# One, Two Step

Wrist pedometers are used by many to count their steps, and notify users when they “reach their 10,000”. These wearable devices quantify step activity and give indiviudals an idea of exactly how much they are moving throughout the day.

Accelerometers are often used within these wearable devices to detect the force acting on the device. The force acting on the accelerometer is correlated to an analog voltage output, which must be processed through a series of op amps to turn a users movement into an electrical output that can be analyzed through signal processing, but what signal processing circuitry is needed following the accelerometer within a wrist pedometer to correlate force acting on the pedometer to steps taken by the user?

In this post we will solve at the following engineering problem associated with pedometers: what signal processing circuitry is needed to convert the analog voltage input from an accelerometer to a binary digital signal that can be correlated to steps taken by a user?

Background

Figure 1. Force acting on wrist pedometer during gait cycle[1].

The average person takes between 0 and 120 steps per a minute. Throughout each gait cycle, a wrist pedometer experiences forces relative to its position, as shown in Figure 1. While standing the force detected by the pedometer is 1G (one times the force of gravity). When a user is pushing against the ground to step forward the force detected by the pedometer can rise above 1G, and while the user is between steps the force detected by the pedometer can go below 1G. The pedometer can detect when a user takes a step by monitoring forces and determining when the 1G threshold is crossed. Many wrist pedometers use a threshold of at least +/- 0.2G to prevent noise and standing movements from being accounted for in step count. So a step count will be equal to crossing the 1.2G and -1.2G thresholds[1].

Figure 2. Voltage Output as a function of force for Analog Devices+/- 2g accelerometer [2]

Accelerometers are often used to relate the force acting on an object to an electrical signal. Analog Devices, a circuitry component manufacturer, produces an +/- 2g accelerometer that relates forces between -2g and +2g to a voltage output, as shown in Figure 2. A linear region exists between +/- 2g, which can be defined by the following simplified function V(g)=(.875*g)+2.5 [2].

Approach

In designing the signal processing circuitry necessary to convert an analog signal from an accelerometer to a binary digital signal, we will do the following:

1.Define the input signal in terms of force acting on a wrist pedometer, and the voltage output of an accelerometer

2.Determine the signal processing necessary to convert the analog signal into binary digital output

3.Select circuit components to complete desired signal processing, and appropriate values for integrated components

4.Use LTSpice to model desired circuitry, and confirm that designed circuit solves the defined engineering problem

Signal Input

It is known that the force acting on a wrist pedometer can be defined by a sine wave function fluctuating +/ 0.5g around 1g, with a frequency of 0-2Hz. Therefore we will define the force acting on the pedometer as F(t)= 0.5sin(t) + 1g. Given the voltage output of analog devices accelerometer is V(g)=(.875*g)+2.5, the voltage output of the accelerometer can be defined as V(t)=0.4105sin(t)+3.375.

Figure 3. Force acting on pedometer throughout gait cycle

Figure 4. Voltage signal generated by accelerometer from force input signal

Signal Processing

To generate a digital binary signal from an analog voltage input signal processing through circuitry is required.

Figure 5. Flow chart of signal processing of input analog signal from accelerometer to binary output signal

First, the input signal should be passed through a low pass filter, with a cutoff frequency of 2Hz to remove high frequency noise from the signal. The force acting on the pedometer, and voltage output of an accelerometer can be defined by sine wave functions. The baseline of accelerometer voltage output exists above zero volts, therefore a subtractor should be used to bring the baseline of this signal to 0V. A full wave rectifier will be used as an AC to DC converter, converting both polarities of the signal to a pulsating DC signal. A compactor will be used to produce a binary DC output that indicates whether the signal is above a given threshold, voltage relative to passing +/- 0.2g force threshold. This binary signal is the system output and can be used to count total steps taken by a user.

Circuit Components

Circuit components were selected to complete necessary signal processing, and assumed to be ideal for simplification of solving this problem.

Low pass filter

Figure 6. Low pass filter

With a cutoff frequency of 2Hz, a low pass filter with a Capacitor of 4.7 nF and resistor of 0.0169 Ohms can be used to filter out high frequency noise

Follower

Figure 7. Op amp acting as follower

Follower used to preserve signal and prevent current flow back to the user

Subtractor

Figure 8. Op amp acting as a subtractor

A subtractor can be used to reduce the baseline signal to zero. Given our voltage input is V(t)=0.4105sin(t)+3.375 V, and the Voltage output of this component is Vout = (R3/R1)*(Vin-Vs), we will set Vs=3.375V DC and R1=R2=R3=100 Ohm to bring the baseline signal down to 0V.

Full Wave Rectifier

Figure 9. Op amps acting as a full wave rectifier

A full wave rectifier will be used to convert all polarities of the input signal to the same polarities. If R1=R2=R3=R4=R5, then if Vin>0 Vout=Vin and Vin<0 Vout=-Vin. Therefore, we will set all the resistors equal to each other to achieve a rectified DC signal.

Comparator

Figure 10. Op Amp acting as a comparator

A comparator will be used to convert the pulsating DC signal to a binary digital output. Op amps functioning as comparators follow the rule that if V+>V- Vout = Vc+ and V->V+ Vout=Vc-. In our ideal circuit, we aim our binary signal to be either 0 or 1.

V+ terminal will be our signal, and we look to determine if this signal represents crossing the 1.2g threshold. To find what the V- terminal should be we need to determine the voltage at this point in the circuit if it has crossed the threshold. Given, V(g)=(.875*g)+2.5, V(g=1.2)=3.52. The signal is brought through a subtractor where it is reduced by 3.375 and afterword is no longer amplified or modified, so the threshold voltage at this point is 0.1534 V. The negative input terminal will be set to be a DC voltage of 0.1534V.

To generate a binary output where 0V= not crossing the threshold and 1V= crossing threshold, the op amp terminals will be set to be Vc+ = 1V and Vc-=0V.

LTSpice Modeling and Verification

Figure 11. LTSpice signal processing circuit following accelerometer to convert analog accelerometer signal input to binary output

LTSpice was used to model the designed circuit, as shown in figure 11. This circuit was simulated using LTSpice software and it’s ability to produce a binary digital output from an analog signal was verified as depicted in figure 12.

Figure 12. Voltage input, green, and output, blue, of signal processing circuit in figure 11

Solution

Our goal was to design signal processing circuitry is needed to convert the analog voltage input from an accelerometer to a binary digital signal that can be correlated to steps taken by a user.

Figure 13. Accelerometer analog output signaling processing circuit to produce binary digital output

A series of signal processing components were integrated within a circuit, depicted in figure 13, to convert an analog voltage signal from an accelerometer into a binary digital signal. This circuit removes high frequency signal noise, reduces the signal baseline, generates a pulsating DC signal, and generates a binary signal output, as shown in figure 14.

Figure 14. Binary digital output of accelerometer signal processing circuit

This binary digital output can be correlated to steps taken, as two square waves is equal to one step taken. These square waves can be counted by an integrated software and used to count user steps. Thus, turning the analog accelerometer voltage output into a binary digital signal.

This binary signal can be used to count steps and step frequency, and when integrated with GPS and other technologies can be used to determine step distance and user speed.

With one two sqaure waves equaling a step, the designed integrated circuit turns user movement into step count, enabling the signal processing necessary to count those 10,000 steps everyone is so desperately trying to reach!

References

[2] “Accelerometer Specifications – Quick Definitions.” Accelerometer Specifications – Quick Definitions | Analog Devices, www.analog.com/en/products/landing-pages/001/accelerometer-specifications-definitions.html.

# Just Trying To Reach 10,000 Or Competing To Step Above The Rest – How Do Wrist Pedometers Count Our Steps?

People everywhere are getting their steps in. Whether they’re attempting to reach 10,000 steps a day or participating in competitions with friends, family, or coworkers to see who can step the most, people are moving – and they want to know exactly how much. Wrist fitness trackers with built in pedometers have become a popular mode for individuals to track their daily activity, but how do these devices work?

Let’s look at Apple Incorporated’s Wrist Pedometer Step Detection technology. This technology uses motion data to determine a force comparison threshold that can be used to accurately count steps while a user is running and walking.

An illustration of a person using a wrist pedometer for step detection, included in United States Patent No. US20140074431A1

Patent title: Wrist Pedometer Step Detection

Patent number: US20140074431A1

Patent filing date: 2012-09-10

Patent issue date: 2014-03-13

Inventor: Yash Rohit Modi

Assignee: Apple Inc

U.S. classification: G01C22/006 Pedometers

How many claims: 18

Forces acting on a wrist pedometer can be associated with user movement, specifically when they’re walking or running. The force of gravity as well as the forces exerted by the user against the force of gravity are measured by the pedometer; changes in forces acting on the device can be used to determine step count as well as type of exercise. While standing the force detected by the pedometer is 1G (one times the force of gravity). When a user is pushing against the ground to step forward the force detected by the pedometer can rise above 1G, and while the user is between steps the force detected by the pedometer can go below 1G. The pedometer can detect when a user takes a step by monitoring forces and determining when the 1G threshold is crossed.

Forces are compared based off magnitude and frequency to accurately count user steps. Other pedometer technologies worn at the trunk have used a 0.2G comparison threshold to account for steps, meaning when the pedometer experiences a for change of at least 0.2G one step will be added onto the step count. This threshold has been set to prevent noise and standing movements from being accounted for in step count.  However, the force differential experienced by wrist pedometers change with alternating steps. With the step on the side opposing the pedometer, the force acting on the pedometer is often less than 0.2G and may not be detected by the device with this threshold in place. To overcome this issue, this devices step algorithm has included frequency of threshold crossing to account for opposing steps. If the comparison threshold has been crossed twice over a set step time, then the technology will account for two steps rather than one. This prevents the technology from missing steps – thus, increasing device accuracy.

Motion data is also utilized in this technology to account for user activity and adjust parameters appropriately count steps . Fast Fourier Transform (FFT) is used to determine dominant frequency of motion and determine user activity. If the dominant frequency is below run threshold, then steps are counted for within walking parameters, described above. If the dominant frequency is above run threshold, then steps are counted for within running parameters. While running, there is a reduction in change of force acting on the pedometer; the change of parameters takes this into account and utilizes this information to properly account for steps.

Unlike other step counting technologies on the market, this product has improved accuracy in step count. The step counting algorithm has parameters that better define noise and non-walking movement as well as a mode to account for the imbalance in force acting on the wrist pedometer during walking. Less steps are unaccounted for and less random movements are counted – making for more accurate step counts.

There are a number of pedometer technologies that exist on the market today. Regardless of brand and step counting algorithm – these technologies are giving indiviudals the ability to count their steps and measure their fitness levels, promoting an active lifestyle for those who utilize them.

Reference