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Implement a weighted least squares VelocityTracker strategy.

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No change to the default strategy.

Bug: 6413587
Change-Id: I08eb6f9a511e65ad637359b55b5993c26ba93b40
This commit is contained in:
Jeff Brown
2012-06-03 14:18:26 -07:00
parent 433927c52f
commit 18f329e948
2 changed files with 145 additions and 22 deletions
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20
include/androidfw/VelocityTracker.h
View File

@@ -138,8 +138,23 @@ public:
*/
class LeastSquaresVelocityTrackerStrategy : public VelocityTrackerStrategy {
public:
enum Weighting {
// No weights applied. All data points are equally reliable.
WEIGHTING_NONE,
// Weight by time delta. Data points clustered together are weighted less.
WEIGHTING_DELTA,
// Weight such that points within a certain horizon are weighed more than those
// outside of that horizon.
WEIGHTING_CENTRAL,
// Weight such that points older than a certain amount are weighed less.
WEIGHTING_RECENT,
};
// Degree must be no greater than Estimator::MAX_DEGREE.
LeastSquaresVelocityTrackerStrategy(uint32_t degree);
LeastSquaresVelocityTrackerStrategy(uint32_t degree, Weighting weighting = WEIGHTING_NONE);
virtual ~LeastSquaresVelocityTrackerStrategy();
virtual void clear();
@@ -167,7 +182,10 @@ private:
}
};
float chooseWeight(uint32_t index) const;
const uint32_t mDegree;
const Weighting mWeighting;
uint32_t mIndex;
Movement mMovements[HISTORY_SIZE];
};

147
libs/androidfw/VelocityTracker.cpp
View File

@@ -161,6 +161,21 @@ VelocityTrackerStrategy* VelocityTracker::createStrategy(const char* strategy) {
// of the velocity when the finger is released.
return new LeastSquaresVelocityTrackerStrategy(3);
}
if (!strcmp("wlsq2-delta", strategy)) {
// 2nd order weighted least squares, delta weighting. Quality: EXPERIMENTAL
return new LeastSquaresVelocityTrackerStrategy(2,
LeastSquaresVelocityTrackerStrategy::WEIGHTING_DELTA);
}
if (!strcmp("wlsq2-central", strategy)) {
// 2nd order weighted least squares, central weighting. Quality: EXPERIMENTAL
return new LeastSquaresVelocityTrackerStrategy(2,
LeastSquaresVelocityTrackerStrategy::WEIGHTING_CENTRAL);
}
if (!strcmp("wlsq2-recent", strategy)) {
// 2nd order weighted least squares, recent weighting. Quality: EXPERIMENTAL
return new LeastSquaresVelocityTrackerStrategy(2,
LeastSquaresVelocityTrackerStrategy::WEIGHTING_RECENT);
}
if (!strcmp("int1", strategy)) {
// 1st order integrating filter. Quality: GOOD.
// Not as good as 'lsq2' because it cannot estimate acceleration but it is
@@ -327,8 +342,9 @@ bool VelocityTracker::getEstimator(uint32_t id, Estimator* outEstimator) const {
const nsecs_t LeastSquaresVelocityTrackerStrategy::HORIZON;
const uint32_t LeastSquaresVelocityTrackerStrategy::HISTORY_SIZE;
LeastSquaresVelocityTrackerStrategy::LeastSquaresVelocityTrackerStrategy(uint32_t degree) :
mDegree(degree) {
LeastSquaresVelocityTrackerStrategy::LeastSquaresVelocityTrackerStrategy(
uint32_t degree, Weighting weighting) :
mDegree(degree), mWeighting(weighting) {
clear();
}
@@ -366,10 +382,23 @@ void LeastSquaresVelocityTrackerStrategy::addMovement(nsecs_t eventTime, BitSet3
*
* Returns true if a solution is found, false otherwise.
*
* The input consists of two vectors of data points X and Y with indices 0..m-1.
* The input consists of two vectors of data points X and Y with indices 0..m-1
* along with a weight vector W of the same size.
*
* The output is a vector B with indices 0..n that describes a polynomial
* that fits the data, such the sum of abs(Y[i] - (B[0] + B[1] X[i] + B[2] X[i]^2 ... B[n] X[i]^n))
* for all i between 0 and m-1 is minimized.
* that fits the data, such the sum of W[i] * W[i] * abs(Y[i] - (B[0] + B[1] X[i]
* + B[2] X[i]^2 ... B[n] X[i]^n)) for all i between 0 and m-1 is minimized.
*
* Accordingly, the weight vector W should be initialized by the caller with the
* reciprocal square root of the variance of the error in each input data point.
* In other words, an ideal choice for W would be W[i] = 1 / var(Y[i]) = 1 / stddev(Y[i]).
* The weights express the relative importance of each data point. If the weights are
* all 1, then the data points are considered to be of equal importance when fitting
* the polynomial. It is a good idea to choose weights that diminish the importance
* of data points that may have higher than usual error margins.
*
* Errors among data points are assumed to be independent. W is represented here
* as a vector although in the literature it is typically taken to be a diagonal matrix.
*
* That is to say, the function that generated the input data can be approximated
* by y(x) ~= B[0] + B[1] x + B[2] x^2 + ... + B[n] x^n.
@@ -379,14 +408,15 @@ void LeastSquaresVelocityTrackerStrategy::addMovement(nsecs_t eventTime, BitSet3
* indicates perfect correspondence.
*
* This function first expands the X vector to a m by n matrix A such that
* A[i][0] = 1, A[i][1] = X[i], A[i][2] = X[i]^2, ..., A[i][n] = X[i]^n.
* A[i][0] = 1, A[i][1] = X[i], A[i][2] = X[i]^2, ..., A[i][n] = X[i]^n, then
* multiplies it by w[i]./
*
* Then it calculates the QR decomposition of A yielding an m by m orthonormal matrix Q
* and an m by n upper triangular matrix R. Because R is upper triangular (lower
* part is all zeroes), we can simplify the decomposition into an m by n matrix
* Q1 and a n by n matrix R1 such that A = Q1 R1.
*
* Finally we solve the system of linear equations given by R1 B = (Qtranspose Y)
* Finally we solve the system of linear equations given by R1 B = (Qtranspose W Y)
* to find B.
*
* For efficiency, we lay out A and Q column-wise in memory because we frequently
@@ -395,17 +425,18 @@ void LeastSquaresVelocityTrackerStrategy::addMovement(nsecs_t eventTime, BitSet3
* http://en.wikipedia.org/wiki/Numerical_methods_for_linear_least_squares
* http://en.wikipedia.org/wiki/Gram-Schmidt
*/
static bool solveLeastSquares(const float* x, const float* y, uint32_t m, uint32_t n,
float* outB, float* outDet) {
static bool solveLeastSquares(const float* x, const float* y,
const float* w, uint32_t m, uint32_t n, float* outB, float* outDet) {
#if DEBUG_STRATEGY
ALOGD("solveLeastSquares: m=%d, n=%d, x=%s, y=%s", int(m), int(n),
vectorToString(x, m).string(), vectorToString(y, m).string());
ALOGD("solveLeastSquares: m=%d, n=%d, x=%s, y=%s, w=%s", int(m), int(n),
vectorToString(x, m).string(), vectorToString(y, m).string(),
vectorToString(w, m).string());
#endif
// Expand the X vector to a matrix A.
// Expand the X vector to a matrix A, pre-multiplied by the weights.
float a[n][m]; // column-major order
for (uint32_t h = 0; h < m; h++) {
a[0][h] = 1;
a[0][h] = w[h];
for (uint32_t i = 1; i < n; i++) {
a[i][h] = a[i - 1][h] * x[h];
}
@@ -462,10 +493,14 @@ static bool solveLeastSquares(const float* x, const float* y, uint32_t m, uint32
ALOGD(" - qr=%s", matrixToString(&qr[0][0], m, n, false /*rowMajor*/).string());
#endif
// Solve R B = Qt Y to find B. This is easy because R is upper triangular.
// Solve R B = Qt W Y to find B. This is easy because R is upper triangular.
// We just work from bottom-right to top-left calculating B's coefficients.
float wy[m];
for (uint32_t h = 0; h < m; h++) {
wy[h] = y[h] * w[h];
}
for (uint32_t i = n; i-- != 0; ) {
outB[i] = vectorDot(&q[i][0], y, m);
outB[i] = vectorDot(&q[i][0], wy, m);
for (uint32_t j = n - 1; j > i; j--) {
outB[i] -= r[i][j] * outB[j];
}
@@ -476,8 +511,9 @@ static bool solveLeastSquares(const float* x, const float* y, uint32_t m, uint32
#endif
// Calculate the coefficient of determination as 1 - (SSerr / SStot) where
// SSerr is the residual sum of squares (squared variance of the error),
// and SStot is the total sum of squares (squared variance of the data).
// SSerr is the residual sum of squares (variance of the error),
// and SStot is the total sum of squares (variance of the data) where each
// has been weighted.
float ymean = 0;
for (uint32_t h = 0; h < m; h++) {
ymean += y[h];
@@ -493,9 +529,9 @@ static bool solveLeastSquares(const float* x, const float* y, uint32_t m, uint32
term *= x[h];
err -= term * outB[i];
}
sserr += err * err;
sserr += w[h] * w[h] * err * err;
float var = y[h] - ymean;
sstot += var * var;
sstot += w[h] * w[h] * var * var;
}
*outDet = sstot > 0.000001f ? 1.0f - (sserr / sstot) : 1;
#if DEBUG_STRATEGY
@@ -513,6 +549,7 @@ bool LeastSquaresVelocityTrackerStrategy::getEstimator(uint32_t id,
// Iterate over movement samples in reverse time order and collect samples.
float x[HISTORY_SIZE];
float y[HISTORY_SIZE];
float w[HISTORY_SIZE];
float time[HISTORY_SIZE];
uint32_t m = 0;
uint32_t index = mIndex;
@@ -531,6 +568,7 @@ bool LeastSquaresVelocityTrackerStrategy::getEstimator(uint32_t id,
const VelocityTracker::Position& position = movement.getPosition(id);
x[m] = position.x;
y[m] = position.y;
w[m] = chooseWeight(index);
time[m] = -age * 0.000000001f;
index = (index == 0 ? HISTORY_SIZE : index) - 1;
} while (++m < HISTORY_SIZE);
@@ -547,8 +585,8 @@ bool LeastSquaresVelocityTrackerStrategy::getEstimator(uint32_t id,
if (degree >= 1) {
float xdet, ydet;
uint32_t n = degree + 1;
if (solveLeastSquares(time, x, m, n, outEstimator->xCoeff, &xdet)
&& solveLeastSquares(time, y, m, n, outEstimator->yCoeff, &ydet)) {
if (solveLeastSquares(time, x, w, m, n, outEstimator->xCoeff, &xdet)
&& solveLeastSquares(time, y, w, m, n, outEstimator->yCoeff, &ydet)) {
outEstimator->time = newestMovement.eventTime;
outEstimator->degree = degree;
outEstimator->confidence = xdet * ydet;
@@ -572,6 +610,73 @@ bool LeastSquaresVelocityTrackerStrategy::getEstimator(uint32_t id,
return true;
}
float LeastSquaresVelocityTrackerStrategy::chooseWeight(uint32_t index) const {
switch (mWeighting) {
case WEIGHTING_DELTA: {
// Weight points based on how much time elapsed between them and the next
// point so that points that "cover" a shorter time span are weighed less.
// delta 0ms: 0.5
// delta 10ms: 1.0
if (index == mIndex) {
return 1.0f;
}
uint32_t nextIndex = (index + 1) % HISTORY_SIZE;
float deltaMillis = (mMovements[nextIndex].eventTime- mMovements[index].eventTime)
* 0.000001f;
if (deltaMillis < 0) {
return 0.5f;
}
if (deltaMillis < 10) {
return 0.5f + deltaMillis * 0.05;
}
return 1.0f;
}
case WEIGHTING_CENTRAL: {
// Weight points based on their age, weighing very recent and very old points less.
// age 0ms: 0.5
// age 10ms: 1.0
// age 50ms: 1.0
// age 60ms: 0.5
float ageMillis = (mMovements[mIndex].eventTime - mMovements[index].eventTime)
* 0.000001f;
if (ageMillis < 0) {
return 0.5f;
}
if (ageMillis < 10) {
return 0.5f + ageMillis * 0.05;
}
if (ageMillis < 50) {
return 1.0f;
}
if (ageMillis < 60) {
return 0.5f + (60 - ageMillis) * 0.05;
}
return 0.5f;
}
case WEIGHTING_RECENT: {
// Weight points based on their age, weighing older points less.
// age 0ms: 1.0
// age 50ms: 1.0
// age 100ms: 0.5
float ageMillis = (mMovements[mIndex].eventTime - mMovements[index].eventTime)
* 0.000001f;
if (ageMillis < 50) {
return 1.0f;
}
if (ageMillis < 100) {
return 0.5f + (100 - ageMillis) * 0.01f;
}
return 0.5f;
}
case WEIGHTING_NONE:
default:
return 1.0f;
}
}
// --- IntegratingVelocityTrackerStrategy ---