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[filter] organize out equations (#6)
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,161 @@ | ||
| /*_ __ _ __ __ _ _ | ||
| | |/ / /\ | | | \/ | /\ | \ | | | ||
| | ' / / \ | | | \ / | / \ | \| | | ||
| | < / /\ \ | | | |\/| | / /\ \ | . ` | | ||
| | . \ / ____ \| |____| | | |/ ____ \| |\ | | ||
| |_|\_\/_/ \_\______|_| |_/_/ \_\_| \_| | ||
| Kalman Filter for C++ | ||
| Version 0.1.0 | ||
| https://github.com/FrancoisCarouge/Kalman | ||
| SPDX-License-Identifier: Unlicense | ||
| This is free and unencumbered software released into the public domain. | ||
| Anyone is free to copy, modify, publish, use, compile, sell, or | ||
| distribute this software, either in source code form or as a compiled | ||
| binary, for any purpose, commercial or non-commercial, and by any | ||
| means. | ||
| In jurisdictions that recognize copyright laws, the author or authors | ||
| of this software dedicate any and all copyright interest in the | ||
| software to the public domain. We make this dedication for the benefit | ||
| of the public at large and to the detriment of our heirs and | ||
| successors. We intend this dedication to be an overt act of | ||
| relinquishment in perpetuity of all present and future rights to this | ||
| software under copyright law. | ||
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, | ||
| EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF | ||
| MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. | ||
| IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR | ||
| OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, | ||
| ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR | ||
| OTHER DEALINGS IN THE SOFTWARE. | ||
| For more information, please refer to <https://unlicense.org> */ | ||
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| #ifndef FCAROUGE_KALMAN_EQUATION_HPP | ||
| #define FCAROUGE_KALMAN_EQUATION_HPP | ||
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| //! @file | ||
| //! @brief Kalman filter main project header. | ||
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| #include <type_traits> | ||
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| namespace fcarouge | ||
| { | ||
| [[nodiscard]] inline constexpr auto extrapolate_state(const auto &x, | ||
| const auto &f) | ||
| { | ||
| using State = std::remove_reference_t<std::remove_cv_t<decltype(x)>>; | ||
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| return State{ f * x }; | ||
| } | ||
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| [[nodiscard]] inline constexpr auto | ||
| extrapolate_state(const auto &x, const auto &f, const auto &g, const auto &u) | ||
| { | ||
| using State = std::remove_reference_t<std::remove_cv_t<decltype(x)>>; | ||
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| return State{ f * x + g * u }; | ||
| } | ||
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| template <template <typename> class Transpose> | ||
| [[nodiscard]] inline constexpr auto | ||
| extrapolate_covariance(const auto &p, const auto &f, const auto &q) | ||
| { | ||
| using estimate_uncertainty_p = | ||
| std::remove_reference_t<std::remove_cv_t<decltype(p)>>; | ||
| using state_transition_f = | ||
| std::remove_reference_t<std::remove_cv_t<decltype(f)>>; | ||
| Transpose<state_transition_f> transpose; | ||
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| return estimate_uncertainty_p{ f * p * transpose(f) + q }; | ||
| } | ||
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| template <template <typename> typename Transpose, | ||
| template <typename> typename Symmetrize> | ||
| inline constexpr void predict(auto &x, auto &p, const auto &f, const auto &q) | ||
| { | ||
| x = extrapolate_state(x, f); | ||
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| using estimate_uncertainty_p = | ||
| std::remove_reference_t<std::remove_cv_t<decltype(p)>>; | ||
| Symmetrize<estimate_uncertainty_p> symmetrize; | ||
| p = symmetrize(extrapolate_covariance<Transpose>(p, f, q)); | ||
| } | ||
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| template <template <typename> typename Transpose, | ||
| template <typename> typename Symmetrize> | ||
| inline constexpr void predict(auto &x, auto &p, const auto &f, const auto &q, | ||
| const auto &g, const auto &u) | ||
| { | ||
| x = extrapolate_state(x, f, g, u); | ||
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| using estimate_uncertainty_p = | ||
| std::remove_reference_t<std::remove_cv_t<decltype(p)>>; | ||
| Symmetrize<estimate_uncertainty_p> symmetrize; | ||
| p = symmetrize(extrapolate_covariance<Transpose>(p, f, q)); | ||
| } | ||
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| [[nodiscard]] inline constexpr auto update_state(const auto &x, const auto &k, | ||
| const auto &z, const auto &h) | ||
| { | ||
| using State = std::remove_reference_t<std::remove_cv_t<decltype(x)>>; | ||
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| return State{ x + k * (z - h * x) }; | ||
| } | ||
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| template <template <typename> typename Transpose, | ||
| template <typename> typename Identity> | ||
| [[nodiscard]] inline constexpr auto | ||
| update_covariance(const auto &p, const auto &k, const auto &h, const auto &r) | ||
| { | ||
| using estimate_uncertainty_p = | ||
| std::remove_reference_t<std::remove_cv_t<decltype(p)>>; | ||
| using gain = std::remove_reference_t<std::remove_cv_t<decltype(k)>>; | ||
| Transpose<estimate_uncertainty_p> transpose_p; | ||
| Transpose<gain> transpose_k; | ||
| Identity<estimate_uncertainty_p> i; | ||
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| return estimate_uncertainty_p{ (i() - k * h) * p * transpose_p(i() - k * h) + | ||
| k * r * transpose_k(k) }; | ||
| } | ||
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| template <template <typename> typename Transpose, | ||
| template <typename, typename> typename Divide> | ||
| [[nodiscard]] inline constexpr auto weight_gain(const auto &p, const auto &h, | ||
| const auto &r) | ||
| { | ||
| using observation_h = std::remove_reference_t<std::remove_cv_t<decltype(h)>>; | ||
| using measurement_uncertainty_r = | ||
| std::remove_reference_t<std::remove_cv_t<decltype(r)>>; | ||
| using gain = std::invoke_result_t<Transpose<observation_h>, observation_h>; | ||
| Transpose<observation_h> transpose_h; | ||
| Divide<gain, measurement_uncertainty_r> divide; | ||
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| return gain{ divide(p * transpose_h(h), h * p * transpose_h(h) + r) }; | ||
| } | ||
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| template <template <typename> typename Transpose, | ||
| template <typename> typename Symmetrize, | ||
| template <typename, typename> typename Divide, | ||
| template <typename> typename Identity> | ||
| inline constexpr void update(auto &x, auto &p, const auto &h, const auto &r, | ||
| const auto &z) | ||
| { | ||
| const auto k{ weight_gain<Transpose, Divide>(p, h, r) }; | ||
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| x = update_state(x, k, z, h); | ||
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| using estimate_uncertainty_p = | ||
| std::remove_reference_t<std::remove_cv_t<decltype(p)>>; | ||
| Symmetrize<estimate_uncertainty_p> symmetrize; | ||
| p = symmetrize(update_covariance<Transpose, Identity>(p, k, h, r)); | ||
| } | ||
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| } // namespace fcarouge | ||
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| #endif // FCAROUGE_KALMAN_EQUATION_HPP |