Update readme.md

readme.md

@@ -1,4 +1,4 @@
-### KFS-suite
+## KFS-suite
 
 This is a collection of three Kalman filter and smoother implementations in Matlab:
 1) A linear Kalman filter and Rauch-Tung-Striebel smoother
@@ -12,31 +12,36 @@ All three filters/smoothers can correctly treat the following:
 - state constraints (a simple projection-based approach is implemented).
 
 All three filters/smoothers return various quantities that might be of interest for further diagnostics or analyses.
-In particular, all three functions return the innovation signals, and the two linear filters return the negative log data likelihood, also known as the *energy*.
-Both innovation and energy can be used as optimization targets for *estimating any of the state-space model parameters*, such as the noise covariances.
+In particular, all three functions return the innovation signals, and the two linear filters return the negative log data likelihood, also known as the **energy**.
+
+Both innovation and energy can be used as optimization targets for **estimating any of the state-space model parameters**, such as the noise covariances.
 (Some of the tests/demo cases show how to do this.)
-Various tests and demos are included to *verify the correctness* of various aspects of the implementation, and to showcase its utility.
-Significant effort has been invested into ensuring the *numerical robustness* and accuracy of the implementation, whereas execution speed was *not* a major concern.
-As a rather unusual feature, the two linear filters/smoothers implement the *sample weighting* approach described in Petersen (2022). 
+
+Various tests and demos are included to **verify the correctness** of various aspects of the implementation, and to showcase its utility.
+Significant effort has been invested into ensuring the **numerical robustness** and accuracy of the implementation, whereas execution speed was *not* a major concern.
+
+As a rather unusual feature, the two linear filters/smoothers implement the **sample weighting** approach described in Petersen (2022). 
 This can be used to perform importance-weighted estimation in the face of model mismatch, covariate shift, and time-varying systems, as described in Petersen (2022) and illustrated in `test_wkfs.m`.
-Finally, as a limitation, currently, only the first filter/smoother (linear KF + RTS) supports inputs, although the other two could be quite trivially extended to also support this.
 
-Concerning the nonlinear filter and smoother, a *general iterative sigma-point quadrature filter and smoother* have been implemented.
-Turning off iterations and choosing the unscented transform as a quadrature scheme, this is equivalent to the classical unscented Rauch-Tung-Striebel smoother.
+Finally, as a limitation, currently, only the first filter/smoother (linear KF + RTS) supports **inputs** ("+B u(k)"), although the other two could be quite trivially extended to also support this.
+
+Concerning the nonlinear filter and smoother, a **general iterative sigma-point quadrature filter and smoother** has been implemented.
+Turning off iterations and choosing the unscented transform as a quadrature scheme, this is equivalent to the classical **unscented Rauch-Tung-Striebel smoother**.
 As an alternative quadrature scheme, the general (also multivariate) Gauss-Hermite quadrature rule is provided for use.
 Since the implementation is modular, alternative quadrature schemes could easily be integrated.
-Concerning the iterative aspect of the implementation, it has been shown in a number of studies that approximative nonlinear (e.g., extended, unscented, or Gauss-Hermite) filters and smoothers can greatly benefit from performing iterative filter/smoother runs.
+
+Concerning the **iterative aspect** of the implementation, it has been shown in a number of studies that approximative nonlinear (e.g., extended, unscented, or Gauss-Hermite) filters and smoothers can greatly benefit from performing iterative filter/smoother runs.
 The included demo case demonstrates this effect very clearly.
 By default, iterations are performed both within individual samples and across whole filter/smoother runs. 
 Dampening is implemented to speed up convergence across iterations.
 
-As the documentation is likely far from complete and clear, *please don't hesitate to ask away in case of any questions.*
+As the documentation is likely far from complete and clear, **please don't hesitate to ask away in case of any questions.**
 My wish is for this toolbox to be useful to as many people as possible.
 (If there is sufficient demand, I might be willing to put together a dedicated PDF documentation in the future.)
 Also, please do not hesitate to contact me in case of any bugs or problems with the code.
 
 
-##### Third-party content
+#### Third-party content
 The following files (in the directory `3rd party code`) have been written by other authors:
 - the `block-matrix-inverse-tools` have been written by **Richard Lange**, see https://github.com/wrongu/block-matrix-inverse-tools
 - `vline2.m` has been written by **K. Stahl**, see https://www.mathworks.com/matlabcentral/fileexchange/29578-improved-vline
@@ -48,7 +53,7 @@ Copyright remains with the original authors, of course.
 Check the original sources (provided above) if in doubt about licensing.
 
 
-##### References
+#### References
 - Arasaratnam and Haykin (2007), Discrete-Time Nonlinear Filtering Algorithms Using Gauss-Hermite Quadrature, Proceedings of the IEEE.
 - Dan Simon (2006), Optimal State Estimation, John Wiley & Sons, Inc.
 - Dan Simon (2009), Kalman filtering with state constraints: a survey of linear and nonlinear algorithms, IET Control Theory and Applications.