I found this script from the EarthEngine user 'kasparhurni', maybe it helps:

//Topographic correction of all Landsat satellite imagery

//USER INPUTS

var startYear = 2015;

var endYear = 2015;

var targetDay = 350;//day of the year around which the mosaic of good observations is built

//startSeason and endSeason define the window to search for 'good' observations for the mosaic

//around the targetDay.

//Window size needs to be a trade-off between availability of good observations

//(large temporal window) while minimizing phenological changes (small temporal window)

var startSeason = '-12-01';

var endSeason = '-12-31';

var studyArea = ee.Geometry.Polygon(

[[[85.1, 27.9], [85.5, 27.9],

[85.5, 27.5], [85.1, 27.5]]]);

////////////////////////////////////////////////////////////////////////////////////////////////

//------------------------------------END OF USER INPUTS--------------------------------------//

////////////////////////////////////////////////////////////////////////////////////////////////

// Definition of Landsat 5/7/8 bands and default band names

var LC8_BANDS = ['B2', 'B3', 'B4', 'B5', 'B6', 'B7'];

var LE7_BANDS = ['B1', 'B2', 'B3', 'B4', 'B5', 'B7'];

var LT5_BANDS = ['B1', 'B2', 'B3', 'B4', 'B5', 'B7'];

var DEF_BANDS = ['blue', 'green', 'red', 'nir', 'swir1', 'swir2'];

//CONVERT TO RADIANS AND CONSTANTS

function radians(img) {

return img.toFloat().multiply(Math.PI).divide(180);}

//SR TIME SERIES SELECTION

//LANDSAT 8 TIME SERIES, MASK CLOUDS USING FMASK, ASSIGN DEFAULT BAND NAMES, SCALE

var getLedapsLC8 = function(year, sensor, box){

var srCollectionT = ee.ImageCollection('LANDSAT/'+sensor+'_SR')

.filterBounds(box)

.filterDate(year+startSeason, year+endSeason)

.map(function(img){

var cloudMask = img.select('cfmask').eq(0);

return img.mask(img.mask().and(cloudMask));

})

.select(LC8_BANDS, DEF_BANDS)

.map(function(img){

return img.select([]).addBands(img.multiply(0.0001));

});

var cloudCollection = ee.ImageCollection('LANDSAT/'+sensor+'_L1T')

.filterBounds(box)

.filterDate(year+startSeason, year+endSeason)

.filterMetadata('CLOUD_COVER', 'less_than', 50)

.map(function(img){

return img.select([]);

});

var innerJoin = ee.Join.inner();

var filterTimeEq = ee.Filter.equals({

leftField: 'system:time_start',

rightField: 'system:time_start'

});

var joinedCollection = innerJoin.apply(srCollectionT, cloudCollection, filterTimeEq);

var srCollection = joinedCollection.map(function(feature){

return ee.Image.cat(feature.get('primary'), feature.get('secondary'));

});

return ee.ImageCollection(srCollection);

};

//LANDSAT 5 and 7 TIME SERIES, MASK CLOUDS USING FMASK AND SR_*_QA, ASSIGN DEFAULT BAND NAMES, SCALE

var getLedapsLT5LE7 = function(year, sensor, box){

var srCollectionT = ee.ImageCollection('LANDSAT/'+sensor+'_SR')

.filterBounds(box)

.filterDate(year+startSeason, year+endSeason)

.map(function(img){

var timg = img.unmask();

var mask = timg.select('sr_cloud_qa')

.add(timg.select('sr_adjacent_cloud_qa'))

.add(timg.select('sr_cloud_shadow_qa'))

.add(timg.select('sr_snow_qa'));

var cloudMask = img.select('cfmask').eq(0).and(mask.eq(0));

return img.mask(img.mask().and(cloudMask));

})

.select(LT5_BANDS, DEF_BANDS)

.map(function(img){

return img.select([]).addBands(img.multiply(0.0001));

});

var cloudCollection = ee.ImageCollection('LANDSAT/'+sensor+'_L1T')

.filterBounds(box)

.filterDate(year+startSeason, year+endSeason)

.filterMetadata('CLOUD_COVER', 'less_than', 50)

.map(function(img){

return img.select([]);

});

var innerJoin = ee.Join.inner();

var filterTimeEq = ee.Filter.equals({

leftField: 'system:time_start',

rightField: 'system:time_start'

});

var joinedCollection = innerJoin.apply(srCollectionT, cloudCollection, filterTimeEq);

var srCollection = joinedCollection.map(function(feature){

return ee.Image.cat(feature.get('primary'), feature.get('secondary'));

});

return ee.ImageCollection(srCollection);

};

//C TOPOGRAPHIC ILLUMINATION CORRECTION

var correctTopo = function(year, box){

//DEM, SLOPE, ASPECT

var DEM = ee.Image("USGS/SRTMGL1_003").clip(box);

// Define a boxcar or low-pass kernel.

var boxcar = ee.Kernel.square({

radius: 3, units: 'pixels', normalize: true

});

// Smooth DEM by convolving with the boxcar kernel.

var DEMs = DEM.convolve(boxcar);

var SLP = radians(ee.Terrain.slope(DEMs));

var ASP = radians(ee.Terrain.aspect(DEMs));

function iteration(img, imglist){

imglist = ee.List(imglist);

img = ee.Image(img);

var emptyImage = img.select([]);

//STUDY AREA AND IMAGE

var footprint = ee.Geometry.Polygon(ee.Number(ee.List(img.get('system:footprint'))));

//VARIABLES FROM METADATA

var AZ = ee.Number(img.get('solar_azimuth_angle'));

var ZE = ee.Number(img.get('solar_zenith_angle'));

var AZ_R = radians(ee.Image(AZ));

var ZE_R = radians(ee.Image(ZE));

//CALCULATE LOCAL ILLUMINATION AND COS OF THE ZENITH ANGLE

var IL = AZ_R.subtract(ASP).cos().multiply(SLP.sin()).multiply(ZE_R.sin())

.add(ZE_R.cos().multiply(SLP.cos()));

var cos_ZE = ZE_R.cos();

//GET REGRESSION COEFFICIENTS (B & M) AND CORRECTION FACTOR FOR EACH BAND & PIXEL

//C for the blue band

var clippedImg1 = img.addBands(1).addBands(IL);

var resultBlue = clippedImg1.select('constant', 'constant_1', 'blue')

.reduceRegion({

reducer: ee.Reducer.linearRegression(2,1),

geometry: footprint,

scale: 30,

maxPixels: 2e9

});

var blueC = (ee.Array(resultBlue.get('coefficients')).get([0,0]))

.divide(ee.Array(resultBlue.get('coefficients')).get([1,0]));

var blueCorr = (cos_ZE.add(blueC)).divide(IL.add(blueC));

//C for the green band

var clippedImg2 = img.addBands(1).addBands(IL);

var resultGreen = clippedImg2.select('constant', 'constant_1', 'green')

.reduceRegion({

reducer: ee.Reducer.linearRegression(2,1),

geometry: footprint,

scale: 30,

maxPixels: 2e9

});

var greenC = (ee.Array(resultGreen.get('coefficients')).get([0,0]))

.divide(ee.Array(resultGreen.get('coefficients')).get([1,0]));

var greenCorr = (cos_ZE.add(greenC)).divide(IL.add(greenC));

//C for the red band

var clippedImg3 = img.addBands(1).addBands(IL);

var resultRed = clippedImg3.select('constant', 'constant_1', 'red')

.reduceRegion({

reducer: ee.Reducer.linearRegression(2,1),

geometry: footprint,

scale: 30,

maxPixels: 2e9

});

var redC = (ee.Array(resultRed.get('coefficients')).get([0,0]))

.divide(ee.Array(resultRed.get('coefficients')).get([1,0]));

var redCorr = (cos_ZE.add(redC)).divide(IL.add(redC));

//C for the nir band

var clippedImg4 = img.addBands(1).addBands(IL);

var resultNir = clippedImg4.select('constant', 'constant_1', 'nir')

.reduceRegion({

reducer: ee.Reducer.linearRegression(2,1),

geometry: footprint,

scale: 30,

maxPixels: 2e9

});

var nirC = (ee.Array(resultNir.get('coefficients')).get([0,0]))

.divide(ee.Array(resultNir.get('coefficients')).get([1,0]));

var nirCorr = (cos_ZE.add(nirC)).divide(IL.add(nirC));

//C for the swir1 band

var clippedImg5 = img.addBands(1).addBands(IL);

var resultSwir1 = clippedImg5.select('constant', 'constant_1', 'swir1')

.reduceRegion({

reducer: ee.Reducer.linearRegression(2,1),

geometry: footprint,

scale: 30,

maxPixels: 2e9

});

var swir1C = (ee.Array(resultSwir1.get('coefficients')).get([0,0]))

.divide(ee.Array(resultSwir1.get('coefficients')).get([1,0]));

var swir1Corr = (cos_ZE.add(swir1C)).divide(IL.add(swir1C));

//C for the swir2 band

var clippedImg6 = img.addBands(1).addBands(IL);

var resultSwir2 = clippedImg6.select('constant', 'constant_1', 'swir2')

.reduceRegion({

reducer: ee.Reducer.linearRegression(2,1),

geometry: footprint,

scale: 30,

maxPixels: 2e9

});

var swir2C = (ee.Array(resultSwir2.get('coefficients')).get([0,0]))

.divide(ee.Array(resultSwir2.get('coefficients')).get([1,0]));

var swir2Corr = (cos_ZE.add(swir2C)).divide(IL.add(swir2C));

//IMAGE CORRECTION

var blueBand = img.select('blue').multiply(blueCorr);

var greenBand = img.select('green').multiply(greenCorr);

var redBand = img.select('red').multiply(redCorr);

var nirBand = img.select('nir').multiply(nirCorr);

var swir1Band = img.select('swir1').multiply(swir1Corr);

var swir2Band = img.select('swir2').multiply(swir2Corr);

var img_TC = img.select().addBands([blueBand, greenBand, redBand, nirBand, swir1Band, swir2Band]);

//ADJUST VALUE RANGE (REFLECTANCE BETWEEN 0 AND 1)

var img_TC1 = img_TC.where(img_TC.lte(0),0);

var img_TC2 = img_TC1.where(img_TC1.gte(1),1);

var outImage = emptyImage.addBands(img_TC2

.select([0,1,2,3,4,5],['blue', 'green', 'red', 'nir', 'swir1', 'swir2']));

return imglist.add(emptyImage.addBands(outImage.select(['blue', 'green', 'red', 'nir', 'swir1', 'swir2'])));

}

var start = ee.List([ee.Image(getCombinedLedapsCollection(year, box).first())]);

return ee.ImageCollection.fromImages(ee.List(getCombinedLedapsCollection(year, box).iterate(iteration, start)).slice(1)).select(['blue', 'green', 'red', 'nir', 'swir1', 'swir2']);

};

//BUILD QUALITY MOSAIC

var targetDayMoasic = function(inCollection, targetDay){

var inCollectionDelta = inCollection.map(function(image) {

var day = ee.Date(image.get('system:time_start')).getRelative('day', 'year');

var delta = image.select(null).addBands(day.subtract(targetDay).abs().multiply(-1)).int16();

return delta.select([0], ['delta']).addBands(image);

});

return inCollectionDelta.qualityMosaic('delta').select([1,2,3,4,5,6]);

};

var buildTargetMosaic = function(year, box, targetDay) {

var collection = correctTopo(year, box);

var tmp = targetDayMoasic(collection, targetDay);

var img = tmp.set('system:time_start', (new Date(year,8,1)).valueOf());

return ee.Image(img);

};

//GET IMAGES

var getCombinedLedapsCollection = function(year, box) {

var LT5 = getLedapsLT5LE7(year, 'LT5', box);

var LE7 = getLedapsLT5LE7(year, 'LE7', box);

var LC8 = getLedapsLC8(year, 'LC8', box);

return ee.ImageCollection(LT5.merge(LE7).merge(LC8)).filterBounds(box);

};

//LOOP THROUGH YEARS

var buildTargetDayNBR = function(startYear, endYear, box, targetDay) {

var imgs = [];

for (var i = startYear; i

please watch this tutorial

https://www.youtube.com/watch?v=qYT9jO5jfCA

https://www.youtube.com/watch?v=qYT9jO5jfCA