Simple Kalman

This repo demos a simple scalar Kalman filter (linear quadratic estimator) in four languages:

1. Rust
2. Zig
3. Venerable C
4. Python

The filter is implemented in a single main file for each language using a very similar style, but they are not all exactly the same. For example, the Rust and Python programs add noise by drawing from a normal distribution while the Zig and C programs draw additive noise points evenly from a linear range.

The programs are simple so comparisons across the languages is limited. But this gives a small flavor and working example code across all four for those interested in taking a look at Rust and/or Zig.

Running the Demos

To run the demos, you will need compilers for all three languages (see below).

With the compilers installed, you can:

1. Build everything by executing build_all.sh in your shell (e.g., bash build_all.sh or zsh build_all.sh).
2. Run the Rust demo via run_rust.sh.
3. Run the Zig demo via run_zig.sh.
4. Run the C demo via run_c.sh.
5. Run the Python demo via run_py.sh.

The Source code

The source code is in src where there is a main file for each of the 4 languages.

Compiling Rust

It is recommended to use rustup. Follow the instructions here.

Compiling Zig

Follow the instructions here for your preferred method of installing the zig compiler on your target platform.

Compiling C

The demos assume GCC is available on your system. On Macs, gcc may be an alias for clang which should work just fine.

The Kalman Filter

All demos run the same Kalman filter model applied to a noisy sinusoid over a single period. The linear Kalman filter model operates only on scalar input and does not include control inputs (e.g., a B * u term). The same terse variable names are used in all language demos and reflect the general mathematical components of the Kalman Filter. These names make more sense for a general non-scalar model where they represent vectors and matrices than the scalar case here. Nonetheless, we use them here for consistency.

• x: State variable (in this case, just a scalar).
• P: A posteriori estimate of variance.
• A: The state transition/physics forward model (again, in this case, just a scalar value).
• H: The observation model.
• Q: Variance for the process noise.
• R: Variance for the observation noise.

The Kalman filter is implemented with a stateful struct in each language and a two-step process to evaluate the output of the filter given a new observation. This common split -- first predict and then update -- is reflected in two separate functions, called serially by advance.