one_euro_rs/

lib.rs

#![no_std]
extern crate num_traits;

use num_traits::float::FloatCore;
use num_traits::float::FloatConst;


/// Representation of a OneEuroFilter.
///
/// # Examples
///
/// ```
/// # use one_euro_rs::OneEuroFilter;
/// let mut one_euro = OneEuroFilter::new(120.0, 1.0, 1.0, 1.0);
///
/// one_euro.filter(1.0);
/// one_euro.filter(1.1);
/// one_euro.filter(0.9);
/// one_euro.filter(99999.9);
/// one_euro.filter(1.01);
/// one_euro.filter(1.04);
/// one_euro.filter(0.00);
/// ```
#[derive(Debug, Clone)]
pub struct OneEuroFilter<T: FloatCore> {
    pub configuration: OneEuroFilterConfiguration<T>,

    filter_dx: LowPassFilter<T>,
    filter_x: LowPassFilter<T>,
    frequency: T,
    time_last: Option<T>,
}

impl<T: FloatCore> OneEuroFilter<T> {
    pub fn new(frequency: T, cutoff_min: T, cutoff_d: T, beta: T) -> OneEuroFilter<T> {
        OneEuroFilter {
            configuration: OneEuroFilterConfiguration {
                frequency,
                cutoff_min,
                cutoff_d,
                beta,
            },
            filter_dx: LowPassFilter::default(),
            filter_x: LowPassFilter::default(),
            frequency: T::zero(),
            time_last: None,
        }
    }

    pub fn from_configuration(configuration: OneEuroFilterConfiguration<T>) -> OneEuroFilter<T> {
        OneEuroFilter {
            configuration,
            filter_dx: LowPassFilter::default(),
            filter_x: LowPassFilter::default(),
            frequency: T::zero(),
            time_last: None,
        }
    }
}

/// Configuration parameters of a One Euro Filter.
#[derive(Debug, Clone)]
pub struct OneEuroFilterConfiguration<T> {
    pub frequency: T,
    pub cutoff_min: T,
    pub cutoff_d: T,
    pub beta: T,
}

#[derive(Debug, Clone)]
struct LowPassFilter<T> {
    x_prev_hat: T,
    x_prev: T,
    used_before: bool,
}

impl<T: FloatCore> Default for LowPassFilter<T> {
    fn default() -> LowPassFilter<T> {
        LowPassFilter {
            x_prev_hat: T::zero(),
            x_prev: T::zero(),
            used_before: false,
        }
    }
}

impl<T: FloatCore> LowPassFilter<T> {
    fn filter(&mut self, x: T, alpha: T) -> T {
        if !self.used_before {
            self.used_before = true;
            self.x_prev_hat = x;
        }
        let x_hat = alpha * x + (T::one() - alpha) * self.x_prev_hat;
        self.x_prev = x;
        self.x_prev_hat = x_hat;

        x_hat
    }
}

impl<T: FloatCore + FloatConst> OneEuroFilter<T> {
    fn alpha(&self, cutoff: T) -> T {
        let te = T::one() / self.frequency;
        let tau = T::one() / ((T::one() + T::one()) * T::PI() * cutoff);
        T::one() / (T::one() + tau / te)
    }

    pub fn filter(&mut self, x: T) -> T {
        if self.time_last.is_none() {
            self.frequency = self.configuration.frequency
        }

        let dx = {
            if self.filter_x.used_before {
                (x - self.filter_x.x_prev) * self.frequency
            } else {
                T::zero()
            }
        };

        let alpha_cutoff_d = self.alpha(self.configuration.cutoff_d);
        let edx = self.filter_dx.filter(dx, alpha_cutoff_d);
        let cutoff = self.configuration.cutoff_min + self.configuration.beta * edx.abs();

        let alpha_cutoff = self.alpha(cutoff);
        self.filter_x.filter(x, alpha_cutoff)
    }

    pub fn filter_with_timestamp(&mut self, value: T, timestamp: T) -> T {
        if let Some(time) = self.time_last {
            self.frequency = T::one() / (timestamp - time);
        }
        self.time_last = Some(timestamp);
        self.filter(value)
    }
}

#[cfg(test)]
mod tests {
    use OneEuroFilter;

    #[test]
    fn check_reference_values() {
        let mut filter = OneEuroFilter::new(120.0, 1.0, 1.0, 1.0);

        // Generated via reference implementation by Nicolas Roussel.
        let reference_data = [
            (0.0, 0.0, 0.021383312440339954, 0.021383312440339954),
            (
                0.008333333333333333,
                0.008333236883050947,
                0.01742723122477257,
                0.021182065986898566,
            ),
            (
                0.016666666666666666,
                0.01666589507244506,
                0.08003600130896155,
                0.02507122551828806,
            ),
            (
                0.025,
                0.024997395914712332,
                0.06320723861275496,
                0.027384681078869957,
            ),
            (
                0.03333333333333333,
                0.03332716083675362,
                0.05210916950674831,
                0.028795253569444068,
            ),
            (
                0.041666666666666664,
                0.041654611386019086,
                0.03845250505680954,
                0.02930589901080003,
            ),
            (
                0.049999999999999996,
                0.049979169270678324,
                0.0722099822511618,
                0.03197015959706569,
            ),
            (
                0.05833333333333333,
                0.058300256399779225,
                0.02932160784122595,
                0.03183779081996437,
            ),
            (
                0.06666666666666667,
                0.066617294923393,
                0.07534775258819933,
                0.03455131229686065,
            ),
            (
                0.075,
                0.07492970727274234,
                0.01444975726594834,
                0.033450268562495056,
            ),
            (
                0.08333333333333333,
                0.08323691620031025,
                0.11823214631976187,
                0.03969360691681312,
            ),
            (
                0.09166666666666666,
                0.09153834481992633,
                0.020560724932967803,
                0.038659964444603935,
            ),
            (
                0.09999999999999999,
                0.09983341664682814,
                0.06886798515412829,
                0.04044889209365102,
            ),
            (
                0.10833333333333332,
                0.10812155563769466,
                0.05431477891849183,
                0.04120743605198477,
            ),
            (
                0.11666666666666665,
                0.11640218623064896,
                0.11088816674546634,
                0.04608596067842302,
            ),
            (
                0.12499999999999999,
                0.12467473338522768,
                0.15246417026650733,
                0.054612750578808725,
            ),
            (
                0.13333333333333333,
                0.13293862262231407,
                0.22538993240526062,
                0.0712877764700402,
            ),
            (
                0.14166666666666666,
                0.14119328006403217,
                0.05594182991184532,
                0.07052290619623662,
            ),
            (
                0.15,
                0.14943813247359922,
                0.05725982551574936,
                0.0698569755632412,
            ),
            (
                0.15833333333333333,
                0.15767260729513352,
                0.21766932536680117,
                0.08365817495696466,
            ),
            (
                0.16666666666666666,
                0.16589613269341502,
                0.2007601388587736,
                0.09383532914257495,
            ),
            (
                0.175,
                0.17410813759359595,
                0.09157106285253577,
                0.09370935091874744,
            ),
            (
                0.18333333333333332,
                0.1823080517208584,
                0.088228146193249,
                0.09341110172433759,
            ),
            (
                0.19166666666666665,
                0.1904953056400167,
                0.15234329965041163,
                0.09764120625132379,
            ),
            (
                0.19999999999999998,
                0.1986693307950612,
                0.27534268915046645,
                0.11590328647805409,
            ),
            (
                0.20833333333333331,
                0.20682955954864102,
                0.19398442244734002,
                0.12208727009847634,
            ),
            (
                0.21666666666666665,
                0.21497542522148327,
                0.15676830657397361,
                0.12443778807075107,
            ),
            (
                0.22499999999999998,
                0.22310636213174542,
                0.23141941948982092,
                0.13372178881465696,
            ),
            (
                0.2333333333333333,
                0.23122180563429853,
                0.1921814228047687,
                0.13808411231753334,
            ),
            (
                0.24166666666666664,
                0.23932119215993858,
                0.18712538549485577,
                0.141617814032818,
            ),
            (
                0.24999999999999997,
                0.2474039592545229,
                0.19787774259254032,
                0.14577334256992833,
            ),
            (
                0.2583333333333333,
                0.2554695456180293,
                0.16427566903547078,
                0.14694954858853326,
            ),
            (
                0.26666666666666666,
                0.26351739114353506,
                0.2689382135380503,
                0.15802260728587997,
            ),
            (
                0.275,
                0.27154693695611287,
                0.1879689454858411,
                0.16003806351785993,
            ),
            (
                0.2833333333333334,
                0.27955762545164153,
                0.3389263330135455,
                0.1789712493370966,
            ),
            (
                0.29166666666666674,
                0.2875489003355282,
                0.3743289228038309,
                0.20085483758034264,
            ),
            (
                0.3000000000000001,
                0.29552020666133966,
                0.22523778285180707,
                0.20257429543059055,
            ),
            (
                0.30833333333333346,
                0.3034709908693401,
                0.2234102771889196,
                0.20401223488450412,
            ),
            (
                0.3166666666666668,
                0.3114007008249325,
                0.3337223909416673,
                0.21660584403135966,
            ),
            (
                0.3250000000000002,
                0.3193087858570011,
                0.247871142449699,
                0.21886665421860532,
            ),
            (
                0.33333333333333354,
                0.32719469679615243,
                0.2653553162626036,
                0.22239537133617218,
            ),
            (
                0.3416666666666669,
                0.33505788601285147,
                0.36019801172028865,
                0.2360858785709737,
            ),
            (
                0.35000000000000026,
                0.34289780745545156,
                0.30019566879806014,
                0.24130730766412706,
            ),
            (
                0.3583333333333336,
                0.35071391668811436,
                0.30191510143882727,
                0.24617855209492934,
            ),
            (
                0.366666666666667,
                0.3585056709286175,
                0.40574679628860755,
                0.26303483882170214,
            ),
            (
                0.37500000000000033,
                0.36627252908604785,
                0.31560501123679313,
                0.2672273667326601,
            ),
            (
                0.3833333333333337,
                0.374013951798377,
                0.3125296360575424,
                0.2707376576333836,
            ),
            (
                0.39166666666666705,
                0.38172940146991646,
                0.28670722687822725,
                0.27184279610815043,
            ),
            (
                0.4000000000000004,
                0.38941834230865086,
                0.48494806642378396,
                0.29722775109458993,
            ),
            (
                0.40833333333333377,
                0.3970802403634453,
                0.3057676190339556,
                0.29782421651984875,
            ),
            (
                0.41666666666666713,
                0.4047145635611251,
                0.3392025907520668,
                0.3010451223803258,
            ),
            (
                0.4250000000000005,
                0.4123207817434252,
                0.451373313991958,
                0.31689750777568787,
            ),
            (
                0.43333333333333385,
                0.4198983667038063,
                0.42280014316631587,
                0.32702048291624436,
            ),
            (
                0.4416666666666672,
                0.42744679222413584,
                0.47764347169315285,
                0.34318048911962207,
            ),
            (
                0.45000000000000057,
                0.43496553411123073,
                0.3696714719381875,
                0.3452119355804641,
            ),
            (
                0.4583333333333339,
                0.4424540702332592,
                0.3808715958526286,
                0.348006384565042,
            ),
            (
                0.4666666666666673,
                0.4499118805560002,
                0.454264977753437,
                0.3582203729462111,
            ),
            (
                0.47500000000000064,
                0.45733844717895605,
                0.4660874966000934,
                0.3686778933808915,
            ),
            (
                0.483333333333334,
                0.4647332543713181,
                0.45860128800701067,
                0.37702180276740554,
            ),
            (
                0.49166666666666736,
                0.47209578860778095,
                0.5094188241701274,
                0.3907497128863644,
            ),
            (
                0.5000000000000007,
                0.47942553860420356,
                0.4684118307156618,
                0.3977914243277588,
            ),
            (
                0.508333333333334,
                0.4867219953531153,
                0.4365075206481011,
                0.4009026580062166,
            ),
            (
                0.5166666666666673,
                0.493984652159063,
                0.45603521874853925,
                0.4055357079721339,
            ),
            (
                0.5250000000000006,
                0.5012130046737984,
                0.4684015329397646,
                0.4109189947079715,
            ),
            (
                0.5333333333333339,
                0.5084065509313016,
                0.4645202718970532,
                0.4153620633347935,
            ),
            (
                0.5416666666666672,
                0.5155647913826402,
                0.517210191573449,
                0.4250368567354933,
            ),
            (
                0.5500000000000005,
                0.5226872289306596,
                0.4565065965259184,
                0.4274585552563856,
            ),
            (
                0.5583333333333338,
                0.5297733689645034,
                0.5588194331338541,
                0.44088119475434656,
            ),
            (
                0.5666666666666671,
                0.5368227193939616,
                0.49725027941468036,
                0.4456068591774484,
            ),
            (
                0.5750000000000004,
                0.5438347906836429,
                0.6191246209440326,
                0.46525017681332514,
            ),
            (
                0.5833333333333337,
                0.5508090958869701,
                0.46770078346217825,
                0.46542448188822877,
            ),
            (
                0.591666666666667,
                0.5577451506799957,
                0.6253504485436888,
                0.4831501978216991,
            ),
            (
                0.6000000000000003,
                0.5646424733950356,
                0.5546640845051478,
                0.48958984214234896,
            ),
            (
                0.6083333333333336,
                0.5715005850541174,
                0.5467010276712442,
                0.49450420092618663,
            ),
            (
                0.6166666666666669,
                0.5783190094022432,
                0.48700350585783414,
                0.4939912403142606,
            ),
            (
                0.6250000000000002,
                0.5850972729404623,
                0.626798588858667,
                0.5078024038623283,
            ),
            (
                0.6333333333333335,
                0.591834904958753,
                0.590454799149603,
                0.5154208016748126,
            ),
            (
                0.6416666666666668,
                0.5985314375687107,
                0.6061122813221334,
                0.5239627769769281,
            ),
            (
                0.6500000000000001,
                0.6051864057360397,
                0.5798493368866869,
                0.5287274488628447,
            ),
            (
                0.6583333333333334,
                0.6117993473128472,
                0.5517691543441483,
                0.5304813847340938,
            ),
            (
                0.6666666666666667,
                0.6183698030697371,
                0.5872204107603417,
                0.5352606534458257,
            ),
            (
                0.675,
                0.6248973167276999,
                0.601772363331665,
                0.5410065532097657,
            ),
            (
                0.6833333333333333,
                0.6313814349897994,
                0.598635022031564,
                0.5458364480873893,
            ),
            (
                0.6916666666666667,
                0.6378217075726509,
                0.5944473151861404,
                0.5497773363636226,
            ),
            (
                0.7,
                0.644217687237691,
                0.6901991655793209,
                0.5644150527847014,
            ),
            (
                0.7083333333333333,
                0.6505689298222357,
                0.5828919075915926,
                0.5657780143958154,
            ),
            (
                0.7166666666666666,
                0.6568749942703246,
                0.6716723629599771,
                0.5759302831343794,
            ),
            (
                0.7249999999999999,
                0.6631354426633496,
                0.6759912059345111,
                0.5854151464543788,
            ),
            (
                0.7333333333333332,
                0.6693498402504661,
                0.6830440804868277,
                0.594637455760675,
            ),
            (
                0.7416666666666665,
                0.6755177554787833,
                0.7233358464359532,
                0.6078416503874263,
            ),
            (
                0.7499999999999998,
                0.681638760023334,
                0.6757010912604849,
                0.6138054835060601,
            ),
            (
                0.7583333333333331,
                0.6877124288168176,
                0.6296392060756821,
                0.6149751534325731,
            ),
            (
                0.7666666666666664,
                0.6937383400791202,
                0.6425005848014446,
                0.6170710936165253,
            ),
            (
                0.7749999999999997,
                0.6997160753466033,
                0.676136211157782,
                0.622019574412074,
            ),
            (
                0.783333333333333,
                0.7056452195011648,
                0.7057791616977066,
                0.6295483905810932,
            ),
            (
                0.7916666666666663,
                0.7115253607990653,
                0.7503197962074777,
                0.6415538546935962,
            ),
            (
                0.7999999999999996,
                0.7173560908995225,
                0.7071988606961395,
                0.6471949311630385,
            ),
            (
                0.8083333333333329,
                0.723137004893067,
                0.6264716899319283,
                0.6458990736715509,
            ),
            (
                0.8166666666666662,
                0.7288677013296613,
                0.6668148954027976,
                0.6474232749060927,
            ),
            (
                0.8249999999999995,
                0.7345477822465782,
                0.7292313055433706,
                0.6546439232613149,
            ),
            (
                0.8333333333333328,
                0.7401768531960367,
                0.6994073241471498,
                0.6581611073291906,
            ),
            (
                0.8416666666666661,
                0.7457545232725942,
                0.7088100478992673,
                0.6621966515532525,
            ),
            (
                0.8499999999999994,
                0.7512804051402924,
                0.7099226815934074,
                0.6659444845073635,
            ),
            (
                0.8583333333333327,
                0.7567541150595556,
                0.7973759014626016,
                0.6790677836478691,
            ),
            (
                0.866666666666666,
                0.7621752729138392,
                0.8129602060627752,
                0.6926488661912626,
            ),
            (
                0.8749999999999993,
                0.7675435022360266,
                0.6839549464843985,
                0.6920835835078416,
            ),
            (
                0.8833333333333326,
                0.772858430234572,
                0.7348047595553453,
                0.695415294214207,
            ),
            (
                0.8916666666666659,
                0.7781196878193893,
                0.7452797482288552,
                0.6993748311227065,
            ),
            (
                0.8999999999999992,
                0.783326909627483,
                0.7041501032842915,
                0.6996943565312455,
            ),
            (
                0.9083333333333325,
                0.7884797340483198,
                0.8385258240953998,
                0.7137622418596969,
            ),
            (
                0.9166666666666659,
                0.7935778032489416,
                0.7101827614107828,
                0.7135292306809413,
            ),
            (
                0.9249999999999992,
                0.7986207631988137,
                0.7083312387746566,
                0.713197402485981,
            ),
            (
                0.9333333333333325,
                0.8036082636944106,
                0.8176481208339658,
                0.7228289186466941,
            ),
            (
                0.9416666666666658,
                0.8085399583835358,
                0.88619144258933,
                0.7404045185867278,
            ),
            (
                0.9499999999999991,
                0.8134155047893732,
                0.7545423431258524,
                0.7414031955973178,
            ),
            (
                0.9583333333333324,
                0.8182345643342707,
                0.9118036778406425,
                0.7602010031264637,
            ),
            (
                0.9666666666666657,
                0.8229968023632521,
                0.7640459403173927,
                0.760466717539167,
            ),
            (
                0.974999999999999,
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                9.650000000000093,
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                9.658333333333426,
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                9.70000000000009,
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                9.716666666666756,
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                9.733333333333421,
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                9.741666666666754,
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                9.750000000000087,
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                9.75833333333342,
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            (
                9.766666666666753,
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                9.775000000000086,
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                9.783333333333418,
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            (
                9.791666666666751,
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            (
                9.800000000000084,
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            (
                9.808333333333417,
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            (
                9.81666666666675,
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            (
                9.825000000000083,
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                9.833333333333416,
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                9.841666666666748,
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                9.850000000000081,
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                9.858333333333414,
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                9.866666666666747,
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            (
                9.87500000000008,
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                9.883333333333413,
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                9.891666666666746,
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            (
                9.900000000000079,
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                -0.37369557839250467,
            ),
            (
                9.908333333333411,
                -0.46492984771348855,
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                -0.37451425066847244,
            ),
            (
                9.916666666666744,
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            (
                9.925000000000077,
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            (
                9.93333333333341,
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            ),
            (
                9.941666666666743,
                -0.49417769656854205,
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            ),
            (
                9.950000000000076,
                -0.5014051281792635,
                -0.5129139172918515,
                -0.42675141626391094,
            ),
            (
                9.958333333333409,
                -0.5085977401909199,
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                -0.4379973223960746,
            ),
            (
                9.966666666666741,
                -0.5157550331194566,
                -0.47276041881867625,
                -0.4408365416376573,
            ),
            (
                9.975000000000074,
                -0.5228765099335189,
                -0.5949689795373625,
                -0.4580015579537443,
            ),
            (
                9.983333333333407,
                -0.5299616760889675,
                -0.5423596008339614,
                -0.46603440604480584,
            ),
            (
                9.99166666666674,
                -0.5370100395632226,
                -0.6137264343370828,
                -0.4824357994176143,
            ),
        ];

        for (timestamp, _signal, noisy, filtered) in reference_data.into_iter() {
            assert_eq!(filter.filter_with_timestamp(*noisy, *timestamp), *filtered);
        }
    }
}