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Webrtc delay-base-bwe代码分析(3): OveruseEstimator模块

该模块是一个卡尔曼滤波，根据当前到达时间差和传输大小的值，对到达时间差进行滤波，计算更精准的到达时间差。

0. 卡尔曼滤波基础公式

从参考文档中获得基础公式及对应变量意义。

公式：

变量：

1. OveruseEstimator的卡尔曼滤波公式

2. 代码分析

2.1 update

void OveruseEstimator::Update(int64_t t_delta,                              double ts_delta,                              int size_delta,                              BandwidthUsage current_hypothesis) {  const double min_frame_period = UpdateMinFramePeriod(ts_delta);  const double t_ts_delta = t_delta - ts_delta;  double fs_delta = size_delta;  ++num_of_deltas_;  if (num_of_deltas_ > kDeltaCounterMax) {    num_of_deltas_ = kDeltaCounterMax;  }  // Update the Kalman filter.  // 误差矩阵  // 加上协方差，为配置初始化值。  // process_noise_ Q  // P(k) = AP(k - 1)AT + Q  // 预测方程2  // 2.3  E_[0][0] += process_noise_[0];  E_[1][1] += process_noise_[1];  if ((current_hypothesis == kBwOverusing && offset_ < prev_offset_) ||      (current_hypothesis == kBwUnderusing && offset_ > prev_offset_)) {    E_[1][1] += 10 * process_noise_[1];  }  // h观测矩阵  // 2.2  const double h[2] = {fs_delta, 1.0};  // P * h转置  // 2.4  const double Eh[2] = {E_[0][0]*h[0] + E_[0][1]*h[1],                        E_[1][0]*h[0] + E_[1][1]*h[1]};  // t_ts_delta 为 zk，residual为 zk - H * xk  // 2.7   const double residual = t_ts_delta - slope_*h[0] - offset_;  const bool in_stable_state = (current_hypothesis == kBwNormal);  const double max_residual = 3.0 * sqrt(var_noise_);  // We try to filter out very late frames. For instance periodic key  // frames doesn't fit the Gaussian model well.  if (fabs(residual) < max_residual) {    UpdateNoiseEstimate(residual, min_frame_period, in_stable_state);  } else {    UpdateNoiseEstimate(residual < 0 ? -max_residual : max_residual,                        min_frame_period, in_stable_state);  }  // denom = h * P * ht + R，var_noise为测量噪声协方差  // 2.5  const double denom = var_noise_ + h[0]*Eh[0] + h[1]*Eh[1];  // K卡尔曼增益矩阵  // K(k) = Eh / (HPkHT + R)   // 校正方程3  // 2.6  const double K[2] = {Eh[0] / denom,                       Eh[1] / denom};  // Ikh I-Kh  // 2.9  const double IKh[2][2] = {{1.0 - K[0]*h[0], -K[0]*h[1]},                            {-K[1]*h[0], 1.0 - K[1]*h[1]}};  const double e00 = E_[0][0];  const double e01 = E_[0][1];  // Update state.  // 使用IKh更新误差矩阵  // P(k) = (I - Kh)P(k - 1)  // 校准方程5  // 2.10  E_[0][0] = e00 * IKh[0][0] + E_[1][0] * IKh[0][1];  E_[0][1] = e01 * IKh[0][0] + E_[1][1] * IKh[0][1];  E_[1][0] = e00 * IKh[1][0] + E_[1][0] * IKh[1][1];  E_[1][1] = e01 * IKh[1][0] + E_[1][1] * IKh[1][1];  // The covariance matrix must be positive semi-definite.  bool positive_semi_definite = E_[0][0] + E_[1][1] >= 0 &&      E_[0][0] * E_[1][1] - E_[0][1] * E_[1][0] >= 0 && E_[0][0] >= 0;  assert(positive_semi_definite);  if (!positive_semi_definite) {    LOG(LS_ERROR) << "The over-use estimator's covariance matrix is no longer "                     "semi-definite.";  }  // 2.8  slope_ = slope_ + K[0] * residual;  prev_offset_ = offset_;  offset_ = offset_ + K[1] * residual;}

2.2 噪声更新

// 这个函数主要提供下面函数需要用到的ts_delta，这里不是直接使用// 本次的ts_delta，而是根据历史时间窗口中最小时间值作为噪声估计中的ts_delta// 这个函数就是在一个固定的时间窗口中按时间顺序存放每一个ts_delta// 当数量超过时就从最早的时间开始pop// 然后遍历整个时间窗口选择最小的时间差值。double OveruseEstimator::UpdateMinFramePeriod(double ts_delta) {  double min_frame_period = ts_delta;  if (ts_delta_hist_.size() >= kMinFramePeriodHistoryLength) {    ts_delta_hist_.pop_front();  }  std::list<double>::iterator it = ts_delta_hist_.begin();  for (; it != ts_delta_hist_.end(); it++) {    min_frame_period = std::min(*it, min_frame_period);  }  ts_delta_hist_.push_back(ts_delta);  return min_frame_period;}void OveruseEstimator::UpdateNoiseEstimate(double residual,                                           double ts_delta,                                           bool stable_state) {  // 仅在Normal状态下更新噪声值。  if (!stable_state) {    return;  }  // Faster filter during startup to faster adapt to the jitter level  // of the network. |alpha| is tuned for 30 frames per second, but is scaled  // according to |ts_delta|.  double alpha = 0.01;  if (num_of_deltas_ > 10*30) {    alpha = 0.002;  }  // Only update the noise estimate if we're not over-using. |beta| is a  // function of alpha and the time delta since the previous update.  // 时间差越大，残差的比重越小  // 由于上面函数控制一个时间窗口，因此一个时间窗口内，其权重基本固定。  const double beta = pow(1 - alpha, ts_delta * 30.0 / 1000.0);  // 更新均值  avg_noise_ = beta * avg_noise_              + (1 - beta) * residual;  // 利用方差更新噪声值。  var_noise_ = beta * var_noise_              + (1 - beta) * (avg_noise_ - residual) * (avg_noise_ - residual);  if (var_noise_ < 1) {    var_noise_ = 1;  }}

参考文档

1 卡尔曼滤波简介