From 9c684c124cf3c703af0454ddd42b11022f4355af Mon Sep 17 00:00:00 2001
From: Raphanus Lo <coldturnip@gmail.com>
Date: Mon, 15 Aug 2022 00:07:26 +0800
Subject: [PATCH] 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               |   96 +
 pkg/indicator/ghfilter_callbacks.go     |   15 +
 pkg/indicator/ghfilter_test.go          | 6151 ++++++++++++++++++++++
 pkg/indicator/kalmanfilter.go           |  108 +
 pkg/indicator/kalmanfilter_callbacks.go |   15 +
 pkg/indicator/kalmanfilter_test.go      | 6191 +++++++++++++++++++++++
 6 files changed, 12576 insertions(+)
 create mode 100644 pkg/indicator/ghfilter.go
 create mode 100644 pkg/indicator/ghfilter_callbacks.go
 create mode 100644 pkg/indicator/ghfilter_test.go
 create mode 100644 pkg/indicator/kalmanfilter.go
 create mode 100644 pkg/indicator/kalmanfilter_callbacks.go
 create mode 100644 pkg/indicator/kalmanfilter_test.go

diff --git a/pkg/indicator/ghfilter.go b/pkg/indicator/ghfilter.go
new file mode 100644
index 000000000..97db2fbd6
--- /dev/null
+++ b/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)
+}
diff --git a/pkg/indicator/ghfilter_callbacks.go b/pkg/indicator/ghfilter_callbacks.go
new file mode 100644
index 000000000..345355a4e
--- /dev/null
+++ b/pkg/indicator/ghfilter_callbacks.go
@@ -0,0 +1,15 @@
+// Code generated by "callbackgen -type GHFilter"; DO NOT EDIT.
+
+package indicator
+
+import ()
+
+func (inc *GHFilter) OnUpdate(cb func(value float64)) {
+	inc.UpdateCallbacks = append(inc.UpdateCallbacks, cb)
+}
+
+func (inc *GHFilter) EmitUpdate(value float64) {
+	for _, cb := range inc.UpdateCallbacks {
+		cb(value)
+	}
+}
diff --git a/pkg/indicator/ghfilter_test.go b/pkg/indicator/ghfilter_test.go
new file mode 100644
index 000000000..ac7439933
--- /dev/null
+++ b/pkg/indicator/ghfilter_test.go
@@ -0,0 +1,6151 @@
+package indicator
+
+import (
+	"encoding/json"
+	"math"
+	"testing"
+
+	"github.com/c9s/bbgo/pkg/types"
+)
+
+// generated from Binance 2022/07/27 00:00
+// https://www.binance.com/api/v3/klines?symbol=ETHUSDT&interval=5m&endTime=1658851200000&limit=1000
+var testGHFilterDataEthusdt5m = []byte(`[
+  {
+    "open": 1591.11,
+    "high": 1593.62,
+    "low": 1589.04,
+    "close": 1590.14
+  },
+  {
+    "open": 1590.14,
+    "high": 1596.51,
+    "low": 1590.13,
+    "close": 1592.06
+  },
+  {
+    "open": 1592.07,
+    "high": 1594.41,
+    "low": 1586.05,
+    "close": 1587.02
+  },
+  {
+    "open": 1587.02,
+    "high": 1588.38,
+    "low": 1583.86,
+    "close": 1585.33
+  },
+  {
+    "open": 1585.34,
+    "high": 1595.2,
+    "low": 1583.74,
+    "close": 1594.69
+  },
+  {
+    "open": 1594.69,
+    "high": 1594.75,
+    "low": 1589.89,
+    "close": 1591.36
+  },
+  {
+    "open": 1591.35,
+    "high": 1592.55,
+    "low": 1586.36,
+    "close": 1588.95
+  },
+  {
+    "open": 1588.95,
+    "high": 1589.75,
+    "low": 1588.39,
+    "close": 1589.38
+  },
+  {
+    "open": 1589.38,
+    "high": 1589.39,
+    "low": 1586.17,
+    "close": 1588.53
+  },
+  {
+    "open": 1588.52,
+    "high": 1588.62,
+    "low": 1581.95,
+    "close": 1583.4
+  },
+  {
+    "open": 1583.4,
+    "high": 1584.67,
+    "low": 1582.1,
+    "close": 1582.36
+  },
+  {
+    "open": 1582.35,
+    "high": 1584.29,
+    "low": 1577.82,
+    "close": 1578.14
+  },
+  {
+    "open": 1578.14,
+    "high": 1581.95,
+    "low": 1575.72,
+    "close": 1581.52
+  },
+  {
+    "open": 1581.52,
+    "high": 1584.86,
+    "low": 1578.51,
+    "close": 1580.88
+  },
+  {
+    "open": 1580.88,
+    "high": 1581.77,
+    "low": 1578.74,
+    "close": 1581.11
+  },
+  {
+    "open": 1581.1,
+    "high": 1582.72,
+    "low": 1579.07,
+    "close": 1579.4
+  },
+  {
+    "open": 1579.4,
+    "high": 1580.93,
+    "low": 1578,
+    "close": 1579.6
+  },
+  {
+    "open": 1579.59,
+    "high": 1583.81,
+    "low": 1579.59,
+    "close": 1582.7
+  },
+  {
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+    "high": 1583,
+    "low": 1577.24,
+    "close": 1579.45
+  },
+  {
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+    "high": 1581.59,
+    "low": 1577.44,
+    "close": 1579.59
+  },
+  {
+    "open": 1579.58,
+    "high": 1581.41,
+    "low": 1579.22,
+    "close": 1580.56
+  },
+  {
+    "open": 1580.57,
+    "high": 1586.23,
+    "low": 1579.86,
+    "close": 1584.23
+  },
+  {
+    "open": 1584.22,
+    "high": 1587.36,
+    "low": 1584.22,
+    "close": 1585.15
+  },
+  {
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+    "high": 1585.15,
+    "low": 1579.83,
+    "close": 1583.75
+  },
+  {
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+  },
+  {
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+  },
+  {
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+  {
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+  },
+  {
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+  },
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+  },
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+  },
+  {
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+  },
+  {
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+  },
+  {
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+  },
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+  },
+  {
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+  },
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+  },
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+  },
+  {
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+  },
+  {
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+    "low": 1522.78,
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+  },
+  {
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+    "low": 1525.3,
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+  {
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+  },
+  {
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+  },
+  {
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+  {
+    "open": 1391.93,
+    "high": 1396.92,
+    "low": 1390.04,
+    "close": 1391.11
+  },
+  {
+    "open": 1391.11,
+    "high": 1394.3,
+    "low": 1383.57,
+    "close": 1385.3
+  },
+  {
+    "open": 1385.31,
+    "high": 1386.85,
+    "low": 1379.45,
+    "close": 1382.74
+  },
+  {
+    "open": 1382.74,
+    "high": 1384.96,
+    "low": 1379.24,
+    "close": 1382.24
+  },
+  {
+    "open": 1382.24,
+    "high": 1384.6,
+    "low": 1380.2,
+    "close": 1380.79
+  },
+  {
+    "open": 1380.78,
+    "high": 1382.77,
+    "low": 1376,
+    "close": 1381.3
+  },
+  {
+    "open": 1381.29,
+    "high": 1384.6,
+    "low": 1379.59,
+    "close": 1382.74
+  },
+  {
+    "open": 1382.75,
+    "high": 1385.95,
+    "low": 1381.72,
+    "close": 1384.68
+  },
+  {
+    "open": 1384.67,
+    "high": 1392.47,
+    "low": 1384.26,
+    "close": 1389.48
+  },
+  {
+    "open": 1389.49,
+    "high": 1392,
+    "low": 1388.82,
+    "close": 1390.13
+  },
+  {
+    "open": 1390.13,
+    "high": 1392.46,
+    "low": 1389.7,
+    "close": 1391.94
+  },
+  {
+    "open": 1391.94,
+    "high": 1393.95,
+    "low": 1388.32,
+    "close": 1388.68
+  },
+  {
+    "open": 1388.68,
+    "high": 1389.35,
+    "low": 1379.59,
+    "close": 1381.72
+  },
+  {
+    "open": 1381.71,
+    "high": 1384.78,
+    "low": 1379.64,
+    "close": 1384.68
+  },
+  {
+    "open": 1384.67,
+    "high": 1384.92,
+    "low": 1381.13,
+    "close": 1383.07
+  },
+  {
+    "open": 1383.07,
+    "high": 1383.24,
+    "low": 1375.5,
+    "close": 1375.74
+  },
+  {
+    "open": 1375.73,
+    "high": 1378.38,
+    "low": 1372.01,
+    "close": 1374.42
+  },
+  {
+    "open": 1374.42,
+    "high": 1377.99,
+    "low": 1366,
+    "close": 1377.51
+  },
+  {
+    "open": 1377.51,
+    "high": 1378.73,
+    "low": 1372.87,
+    "close": 1375.18
+  },
+  {
+    "open": 1375.18,
+    "high": 1378.38,
+    "low": 1371.96,
+    "close": 1376.76
+  },
+  {
+    "open": 1376.77,
+    "high": 1377.59,
+    "low": 1370.81,
+    "close": 1370.95
+  },
+  {
+    "open": 1370.95,
+    "high": 1374.62,
+    "low": 1363.87,
+    "close": 1367.88
+  },
+  {
+    "open": 1367.88,
+    "high": 1372,
+    "low": 1365.03,
+    "close": 1368.68
+  },
+  {
+    "open": 1368.67,
+    "high": 1373.02,
+    "low": 1367,
+    "close": 1370.9
+  }
+]`)
+
+func Test_GHFilter(t *testing.T) {
+	type args struct {
+		allKLines []types.KLine
+		window    int
+	}
+	var klines []types.KLine
+	if err := json.Unmarshal(testGHFilterDataEthusdt5m, &klines); err != nil {
+		panic(err)
+	}
+	tests := []struct {
+		name string
+		args args
+		want float64
+	}{
+		{
+			name: "ETHUSDT G-H Filter 7",
+			args: args{
+				allKLines: klines,
+				window:    7,
+			},
+			want: 1373.71,
+		},
+		{
+			name: "ETHUSDT G-H Filter 25",
+			args: args{
+				allKLines: klines,
+				window:    25,
+			},
+			want: 1376.21,
+		},
+		{
+			name: "ETHUSDT G-H Filter 99",
+			args: args{
+				allKLines: klines,
+				window:    99,
+			},
+			want: 1378.96,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			filter := &GHFilter{IntervalWindow: types.IntervalWindow{Window: tt.args.window}}
+			for _, k := range klines {
+				filter.PushK(k)
+			}
+			got := filter.Last()
+			got = math.Trunc(got*100.0) / 100.0
+			if got != tt.want {
+				t.Errorf("GHFilter.Last() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func Test_GHFilterEstimationAccurate(t *testing.T) {
+	type args struct {
+		allKLines []types.KLine
+		priceF    KLineValueMapper
+		window    int
+	}
+	var klines []types.KLine
+	if err := json.Unmarshal(testGHFilterDataEthusdt5m, &klines); err != nil {
+		panic(err)
+	}
+	tests := []struct {
+		name string
+		args args
+		want float64
+	}{
+		{
+			name: "ETHUSDT G-H Filter square error 7",
+			args: args{
+				allKLines: klines,
+				window:    7,
+			},
+		},
+		{
+			name: "ETHUSDT G-H Filter square error 25",
+			args: args{
+				allKLines: klines,
+				window:    25,
+			},
+		},
+		{
+			name: "ETHUSDT G-H Filter square error 99",
+			args: args{
+				allKLines: klines,
+				window:    99,
+			},
+		},
+	}
+	klineSquareError := func(base float64, k types.KLine) float64 {
+		openDiff := math.Abs(k.Open.Float64() - base)
+		highDiff := math.Abs(k.High.Float64() - base)
+		lowDiff := math.Abs(k.Low.Float64() - base)
+		closeDiff := math.Abs(k.Close.Float64() - base)
+		return openDiff*openDiff + highDiff*highDiff + lowDiff*lowDiff + closeDiff*closeDiff
+	}
+	closeSquareError := func(base float64, k types.KLine) float64 {
+		closeDiff := math.Abs(k.Close.Float64() - base)
+		return closeDiff * closeDiff
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			filter := &GHFilter{IntervalWindow: types.IntervalWindow{Window: tt.args.window}}
+			ewma := &EWMA{IntervalWindow: types.IntervalWindow{Window: tt.args.window}}
+
+			var filterDiff2Sum, ewmaDiff2Sum float64
+			var filterCloseDiff2Sum, ewmaCloseDiff2Sum float64
+			for i, k := range klines {
+				// square error between last estimated state and current actual state
+				if i > 0 {
+					filterDiff2Sum += klineSquareError(filter.Last(), k)
+					ewmaDiff2Sum += klineSquareError(ewma.Last(), k)
+					filterCloseDiff2Sum += closeSquareError(filter.Last(), k)
+					ewmaCloseDiff2Sum += closeSquareError(ewma.Last(), k)
+				}
+
+				// update estimations
+				filter.PushK(k)
+				ewma.PushK(k)
+			}
+			numEstimations := len(klines) - 1
+			filterSquareErr := math.Sqrt(filterDiff2Sum / float64(numEstimations*4))
+			ewmaSquareErr := math.Sqrt(ewmaDiff2Sum / float64(numEstimations*4))
+			if filterSquareErr > ewmaSquareErr {
+				t.Errorf("filter K-Line square error %f > EWMA K-Line square error %v", filterSquareErr, ewmaSquareErr)
+			}
+			filterCloseSquareErr := math.Sqrt(filterCloseDiff2Sum / float64(numEstimations))
+			ewmaCloseSquareErr := math.Sqrt(ewmaCloseDiff2Sum / float64(numEstimations))
+			if filterCloseSquareErr > ewmaCloseSquareErr {
+				t.Errorf("filter close price square error %f > EWMA close price square error %v", filterCloseSquareErr, ewmaCloseSquareErr)
+			}
+		})
+	}
+}
diff --git a/pkg/indicator/kalmanfilter.go b/pkg/indicator/kalmanfilter.go
new file mode 100644
index 000000000..c49f22388
--- /dev/null
+++ b/pkg/indicator/kalmanfilter.go
@@ -0,0 +1,108 @@
+package indicator
+
+import (
+	"github.com/c9s/bbgo/pkg/datatype/floats"
+	"github.com/c9s/bbgo/pkg/types"
+	"math"
+)
+
+// Refer: https://www.kalmanfilter.net/kalman1d.html
+// One-dimensional Kalman filter
+
+//go:generate callbackgen -type KalmanFilter
+type KalmanFilter struct {
+	types.SeriesBase
+	types.IntervalWindow
+	AdditionalSmoothWindow uint
+	amp2                   *types.Queue // measurement uncertainty
+	k                      float64      // Kalman gain
+	measurements           *types.Queue
+	Values                 floats.Slice
+
+	UpdateCallbacks []func(value float64)
+}
+
+func (inc *KalmanFilter) Update(value float64) {
+	var measureMove = value
+	if inc.measurements != nil {
+		measureMove = value - inc.measurements.Last()
+	}
+	inc.update(value, math.Abs(measureMove))
+}
+
+func (inc *KalmanFilter) update(value, amp float64) {
+	if len(inc.Values) == 0 {
+		inc.amp2 = types.NewQueue(inc.Window)
+		inc.amp2.Update(amp * amp)
+		inc.measurements = types.NewQueue(inc.Window)
+		inc.measurements.Update(value)
+		inc.Values.Push(value)
+		return
+	}
+
+	// measurement
+	inc.measurements.Update(value)
+	inc.amp2.Update(amp * amp)
+	q := math.Sqrt(types.Mean(inc.amp2)) * float64(1+inc.AdditionalSmoothWindow)
+
+	// update
+	lastPredict := inc.Values.Last()
+	curState := value + (value - lastPredict)
+	estimated := lastPredict + inc.k*(curState-lastPredict)
+
+	// predict
+	inc.Values.Push(estimated)
+	p := math.Abs(curState - estimated)
+	inc.k = p / (p + q)
+}
+
+func (inc *KalmanFilter) Index(i int) float64 {
+	if inc.Values == nil {
+		return 0.0
+	}
+	return inc.Values.Index(i)
+}
+
+func (inc *KalmanFilter) Length() int {
+	if inc.Values == nil {
+		return 0
+	}
+	return inc.Values.Length()
+}
+
+func (inc *KalmanFilter) Last() float64 {
+	if inc.Values == nil {
+		return 0.0
+	}
+	return inc.Values.Last()
+}
+
+var _ types.SeriesExtend = &KalmanFilter{}
+
+func (inc *KalmanFilter) PushK(k types.KLine) {
+	inc.update(k.Close.Float64(), (k.High.Float64()-k.Low.Float64())/2)
+}
+
+func (inc *KalmanFilter) 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 *KalmanFilter) handleKLineWindowUpdate(interval types.Interval, window types.KLineWindow) {
+	if inc.Interval != interval {
+		return
+	}
+	inc.CalculateAndUpdate(window)
+}
+
+func (inc *KalmanFilter) Bind(updater KLineWindowUpdater) {
+	updater.OnKLineWindowUpdate(inc.handleKLineWindowUpdate)
+}
diff --git a/pkg/indicator/kalmanfilter_callbacks.go b/pkg/indicator/kalmanfilter_callbacks.go
new file mode 100644
index 000000000..3dff5fc49
--- /dev/null
+++ b/pkg/indicator/kalmanfilter_callbacks.go
@@ -0,0 +1,15 @@
+// Code generated by "callbackgen -type KalmanFilter"; DO NOT EDIT.
+
+package indicator
+
+import ()
+
+func (inc *KalmanFilter) OnUpdate(cb func(value float64)) {
+	inc.UpdateCallbacks = append(inc.UpdateCallbacks, cb)
+}
+
+func (inc *KalmanFilter) EmitUpdate(value float64) {
+	for _, cb := range inc.UpdateCallbacks {
+		cb(value)
+	}
+}
diff --git a/pkg/indicator/kalmanfilter_test.go b/pkg/indicator/kalmanfilter_test.go
new file mode 100644
index 000000000..250656047
--- /dev/null
+++ b/pkg/indicator/kalmanfilter_test.go
@@ -0,0 +1,6191 @@
+package indicator
+
+import (
+	"encoding/json"
+	"math"
+	"testing"
+
+	"github.com/c9s/bbgo/pkg/types"
+)
+
+// generated from Binance 2022/07/27 00:00
+// https://www.binance.com/api/v3/klines?symbol=ETHUSDT&interval=5m&endTime=1658851200000&limit=1000
+var testKalmanFilterDataEthusdt5m = []byte(`[
+  {
+    "open": 1591.11,
+    "high": 1593.62,
+    "low": 1589.04,
+    "close": 1590.14
+  },
+  {
+    "open": 1590.14,
+    "high": 1596.51,
+    "low": 1590.13,
+    "close": 1592.06
+  },
+  {
+    "open": 1592.07,
+    "high": 1594.41,
+    "low": 1586.05,
+    "close": 1587.02
+  },
+  {
+    "open": 1587.02,
+    "high": 1588.38,
+    "low": 1583.86,
+    "close": 1585.33
+  },
+  {
+    "open": 1585.34,
+    "high": 1595.2,
+    "low": 1583.74,
+    "close": 1594.69
+  },
+  {
+    "open": 1594.69,
+    "high": 1594.75,
+    "low": 1589.89,
+    "close": 1591.36
+  },
+  {
+    "open": 1591.35,
+    "high": 1592.55,
+    "low": 1586.36,
+    "close": 1588.95
+  },
+  {
+    "open": 1588.95,
+    "high": 1589.75,
+    "low": 1588.39,
+    "close": 1589.38
+  },
+  {
+    "open": 1589.38,
+    "high": 1589.39,
+    "low": 1586.17,
+    "close": 1588.53
+  },
+  {
+    "open": 1588.52,
+    "high": 1588.62,
+    "low": 1581.95,
+    "close": 1583.4
+  },
+  {
+    "open": 1583.4,
+    "high": 1584.67,
+    "low": 1582.1,
+    "close": 1582.36
+  },
+  {
+    "open": 1582.35,
+    "high": 1584.29,
+    "low": 1577.82,
+    "close": 1578.14
+  },
+  {
+    "open": 1578.14,
+    "high": 1581.95,
+    "low": 1575.72,
+    "close": 1581.52
+  },
+  {
+    "open": 1581.52,
+    "high": 1584.86,
+    "low": 1578.51,
+    "close": 1580.88
+  },
+  {
+    "open": 1580.88,
+    "high": 1581.77,
+    "low": 1578.74,
+    "close": 1581.11
+  },
+  {
+    "open": 1581.1,
+    "high": 1582.72,
+    "low": 1579.07,
+    "close": 1579.4
+  },
+  {
+    "open": 1579.4,
+    "high": 1580.93,
+    "low": 1578,
+    "close": 1579.6
+  },
+  {
+    "open": 1579.59,
+    "high": 1583.81,
+    "low": 1579.59,
+    "close": 1582.7
+  },
+  {
+    "open": 1582.7,
+    "high": 1583,
+    "low": 1577.24,
+    "close": 1579.45
+  },
+  {
+    "open": 1579.46,
+    "high": 1581.59,
+    "low": 1577.44,
+    "close": 1579.59
+  },
+  {
+    "open": 1579.58,
+    "high": 1581.41,
+    "low": 1579.22,
+    "close": 1580.56
+  },
+  {
+    "open": 1580.57,
+    "high": 1586.23,
+    "low": 1579.86,
+    "close": 1584.23
+  },
+  {
+    "open": 1584.22,
+    "high": 1587.36,
+    "low": 1584.22,
+    "close": 1585.15
+  },
+  {
+    "open": 1585.15,
+    "high": 1585.15,
+    "low": 1579.83,
+    "close": 1583.75
+  },
+  {
+    "open": 1583.74,
+    "high": 1592.49,
+    "low": 1583.45,
+    "close": 1587.76
+  },
+  {
+    "open": 1587.76,
+    "high": 1590.7,
+    "low": 1585.62,
+    "close": 1587.5
+  },
+  {
+    "open": 1587.51,
+    "high": 1587.51,
+    "low": 1579.53,
+    "close": 1581.16
+  },
+  {
+    "open": 1581.15,
+    "high": 1585.71,
+    "low": 1581.15,
+    "close": 1582.47
+  },
+  {
+    "open": 1582.46,
+    "high": 1582.86,
+    "low": 1567.58,
+    "close": 1571.52
+  },
+  {
+    "open": 1571.53,
+    "high": 1577.8,
+    "low": 1571.03,
+    "close": 1575.16
+  },
+  {
+    "open": 1575.16,
+    "high": 1578.06,
+    "low": 1572.18,
+    "close": 1576.66
+  },
+  {
+    "open": 1576.66,
+    "high": 1578,
+    "low": 1574.62,
+    "close": 1577.21
+  },
+  {
+    "open": 1577.2,
+    "high": 1584.57,
+    "low": 1576.61,
+    "close": 1584.05
+  },
+  {
+    "open": 1584.06,
+    "high": 1585.61,
+    "low": 1580,
+    "close": 1582.08
+  },
+  {
+    "open": 1582.08,
+    "high": 1583.4,
+    "low": 1579.43,
+    "close": 1579.43
+  },
+  {
+    "open": 1579.43,
+    "high": 1579.98,
+    "low": 1574.53,
+    "close": 1575.06
+  },
+  {
+    "open": 1575.06,
+    "high": 1578.52,
+    "low": 1574.57,
+    "close": 1576.49
+  },
+  {
+    "open": 1576.5,
+    "high": 1577,
+    "low": 1572.5,
+    "close": 1573.26
+  },
+  {
+    "open": 1573.26,
+    "high": 1579.41,
+    "low": 1573.06,
+    "close": 1578.35
+  },
+  {
+    "open": 1578.35,
+    "high": 1585,
+    "low": 1577.16,
+    "close": 1584.32
+  },
+  {
+    "open": 1584.31,
+    "high": 1587.97,
+    "low": 1580.67,
+    "close": 1585.7
+  },
+  {
+    "open": 1585.7,
+    "high": 1588.35,
+    "low": 1584.37,
+    "close": 1585.95
+  },
+  {
+    "open": 1585.94,
+    "high": 1587.09,
+    "low": 1580.66,
+    "close": 1580.97
+  },
+  {
+    "open": 1580.97,
+    "high": 1583.38,
+    "low": 1577,
+    "close": 1581.64
+  },
+  {
+    "open": 1581.64,
+    "high": 1586.79,
+    "low": 1581.22,
+    "close": 1585.42
+  },
+  {
+    "open": 1585.42,
+    "high": 1585.42,
+    "low": 1581.67,
+    "close": 1582.37
+  },
+  {
+    "open": 1582.38,
+    "high": 1584.86,
+    "low": 1581.01,
+    "close": 1581.02
+  },
+  {
+    "open": 1581.03,
+    "high": 1582.05,
+    "low": 1578.99,
+    "close": 1579.46
+  },
+  {
+    "open": 1579.46,
+    "high": 1579.89,
+    "low": 1566.85,
+    "close": 1567.99
+  },
+  {
+    "open": 1567.99,
+    "high": 1567.99,
+    "low": 1553.2,
+    "close": 1554.87
+  },
+  {
+    "open": 1554.87,
+    "high": 1558,
+    "low": 1546.9,
+    "close": 1550.4
+  },
+  {
+    "open": 1550.4,
+    "high": 1554.98,
+    "low": 1546.27,
+    "close": 1549.67
+  },
+  {
+    "open": 1549.68,
+    "high": 1555,
+    "low": 1546.97,
+    "close": 1553.88
+  },
+  {
+    "open": 1553.89,
+    "high": 1557.86,
+    "low": 1553.6,
+    "close": 1557.85
+  },
+  {
+    "open": 1557.86,
+    "high": 1558.37,
+    "low": 1554.9,
+    "close": 1556.3
+  },
+  {
+    "open": 1556.31,
+    "high": 1557.4,
+    "low": 1552.81,
+    "close": 1557.18
+  },
+  {
+    "open": 1557.18,
+    "high": 1563.78,
+    "low": 1556.5,
+    "close": 1562.72
+  },
+  {
+    "open": 1562.72,
+    "high": 1564.11,
+    "low": 1558.76,
+    "close": 1560.64
+  },
+  {
+    "open": 1560.64,
+    "high": 1562.31,
+    "low": 1560.5,
+    "close": 1561.24
+  },
+  {
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+  },
+  {
+    "open": 1423.26,
+    "high": 1423.26,
+    "low": 1420.76,
+    "close": 1420.82
+  },
+  {
+    "open": 1420.82,
+    "high": 1421.01,
+    "low": 1418.92,
+    "close": 1419.11
+  },
+  {
+    "open": 1419.11,
+    "high": 1421.25,
+    "low": 1419,
+    "close": 1421
+  },
+  {
+    "open": 1421.01,
+    "high": 1422.98,
+    "low": 1417.66,
+    "close": 1418.53
+  },
+  {
+    "open": 1418.52,
+    "high": 1419.44,
+    "low": 1415.01,
+    "close": 1415.47
+  },
+  {
+    "open": 1415.47,
+    "high": 1417.15,
+    "low": 1413.71,
+    "close": 1414.16
+  },
+  {
+    "open": 1414.15,
+    "high": 1416.22,
+    "low": 1413.37,
+    "close": 1414.09
+  },
+  {
+    "open": 1414.1,
+    "high": 1416.01,
+    "low": 1413,
+    "close": 1415.83
+  },
+  {
+    "open": 1415.84,
+    "high": 1418.37,
+    "low": 1413.65,
+    "close": 1414.5
+  },
+  {
+    "open": 1414.46,
+    "high": 1414.96,
+    "low": 1408.49,
+    "close": 1411.92
+  },
+  {
+    "open": 1411.92,
+    "high": 1412.58,
+    "low": 1409.72,
+    "close": 1412.57
+  },
+  {
+    "open": 1412.57,
+    "high": 1413.05,
+    "low": 1411.23,
+    "close": 1411.32
+  },
+  {
+    "open": 1411.32,
+    "high": 1412.81,
+    "low": 1408.13,
+    "close": 1409.79
+  },
+  {
+    "open": 1409.79,
+    "high": 1412.35,
+    "low": 1409.34,
+    "close": 1410.44
+  },
+  {
+    "open": 1410.43,
+    "high": 1412.92,
+    "low": 1408.61,
+    "close": 1412.09
+  },
+  {
+    "open": 1412.1,
+    "high": 1412.84,
+    "low": 1410.56,
+    "close": 1410.57
+  },
+  {
+    "open": 1410.56,
+    "high": 1411.32,
+    "low": 1409.19,
+    "close": 1409.59
+  },
+  {
+    "open": 1409.6,
+    "high": 1412.09,
+    "low": 1407.68,
+    "close": 1410.42
+  },
+  {
+    "open": 1410.43,
+    "high": 1414.86,
+    "low": 1409.94,
+    "close": 1414.1
+  },
+  {
+    "open": 1414.11,
+    "high": 1414.47,
+    "low": 1412.17,
+    "close": 1412.65
+  },
+  {
+    "open": 1412.66,
+    "high": 1413.85,
+    "low": 1411.93,
+    "close": 1413.43
+  },
+  {
+    "open": 1413.44,
+    "high": 1415.79,
+    "low": 1412.99,
+    "close": 1413.51
+  },
+  {
+    "open": 1413.52,
+    "high": 1414.6,
+    "low": 1410.26,
+    "close": 1410.34
+  },
+  {
+    "open": 1410.33,
+    "high": 1413.83,
+    "low": 1410.33,
+    "close": 1413.39
+  },
+  {
+    "open": 1413.38,
+    "high": 1414.82,
+    "low": 1406.46,
+    "close": 1407.52
+  },
+  {
+    "open": 1407.52,
+    "high": 1413.46,
+    "low": 1385.08,
+    "close": 1406.33
+  },
+  {
+    "open": 1406.33,
+    "high": 1406.42,
+    "low": 1396.54,
+    "close": 1403.7
+  },
+  {
+    "open": 1403.69,
+    "high": 1413.95,
+    "low": 1403.69,
+    "close": 1411.91
+  },
+  {
+    "open": 1411.92,
+    "high": 1420.39,
+    "low": 1411.91,
+    "close": 1414.33
+  },
+  {
+    "open": 1414.34,
+    "high": 1414.52,
+    "low": 1405.66,
+    "close": 1405.79
+  },
+  {
+    "open": 1405.8,
+    "high": 1409.11,
+    "low": 1399,
+    "close": 1399.24
+  },
+  {
+    "open": 1399.23,
+    "high": 1405.73,
+    "low": 1399.23,
+    "close": 1400.56
+  },
+  {
+    "open": 1400.55,
+    "high": 1402,
+    "low": 1396.96,
+    "close": 1400.96
+  },
+  {
+    "open": 1400.96,
+    "high": 1401.35,
+    "low": 1390.31,
+    "close": 1394.24
+  },
+  {
+    "open": 1394.24,
+    "high": 1395.43,
+    "low": 1387.54,
+    "close": 1389.76
+  },
+  {
+    "open": 1389.87,
+    "high": 1390.95,
+    "low": 1381.54,
+    "close": 1384.88
+  },
+  {
+    "open": 1384.87,
+    "high": 1388.96,
+    "low": 1383.78,
+    "close": 1388.13
+  },
+  {
+    "open": 1388.13,
+    "high": 1393.11,
+    "low": 1387.84,
+    "close": 1391.98
+  },
+  {
+    "open": 1391.99,
+    "high": 1393.4,
+    "low": 1387.03,
+    "close": 1391.28
+  },
+  {
+    "open": 1391.38,
+    "high": 1391.68,
+    "low": 1384.04,
+    "close": 1384.51
+  },
+  {
+    "open": 1384.52,
+    "high": 1387.12,
+    "low": 1369.29,
+    "close": 1377.99
+  },
+  {
+    "open": 1377.99,
+    "high": 1384.82,
+    "low": 1371,
+    "close": 1383.01
+  },
+  {
+    "open": 1383.01,
+    "high": 1388,
+    "low": 1381.75,
+    "close": 1383.05
+  },
+  {
+    "open": 1383.06,
+    "high": 1388.47,
+    "low": 1383.05,
+    "close": 1387.82
+  },
+  {
+    "open": 1387.82,
+    "high": 1390,
+    "low": 1382.78,
+    "close": 1388.01
+  },
+  {
+    "open": 1388,
+    "high": 1392.96,
+    "low": 1386.5,
+    "close": 1391.27
+  },
+  {
+    "open": 1391.2,
+    "high": 1392.61,
+    "low": 1387.5,
+    "close": 1389.07
+  },
+  {
+    "open": 1389.07,
+    "high": 1389.07,
+    "low": 1382.39,
+    "close": 1385.3
+  },
+  {
+    "open": 1385.3,
+    "high": 1392,
+    "low": 1384.63,
+    "close": 1387.41
+  },
+  {
+    "open": 1387.41,
+    "high": 1390.71,
+    "low": 1386.5,
+    "close": 1389.12
+  },
+  {
+    "open": 1389.11,
+    "high": 1392.6,
+    "low": 1382.5,
+    "close": 1391.93
+  },
+  {
+    "open": 1391.93,
+    "high": 1396.92,
+    "low": 1390.04,
+    "close": 1391.11
+  },
+  {
+    "open": 1391.11,
+    "high": 1394.3,
+    "low": 1383.57,
+    "close": 1385.3
+  },
+  {
+    "open": 1385.31,
+    "high": 1386.85,
+    "low": 1379.45,
+    "close": 1382.74
+  },
+  {
+    "open": 1382.74,
+    "high": 1384.96,
+    "low": 1379.24,
+    "close": 1382.24
+  },
+  {
+    "open": 1382.24,
+    "high": 1384.6,
+    "low": 1380.2,
+    "close": 1380.79
+  },
+  {
+    "open": 1380.78,
+    "high": 1382.77,
+    "low": 1376,
+    "close": 1381.3
+  },
+  {
+    "open": 1381.29,
+    "high": 1384.6,
+    "low": 1379.59,
+    "close": 1382.74
+  },
+  {
+    "open": 1382.75,
+    "high": 1385.95,
+    "low": 1381.72,
+    "close": 1384.68
+  },
+  {
+    "open": 1384.67,
+    "high": 1392.47,
+    "low": 1384.26,
+    "close": 1389.48
+  },
+  {
+    "open": 1389.49,
+    "high": 1392,
+    "low": 1388.82,
+    "close": 1390.13
+  },
+  {
+    "open": 1390.13,
+    "high": 1392.46,
+    "low": 1389.7,
+    "close": 1391.94
+  },
+  {
+    "open": 1391.94,
+    "high": 1393.95,
+    "low": 1388.32,
+    "close": 1388.68
+  },
+  {
+    "open": 1388.68,
+    "high": 1389.35,
+    "low": 1379.59,
+    "close": 1381.72
+  },
+  {
+    "open": 1381.71,
+    "high": 1384.78,
+    "low": 1379.64,
+    "close": 1384.68
+  },
+  {
+    "open": 1384.67,
+    "high": 1384.92,
+    "low": 1381.13,
+    "close": 1383.07
+  },
+  {
+    "open": 1383.07,
+    "high": 1383.24,
+    "low": 1375.5,
+    "close": 1375.74
+  },
+  {
+    "open": 1375.73,
+    "high": 1378.38,
+    "low": 1372.01,
+    "close": 1374.42
+  },
+  {
+    "open": 1374.42,
+    "high": 1377.99,
+    "low": 1366,
+    "close": 1377.51
+  },
+  {
+    "open": 1377.51,
+    "high": 1378.73,
+    "low": 1372.87,
+    "close": 1375.18
+  },
+  {
+    "open": 1375.18,
+    "high": 1378.38,
+    "low": 1371.96,
+    "close": 1376.76
+  },
+  {
+    "open": 1376.77,
+    "high": 1377.59,
+    "low": 1370.81,
+    "close": 1370.95
+  },
+  {
+    "open": 1370.95,
+    "high": 1374.62,
+    "low": 1363.87,
+    "close": 1367.88
+  },
+  {
+    "open": 1367.88,
+    "high": 1372,
+    "low": 1365.03,
+    "close": 1368.68
+  },
+  {
+    "open": 1368.67,
+    "high": 1373.02,
+    "low": 1367,
+    "close": 1370.9
+  }
+]`)
+
+func Test_KalmanFilter(t *testing.T) {
+	type args struct {
+		allKLines              []types.KLine
+		window                 int
+		additionalSmoothWindow uint
+	}
+	var klines []types.KLine
+	if err := json.Unmarshal(testKalmanFilterDataEthusdt5m, &klines); err != nil {
+		panic(err)
+	}
+	tests := []struct {
+		name string
+		args args
+		want float64
+	}{
+		{
+			name: "ETHUSDT Kalman Filter 7",
+			args: args{
+				allKLines:              klines,
+				window:                 7,
+				additionalSmoothWindow: 3,
+			},
+			want: 1369.24,
+		},
+		{
+			name: "ETHUSDT Kalman Filter 25",
+			args: args{
+				allKLines:              klines,
+				window:                 25,
+				additionalSmoothWindow: 0,
+			},
+			want: 1369.84,
+		},
+		{
+			name: "ETHUSDT Kalman Filter 99",
+			args: args{
+				allKLines:              klines,
+				window:                 99,
+				additionalSmoothWindow: 0,
+			},
+			want: 1369.95,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			filter := &KalmanFilter{
+				IntervalWindow:         types.IntervalWindow{Window: tt.args.window},
+				AdditionalSmoothWindow: tt.args.additionalSmoothWindow,
+			}
+			for _, k := range klines {
+				filter.PushK(k)
+			}
+			got := filter.Last()
+			got = math.Trunc(got*100.0) / 100.0
+			if got != tt.want {
+				t.Errorf("KalmanFilter.Last() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func Test_KalmanFilterEstimationAccurate(t *testing.T) {
+	type args struct {
+		allKLines   []types.KLine
+		partialInfo bool
+		window      int
+	}
+	var klines []types.KLine
+	if err := json.Unmarshal(testKalmanFilterDataEthusdt5m, &klines); err != nil {
+		panic(err)
+	}
+	tests := []struct {
+		name string
+		args args
+		want float64
+	}{
+		{
+			name: "ETHUSDT Kalman Filter full K-line square error 7",
+			args: args{
+				allKLines:   klines,
+				partialInfo: false,
+				window:      7,
+			},
+		},
+		{
+			name: "ETHUSDT Kalman Filter full K-line square error 25",
+			args: args{
+				allKLines:   klines,
+				partialInfo: false,
+				window:      25,
+			},
+		},
+		{
+			name: "ETHUSDT Kalman Filter full K-line square error 99",
+			args: args{
+				allKLines:   klines,
+				partialInfo: false,
+				window:      99,
+			},
+		},
+		{
+			name: "ETHUSDT Kalman Filter partial K-line square error 7",
+			args: args{
+				allKLines:   klines,
+				partialInfo: true,
+				window:      7,
+			},
+		},
+		{
+			name: "ETHUSDT Kalman Filter partial K-line square error 25",
+			args: args{
+				allKLines:   klines,
+				partialInfo: true,
+				window:      25,
+			},
+		},
+		{
+			name: "ETHUSDT Kalman Filter partial K-line square error 99",
+			args: args{
+				allKLines:   klines,
+				partialInfo: true,
+				window:      99,
+			},
+		},
+	}
+	klineSquareError := func(base float64, k types.KLine) float64 {
+		openDiff := math.Abs(k.Open.Float64() - base)
+		highDiff := math.Abs(k.High.Float64() - base)
+		lowDiff := math.Abs(k.Low.Float64() - base)
+		closeDiff := math.Abs(k.Close.Float64() - base)
+		return openDiff*openDiff + highDiff*highDiff + lowDiff*lowDiff + closeDiff*closeDiff
+	}
+	closeSquareError := func(base float64, k types.KLine) float64 {
+		closeDiff := math.Abs(k.Close.Float64() - base)
+		return closeDiff * closeDiff
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			filter := &KalmanFilter{IntervalWindow: types.IntervalWindow{Window: tt.args.window}}
+			ewma := &EWMA{IntervalWindow: types.IntervalWindow{Window: tt.args.window}}
+
+			var filterDiff2Sum, ewmaDiff2Sum float64
+			var filterCloseDiff2Sum, ewmaCloseDiff2Sum float64
+			var numEstimations = 0
+			for _, k := range klines {
+				// square error between last estimated state and current actual state
+				if ewma.Length() > 0 {
+					filterDiff2Sum += klineSquareError(filter.Last(), k)
+					ewmaDiff2Sum += klineSquareError(ewma.Last(), k)
+					filterCloseDiff2Sum += closeSquareError(filter.Last(), k)
+					ewmaCloseDiff2Sum += closeSquareError(ewma.Last(), k)
+					numEstimations++
+				}
+
+				// update estimations
+				if tt.args.partialInfo {
+					filter.Update(k.Close.Float64())
+					ewma.Update(k.Close.Float64())
+				} else {
+					filter.PushK(k)
+					ewma.PushK(k)
+				}
+			}
+			filterSquareErr := math.Sqrt(filterDiff2Sum / float64(numEstimations*4))
+			ewmaSquareErr := math.Sqrt(ewmaDiff2Sum / float64(numEstimations*4))
+			if filterSquareErr > ewmaSquareErr {
+				t.Errorf("filter K-Line square error %f > EWMA K-Line square error %v", filterSquareErr, ewmaSquareErr)
+			}
+			filterCloseSquareErr := math.Sqrt(filterCloseDiff2Sum / float64(numEstimations))
+			ewmaCloseSquareErr := math.Sqrt(ewmaCloseDiff2Sum / float64(numEstimations))
+			if filterCloseSquareErr > ewmaCloseSquareErr {
+				t.Errorf("filter close price square error %f > EWMA close price square error %v", filterCloseSquareErr, ewmaCloseSquareErr)
+			}
+		})
+	}
+}