Kalman Based VWAP [EdgeTerminal]

Kalman VWAP is a different take on volume-weighted average price (VWAP) indicator where we enhance the results with Kalman filtering and dynamic wave visualization for a more smooth and improved trend identification and volatility analysis.

A little bit about Kalman Filter:
Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided showing how the filter relates to maximum likelihood statistics

This indicator combines:
Volume-Weighted Average Price (VWAP) for institutional price levels
Kalman filtering for noise reduction and trend smoothing
Dynamic wave visualization for volatility zones

This creates a robust indicator that helps traders identify trends, support/resistance zones, and potential reversal points with high precision.

What makes this even more special is the fact that we use open price as a data source instead of usual close price. This allows you to tune the indicator more accurately when back testing it and generally get results that are closer to real time market data.

The math:
In case if you're interested in the math of this indicator, the indicator employs a state-space Kalman filter model:
State Equation: x_t = x_{t-1} + w_t
Measurement Equation: z_t = x_t + v_t

x_t is the filtered VWAP state
w_t is process noise ~ N(0, Q)
v_t is measurement noise ~ N(0, R)
z_t is the traditional VWAP measurement

The Kalman filter recursively updates through:
Prediction: x̂_t|t-1 = x̂_{t-1}
Update: x̂_t = x̂_t|t-1 + K_t(z_t - x̂_t|t-1)
Where K_t is the Kalman gain, optimally balancing between prediction and measurement.

Input Parameters
Measurement Noise: Controls signal smoothing (0.0001 to 1.0)
Process Noise: Adjusts trend responsiveness (0.0001 to 1.0)
Wave Size: Multiplier for volatility bands (0.1 to 5.0)
Trend Lookback: Period for trend determination (1 to 100)
Bull/Bear Colors: Customizable color schemes

Application:
I recommend using this along other indicators. This is best used for assets that don't have a close time, such as BTC but can be used with anything as long as the data is there.

With default settings, this works better for swing trades but you can adjust it for day trading as well, by adjusting the lookback and also process noise.