Matrix math and 'stubbed' kalman filter implementation

[cowsed]

Description

Add simple matrix and cmsis-dsp matrix to airbrakes project. Also stub out implementation of 'simple' kalman filter. Subject to change as the model changes but im working to avoid 10000000 line PRs because i love my reviewers

The matrix files could be added as 'library' level files but given the rate of change for airbrakes and the fact that we have no use for the matrices elsewhere, I believe the should live in the app/ for airbrakes. There is also a chance that once the filter design has solidified, it makes sense to implement the entire control system as one function with direct calls to the cmsis matrix library. However, bc readability is important i have the matrix types. If the time comes, the 'optimized' version with direct calls can be implemented with the 'readable' version acting as a reference to verify functionality.

Based on the super cool specs we have been given / drawn up

Type of change

Please delete options that are not relevant.

• New feature (non-breaking change which adds functionality)

How Has This Been Tested?

sw_board tests for determining matrix correctness and speeds on arm w/ cmsis
native_sim tests for ability to test independently of hardware
control_freak hardware in case all the other hardware explodes

sw_board

Size Opts
Addition Manual: (4x4 + 4x4) 16 us, 1142 cycles
Addition CMSIS:  (4x4 + 4x4) 16 us, 1179 cycles
Multiply Manual: (4x4 * 4x1) 25 us, 1828 cycles
Multiply CMSIS:  (4x4 * 4x1) 23 us, 1647 cycles

Speed Opts
Addition Manual: (4x4 + 4x4) 15 us, 1107 cycles
Addition CMSIS:  (4x4 + 4x4) 15 us, 1088 cycles
Multiply Manual: (4x4 * 4x1) 24 us, 1708 cycles
Multiply CMSIS:  (4x4 * 4x1) 21 us, 1507 cycles

these dang arm engineers seem to know a thing or two.

Checklist:

• New functionality is documented in the necessary spots (i.e new functions documented in the header)
• Unit tests cover any new functionality or edge cases that the PR was meant to resolve (if applicable)
• The CI checks are passing
• I reviewed my own code in the GitHub diff and am sure that each change is intentional
• I feel comfortable about this code flying in a rocket

[cowsed]

pragma once is awesome and ill be really sad if The Powers That Be say we shouldnt use it
(all the compilers we have ever used for our hardware and native sim support it wholly and completely [sdcc doesnt so no stm8s but also none of our code would work on an stm8 lol])

[AarC10]

We can do pragma once tbh. I do it in our other codebases lol. I just stuck with the standard for Zephyr when we started out

[cowsed]

can verify that the type checking for matrix dimensions is all good at compile time. hurray for modern c++ versions

[cowsed]

could also static_assert their results but that was extra work

[AarC10]

Looks pretty good. Just drop the sample for benchmarking for repro and also I'm curious about your error handling. I'm looking at the return status and maybe we should alert the user that their inputs are bad?
https://arm-software.github.io/CMSIS_5/DSP/html/arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6

[cowsed]

Looks pretty good. Just drop the sample for benchmarking for repro and also I'm curious about your error handling. I'm looking at the return status and maybe we should alert the user that their inputs are bad? https://arm-software.github.io/CMSIS_5/DSP/html/arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6

For the functions implemented here (add, subtract, multiply) the template static_asserts prevent the conditions that would bring about the error codes. Even multiplication and addition by NaN is defined.

For things like decompositions and inverses, there has to be some sort of error handling since they can fail and if/when implemented they will include return codes std::options or something.
Also, trying to get a return code into operator overloads kinda doesnt work and i think the readability of operators is well worth it given the guarantees from the template/type checker.

[cowsed]

Benchmark included in the math directory not as a sample bc of reasons stated in PR description about current narrow-applicability. But it is there for testing as work is done for airbrakes and should lend itself pretty easily to turning into a 'real' sample later

(also im on campus with no hardware so theres a chance that doesn't work in which case don't approve and ill fix it tn but it does compile)