feature: add G-H filter and Kalman filter

- implement G-H (alpha beta) filter and Kalman filter
- compare the predict accurateness with other indicator

pkg/indicator/ghfilter.go

@@ -0,0 +1,96 @@
+package indicator
+
+import (
+	"github.com/c9s/bbgo/pkg/datatype/floats"
+	"github.com/c9s/bbgo/pkg/types"
+	"math"
+)
+
+// Refer: https://jamesgoulding.com/Research_II/Ehlers/Ehlers%20(Optimal%20Tracking%20Filters).doc
+// Ehler's Optimal Tracking Filter, an alpha-beta filter, also called g-h filter
+
+//go:generate callbackgen -type GHFilter
+type GHFilter struct {
+	types.SeriesBase
+	types.IntervalWindow
+	a               float64 // maneuverability uncertainty
+	b               float64 // measurement uncertainty
+	lastMeasurement float64
+	Values          floats.Slice
+
+	UpdateCallbacks []func(value float64)
+}
+
+func (inc *GHFilter) Update(value float64) {
+	inc.update(value, math.Abs(value-inc.lastMeasurement))
+}
+
+func (inc *GHFilter) update(value, uncertainty float64) {
+	if len(inc.Values) == 0 {
+		inc.a = 0
+		inc.b = uncertainty / 2
+		inc.lastMeasurement = value
+		inc.Values.Push(value)
+		return
+	}
+	multiplier := 2.0 / float64(1+inc.Window) // EMA multiplier
+	inc.a = multiplier*(value-inc.lastMeasurement) + (1-multiplier)*inc.a
+	inc.b = multiplier*uncertainty/2 + (1-multiplier)*inc.b
+	lambda := inc.a / inc.b
+	lambda2 := lambda * lambda
+	alpha := (-lambda2 + math.Sqrt(lambda2*lambda2+16*lambda2)) / 8
+	filtered := alpha*value + (1-alpha)*inc.Values.Last()
+	inc.Values.Push(filtered)
+	inc.lastMeasurement = value
+}
+
+func (inc *GHFilter) Index(i int) float64 {
+	if inc.Values == nil {
+		return 0.0
+	}
+	return inc.Values.Index(i)
+}
+
+func (inc *GHFilter) Length() int {
+	if inc.Values == nil {
+		return 0
+	}
+	return inc.Values.Length()
+}
+
+func (inc *GHFilter) Last() float64 {
+	if inc.Values == nil {
+		return 0.0
+	}
+	return inc.Values.Last()
+}
+
+var _ types.SeriesExtend = &GHFilter{}
+
+func (inc *GHFilter) PushK(k types.KLine) {
+	inc.update(k.Close.Float64(), k.High.Float64()-k.Low.Float64())
+}
+
+func (inc *GHFilter) CalculateAndUpdate(allKLines []types.KLine) {
+	if inc.Values != nil {
+		k := allKLines[len(allKLines)-1]
+		inc.PushK(k)
+		inc.EmitUpdate(inc.Last())
+		return
+	}
+	for _, k := range allKLines {
+		inc.PushK(k)
+		inc.EmitUpdate(inc.Last())
+	}
+}
+
+func (inc *GHFilter) handleKLineWindowUpdate(interval types.Interval, window types.KLineWindow) {
+	if inc.Interval != interval {
+		return
+	}
+	inc.CalculateAndUpdate(window)
+}
+
+func (inc *GHFilter) Bind(updater KLineWindowUpdater) {
+	updater.OnKLineWindowUpdate(inc.handleKLineWindowUpdate)
+}