WebRTC QoS方法十三.2（Jitter延时的计算）

一、背景介绍

一些报文在网络传输中，会存在丢包重传和延时的情况。渲染时需要进行适当缓存，等待丢失被重传的报文或者正在路上传输的报文。

jitter延时计算是确认需要缓存的时间

另外，在检测到帧有重传情况时，也可适当在渲染时间内增加RTT延时时间，等待丢失重传的报文

二、jitter实现原理

JitterDelay由两部分延迟造成：传输大帧引起的延迟和网络噪声引起的延迟。计算公式如下：

其中：

estimate[0]：信道传输速率的倒数
MaxFrameSize：表示自会话开始以来所收到的最大帧size
AvgFrameSize：表示平均帧大小，排除keyframe等超大帧

kNoiseStdDevs： 表示噪声系数2.33
var_noise_ms2_： 表示噪声方差
kNoiseStdDevOffset: 表示噪声扣除常数30

实现函数：

JitterEstimator::CalculateEstimate

1、传输大帧引起的延迟

传输大帧引起的延迟

这个公式的原理是：[milliseconds] = [1 / bytes per millisecond] * [bytes]

实现函数：

double FrameDelayVariationKalmanFilter::GetFrameDelayVariationEstimateSizeBased(
    double frame_size_variation_bytes) const {
  // Unit: [1 / bytes per millisecond] * [bytes] = [milliseconds].
  return estimate_[0] * frame_size_variation_bytes;
}

filtered_max_frame_size_bytes

= std::max<double>(kPsi * max_frame_size_bytes_, frame_size.bytes());

constexpr double kPsi = 0.9999;

filtered_avg_frame_size_bytes

是每一帧的加权平均值，但是需要排除key frame这种超大帧

estimate_[0]参数计算：

使用一个简化卡尔曼滤波算法，在处理帧延迟变化(frame_delay_variation_ms)的估计，考虑了帧大小变化(frame_size_variation_bytes)和最大帧大小(max_frame_size_bytes)作为输入参数。

void FrameDelayVariationKalmanFilter::PredictAndUpdate(
    double frame_delay_variation_ms,
    double frame_size_variation_bytes,
    double max_frame_size_bytes,
    double var_noise) {
  // Sanity checks.
  if (max_frame_size_bytes < 1) {
    return;
  }
  if (var_noise <= 0.0) {
    return;
  }

  // This member function follows the data flow in
  // https://en.wikipedia.org/wiki/Kalman_filter#Details.

  // 1) Estimate prediction: `x = F*x`.
  // For this model, there is no need to explicitly predict the estimate, since
  // the state transition matrix is the identity.

  // 2) Estimate covariance prediction: `P = F*P*F' + Q`.
  // Again, since the state transition matrix is the identity, this update
  // is performed by simply adding the process noise covariance.
  estimate_cov_[0][0] += process_noise_cov_diag_[0];
  estimate_cov_[1][1] += process_noise_cov_diag_[1];

  // 3) Innovation: `y = z - H*x`.
  // This is the part of the measurement that cannot be explained by the current
  // estimate.
  double innovation =
      frame_delay_variation_ms -
      GetFrameDelayVariationEstimateTotal(frame_size_variation_bytes);

  // 4) Innovation variance: `s = H*P*H' + r`.
  double estim_cov_times_obs[2];
  estim_cov_times_obs[0] =
      estimate_cov_[0][0] * frame_size_variation_bytes + estimate_cov_[0][1];
  estim_cov_times_obs[1] =
      estimate_cov_[1][0] * frame_size_variation_bytes + estimate_cov_[1][1];
  double observation_noise_stddev =
      (300.0 * exp(-fabs(frame_size_variation_bytes) /
                   (1e0 * max_frame_size_bytes)) +
       1) *
      sqrt(var_noise);
  if (observation_noise_stddev < 1.0) {
    observation_noise_stddev = 1.0;
  }
  // TODO(brandtr): Shouldn't we add observation_noise_stddev^2 here? Otherwise,
  // the dimensional analysis fails.
  double innovation_var = frame_size_variation_bytes * estim_cov_times_obs[0] +
                          estim_cov_times_obs[1] + observation_noise_stddev;
  if ((innovation_var < 1e-9 && innovation_var >= 0) ||
      (innovation_var > -1e-9 && innovation_var <= 0)) {
    RTC_DCHECK_NOTREACHED();
    return;
  }

  // 5) Optimal Kalman gain: `K = P*H'/s`.
  // How much to trust the model vs. how much to trust the measurement.
  double kalman_gain[2];
  kalman_gain[0] = estim_cov_times_obs[0] / innovation_var;
  kalman_gain[1] = estim_cov_times_obs[1] / innovation_var;

  // 6) Estimate update: `x = x + K*y`.
  // Optimally weight the new information in the innovation and add it to the
  // old estimate.
  estimate_[0] += kalman_gain[0] * innovation;
  estimate_[1] += kalman_gain[1] * innovation;

  // (This clamping is not part of the linear Kalman filter.)
  if (estimate_[0] < kMaxBandwidth) {
    estimate_[0] = kMaxBandwidth;
  }

  // 7) Estimate covariance update: `P = (I - K*H)*P`
  double t00 = estimate_cov_[0][0];
  double t01 = estimate_cov_[0][1];
  estimate_cov_[0][0] =
      (1 - kalman_gain[0] * frame_size_variation_bytes) * t00 -
      kalman_gain[0] * estimate_cov_[1][0];
  estimate_cov_[0][1] =
      (1 - kalman_gain[0] * frame_size_variation_bytes) * t01 -
      kalman_gain[0] * estimate_cov_[1][1];
  estimate_cov_[1][0] = estimate_cov_[1][0] * (1 - kalman_gain[1]) -
                        kalman_gain[1] * frame_size_variation_bytes * t00;
  estimate_cov_[1][1] = estimate_cov_[1][1] * (1 - kalman_gain[1]) -
                        kalman_gain[1] * frame_size_variation_bytes * t01;

  // Covariance matrix, must be positive semi-definite.
  RTC_DCHECK(estimate_cov_[0][0] + estimate_cov_[1][1] >= 0 &&
             estimate_cov_[0][0] * estimate_cov_[1][1] -
                     estimate_cov_[0][1] * estimate_cov_[1][0] >=
                 0 &&
             estimate_cov_[0][0] >= 0);
}

2、网络噪声引起的延迟

网络噪声引起的延迟

constexpr double kNoiseStdDevs = 2.33; //噪声系数

constexpr double kNoiseStdDevOffset = 30.0;//噪声扣除常数

var_noise_ms2_ //噪声方差

实现函数：

噪声方差var_noise_ms2计算

var_noise_ms2 = alpha * var_noise_ms2_ +
(1 - alpha) *(d_dT - avg_noise_ms_) *(d_dT - avg_noise_ms_);

实现函数：JitterEstimator::EstimateRandomJitter

其中：

d_dT = 实际FrameDelay - 评估FrameDelay

         在JitterEstimator::UpdateEstimate函数实现

         ![](https://i-blog.csdnimg.cn/direct/90f0522e6e2941b58810bed37a4dbb79.png)

实际FrameDelay = （两帧之间实际接收gap - 两帧之间实际发送gap）

         在InterFrameDelayVariationCalculator::Calculate函数实现

absl::optional<TimeDelta> InterFrameDelayVariationCalculator::Calculate(
    uint32_t rtp_timestamp,
    Timestamp now) {
  int64_t rtp_timestamp_unwrapped = unwrapper_.Unwrap(rtp_timestamp);

  if (!prev_wall_clock_) {
    prev_wall_clock_ = now;
    prev_rtp_timestamp_unwrapped_ = rtp_timestamp_unwrapped;
    // Inter-frame delay variation is undefined for a single frame.
    // TODO(brandtr): Should this return absl::nullopt instead?
    return TimeDelta::Zero();
  }

  // Account for reordering in jitter variance estimate in the future?
  // Note that this also captures incomplete frames which are grabbed for
  // decoding after a later frame has been complete, i.e. real packet losses.
  uint32_t cropped_prev = static_cast<uint32_t>(prev_rtp_timestamp_unwrapped_);
  if (rtp_timestamp_unwrapped < prev_rtp_timestamp_unwrapped_ ||
      !IsNewerTimestamp(rtp_timestamp, cropped_prev)) {
    return absl::nullopt;
  }

  // Compute the compensated timestamp difference.
  TimeDelta delta_wall = now - *prev_wall_clock_;
  int64_t d_rtp_ticks = rtp_timestamp_unwrapped - prev_rtp_timestamp_unwrapped_;
  TimeDelta delta_rtp = d_rtp_ticks / k90kHz;

  // The inter-frame delay variation is the second order difference between the
  // RTP and wall clocks of the two frames, or in other words, the first order
  // difference between `delta_rtp` and `delta_wall`.
  TimeDelta inter_frame_delay_variation = delta_wall - delta_rtp;

  prev_wall_clock_ = now;
  prev_rtp_timestamp_unwrapped_ = rtp_timestamp_unwrapped;

  return inter_frame_delay_variation;
}

评估FrameDelay = estimate[0] * (FrameSize – PreFrameSize) + estimate[1]

评估FrameDelay实现函数：

double FrameDelayVariationKalmanFilter::GetFrameDelayVariationEstimateTotal(
    double frame_size_variation_bytes) const {
  double frame_transmission_delay_ms =
      GetFrameDelayVariationEstimateSizeBased(frame_size_variation_bytes);
  double link_queuing_delay_ms = estimate_[1];
  return frame_transmission_delay_ms + link_queuing_delay_ms;
}

3、jitter延时更新流程

三、RTT延时计算

VideoStreamBufferController::OnFrameReady函数，在判断帧有重传情况时，还会根据实际情况，在渲染帧时间里面增加RTT值。

JitterEstimator::GetJitterEstimate根据实际配置，可以在渲染时间中适当增加一定比例的RTT延时值。

四、参考

WebRTC视频接收缓冲区基于KalmanFilter的延迟模型 - 简书在WebRTC的视频处理流水线中，接收端缓冲区JitterBuffer是关键的组成部分：它负责RTP数据包乱序重排和组帧，RTP丢包重传，请求重传关键帧，估算缓冲区延迟等功能...https://www.jianshu.com/p/bb34995c549a