#no-std #estimation #filtering #ukf

no-std yakf

Yet Another Kalman Filter Implementation, as well as, Lie Theory (Lie group, algebra, vector) on SO(3) and SE(3). [no_std] is supported by default.

9 releases

Uses new Rust 2021

new 0.1.11 Jul 6, 2022
0.1.10 Jul 4, 2022
0.1.9 Jun 25, 2022

#6 in Robotics

Download history 30/week @ 2022-06-08 105/week @ 2022-06-15 33/week @ 2022-06-22 31/week @ 2022-06-29

199 downloads per month



yakf - Yet Another Kalman Filter

Yet Another Kalman Filter Implementation, as well as,

Lie Theory (Lie group, algebra, vector) on SO(3) and SE(3).

[no_std] is supported by default.

Current implementation status

Filter Status

  • UKF ✅
  • EKF (Only dynamically-sized version) ✅

Sampling Method Status

  • Minimal Skew Simplex Sampling (n+2) ✅
  • Symmetrically-Distributed Sampling Method (2n+1) ✅

Static V.S Dynamic Cases

  • For statically-sized state whose dimension is known in compile time, refer to yakf::filters
  • For dynamically-sized state whose dimension may vary in run time, refer to yakf::dfilters

Lie Group Status

  • SO(3) ✅, refer to yakf::lie::so3
  • SE(3) ✅, refer to yakf::lie::se3

Lie Group Examples

  • (non-generic) Kalman Filter Example on SO(3) ✅ see examples/so3_kf.rs for instance
  • (non-generic) Kalman Filter Example on SE(3) ✅ see examples/se3_kf.rs for instance

NOTE that some functions havn't been thoroughly tested, so please let me know if there is any error.

UKF Usage

Add this to your Cargo.toml:

yakf = "0.1"

Example (statically-sized):

/// import yakf crate
extern crate yakf;
/// import State trait, UKF filter struct, and MSSS sampling method struct
use yakf::kf::{
    MinimalSkewSimplexSampling as MSSS, State, SymmetricallyDistributedSampling as SDS, UKF,

/// import Re-exports of hifitime (for time) and nalgebra (for matrix)
use yakf::{
    time::{Duration, Epoch, Unit},

fn main() {
    use crate::linalg::{Const, OMatrix, OVector, U2};
    use rand::prelude::*;

    /// define a custom struct to be the state. e.g., BikeState, has a 2-D vector x (x[0]: position, x[1]: velocity) and a timestamped time t.
    pub struct BikeState {
        pub x: OVector<f64, U2>,
        pub t: Epoch,

    /// for example, you can define your own methods.
    impl BikeState {
        pub fn new(state: OVector<f64, U2>, epoch: Epoch) -> Self {
            BikeState { x: state, t: epoch }
        pub fn zeros() -> Self {
            Self {
                x: OVector::<f64, U2>::zeros(),
                t: Epoch::from_gregorian_tai(2022, 5, 10, 0, 0, 0, 0),

    /// you **MUST** implement State<T,U> for your custom state struct.
    impl State<U2, Const<1>> for BikeState {
        fn state(&self) -> &OVector<f64, U2> {
        fn set_state(&mut self, state: OVector<f64, U2>) {
            self.x = state;

        fn epoch(&self) -> Epoch {
        fn set_epoch(&mut self, epoch: Epoch) {
            self.t = epoch;
    // you SHOULD provide a function `dynamics` for UKF propagating the state.
    // for example,
    let dynamics = |x: &OVector<f64, U2>, _ext: &OVector<f64, Const<1>>, dt: Duration| {
        OVector::<f64, U2>::new(x[0] + x[1] * dt.in_seconds(), x[1])

    // you SHOULD ALSO provide a function for UKF yielding measurements based on given state.
    // for example, assume the measuring has a 2-D measurement.
    let measure_model = |x: &OVector<f64, U2>| OVector::<f64, U2>::new(x[0], x[1]);

    // you SHOULD ALSO specify a sampling method for UKF.
    // for example, you can specify a MSSS method
    type T2 = Const<4>;
    let samling_method = MSSS::<U2, T2>::build(0.6).unwrap();

    // or you can specify a SDS method as an alternative.
    type _T2 = Const<5>;

    let _samling_method = SDS::<U2, _T2>::build(1e-3, None, None).unwrap();

    // finally, build the UKF.
    let mut ukf = UKF::<U2, T2, U2, Const<1>, BikeState>::build(
        OMatrix::<f64, U2, U2>::from_diagonal_element(10.0),
        OMatrix::<f64, U2, U2>::from_diagonal_element(1.0),
        OMatrix::<f64, U2, U2>::from_diagonal(&OVector::<f64, U2>::new(1.0, 0.001)),

    // you can then use ukf to estimate the state vector.

    let mut rng = rand::thread_rng();
    let mut add_noisies = |mut y: OVector<f64, U2>| {
        y[0] += rng.gen_range(-3.0..3.0);
        y[1] += rng.gen_range(-0.1..0.1);
    let s = OVector::<f64, U2>::new(-5.0, 1.0);
    let t = Epoch::now().unwrap();
    let mut bike_actual = BikeState::new(s, t);

        "bike actual = {:?}, ukf estimate = {:?}",
    let mut actual_normed_noise: Vec<f64> = Vec::new();
    let mut estimate_normed_error: Vec<f64> = Vec::new();
    let nums_measure = 500_usize;

    // you can set an arbitary time base for ukf.
    // a timing system would help in aligning data.
    let ukf_base_epoch = ukf.current_estimate().epoch();

    for i in 0..nums_measure {
        let dt = Duration::from_f64(1.0, Unit::Second);
        let m_epoch = ukf_base_epoch + dt;

        Remark 1. Note that the actual dynamics doesn't need to be exactly the same with that used by ukf.
                Actually, the dynamics used by ukf is only a Model abstracted from the actual one.
                But in this example, assume they are the same. Case is the same for measuring model.

        Remark 2. For the same reason, the delta_t used by actual dynamics is not neccesarily the same
                with dt (the one used by ukf estimation) and, actually, delta_t should be much smaller than dt
                in real world. However, for simplity, this example just let them be the same, i.e. delta_t = dt.
        let _ = bike_actual.propagate(&dynamics, dt, OVector::<f64, Const<1>>::zeros());

        // use measuring model to simulate a measurement, and add some noises on it.
        let mut meas = measure_model(&bike_actual.state());
        meas = add_noisies(meas);

        // every time the measurement is ready, ukf is trigger to update.
        ukf.feed_and_update(meas, m_epoch, OVector::<f64, Const<1>>::zeros());
        if i > nums_measure / 3 {
            actual_normed_noise.push((&meas - bike_actual.state()).norm());
                .push((ukf.current_estimate().state() - bike_actual.state()).norm());

            "bike actual = {:?}, meas = {:.3?}, ukf estimate = {:.3?}",
    let nums = actual_normed_noise.len();
    let noise_metric: f64 = actual_normed_noise
        .fold(0.0, |acc, x| acc + x / nums as f64);
    let error_metric: f64 = estimate_normed_error
        .fold(0.0, |acc, x| acc + x / nums as f64);
        "noise_metric = {:?}, error_metric = {:?}",
        noise_metric, error_metric
    assert!(error_metric < noise_metric);

You may see the output as

.. .. ..
actual = [493.0, 1.0], meas = [493.281, 1.073], estimate = [492.553, 1.073]
actual = [494.0, 1.0], meas = [492.615, 0.941], estimate = [492.598, 0.941]
actual = [495.0, 1.0], meas = [496.849, 1.019], estimate = [495.710, 1.019]
noise_metric = 1.5346849337852513, error_metric = 1.2218914483371828

SO(3)/SE(3) Usage

The element in SO(3) is stored as an Enum type, named by SO3. One can create such an element by methods from_vec, from_grp, from_alg. Either will be Ok, since an element can be expressed in all the three forms, and there exists a one-on-one mapping relationship among them.

For example, one can create a SO3 element so from a 3-d vector:

let so = SO3::from_vec(Vec3::new(0.3, 0.6, -0.9));

If you want use its vector form, just call

let v = so.to_vec();

if you want use its group form, just call

let g = so.to_group();

and if you want use its algebra form, just call

let a = so.to_alg();

As you know, all v, g, a stand for the same SO3 element so (limited in a proper range).

Currently, some neccessary methods have been implemented for SO3.

The design of SE(3) is consensus with SO(3).


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