1 Introduction Modern fitness tracking apps such as Strava and Garmin Connect make extensive use of sensor data to provide insights into a user’s exercise program. This project will concentrate on the...

1 Introduction Modern fitness tracking apps such as Strava and Garmin Connect make extensive use of sensor data to provide insights into a user’s exercise program. This project will concentrate on the analysis of GPS data collected during a mountain bike ride in the Stockrington State Conservation Area. The GPS track log is presented in a csv file containing timestamps, latitude, longitude, and elevation columns recorded at 1 second intervals. In this project you will analyse this GPS data to create some common analysis metrics provided by fitness tracking services. Some effort will also be made to interpolate missing data in places where the GPS signal was lost. 2 Tasks 1. Open the provided .csv file in a text editor and take note of the column headings containing the latitude, longitude, and elevation values for each GPS data point. 2. Write a Python script which opens the .csv file and loads the three columns into numpy arrays. Note that adding .values to the variable returned by pd.read csv() returns a numpy array. 3. In the “random walk” lab task (Week 5 lab, Task 2) two numpy arrays were interpreted as lists of x and y coordinates and plotted as such. Do the same thing for the GPS data points, paying close attention to whether plot(lat,lon) or plot(lon,lat) produces a plot in the standard map orientation of “North up”. The GPS data starts and finishes on the East side. NB: Plotting a “map” in this way interprets latitude and longitude angles as x-y coordinates. It is known as an equirectangular projection and is a gross approximation of what a more accurate map projection would look like. It is, however, useful visual tool due to its simplicity. 4. Read in the “time” column into an array of strings (NB: The .values extension will provide an array of strings) 5. Print the first value and ensure that you get: 2021-01-05 23:48:56+00:00. The format is: YY-MM-DD HH:MM:SS+. The UTC offset is zero, indicating that the timestamps are in GMT. (Very optional) Add 11 hours if you would like to convert them to Australian Eastern Daylight Savings Time. 6. From the array of time strings, create an array where each element is the number of seconds which has past since the previous GPS point. The points are mostly 1 second apart but there may be missing data points or errors so you cannot assume that the n’th data point is n seconds from the start. To create this array you can use the following example as a template: import datetime time1Str = ’2021-01-05 23:48:56+00:00’ time1Obj = datetime.datetime.strptime(time1Str, ’%Y-%m-%d %H:%M:%S+00:00’) time2Str = ’2021-01-06 00:49:57+00:00’ Last compiled: 2021-04-12 10:14:44+10:00 Page 1 of 4 Brenton Schulz Project: ENGG1003 - Programming Assignment 1 GPS Data Analysis, 2021-04-12 ENGG1003- Introduction to Procedural Programming time2Obj = datetime.datetime.strptime(time2Str, ’%Y-%m-%d %H:%M:%S+00:00’) timeDiff = time2Obj - time1Obj print(timeDiff.seconds) In this example time1Str is a string and the datetime.datetime.strptime() function converts that string to a time “object”. Arithmetic can then be performed with these time objects. The results of these arithmetic operations will then contain a .seconds variable. Since there are several thousand GPS points you will need to perform processing in a loop to create the full array. 7. Create an array containing the distance travelled between each GPS point. To do this you will need an equation which translates changes in latitude and longitude to distance. There are many ways to do this, but you are given the choice between the following two options (worth different marks): • Using an equirectangular approximation: x = ∆λ cos φm y = ∆φ d = R p x 2 + y 2 where: – φm is “average latitude”. Use cos φm = 0.839 – ∆φ is change in latitude in radians – ∆λ is change in longitude in radians – R is the radius of Earth, 6371 km. – d is the distance traveled. NB: This will have the same units as R! • Using the haversine formula: a = sin2 ∆φ 2 + cos φ1 cos φ2 sin2 ∆λ 2 c = 2atan2(√ a, √ 1 − a) d = Rc where: – ∆φ is the change in latitude – φ1 is the latitude of the first point – φ2 is the latitude of the second point – ∆λ is the change in longitude – R is the radius of Earth, 6371 km – atan2() is the “four quadrant” inverse-tan() function. Use numpy.arctan2(). – d is the distance traveled. NB: This will have the same units as R! Note that: • The length of the array containing distances will contain 1 fewer elements than the array of points. Store the distance between the 1st and 2nd point in the first element of this array and all other values thereafter. • The numpy trig functions take arguments in radians. Last compiled: 2021-04-12 10:14:44+10:00 Page 2 of 4 Brenton Schulz Project: ENGG1003 - Programming Assignment 1 GPS Data Analysis, 2021-04-12 ENGG1003- Introduction to Procedural Programming • Changes in elevation are ignored. Only calculate the “2D” distance. 8. Plot the timespan array. If the data was “complete” this will be a horizontal line at y = 1. Are there gaps in the data? 9. Create another array and store the average speed traveled between each GPS point. Note that speed = distance time and you already have distance and timespan arrays. The speed can be calculated as a single line of code operating on these arrays. 10. Plot Speed vs Time. Are there any points which are obviously unrealistic or outliers? This was a mountain bike ride - the maximum speed will have been around 50 km/hr. Note that outliers are an indication that the time calculation is possibly incorrect - gaps in the GPS data should still result in a correct average speed during the gap, not an outlier. 11. From the plot of timespans, observe that all timespans greater than 1 second indicate that the GPS signal was lost. Use linear interpolation to calculate an estimate for latitude, longitude, and elevation at all 1 second intervals for which a GPS measurement does not exist. Note that latitude, longitude, and elevation are three different functions of time. This implies that the interpolation is performed on latitude, longitude, and elevation independently (ie: with three calls to the scipy.interp1d() function). The output of the interpolation process will be a new array of GPS points without any gaps (ie: with 1 second between each point). Plot the latitude and longitude points as a “map” on top of the original data, indicating the interpolated data with red X’s. ie: with plt.plot(...,...,’rx’). Zoom in to the section on the Western edge, shown in Figure 1, to show that your interpolation worked. From the interpolated GPS data, calculate a “complete” array of speed vs. time and plot it vs time in seconds since the start of the GPS track. During the interpolated sections speed will be constant (ie: a horizontal line). Also create a plot of interpolated elevation vs time. Note that the length of all interpolated arrays will be longer than the original GPS track. Figure 1: The largest gap in GPS data is along the Western edge due to a disused railway tunnel. Last compiled: 2021-04-12 10:14:44+10:00 Page 3 of 4 Brenton Schulz Project: ENGG1003 - Programming Assignment 1 GPS Data Analysis, 2021-04-12 ENGG1003- Introduction to Procedural Programming 12. Given the interpolated elevation data, create an array of elevation changes between each data point then calculate a lower bound 1 estimate for the rider’s power output. This can be calculated given the following equation for gravitational potential energy: E = mgH. (1) Equation 1 returns a value in Joules assuming that: • The rider, bike, and equipment weight, m, is 100 kg • g = 9.8 ms−2 • H differences are in meters Given that data points are 1 second apart the value of E also happens to be equal to the power output in Watts. Create a plot of this power output as a function of time. Assume that the power output on any downhill sections is zero. 13. From the power output data calculate a lower-bound estimate for the average power output throughout the ride. The “true” power output was not measured (power meters are expensive!) but for reference the average food energy consumption was measured from heart rate data to be approximately 800 W which, assuming a biochemical efficiency of 20 %, results in an average human power output at the pedals of 160 W. Given this, estimate the average power lost due to all other sources (rolling resistance, drivetrain loss, braking, suspension damping, deforming the soil, etc). Is your result realistic? 14. (Spoilers) The power estimate using raw elevation data is unrealistically high. Repeat the calculation, but filter the elevation data first with the following code: import scipy.signal as sig [b,a] = sig.butter(2,0.01) eleFiltered = sig.lfilter(b,a,ele) Plot the raw and “filtered” data to observe the effect - the “noise” in the elevation data has been removed and the data smoothed out. Is the power estimate more realistic now?