, Durand-Kerner, Cholesky, DARE, Runge-Kutta ODE Integrators (RK4 + Dormand-Prince), Spectral Radius & Discrete Stability Margin, QR Decomposition (Householder / Givens), LU Decomposition with Partial Pivoting, Singular Value Decomposition (Golub-Kahan), Symplectic Integrators (Semi-Implicit Euler, Velocity Verlet), Damped Pseudo-Inverse + Null-Space Projector |
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| [Nonlinear Control](doc/nonlinear_control/README.md) | Feedback Linearization, Backstepping Control, Model Reference Adaptive Control (MRAC) |
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| [Robust Control](doc/robust_control/README.md) | Active Disturbance Rejection Control (ADRC + ESO), Sliding Mode Control (SMC), Disturbance Observer (DOB), H∞ State-Feedback Control |
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| [Performance Optimization](doc/performance-optimization/README.md) | Compiler optimizations |
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| [Nonlinear Control](doc/nonlinear_control/README.md) | Feedback Linearization, Backstepping Control, Model Reference Adaptive Control (MRAC) |
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| [Robust Control](doc/robust_control/README.md) | Active Disturbance Rejection Control (ADRC + ESO), Sliding Mode Control (SMC), Disturbance Observer (DOB), H∞ State-Feedback Control |
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| [Performance Optimization](doc/performance-optimization/README.md) | Compiler optimizations |
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Each category page lists its algorithms with a brief description and links to the detailed documentation.
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‎ROADMAP.md‎

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## Master list (by priority)
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| # | Component | Target module | Difficulty |
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|----|------------------------------------------------------|-------------------------|------------|
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| 64 | Levenberg–Marquardt (retraction, pluggable damping) | `optimization` | ★★★☆☆ |
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| 65 | Dense convex QP (Goldfarb–Idnani dual active set) | `solvers` | ★★★★☆ |
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| # | Component | Target module | Difficulty |
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|----|-----------------------------------------------------|----------------|------------|
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| 64 | Levenberg–Marquardt (retraction, pluggable damping) | `optimization` | ★★★☆☆ |
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| 65 | Dense convex QP (Goldfarb–Idnani dual active set) | `solvers` | ★★★★☆ |
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Items 53–65 are the generic building blocks of robotics-toolbox-cpp's roadmap (referenced there as
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NT53–NT65); each also serves non-robotics consumers (motor control, navigation, calibration). All are

‎doc/estimators/README.md‎

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## Offline Estimators (Batch)
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| Algorithm | Description |
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|--------------------------------------------------------|---------------------------------------------------------------------------|
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| [Linear Regression](LinearRegression.md) | Ordinary least-squares regression using the normal equation |
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| [Polynomial Fitting](PolynomialFitting.md) | Degree-d polynomial fit via Vandermonde normal equations |
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| [Total Least Squares](TotalLeastSquares.md) | Errors-in-variables fit (noisy regressors) via the SVD of `[A | b]` |
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| [Yule-Walker](YuleWalker.md) | Autoregressive model parameter estimation via the Yule-Walker equations |
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| [Expectation-Maximization](ExpectationMaximization.md) | EM algorithm for Kalman filter parameter identification (Shumway-Stoffer) |
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| Algorithm | Description |
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|--------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------|
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| [Linear Regression](LinearRegression.md) | Ordinary least-squares regression using the normal equation |
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| [Polynomial Fitting](PolynomialFitting.md) | Degree-d polynomial fit via Vandermonde normal equations |
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| [Total Least Squares](TotalLeastSquares.md) | Errors-in-variables fit (noisy regressors) via the SVD of `[A | b]` |
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| [Yule-Walker](YuleWalker.md) | Autoregressive model parameter estimation via the Yule-Walker equations |
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| [Expectation-Maximization](ExpectationMaximization.md) | EM algorithm for Kalman filter parameter identification (Shumway-Stoffer) |
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| [Incremental QR Least Squares](IncrementalQrLeastSquares.md) | Streaming Givens QR in fixed memory with a rank-revealing SVD solve (minimum-norm, identifiable combinations) |
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## Online Estimators (Streaming)

‎doc/math/CubicSpline.md‎

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### End conditions
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| Condition | First row | Last row |
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|-----------|-----------|----------|
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| Condition | First row | Last row |
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|-------------------------------------------------|--------------------------------------------|----------------------------------------------------------------|
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| **Clamped** (end slopes $\sigma_0$, $\sigma_1$) | $2h_0 M_0 + h_0 M_1 = 6\,(s_0 - \sigma_0)$ | $h_{K-2} M_{K-2} + 2h_{K-2} M_{K-1} = 6\,(\sigma_1 - s_{K-2})$ |
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| **Natural** | $M_0 = 0$ | $M_{K-1} = 0$ |
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| **Natural** | $M_0 = 0$ | $M_{K-1} = 0$ |
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Clamping fixes the end slopes and leaves the end second derivatives free; natural ends do the reverse. Default slopes are zero.
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## Complexity Analysis
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| Operation | Time | Space | Notes |
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|-----------|------|-------|-------|
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| Factorization | $O(K)$ | three bands | Once per fit, shared by all channels |
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| Fit | $O(D\,K)$ | $K_{\max}(2 + 2D)$ scalars | $D$ channels, each one right-hand side build and one solve of $O(K)$; no iteration |
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| Evaluate | $O(\log K + D)$ | $O(1)$ | Binary search, then three Horner polynomials per channel |
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| Operation | Time | Space | Notes |
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|---------------|-----------------|----------------------------|------------------------------------------------------------------------------------|
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| Factorization | $O(K)$ | three bands | Once per fit, shared by all channels |
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| Fit | $O(D\,K)$ | $K_{\max}(2 + 2D)$ scalars | $D$ channels, each one right-hand side build and one solve of $O(K)$; no iteration |
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| Evaluate | $O(\log K + D)$ | $O(1)$ | Binary search, then three Horner polynomials per channel |
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Storage holds the knots, their reciprocal spans, the values and the second derivatives: $K_{\max}(2 + 2D)$ scalars, where $K_{\max}$ is the compile-time capacity, plus the three bands of the solver. All of it is bounded and on the stack or inside the object; no heap.
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$$\begin{pmatrix} 2 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 2 \end{pmatrix} M = \begin{pmatrix} 6 \\ -12 \\ 6 \end{pmatrix}$$
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|-----|-------------|--------|---------------|------------|
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| 0 | $2$ | $1/2$ | $3$ | $3 + 3 = 6$ |
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| 1 | $4 - 1/2 = 7/2$ | $2/7$ | $-30/7$ | $-30/7 - 12/7 = -6$ |
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| 2 | $2 - 2/7 = 12/7$ | unused | $6$ | $6$ |
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| $k$ | Pivot $p_k$ | $c'_k$ | Forward $y_k$ | Back $M_k$ |
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|-----|------------------|--------|---------------|---------------------|
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| 0 | $2$ | $1/2$ | $3$ | $3 + 3 = 6$ |
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| 1 | $4 - 1/2 = 7/2$ | $2/7$ | $-30/7$ | $-30/7 - 12/7 = -6$ |
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| 2 | $2 - 2/7 = 12/7$ | unused | $6$ | $6$ |
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So $M = (6, -6, 6)$. Interval 0 has $\beta_0 = 1 - (12 - 6)/6 = 0$ and $d_0 = -2$, giving $y(\tau) = 3\tau^2 - 2\tau^3$. Hence $y(0.5) = 0.75 - 0.25 = 0.5$, $y'(0.5) = 3 - 1.5 = 1.5$ and $y''(0.5) = 0$. The curve leaves and enters every knot flat, like a smooth step.
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## Connections to Other Algorithms
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| Algorithm | Relationship |
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| [Tridiagonal Solver](TridiagonalSolver.md) | Solves the second-derivative system; its factorization is reused across channels |
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| Algorithm | Relationship |
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|---------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------|
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| [Tridiagonal Solver](TridiagonalSolver.md) | Solves the second-derivative system; its factorization is reused across channels |
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| [Polynomial Profile](../motion_profiles/PolynomialProfile.md) | The two-knot clamped case is the same cubic Hermite polynomial; the spline generalizes it to many knots with $C^2$ joins |
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| Polynomial fitting | Least-squares fit instead of interpolation |
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| Polynomial fitting | Least-squares fit instead of interpolation |
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## References & Further Reading
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