Use unicode characters in docs equations (#3487)

javac and javadoc needed the encoding set to UTF-8.

wpimath/src/main/java/edu/wpi/first/math/Matrix.java

@@ -290,7 +290,7 @@ public class Matrix<R extends Num, C extends Num> {
   }
 
   /**
-   * Calculates the transpose, M^T of this matrix.
+   * Calculates the transpose, Mᵀ of this matrix.
    *
    * @return The transpose matrix.
    */

wpimath/src/main/java/edu/wpi/first/math/StateSpaceUtil.java

@@ -88,8 +88,8 @@ public final class StateSpaceUtil {
    * Returns true if (A, B) is a stabilizable pair.
    *
    * <p>(A,B) is stabilizable if and only if the uncontrollable eigenvalues of A, if any, have
-   * absolute values less than one, where an eigenvalue is uncontrollable if rank(lambda * I - A, B)
-   * %3C n where n is number of states.
+   * absolute values less than one, where an eigenvalue is uncontrollable if rank(λI - A, B) %3C n
+   * where n is number of states.
    *
    * @param <States> Num representing the size of A.
    * @param <Inputs> Num representing the columns of B.

wpimath/src/main/java/edu/wpi/first/math/controller/LinearQuadraticRegulator.java

@@ -103,8 +103,8 @@ public class LinearQuadraticRegulator<States extends Num, Inputs extends Num, Ou
 
     var S = Drake.discreteAlgebraicRiccatiEquation(discA, discB, Q, R);
 
+    // K = (BᵀSB + R)⁻¹BᵀSA
     var temp = discB.transpose().times(S).times(discB).plus(R);
-
     m_K = temp.solve(discB.transpose().times(S).times(discA));
 
     m_r = new Matrix<>(new SimpleMatrix(B.getNumRows(), 1));
@@ -137,8 +137,8 @@ public class LinearQuadraticRegulator<States extends Num, Inputs extends Num, Ou
 
     var S = Drake.discreteAlgebraicRiccatiEquation(discA, discB, Q, R, N);
 
+    // K = (BᵀSB + R)⁻¹(BᵀSA + Nᵀ)
     var temp = discB.transpose().times(S).times(discB).plus(R);
-
     m_K = temp.solve(discB.transpose().times(S).times(discA).plus(N.transpose()));
 
     m_r = new Matrix<>(new SimpleMatrix(B.getNumRows(), 1));

wpimath/src/main/java/edu/wpi/first/math/estimator/DifferentialDrivePoseEstimator.java

@@ -36,15 +36,15 @@ import java.util.function.BiConsumer;
  *
  * <p>Our state-space system is:
  *
- * <p><strong> x = [[x, y, theta, dist_l, dist_r]]^T </strong> in the field coordinate system
- * (dist_* are wheel distances.)
+ * <p><strong> x = [[x, y, theta, dist_l, dist_r]]ᵀ </strong> in the field coordinate system (dist_*
+ * are wheel distances.)
  *
- * <p><strong> u = [[vx, vy, omega]]^T </strong> (robot-relative velocities) -- NB: using velocities
+ * <p><strong> u = [[vx, vy, omega]]ᵀ </strong> (robot-relative velocities) -- NB: using velocities
  * make things considerably easier, because it means that teams don't have to worry about getting an
  * accurate model. Basically, we suspect that it's easier for teams to get good encoder data than it
  * is for them to perform system identification well enough to get a good model.
  *
- * <p><strong>y = [[x, y, theta]]^T </strong> from vision, or <strong>y = [[dist_l, dist_r, theta]]
+ * <p><strong>y = [[x, y, theta]]ᵀ </strong> from vision, or <strong>y = [[dist_l, dist_r, theta]]
  * </strong> from encoders and gyro.
  */
 public class DifferentialDrivePoseEstimator {
@@ -66,14 +66,14 @@ public class DifferentialDrivePoseEstimator {
    * @param gyroAngle The current gyro angle.
    * @param initialPoseMeters The starting pose estimate.
    * @param stateStdDevs Standard deviations of model states. Increase these numbers to trust your
-   *     model's state estimates less. This matrix is in the form [x, y, theta, dist_l, dist_r]^T,
+   *     model's state estimates less. This matrix is in the form [x, y, theta, dist_l, dist_r]ᵀ,
    *     with units in meters and radians.
    * @param localMeasurementStdDevs Standard deviations of the encoder and gyro measurements.
    *     Increase these numbers to trust sensor readings from encoders and gyros less. This matrix
-   *     is in the form [dist_l, dist_r, theta]^T, with units in meters and radians.
+   *     is in the form [dist_l, dist_r, theta]ᵀ, with units in meters and radians.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public DifferentialDrivePoseEstimator(
       Rotation2d gyroAngle,
@@ -96,14 +96,14 @@ public class DifferentialDrivePoseEstimator {
    * @param gyroAngle The current gyro angle.
    * @param initialPoseMeters The starting pose estimate.
    * @param stateStdDevs Standard deviations of model states. Increase these numbers to trust your
-   *     model's state estimates less. This matrix is in the form [x, y, theta, dist_l, dist_r]^T,
+   *     model's state estimates less. This matrix is in the form [x, y, theta, dist_l, dist_r]ᵀ,
    *     with units in meters and radians.
    * @param localMeasurementStdDevs Standard deviations of the encoder and gyro measurements.
    *     Increase these numbers to trust sensor readings from encoders and gyros less. This matrix
-   *     is in the form [dist_l, dist_r, theta]^T, with units in meters and radians.
+   *     is in the form [dist_l, dist_r, theta]ᵀ, with units in meters and radians.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    * @param nominalDtSeconds The time in seconds between each robot loop.
    */
   @SuppressWarnings("ParameterName")
@@ -160,7 +160,7 @@ public class DifferentialDrivePoseEstimator {
    *
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public void setVisionMeasurementStdDevs(Matrix<N3, N1> visionMeasurementStdDevs) {
     m_visionContR = StateSpaceUtil.makeCovarianceMatrix(Nat.N3(), visionMeasurementStdDevs);
@@ -279,7 +279,7 @@ public class DifferentialDrivePoseEstimator {
    *     source in this case.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public void addVisionMeasurement(
       Pose2d visionRobotPoseMeters,

wpimath/src/main/java/edu/wpi/first/math/estimator/ExtendedKalmanFilter.java

@@ -141,7 +141,7 @@ public class ExtendedKalmanFilter<States extends Num, Inputs extends Num, Output
 
     final var discR = Discretization.discretizeR(m_contR, dtSeconds);
 
-    // IsStabilizable(A^T, C^T) will tell us if the system is observable.
+    // IsStabilizable(Aᵀ, Cᵀ) will tell us if the system is observable.
     boolean isObservable = StateSpaceUtil.isStabilizable(discA.transpose(), C.transpose());
     if (isObservable && outputs.getNum() <= states.getNum()) {
       m_initP =
@@ -267,7 +267,10 @@ public class ExtendedKalmanFilter<States extends Num, Inputs extends Num, Output
     final var discQ = discPair.getSecond();
 
     m_xHat = NumericalIntegration.rk4(f, m_xHat, u, dtSeconds);
+
+    // Pₖ₊₁⁻ = APₖ⁻Aᵀ + Q
     m_P = discA.times(m_P).times(discA.transpose()).plus(discQ);
+
     m_dtSeconds = dtSeconds;
   }
 
@@ -338,23 +341,24 @@ public class ExtendedKalmanFilter<States extends Num, Inputs extends Num, Output
 
     final var S = C.times(m_P).times(C.transpose()).plus(discR);
 
-    // We want to put K = PC^T S^-1 into Ax = b form so we can solve it more
+    // We want to put K = PCᵀS⁻¹ into Ax = b form so we can solve it more
     // efficiently.
     //
-    // K = PC^T S^-1
-    // KS = PC^T
-    // (KS)^T = (PC^T)^T
-    // S^T K^T = CP^T
+    // K = PCᵀS⁻¹
+    // KS = PCᵀ
+    // (KS)ᵀ = (PCᵀ)ᵀ
+    // SᵀKᵀ = CPᵀ
     //
     // The solution of Ax = b can be found via x = A.solve(b).
     //
-    // K^T = S^T.solve(CP^T)
-    // K = (S^T.solve(CP^T))^T
-    //
-    // Now we have the Kalman gain
+    // Kᵀ = Sᵀ.solve(CPᵀ)
+    // K = (Sᵀ.solve(CPᵀ))ᵀ
     final Matrix<States, Rows> K = S.transpose().solve(C.times(m_P.transpose())).transpose();
 
+    // x̂ₖ₊₁⁺ = x̂ₖ₊₁⁻ + K(y − h(x̂ₖ₊₁⁻, uₖ₊₁))
     m_xHat = addFuncX.apply(m_xHat, K.times(residualFuncY.apply(y, h.apply(m_xHat, u))));
+
+    // Pₖ₊₁⁺ = (I − KC)Pₖ₊₁⁻
     m_P = Matrix.eye(m_states).minus(K.times(C)).times(m_P);
   }
 }

wpimath/src/main/java/edu/wpi/first/math/estimator/KalmanFilter.java

@@ -76,7 +76,7 @@ public class KalmanFilter<States extends Num, Inputs extends Num, Outputs extend
 
     var C = plant.getC();
 
-    // isStabilizable(A^T, C^T) will tell us if the system is observable.
+    // isStabilizable(Aᵀ, Cᵀ) will tell us if the system is observable.
     var isObservable = StateSpaceUtil.isStabilizable(discA.transpose(), C.transpose());
     if (!isObservable) {
       MathSharedStore.reportError(
@@ -90,20 +90,21 @@ public class KalmanFilter<States extends Num, Inputs extends Num, Outputs extend
         new Matrix<>(
             Drake.discreteAlgebraicRiccatiEquation(discA.transpose(), C.transpose(), discQ, discR));
 
+    // S = CPCᵀ + R
     var S = C.times(P).times(C.transpose()).plus(discR);
 
-    // We want to put K = PC^T S^-1 into Ax = b form so we can solve it more
+    // We want to put K = PCᵀS⁻¹ into Ax = b form so we can solve it more
     // efficiently.
     //
-    // K = PC^T S^-1
-    // KS = PC^T
-    // (KS)^T = (PC^T)^T
-    // S^T K^T = CP^T
+    // K = PCᵀS⁻¹
+    // KS = PCᵀ
+    // (KS)ᵀ = (PCᵀ)ᵀ
+    // SᵀKᵀ = CPᵀ
     //
     // The solution of Ax = b can be found via x = A.solve(b).
     //
-    // K^T = S^T.solve(CP^T)
-    // K = (S^T.solve(CP^T))^T
+    // Kᵀ = Sᵀ.solve(CPᵀ)
+    // K = (Sᵀ.solve(CPᵀ))ᵀ
     m_K =
         new Matrix<>(
             S.transpose().getStorage().solve((C.times(P.transpose())).getStorage()).transpose());
@@ -194,6 +195,7 @@ public class KalmanFilter<States extends Num, Inputs extends Num, Outputs extend
   public void correct(Matrix<Inputs, N1> u, Matrix<Outputs, N1> y) {
     final var C = m_plant.getC();
     final var D = m_plant.getD();
+    // x̂ₖ₊₁⁺ = x̂ₖ₊₁⁻ + K(y − (Cx̂ₖ₊₁⁻ + Duₖ₊₁))
     m_xHat = m_xHat.plus(m_K.times(y.minus(C.times(m_xHat).plus(D.times(u)))));
   }
 }

wpimath/src/main/java/edu/wpi/first/math/estimator/MecanumDrivePoseEstimator.java

@@ -34,12 +34,12 @@ import java.util.function.BiConsumer;
  *
  * <p>Our state-space system is:
  *
- * <p><strong> x = [[x, y, theta]]^T </strong> in the field-coordinate system.
+ * <p><strong> x = [[x, y, theta]]ᵀ </strong> in the field-coordinate system.
  *
- * <p><strong> u = [[vx, vy, theta]]^T </strong> in the field-coordinate system.
+ * <p><strong> u = [[vx, vy, theta]]ᵀ </strong> in the field-coordinate system.
  *
- * <p><strong> y = [[x, y, theta]]^T </strong> in field coords from vision, or <strong> y =
- * [[theta]]^T </strong> from the gyro.
+ * <p><strong> y = [[x, y, theta]]ᵀ </strong> in field coords from vision, or <strong> y =
+ * [[theta]]ᵀ </strong> from the gyro.
  */
 public class MecanumDrivePoseEstimator {
   private final UnscentedKalmanFilter<N3, N3, N1> m_observer;
@@ -62,14 +62,14 @@ public class MecanumDrivePoseEstimator {
    * @param initialPoseMeters The starting pose estimate.
    * @param kinematics A correctly-configured kinematics object for your drivetrain.
    * @param stateStdDevs Standard deviations of model states. Increase these numbers to trust your
-   *     model's state estimates less. This matrix is in the form [x, y, theta]^T, with units in
+   *     model's state estimates less. This matrix is in the form [x, y, theta]ᵀ, with units in
    *     meters and radians.
    * @param localMeasurementStdDevs Standard deviations of the encoder and gyro measurements.
    *     Increase these numbers to trust sensor readings from encoders and gyros less. This matrix
    *     is in the form [theta], with units in radians.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public MecanumDrivePoseEstimator(
       Rotation2d gyroAngle,
@@ -95,14 +95,14 @@ public class MecanumDrivePoseEstimator {
    * @param initialPoseMeters The starting pose estimate.
    * @param kinematics A correctly-configured kinematics object for your drivetrain.
    * @param stateStdDevs Standard deviations of model states. Increase these numbers to trust your
-   *     model's state estimates less. This matrix is in the form [x, y, theta]^T, with units in
+   *     model's state estimates less. This matrix is in the form [x, y, theta]ᵀ, with units in
    *     meters and radians.
    * @param localMeasurementStdDevs Standard deviations of the encoder and gyro measurements.
    *     Increase these numbers to trust sensor readings from encoders and gyros less. This matrix
    *     is in the form [theta], with units in radians.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    * @param nominalDtSeconds The time in seconds between each robot loop.
    */
   @SuppressWarnings("ParameterName")
@@ -161,7 +161,7 @@ public class MecanumDrivePoseEstimator {
    *
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public void setVisionMeasurementStdDevs(Matrix<N3, N1> visionMeasurementStdDevs) {
     m_visionContR = StateSpaceUtil.makeCovarianceMatrix(Nat.N3(), visionMeasurementStdDevs);
@@ -242,7 +242,7 @@ public class MecanumDrivePoseEstimator {
    *     Timer.getFPGATimestamp as your time source in this case.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public void addVisionMeasurement(
       Pose2d visionRobotPoseMeters,

wpimath/src/main/java/edu/wpi/first/math/estimator/SwerveDrivePoseEstimator.java

@@ -34,12 +34,12 @@ import java.util.function.BiConsumer;
  *
  * <p>Our state-space system is:
  *
- * <p><strong> x = [[x, y, theta]]^T </strong> in the field-coordinate system.
+ * <p><strong> x = [[x, y, theta]]ᵀ </strong> in the field-coordinate system.
  *
- * <p><strong> u = [[vx, vy, omega]]^T </strong> in the field-coordinate system.
+ * <p><strong> u = [[vx, vy, omega]]ᵀ </strong> in the field-coordinate system.
  *
- * <p><strong> y = [[x, y, theta]]^T </strong> in field coords from vision, or <strong> y =
- * [[theta]]^T </strong> from the gyro.
+ * <p><strong> y = [[x, y, theta]]ᵀ </strong> in field coords from vision, or <strong> y =
+ * [[theta]]ᵀ </strong> from the gyro.
  */
 public class SwerveDrivePoseEstimator {
   private final UnscentedKalmanFilter<N3, N3, N1> m_observer;
@@ -62,14 +62,14 @@ public class SwerveDrivePoseEstimator {
    * @param initialPoseMeters The starting pose estimate.
    * @param kinematics A correctly-configured kinematics object for your drivetrain.
    * @param stateStdDevs Standard deviations of model states. Increase these numbers to trust your
-   *     model's state estimates less. This matrix is in the form [x, y, theta]^T, with units in
+   *     model's state estimates less. This matrix is in the form [x, y, theta]ᵀ, with units in
    *     meters and radians.
    * @param localMeasurementStdDevs Standard deviations of the encoder and gyro measurements.
    *     Increase these numbers to trust sensor readings from encoders and gyros less. This matrix
    *     is in the form [theta], with units in radians.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public SwerveDrivePoseEstimator(
       Rotation2d gyroAngle,
@@ -95,14 +95,14 @@ public class SwerveDrivePoseEstimator {
    * @param initialPoseMeters The starting pose estimate.
    * @param kinematics A correctly-configured kinematics object for your drivetrain.
    * @param stateStdDevs Standard deviations of model states. Increase these numbers to trust your
-   *     model's state estimates less. This matrix is in the form [x, y, theta]^T, with units in
+   *     model's state estimates less. This matrix is in the form [x, y, theta]ᵀ, with units in
    *     meters and radians.
    * @param localMeasurementStdDevs Standard deviations of the encoder and gyro measurements.
    *     Increase these numbers to trust sensor readings from encoders and gyros less. This matrix
    *     is in the form [theta], with units in radians.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    * @param nominalDtSeconds The time in seconds between each robot loop.
    */
   @SuppressWarnings("ParameterName")
@@ -161,7 +161,7 @@ public class SwerveDrivePoseEstimator {
    *
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public void setVisionMeasurementStdDevs(Matrix<N3, N1> visionMeasurementStdDevs) {
     m_visionContR = StateSpaceUtil.makeCovarianceMatrix(Nat.N3(), visionMeasurementStdDevs);
@@ -242,7 +242,7 @@ public class SwerveDrivePoseEstimator {
    *     Timer.getFPGATimestamp as your time source in this case.
    * @param visionMeasurementStdDevs Standard deviations of the vision measurements. Increase these
    *     numbers to trust global measurements from vision less. This matrix is in the form [x, y,
-   *     theta]^T, with units in meters and radians.
+   *     theta]ᵀ, with units in meters and radians.
    */
   public void addVisionMeasurement(
       Pose2d visionRobotPoseMeters,

wpimath/src/main/java/edu/wpi/first/math/estimator/UnscentedKalmanFilter.java

@@ -171,7 +171,9 @@ public class UnscentedKalmanFilter<States extends Num, Inputs extends Num, Outpu
     }
 
     // New mean is usually just the sum of the sigmas * weight:
-    // dot = \Sigma^n_1 (W[k]*Xi[k])
+    //       n
+    // dot = Σ W[k] Xᵢ[k]
+    //      k=1
     Matrix<C, N1> x = meanFunc.apply(sigmas, Wm);
 
     // New covariance is the sum of the outer product of the residuals times the
@@ -403,22 +405,24 @@ public class UnscentedKalmanFilter<States extends Num, Inputs extends Num, Outpu
     // Compute cross covariance of the state and the measurements
     Matrix<States, R> Pxy = new Matrix<>(m_states, rows);
     for (int i = 0; i < m_pts.getNumSigmas(); i++) {
-      // Pxy += (sigmas_f[:, i] - xHat) * (sigmas_h[:, i] - yHat)^T * W_c[i]
+      // Pxy += (sigmas_f[:, i] - x̂)(sigmas_h[:, i] - ŷ)ᵀ W_c[i]
       var dx = residualFuncX.apply(m_sigmasF.extractColumnVector(i), m_xHat);
       var dy = residualFuncY.apply(sigmasH.extractColumnVector(i), yHat).transpose();
 
       Pxy = Pxy.plus(dx.times(dy).times(m_pts.getWc(i)));
     }
 
-    // K = P_{xy} Py^-1
-    // K^T = P_y^T^-1 P_{xy}^T
-    // P_y^T K^T = P_{xy}^T
-    // K^T = P_y^T.solve(P_{xy}^T)
-    // K = (P_y^T.solve(P_{xy}^T)^T
+    // K = P_{xy} P_y⁻¹
+    // Kᵀ = P_yᵀ⁻¹ P_{xy}ᵀ
+    // P_yᵀKᵀ = P_{xy}ᵀ
+    // Kᵀ = P_yᵀ.solve(P_{xy}ᵀ)
+    // K = (P_yᵀ.solve(P_{xy}ᵀ)ᵀ
     Matrix<States, R> K = new Matrix<>(Py.transpose().solve(Pxy.transpose()).transpose());
 
-    // xHat + K * (y - yHat)
+    // x̂ₖ₊₁⁺ = x̂ₖ₊₁⁻ + K(y − ŷ)
     m_xHat = addFuncX.apply(m_xHat, K.times(residualFuncY.apply(y, yHat)));
+
+    // Pₖ₊₁⁺ = Pₖ₊₁⁻ − KP_yKᵀ
     m_P = m_P.minus(K.times(Py).times(K.transpose()));
   }
 }

wpimath/src/main/java/edu/wpi/first/math/filter/LinearFilter.java

@@ -13,8 +13,8 @@ import java.util.Arrays;
  * This class implements a linear, digital filter. All types of FIR and IIR filters are supported.
  * Static factory methods are provided to create commonly used types of filters.
  *
- * <p>Filters are of the form: y[n] = (b0*x[n] + b1*x[n-1] + ... + bP*x[n-P]) - (a0*y[n-1] +
- * a2*y[n-2] + ... + aQ*y[n-Q])
+ * <p>Filters are of the form: y[n] = (b0 x[n] + b1 x[n-1] + ... + bP x[n-P]) - (a0 y[n-1] + a2
+ * y[n-2] + ... + aQ y[n-Q])
  *
  * <p>Where: y[n] is the output at time "n" x[n] is the input at time "n" y[n-1] is the output from
  * the LAST time step ("n-1") x[n-1] is the input from the LAST time step ("n-1") b0...bP are the
@@ -71,8 +71,8 @@ public class LinearFilter {
   }
 
   /**
-   * Creates a one-pole IIR low-pass filter of the form: y[n] = (1-gain)*x[n] + gain*y[n-1] where
-   * gain = e^(-dt / T), T is the time constant in seconds.
+   * Creates a one-pole IIR low-pass filter of the form: y[n] = (1-gain) x[n] + gain y[n-1] where
+   * gain = e<sup>-dt / T</sup>, T is the time constant in seconds.
    *
    * <p>Note: T = 1 / (2 pi f) where f is the cutoff frequency in Hz, the frequency above which the
    * input starts to attenuate.
@@ -92,8 +92,8 @@ public class LinearFilter {
   }
 
   /**
-   * Creates a first-order high-pass filter of the form: y[n] = gain*x[n] + (-gain)*x[n-1] +
-   * gain*y[n-1] where gain = e^(-dt / T), T is the time constant in seconds.
+   * Creates a first-order high-pass filter of the form: y[n] = gain x[n] + (-gain) x[n-1] + gain
+   * y[n-1] where gain = e<sup>-dt / T</sup>, T is the time constant in seconds.
    *
    * <p>Note: T = 1 / (2 pi f) where f is the cutoff frequency in Hz, the frequency below which the
    * input starts to attenuate.
@@ -113,8 +113,7 @@ public class LinearFilter {
   }
 
   /**
-   * Creates a K-tap FIR moving average filter of the form: y[n] = 1/k * (x[k] + x[k-1] + ... +
-   * x[0]).
+   * Creates a K-tap FIR moving average filter of the form: y[n] = 1/k (x[k] + x[k-1] + ... + x[0]).
    *
    * <p>This filter is always stable.
    *

wpimath/src/main/java/edu/wpi/first/math/system/Discretization.java

@@ -64,6 +64,7 @@ public final class Discretization {
   /**
    * Discretizes the given continuous A and Q matrices.
    *
+   * @param <States> Nat representing the number of states.
    * @param contA Continuous system matrix.
    * @param contQ Continuous process noise covariance matrix.
    * @param dtSeconds Discretization timestep.
@@ -128,11 +129,11 @@ public final class Discretization {
     Matrix<States, States> lastTerm = Q.copy();
     double lastCoeff = dtSeconds;
 
-    // A^T^n
+    // Aᵀⁿ
     Matrix<States, States> Atn = contA.transpose();
     Matrix<States, States> phi12 = lastTerm.times(lastCoeff);
 
-    // i = 6 i.e. 6th order should be enough precision
+    // i = 6 i.e. 5th order should be enough precision
     for (int i = 2; i < 6; ++i) {
       lastTerm = contA.times(-1).times(lastTerm).plus(Q.times(Atn));
       lastCoeff *= dtSeconds / ((double) i);

wpimath/src/main/java/edu/wpi/first/math/system/plant/LinearSystemId.java

@@ -18,7 +18,7 @@ public final class LinearSystemId {
 
   /**
    * Create a state-space model of an elevator system. The states of the system are [position,
-   * velocity]^T, inputs are [voltage], and outputs are [position].
+   * velocity]ᵀ, inputs are [voltage], and outputs are [position].
    *
    * @param motor The motor (or gearbox) attached to the arm.
    * @param massKg The mass of the elevator carriage, in kilograms.
@@ -72,7 +72,7 @@ public final class LinearSystemId {
 
   /**
    * Create a state-space model of a differential drive drivetrain. In this model, the states are
-   * [v_left, v_right]^T, inputs are [V_left, V_right]^T and outputs are [v_left, v_right]^T.
+   * [v_left, v_right]ᵀ, inputs are [V_left, V_right]ᵀ and outputs are [v_left, v_right]ᵀ.
    *
    * @param motor the gearbox representing the motors driving the drivetrain.
    * @param massKg the mass of the robot.
@@ -157,7 +157,7 @@ public final class LinearSystemId {
   /**
    * Identify a position system from it's kV (volts/(unit/sec)) and kA (volts/(unit/sec^2). These
    * constants cam be found using frc-characterization. The states of the system are [position,
-   * velocity]^T, inputs are [voltage], and outputs are [position].
+   * velocity]ᵀ, inputs are [voltage], and outputs are [position].
    *
    * <p>The distance unit you choose MUST be an SI unit (i.e. meters or radians). You can use the
    * {@link edu.wpi.first.math.util.Units} class for converting between unit types.
@@ -181,8 +181,8 @@ public final class LinearSystemId {
    * Identify a standard differential drive drivetrain, given the drivetrain's kV and kA in both
    * linear (volts/(meter/sec) and volts/(meter/sec^2)) and angular (volts/(meter/sec) and
    * volts/(meter/sec^2)) cases. This can be found using frc-characterization. The states of the
-   * system are [left velocity, right velocity]^T, inputs are [left voltage, right voltage]^T, and
-   * outputs are [left velocity, right velocity]^T.
+   * system are [left velocity, right velocity]ᵀ, inputs are [left voltage, right voltage]ᵀ, and
+   * outputs are [left velocity, right velocity]ᵀ.
    *
    * @param kVLinear The linear velocity gain, volts per (meter per second).
    * @param kALinear The linear acceleration gain, volts per (meter per second squared).
@@ -211,8 +211,8 @@ public final class LinearSystemId {
    * Identify a standard differential drive drivetrain, given the drivetrain's kV and kA in both
    * linear (volts/(meter/sec) and volts/(meter/sec^2)) and angular (volts/(radian/sec) and
    * volts/(radian/sec^2)) cases. This can be found using frc-characterization. The states of the
-   * system are [left velocity, right velocity]^T, inputs are [left voltage, right voltage]^T, and
-   * outputs are [left velocity, right velocity]^T.
+   * system are [left velocity, right velocity]ᵀ, inputs are [left voltage, right voltage]ᵀ, and
+   * outputs are [left velocity, right velocity]ᵀ.
    *
    * @param kVLinear The linear velocity gain, volts per (meter per second).
    * @param kALinear The linear acceleration gain, volts per (meter per second squared).