question: How does your phone (or a pedometer) tell the difference between a step and random movement?
comment: You might be a bit disappointed by this answer, but most of the time, you're not moving your phone so abruptly that the "shock" (change in acceleration) to it is anywhere near the shock that comes from it being in your pocket/bag and your heel hitting the ground when you walk. And your phone knows when you're tapping on the screen, so it can filter out any "shocks" that come from your fingers hitting the screen. So if you drop your phone on the ground accidentally, or if you text a lot while walking, you might overestimate the number of steps a couple times. But this doesn't happen often. And hopefully you're walking enough that these tiny extra counts don't matter!
passages: The Sony Ericsson W710 and W580 Walkman phones use embedded 2 axis MEMS inertial sensors to detect the steps a user takes. The W710 is a clamshell phone and displays the user's steps on the external display. The W710 must be closed in order for it to count steps. When the step counter is activated, it counts detected steps during the day, and at midnight it stores the counter in a day-by-day history and resets it to zero.
  
  Section::::Integration in personal electronic devices.:Nintendo DS/Nintendo 3DS/Wii U.
   Section::::Accuracy.
  
  The accuracy of step counters varies widely between devices. Typically, step counters are reasonably accurate at a walking pace on a flat surface if the device is placed in its optimal position (usually vertically on the belt clip).
   Although traditional step counters are affected dramatically when placed at different angles and locations, recent advances have made them more robust to those non-ideal placements. Still, most step counters falsely count steps when a user is driving a car or makes other habitual motions that the device encounters throughout the day. This error accumulates for users with moderate commutes to work. Accuracy also depends on the step-length the user enters.
  
  The best pedometers are accurate to within ± 5% error.
  
  Section::::Integration in personal electronic devices.
  
  Section::::Integration in personal electronic devices.:Apple products.
  
  Section::::Integration in personal electronic devices.:Apple products.:Apple iPod Nano.
   The Nintendo 3DS, released March 27, 2011, features an internal pedometer that counts and records daily step counts while in sleep mode. Every hundred steps earns a Play Coin, which can be spent on a variety of extras and bonuses. This pedometer is easily fooled, however, and 'steps' can be created by simply lifting the device up and down in the hand with a motion similar to walking.
   The Apple Watch extended step-counting capability to Apple's first wearable device using the accelerometer and gyroscope integrated in the Apple S1 SIP (System in package). Apple Watch works in parallel with a connected iPhone to improve accuracy of the user's step count.
  
  Section::::Integration in personal electronic devices.:Fitbit.
   By considering a small "window" of the signal, these algorithms look for evidence of a step occurring within the window. The window "slides" across the time series, one time step at a time. The evidence for a step is tested by statistical procedures, for example, by use of the two-sample Student's t-test. Alternatively, a nonlinear filter such as the median filter is applied to the signal. Filters such as these attempt to remove the noise whilst preserving the abrupt steps.
  
  Section::::Algorithms.:Global.
   When the step detection must be performed as and when the data arrives, then online algorithms are usually used, 
  
  and it becomes a special case of sequential analysis.
  
  Such algorithms include the classical CUSUM method applied to changes in mean.
  
  By contrast, "offline" algorithms are applied to the data potentially long after it has been received. Most offline algorithms for step detection in digital data can be categorised as "top-down", "bottom-up", "sliding window", or "global" methods.
  
  Section::::Algorithms.:Top-down.
   In a simple implementation, the user holds their phone in front of them and each step causes position to move forward a fixed distance in the direction measured by the compass. Accuracy is limited by the sensor precision, magnetic disturbances inside structures, and unknown variables such as carrying position and stride length. Another challenge is differentiating walking from running, and recognizing movements like bicycling, climbing stairs, or riding an elevator.
   Nokia Step Counter is a free application available at Nokia Beta Labs which works on a wide range of N-Series Nokia phones. The pedometer application tracks steps taken, time elapsed and distance traveled. This application can be left running all day as it is not a huge drain on the battery.
  
  Section::::Integration in personal electronic devices.:Sony Ericsson W710 Walkman phone, W580 Walkman phone.
   Section::::Gait Training Using Assistive Devices.:Stairs.
  
  Section::::Gait Training Using Assistive Devices.:Stairs.:Ascending Stairs.
   Pedometer
  
  A pedometer is a device, usually portable and electronic or electromechanical, that counts each step a person takes by detecting the motion of the person's hands or hips. Because the distance of each person's step varies, an informal calibration, performed by the user, is required if presentation of the distance covered in a unit of length (such as in kilometers or miles) is desired, though there are now pedometers that use electronics and software to automatically determine how a person's step varies. Distance traveled (by walking or any other means) can be measured directly by a GPS receiver.
   The technology for a pedometer includes a mechanical sensor and software to count steps. Early forms used a mechanical switch to detect steps together with a simple counter. If one shakes these devices, one hears a lead ball sliding back and forth, or a pendulum striking stops as it swings. Today advanced step counters rely on MEMS inertial sensors and sophisticated software to detect steps. These MEMS sensors have either 1-, 2- or 3-axis detection of acceleration. The use of MEMS inertial sensors permits more accurate detection of steps and fewer false positives. The software technology used to interpret the output of the inertial sensor and "make sense of accurate steps" varies widely. The problem is compounded by the fact that in modern day-to-day life, such step-counters are expected to count accurately on locations where users frequently carry their devices (attached to the belt, shirt/pants pocket, hand bag, backpack). In recent years more advanced approaches to measure steps have been made with the use of computer vision.
   BULLET::::5. Inertial (cameraless) systems based on MEMS inertial sensors, biomechanical models, and sensor fusion algorithms. These full-body or partial body systems can be used indoors and outdoors regardless of lighting conditions.
  
  Section::::Techniques.:Markerless gait capture.
   These algorithms start with the assumption that there are no steps and introduce possible candidate steps one at a time, testing each candidate to find the one that minimizes some criteria (such as the least-squares fit of the estimated, underlying piecewise constant signal). An example is the "stepwise jump placement" algorithm, first studied in geophysical problems, that has found recent uses in modern biophysics.
  
  Section::::Algorithms.:Bottom-up.
   Bottom-up algorithms take the "opposite" approach to top-down methods, first assuming that there is a step in between every sample in the digital signal, and then successively merging steps based on some criteria tested for every candidate merge.
  
  Section::::Algorithms.:Sliding window.
   Before phone-based systems existed, many custom PDR systems existed. While a pedometer can only be used to measure linear distance traveled, PDR systems have an embedded magnetometer for heading measurement. Custom PDR systems can take many forms including special boots, belts, and watches, where the variability of carrying position has been minimized to better utilize magnetometer heading. True dead reckoning is fairly complicated, as it is not only important to minimize basic drift, but also to handle different carrying scenarios and movements, as well as hardware differences across phone models.
  
  Section::::Directional dead reckoning.
   One way to identify specific people is by how they walk. Gait-recognition software can be used to record a person's gait or gait feature profile in a database for the purpose of recognizing that person later, even if they are wearing a disguise.
  
  Section::::Sensor usage.:Wi-Fi-based activity recognition.
   The data sent by the device every second is cumulative, since the device was first used, and thus can be very revealing of a user's exercise habits and life in general. The data is: number of steps run, number of steps walked, distance run, distance walked, and number of hours device has been on.
  
  Section::::Online integration.
   Section::::General information.
   The app also calculates other data such as the distance traveled, the number of calories burned and the number of steps taken at a good pace. According to the application information, a good rhythm is obtained when a rate of at least 100 steps per minute is maintained for ten minutes.
  
  At the visual level, we can use the data with different graphics:
  
  BULLET::::- On a 24-hour day with a histogram showing activity (number of steps) in 24-minute increments (60 slices of 24 minutes in one day)
   • First Phase :
  
  • Second Phase: 
  
  • Set the new step size as S = S/2
  
  • Repeat the SES search procedure until S=1
  
  • Select the location with lowest weight as motion vector
  
  SES is computationally very efficient as compared to TSS. However the peak signal-to-noise ratio achieved is poor as compared to TSS as the error surfaces are not strictly unimodal in reality. 34.0444094
  
  Section::::Algorithms.:Four Step Search.
   Pedestrian dead reckoning and other approaches for positioning of pedestrians propose an inertial measurement unit carried by the pedestrian either by measuring steps indirectly (step counting) or in a foot mounted approach, sometimes referring to maps or other additional sensors to constrain the inherent sensor drift encountered with inertial navigation. The MEMS inertial sensors suffer from internal noises which result in cubically growing position error with time. To reduce the error growth in such devices a Kalman Filtering based approach is often used.
   PeSEAS and PerMIATE software automate and record the movement observed in the WAMI video. This technology uses software to track and record the movements of pedestrians and vehicles using automatic object recognition software across the entire frame, generating "tracklets" or chronographs of every car and pedestrian movements. 24/7 deployment of this technology has been suggested by the DHS on spy blimps such as the recently killed Blue Devil Airship.
   The following table shows the types of mobile sensors from which each software package is capable of collecting sensor data. Note that the type of data collected depends on availability of the appropriate sensor hardware on a specific smartphone. Some software packages collect raw sensor data (e.g. Beiwe) whereas others collect summaries of such data (e.g. ResearchKit).
  
  Section::::Sensor and data that can be captured (part 2).
   Section::::Integration in personal electronic devices.:Pedometers for Smartphones/MP3 players.
  
  Since most smartphones, iPod Touches and some MP3 players are enhanced with an integrated accelerometer it is possible to introduce pedometer functionality to these devices. This option was successfully realized by a number of smartphone application developers, enabling any fitness savvy smartphone owner to track the number of steps taken as well as distance traveled and calories used.
  
  Section::::Integration in personal electronic devices.:NTT DoCoMo Fujitsu Pedometer Phone.
  
presuppositions: A step and a random movement are both equally detectable by a phone. Your phone can tell the difference between a step and random movement.
corrections: A random movement is not abrupt enough to cause a "shock" that a phone will recognize. Your phone cannot tell the difference between a step and random movement, but most of the time random movement doesn't create enough change in acceleration.
raw_presuppositions: A step and a random movement are both equally detectable by a phone. Your phone can tell the difference between a step and random movement.
raw_corrections: A random movement is not abrupt enough to cause a "shock" that a phone will recognize. Your phone cannot tell the difference between a step and random movement, but most of the time random movement doesn't create enough change in acceleration.