[sample] add 2D vehicule location example

.github/workflows/deploy_test_coverage_coveralls.yml

@@ -26,7 +26,7 @@ jobs:
             cmake --build . ;
             sudo make install ) )
     - name: Build
-      run: gcc-11 sample/*.cpp source/*.cpp test/*.cpp -Iinclude -I/usr/local/include/eigen3 -O0 -g -std=c++23 -fmodules-ts --coverage -lstdc++
+      run: gcc-11 sample/*.cpp source/*.cpp test/*.cpp -Iinclude -I/usr/local/include/eigen3 -O0 -g -std=c++23 -fmodules-ts --coverage -lstdc++ -lm
     - name: "Coverage: Base"
       run: |
         lcov --rc lcov_branch_coverage=1 --gcov-tool gcov-11 --capture --initial --directory . --output-file base.info

.github/workflows/verify_test_memory_valgrind.yml

@@ -26,6 +26,6 @@ jobs:
             cmake --build . ;
             sudo make install ) )
     - name: Build
-      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -g -O0 -std=c++23 -lstdc++
+      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -g -O0 -std=c++23 -lstdc++ -lm
     - name: Test
       run: valgrind --verbose ./a.out

.github/workflows/verify_test_sanitizer_address.yml

@@ -26,6 +26,6 @@ jobs:
             cmake --build . ;
             sudo make install ) )
     - name: Build
-      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -std=c++23 -g -fsanitize=address -fsanitize-address-use-after-scope -fno-omit-frame-pointer -lstdc++
+      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -std=c++23 -g -fsanitize=address -fsanitize-address-use-after-scope -fno-omit-frame-pointer -lstdc++ -lm
     - name: Test
       run: ASAN_OPTIONS=verbosity=2:strict_string_checks=1:detect_stack_use_after_return=1:check_initialization_order=1:strict_init_order=1 ./a.out

.github/workflows/verify_test_sanitizer_leak.yml

@@ -26,6 +26,6 @@ jobs:
             cmake --build . ;
             sudo make install ) )
     - name: Build
-      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -std=c++23 -g -fsanitize=leak -lstdc++
+      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -std=c++23 -g -fsanitize=leak -lstdc++ -lm
     - name: Test
       run: LSAN_OPTIONS=verbosity=2 ./a.out

.github/workflows/verify_test_sanitizer_thread.yml

@@ -26,6 +26,6 @@ jobs:
             cmake --build . ;
             sudo make install ) )
     - name: Build
-      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -std=c++23 -g -fsanitize=thread -lstdc++
+      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -std=c++23 -g -fsanitize=thread -lstdc++ -lm
     - name: Test
       run: TSAN_OPTIONS=verbosity=2 ./a.out

.github/workflows/verify_test_sanitizer_undefined_behavior.yml

@@ -26,6 +26,6 @@ jobs:
             cmake --build . ;
             sudo make install ) )
     - name: Build
-      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -std=c++23 -g -fsanitize=undefined -lstdc++
+      run: gcc-11 sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -std=c++23 -g -fsanitize=undefined -lstdc++ -lm
     - name: Test
       run: UBSAN_OPTIONS=verbosity=2 ./a.out

.github/workflows/verify_test_ubuntu-20-04_gcc-trunk.yml

@@ -25,6 +25,6 @@ jobs:
             cmake --build . ;
             sudo make install ) )
     - name: Build
-      run: LD_LIBRARY_PATH=/opt/gcc-latest/lib64 LD_RUN_PATH=/opt/gcc-latest/lib64 /opt/gcc-latest/bin/gcc sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -Wall -Wextra -pedantic -std=c++23 -lstdc++
+      run: LD_LIBRARY_PATH=/opt/gcc-latest/lib64 LD_RUN_PATH=/opt/gcc-latest/lib64 /opt/gcc-latest/bin/gcc sample/*.cpp test/*.cpp source/*.cpp -Iinclude -I/usr/local/include/eigen3 -Wall -Wextra -pedantic -std=c++23 -lstdc++ -lm
     - name: Run
       run: ./a.out

.github/workflows/verify_test_windows-2019_msvc.yml

@@ -14,7 +14,9 @@ jobs:
       uses: actions/checkout@v3
     - name: Install
       uses: ilammy/msvc-dev-cmd@v1.10.0
-    - name: Version
-      run: cl
+    - name: Install Eigen
+      run: vcpkg install eigen3
     - name: Build
-      run: cl /EHsc /std:c++latest /I include /TP sample/*.cpp source/*.cpp test/*.cpp
+      run: cl /EHsc /std:c++latest /I include /I C:\vcpkg\packages\eigen3_x86-windows\include\eigen3 /TP sample/*.cpp source/*.cpp test/*.cpp /Fe:kalman.exe
+    - name: Run
+      run: ./kalman.exe

README.md

@@ -52,11 +52,11 @@ using kalman = fcarouge::kalman<double>;
 
 kalman k;
 
-k.state_x = kalman::state{ 60 };
-k.estimate_uncertainty_p = kalman::estimate_uncertainty{ 15 * 15 };
-k.transition_observation_h = []() { return kalman::observation{ 1 }; };
-k.noise_observation_r = []() {
-  return kalman::observation_noise_uncertainty{ 5 * 5 };
+k.state_x = 60;
+k.estimate_uncertainty_p = 225;
+k.transition_observation_h = [] { return kalman::observation{ 1 }; };
+k.noise_observation_r = [] {
+  return kalman::observation_noise_uncertainty{ 25 };
 };
 
 k.update(48.54);
@@ -74,7 +74,7 @@ const double gravitational_acceleration{ -9.8 }; // m.s^-2
 const std::chrono::milliseconds delta_time{ 250 };
 kalman k;
 
-k.state_x = kalman::state{ 0, 0 };
+k.state_x = { 0, 0 };
 k.estimate_uncertainty_p =
     kalman::estimate_uncertainty{ { 500, 0 }, { 0, 500 } };
 k.transition_state_f = [](const std::chrono::milliseconds &delta_time) {
@@ -92,8 +92,8 @@ k.transition_control_g = [](const std::chrono::milliseconds &delta_time) {
   const auto dt{ std::chrono::duration<double>(delta_time).count() };
   return kalman::control{ 0.0313, dt };
 };
-k.transition_observation_h = []() { return kalman::observation{ { 1, 0 } }; };
-k.noise_observation_r = []() {
+k.transition_observation_h = [] { return kalman::observation{ { 1, 0 } }; };
+k.noise_observation_r = [] {
   return kalman::observation_noise_uncertainty{ 400 };
 };
 

include/fcarouge/kalman.hpp

@@ -90,11 +90,11 @@ class kalman
   // Functors could be replaced by the standard general-purpose polymorphic
   // function wrapper `std::function` if lambda captures are needed.
 
-  observation (*transition_observation_h)() = []() {
+  observation (*transition_observation_h)() = [] {
     return observation{ Identity<observation>()() };
   };
 
-  observation_noise_uncertainty (*noise_observation_r)() = []() {
+  observation_noise_uncertainty (*noise_observation_r)() = [] {
     return observation_noise_uncertainty{};
   };
 

sample/building_height.cpp

@@ -21,20 +21,20 @@ namespace
 //! 55.01m, 55.15m, 49.89m, 40.85m, 46.72m, 50.05m, 51.27m, 49.95m.
 //!
 //! @example building_height.cpp
-[[maybe_unused]] constexpr auto building_height{ []() {
-  // One-dimensional filter, constant system dynamic model.
+[[maybe_unused]] constexpr auto building_height{ [] {
+  // A one-dimensional filter, constant system dynamic model.
   using kalman = kalman<float>;
   kalman k;
 
   // Initialization
   // One can estimate the building height simply by looking at it. The estimated
   // building height is: 60 meters.
-  k.state_x = kalman::state{ 60 };
+  k.state_x = 60;
 
   // Now we shall initialize the estimate uncertainty. A human’s estimation
   // error (standard deviation) is about 15 meters: σ = 15. Consequently the
   // variance is 225: σ^2 = 225.
-  k.estimate_uncertainty_p = kalman::estimate_uncertainty{ 15 * 15 };
+  k.estimate_uncertainty_p = 225;
 
   // Prediction
   // Now, we shall predict the next state based on the initialization values.
@@ -49,8 +49,8 @@ namespace
   // The first measurement is: z1 = 48.54m. Since the standard deviation σ of
   // the altimeter measurement error is 5, the variance σ^2 would be 25, thus
   // the measurement uncertainty is: r1 = 25.
-  k.noise_observation_r = []() {
-    return kalman::observation_noise_uncertainty{ 5 * 5 };
+  k.noise_observation_r = [] {
+    return kalman::observation_noise_uncertainty{ 25 };
   };
   k.update(48.54);
 

sample/liquid_temperature.cpp

@@ -26,29 +26,29 @@ namespace
 //! 50.023°C, and 49.99°C.
 //!
 //! @example liquid_temperature.cpp
-[[maybe_unused]] constexpr auto liquid_temperature{ []() {
-  // One-dimensional filter, constant system dynamic model.
+[[maybe_unused]] constexpr auto liquid_temperature{ [] {
+  // A one-dimensional filter, constant system dynamic model.
   using kalman = kalman<float>;
   kalman k;
 
   // Initialization
   // Before the first iteration, we must initialize the Kalman filter and
   // predict the next state (which is the first state). We don't know what the
   // temperature of the liquid is, and our guess is 10°C.
-  k.state_x = kalman::state{ 10 };
+  k.state_x = 10;
 
   // Our guess is very imprecise, so we set our initialization estimate error σ
   // to 100. The estimate uncertainty of the initialization is the error
   // variance σ^2: p0,0 = 100^2 = 10,000. This variance is very high. If we
   // initialize with a more meaningful value, we will get faster Kalman filter
   // convergence.
-  k.estimate_uncertainty_p = kalman::estimate_uncertainty{ 100 * 100 };
+  k.estimate_uncertainty_p = 100 * 100;
 
   // Prediction
   // Now, we shall predict the next state based on the initialization values. We
   // think that we have an accurate model, thus we set the process noise
   // variance q to 0.0001.
-  k.noise_process_q = []() {
+  k.noise_process_q = [] {
     return kalman::process_noise_uncertainty{ 0.0001 };
   };
 
@@ -67,13 +67,13 @@ namespace
   // 0.1, the variance σ^2 would be 0.01, thus the measurement uncertainty is:
   // r1 = 0.01. The measurement error (standard deviation) is 0.1 degrees
   // Celsius.
-  k.noise_observation_r = []() {
+  k.noise_observation_r = [] {
     return kalman::observation_noise_uncertainty{ 0.1 * 0.1 };
   };
 
   k.update(49.95);
 
-  // And so on.
+  // And so on, every measurements period: Δt = 5s (constant).
   k.predict();
   k.update(49.967);
   k.predict();
@@ -92,15 +92,17 @@ namespace
   k.update(50.023);
   k.predict();
   k.update(49.99);
-  k.predict();
 
   // The estimate uncertainty quickly goes down, after 10 measurements:
-  assert(49.988 - 0.0001 < k.state_x && k.state_x < 49.988 + 0.0001 &&
-         "The filter estimates the liquid temperature at 49.988°C.");
   assert(0.0013 - 0.0001 < k.estimate_uncertainty_p &&
          k.estimate_uncertainty_p < 0.0013 + 0.0001 &&
          "The estimate uncertainty is 0.0013, i.e. the estimate error standard "
          "deviation is: 0.036°C.");
+
+  k.predict();
+
+  assert(49.988 - 0.0001 < k.state_x && k.state_x < 49.988 + 0.0001 &&
+         "The filter estimates the liquid temperature at 49.988°C.");
   // So we can say that the liquid temperature estimate is: 49.988 ± 0.036°C.
   // In this example we've measured a liquid temperature using the
   // one-dimensional Kalman filter. Although the system dynamics include a