NXP NTM88 User guide

Brand: NXP

Model: NTM88

Type: User guide

UM11362

NTM88 Dual-Axis Location Angle Project – Algorithms

Rev. 1 — 27 March 2020 User manual

1 Introduction

This document provides an overview of the algorithms used in the NTM88_LocAngle_XZ

project source code functions, including:

• The wheel rotation period measurement algorithm in function u8fXGetRotPeriod()

• The wheel rotation direction finding algorithm in function u8fFindWheelDir()

• The RF packet transmission timing algorithm in function Xmit_RF_Packets_Loop()

• The low pass filters (LPF) 4-pole and 2-pole algorithms used in the rotation direction

finding function u8fFindWheelDir() and the rotation period measurement function

u8fXGetRotPeriod()

This document complements the NTM88 Dual-Axis Location Angle Project – Software

user manual, which describes how these algorithms are implemented and offers details

on the project source code.

The NTM88_LocAngle_XZ project was designed as a reference project with limited

performance verification. Users are encouraged to experiment and modify the algorithms

and the project code to suit their application requirements.

2 Rotation period measurement

Wheel rotation speed measurement is performed in function u8fXGetRotPeriod(). The

algorithm is implemented as a state sequencer with state variable u8MoveState. During

wheel rotation, a sequence of samples read from the TPMS accelerometer X is passed

through the LPF to attenuate noise and distortions, and the period of the resulting sine

wave is measured. The peak-to-peak value of the sine wave is equivalent to acceleration

X changing in the range ±1 g. In the ideal scenario, accelerometer X's sensitivity axis

is tangent to the wheel's circle and the sequence of accelerometer X samples is a

sine wave with an average value of 0. In practice, due to installation inaccuracies,

accelerometer X is not perfectly tangent to the wheel and is influenced by centripetal

acceleration. As a result, the sine wave average value is not 0, and the value changes

with the wheel rotation speed. In the period measurement function, the centripetal

acceleration estimate is calculated in variable i16AccXCnt_cpt and is then subtracted

from all subsequent accelerometer X readings. This allows the dynamic range of the

signal being processed by the LPF to be limited.

To save processing time, two possible cases are considered, depending on whether

the first sample of accelerometer X data sequence happens to be on the rising or falling

sine wave slope. The state sequencer follows the sequence shown in Figure 1 in case

the rising slope is detected first and the sequence shown in Figure 2 in case the falling

slope is detected first. Detection of the slope at the beginning of the sequence is done in

state 1. If the rising slope is detected first, the control path follows states 1, 2, 3, 4, 5, 21,

22. If the falling slope is detected first, the control path follows states 1, 12, 13, 14, 15,

21, 22. In both Figure 1 and Figure 2, the sine wave curve represents the signal on the

output of the LPF.

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The sequence of events when the sine wave rising slope is detected in state 1 is

described below with reference to the characteristic sine wave points shown in Figure 1.

aaa-036887

MAX1

MIN1

MAX2

i16XLPF_out

i16XSamp_max1

i16XSamp_min1

u16FRC_PrdStart

PERIOD

u16FRC_Prd

u16FRC_PrdEnd

X_PRD_LVL_CNT

X_RISE_FALL_CNT

i16XSamp_max2

u16FRC_0cr

time

X_PRD_LVL_CNT

1 2 3 ... -sequencer state in u8MoveState

Figure 1. Period measurement when an accelerometer X rising slope is detected first

Point A – Read the first accelerometer X sine wave sample. Control remains in state 1.

Point B – Accelerometer X LPF output count in i16XLPF_out has increased by more

than X_RISE_FALL_CNT from Point A, triggering a decision that a rising slope has been

detected. Transfer control to state 2.

Points MAX1 and C – Monitor the sine wave in state 2 to find the maximum peak count

at point MAX1 and save that value in i16XSamp_max1. Wait until the sine wave count

drops from i16XSamp_max1 by X_PRD_LVL_CNT at Point C. When that occurs, read

the FRC count and save the value in u16FRC_PrdStart. Using the last two sample

counts, apply an interpolation correction to u16FRC_PrdStart to improve the accuracy of

the period starting time. Transfer control to state 3.

Points MIN1 and D – Monitor the sine wave in state 3 to find the minimum peak count at

Point MIN1 and save the value in i16XSamp_min1. Then wait until the sine wave count

increases from i16XSamp_min1 by X_PRD_LVL_CNT at Point D. At this point, make the

decision that the sine wave minimum MIN1 has been detected. Transfer control to state 4

to wait for the following maximum MAX2.

Points MAX2 and E − Monitor the sine wave in state 4 to find the maximum peak count

at point MAX2 and save that value in i16XSamp_max2. Then wait until the sine wave

count drops from i16XSamp_max2 by X_PRD_LVL_CNT at Point E. At Point E, read

the FRC count and save the value in u16FRC_PrdEnd. Using the last two sample

counts, apply an interpolation correction to u16FRC_PrdEnd to improve the accuracy

of the period ending time. To calculate the period length in terms of the FRC count,

subtract u16FRC_PrdStart from u16FRC_PrdEnd and store the result in u16FRC_Prd.

Then, using the FRC calibration result stored in u16usPerPrd, convert the period length

u16FRC_Prd to milliseconds and store the result in u16XPrd_ms. Finally, calculate the

average of the sine wave's last two maximums in i16XSamp_max1 and i16XSamp_max2

and minimum i16XSamp_min1. Save that value in i16XSamp_0crLvl to be used as the

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sine wave 0-crossing count level. Then transfer control to state 5 to wait for the sine

wave 0-crossing point (Point F)

Point F – The accelerometer X sine wave 0-crossing point in state 5. In state 5, monitor

the accelerometer X signal on the output of the LPF. If LPF did not introduce any signal

delay, this point would be equivalent to a location angle of 0° on the car's right-side

wheel (top) and an angle of 180° on the left-side wheel (bottom). In practice, because

the LPF delay is always greater than 0 (several milliseconds), Point F is detected with

a delay equal to the LPF signal delay time. Using an interpolation between the last two

LPF output samples, calculate the value of the FRC counter precisely at the 0-crossing

point F and save the value in variable u16FRC_0cr. u16FRC_0cr is used as a reference

for determining the starting time of the RF packet transmission in state 22 in function

Xmit_RF_Packet_Loop(). Then transfer control to function Xmit_RF_Packet_Loop() in

state 21 to find the target angle in array cai16TargetAngle[] where the first RF packet

must be transmitted.

The sequence of events when the sine wave falling slope is detected in state 1 is

described below with references to the characteristic sine wave points shown in Figure 2.

aaa-036888

MIN1

MAX1

MIN2

i16XLPF_out

i16XSamp_min1

i16XSamp_max1

u16FRC_PrdStart

PERIOD

u16FRC_Prd

u16FRC_PrdEnd

X_PRD_LVL_CNT

X_RISE_FALL_CNT

i16XSamp_min2

u16FRC_0cr

time

X_PRD_LVL_CNT

1 12 13 ... -sequencer state in u8MoveState

Figure 2. Period measurement when an accelerometer X falling slope is detected first

Point A – Read the first accelerometer X sine wave sample. Control remains in state 1.

Point G – Accelerometer X LPF output count in i16XLPF_out has decreased by more

than X_RISE_FALL_CNT count from Point A, triggering a decision that a falling slope

has been detected. Transfer control to state 12.

Points MIN1 and H – Monitor the sine wave in state 12 to find the minimum peak count

at point MIN1 and save that value in i16XSamp_min1. Wait until the sine wave count

increases from i16XSamp_min1 by X_PRD_LVL_CNT at point H. When that occurs,

read the FRC count and save the value in u16FRC_PrdStart. Using the last two sample

counts, apply an interpolation correction to u16FRC_PrdStart to improve the accuracy of

the period starting time. Transfer control to state 13.

Points MAX1 and I – Monitor the sine wave in state 13 to find the maximum peak count

at point MAX1 and save that value in i16XSamp_max1. Then wait until the sine wave

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count drops from i16XSamp_max1 by X_PRD_LVL_CNT at Point I. At this point, decide

that the sine wave maximum MAX1 has been detected. Transfer control to state 14 to

wait for the following minimum MIN2.

Points MIN2 and J – Monitor the sine wave in state 14 to find the minimum peak count

at point MIN2 and save that value in i16XSamp_min2. Then wait until the sine wave

count increases from i16XSamp_min2 by X_PRD_LVL_CNT at Point J. At Point J,

read the FRC count and save that value in u16FRC_PrdEnd. Using the last two sample

counts, apply an interpolation correction to u16FRC_PrdEnd to improve the accuracy

of the period ending time. To calculate the period length in terms of the FRC count,

subtract u16FRC_PrdStart from u16FRC_PrdEnd and store the result in u16FRC_Prd.

Then, using the FRC calibration result stored in u16usPerPrd, convert the period length

u16FRC_Prd to milliseconds and store the result in u16XPrd_ms. Finally, calculate the

average of the sine wave's last two minimums in i16XSamp_min1 and i16XSamp_min2

and maximum i16XSamp_max1 and store the result in i16XSamp_0crLvl to be used as

the sine wave 0-crossing count level. Then transfer control to state 15 to wait for the sine

wave 0-crossing point K.

Point K – The accelerometer X sine wave 0-crossing point in state 15. In state 15,

monitor the accelerometer X signal on the output of the LPF. If LPF did not introduce any

signal delay, this point would be equivalent to a location angle of 180° on the car's right-

side wheel (bottom) and an angle of 0° on the left-side wheel (top). In practice, because

the LPF delay is always greater than 0 (several milliseconds), Point K is detected with

a delay equal to the LPF signal delay time. Using interpolation between the last two

LPF output samples, calculate the value of the FRC counter at precisely the 0-crossing

point K and save the result in variable u16FRC_0cr. u16FRC_0cr is used as a reference

to determine the starting time of the RF packet transmission in state 22 in function

Xmit_RF_Packet_Loop(). Then transfer control to function Xmit_RF_Packet_Loop() in

state 21 to find the target angle in array cai16TargetAngle[] where the first RF packet

should be transmitted.

An example of raw counts of accelerometer X output at different wheel location angles is

shown in Figure 3. The sine wave peak count equivalent to ±1 g is approximately ±105.

After processing the sine wave by the LPF in function RunLPF_IIR16x16() using fixed-

point arithmetic, the LPF output signal in variable i16XLPF_out can be considered as

an integer number in the range of ±1680 (LPF gain equal to 16). All period measuring

operations are performed on the filtered LPF output signal in i16XLPF_out.

aaa-036889

2155

2050

105

0º

180º

270º

0º

90º 180º

time180º

90º19452155

2050

270º

a) b)

105

1945

Figure 3. Accelerator X raw count readings at different location angles (right side wheel)

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3 Finding wheel rotation direction

Wheel rotation direction, clockwise (CW) or counter-clockwise (CCW), is determined

using the readings of both TPMS accelerometers X and Z. When the wheel rotates,

the sequences of samples from both accelerometers are sine waves with peak-to-

peak values representing ±1 g gravity acceleration. In addition, accelerometer Z data

includes a constant acceleration component proportional to wheel rotation speed

—centripetal acceleration. Accelerometer X may also include a small amount of

centripetal acceleration due to an inaccurate TPMS mounting position. The phase

relation between the X and Z sine waves provides information about the wheel rotation

direction. When the wheel rotates in CW direction, the accelerometer Z sine wave is

leading the accelerometer X sine wave by 90°. When the wheel rotates in CCW direction,

the accelerometer Z sine wave is lagging the accelerometer X sine wave by 90°. The

captured sine wave plots are shown in Figure 4 for CW rotation direction and in Figure 5

for CCW rotation direction.

Sample Nr

0 604020 503010

aaa-036891

-1000

1000

2000

-500

-1500

500

1500

Count

-2000

Figure 4. X and Z acceleration sine waves when the wheel rotates in CW direction

Sample Nr

0 604020 503010

aaa-036892

-1000

1000

2000

-500

-1500

500

1500

Count

-2000

Figure 5. X and Z acceleration sine waves when the wheel rotates in CCW direction

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The wheel rotation direction finding algorithm is implemented in function

u8fFindWheelDir(). After reading each of the accelerometer X and Z samples, first the

estimate of the respective centripetal acceleration is subtracted and then the resulting

sine wave samples are passed through their LPFs. The values from the LPF outputs

are then processed by the direction-determining state sequencer. Beginning in state

1, the state sequencer looks for the falling or rising sine wave slope. If a rising slope is

detected first, control transfers to state 2 to wait for the sine wave maximum. At each

accelerometer X sample (which could be the sine wave X maximum) the values of both

samples X and Z are saved. When the X sine wave value, after passing its maximum,

drops by D_X_DIR_CNT below its maximum, the new value of the accelerometer Z

sample is recorded. The two recorded samples of acceleration Z are used to determine

if the slope of sine wave Z in the vicinity of the sine wave X maximum is rising or falling.

Then the decision is made on the wheel rotation direction: if sine wave Z is falling

where sine wave X has its maximum, the direction is CW; if sine wave Z is rising at the

moment of sine wave X maximum, the direction is CCW. Similar logic and processing is

performed in state 3 when the first detected sine wave X slope is falling instead of rising.

In such a case, the program waits in state 3 for the sine wave X minimum. Depending

on whether sine wave Z has a rising or a falling slope at the sine wave X minimum, a

decision is made on the wheel rotation direction.

Using a software conditional compilation switch, the rotation direction monitoring function

can be configured to use 2-pole or 4-pole LPFs for filtering accelerometer X and Z

signals. Using 4-pole LPFs provides better noise attenuation but requires a longer

execution time, which results in a lower maximum car speed at which the direction finding

function will work.

When monitoring the acceleration sine waves X and Z in the wheel direction finding

function using the 2-pole LPFs, the minimum sampling period is Ts=3.3 ms equivalent to

the maximum sampling frequency Fs=303.0 Hz. The minimum sampling period is limited

by the sum of the execution times of all major functions that must be executed on each

pass of the program loop. These are:

Reading accelerometer X – 0.85 ms

Reading accelerometer Z – 0.85 ms

2-pole accelerometer X LPF – 0.78 ms

2-pole accelerometer Z LPF – 0.78 ms

The total minimum execution time is 0.85 ms + 0.85 ms + 0.78 ms + 0.78 ms ≈ 3.3 ms.

This limits the maximum wheel rotation period at which the direction finding algorithm will

work reliably to ≈ 60 ms. Therefore, using the 2-pole LPFs, the wheel rotation direction

can be determined at car speeds up to a maximum of ≈130 km/h (estimation done for tire

size 245/45R18).

With 4-pole LPFs used in the direction finding function, the above functions execution

times are:

Reading accelerometer X – 0.85 ms

Reading accelerometer Z – 0.85 ms

4-pole accelerometer X LPF – 1.6 ms

4-pole accelerometer Z LPF – 1.6 ms

The total minimum execution time is 0.85 ms + 0.85 ms + 1.6 ms +1.6 ms ≈ 4.9ms. This

limits the maximum wheel rotation period at which the direction finding algorithm will work

reliably to ≈ 88 ms. Therefore, using the 4-pole LPFs, the wheel rotation direction can be

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determined at car speeds up to a maximum of ≈ 90 km/h (estimation done for tire size

245/45R18).

4 Packet transmission

The calculation of RF packet transmission times and the transmission of packets is

handled in function Xmit_RF_Packet_Loop(). The function implements a simple state

sequencer that is a continuation of the sequencer started in function u8fXGetRotPeriod()

with state variable u8MoveState.

State 21 is entered when control transfers from either state 5 or state 15. If the

previous state was 5, control transferred to state 21 at Figure 1 Point F, coinciding

with a 0-crossing at TPMS location angle 0°. The initial angle value passed in variable

u8InitAng_0cr is 0. If the previous state was 15, control transferred to state 21 at Figure 2

Point K, coinciding with a 0-crossing at TPMS location angle 180°. The initial angle value

passed in variable u8InitAng_0cr is 180. In state 21, the delay from 0-crossing Points

F or K to the start of the first RF packet transmission is calculated in terms of the FRC

count in variable u16FRCTargAngDly using the initial angle in u8InitAng_0cr.

After calculating the delay in u16FRCTargAngDly, control transfers to state 22. In state

22, the function waits the required delay time for the appropriate moment to start the

next RF packet transmission. The delay is determined by the starting FRC count in

u16FRC_0cr and the delay duration count in u16FRCTargAngDly. After the packet

transmission has started, the program cycles through the remaining target angles

defined in the cai16TargetAngle[] array to find the next suitable angle for transmitting

a packet. After all TARGET_ANG_MAX target angles are processed, the function

Xmit_RF_Packets_Loop() exits and control returns to the main() function.

Calculation of the time delay from the last 0-crossing after the period measurement in

state 5 at point F to the start of the first RF packet transmission is explained below for

the case shown in Figure 1 The same algorithm applies to Figure 2 and 0-crossing point

K. The only difference is that Point F is assumed to coincide with a TPMS location angle

of 0° and Point K is at location angle of 180°. In both cases, the wheel is assumed to be

on the right-side of the car and rotating in a clockwise direction. Figure 6 (a) shows the

events on a time axis and Figure 6 (b) shows the corresponding points marked on the

rotating wheel.

aaa-036893

TA0

i16DegAng2

u16DlyAng3

u16DlyAng1

LPF delay

code execution time

packet transmit time

a) b)

0º

180º

Figure 6. Calculation of the earliest target angle TA0

Figure 7 shows the processing of a sequence of target angles listed in the

cai16TargetAngle[] array.

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aaa-036895

F M

delaydelay

u16FRCTargAngDly

LPF delay packet transmit time

delay

packet transmit time

N P

first target

angle

first packet

transmit start

next packet

transmit start

Q R

next target

angle

next packet

transmit start

0º

Figure 7. Calculation of consecutive RF packets start times

Calculations of the first time delay from Point F to the start of the first RF packet are

performed in state 21 when the TPMS is in the Point F location. The variable u16DlyAng3

is used to calculate the sum of the packet transmission time and the MCU code

execution time. Then the sum of u16DlyAng3 and the signal delay introduced by the

LPF is calculated and stored in u16DlyAng1. Using the wheel rotation period measured

previously, the delay in u16DlyAng1 is converted to degrees in u16DegAng1. The value

represents the minimum difference required from the 0° location angle point to the

earliest possible target angle TA0 in Figure 6 (a). If RF packet transmission starts at this

moment, the target angle (where the packet transmission would end) would be at the

angle i16DegAng2 = u8InitAng_0cr + u16DlyAng1, where u8InitAng_0cr=0.

Next, the sum of the packet transmission time and the MCU code execution time is

calculated and saved in u16DlyAng3 to be used in future processing as a minimum time

delay between two consecutive target angles. The time delay in u16DlyAng3 is converted

to degrees and saved in u16DegAng3. This value becomes the minimum required

difference from the current target angle to the next angle listed in cai16TargetAngle[]

array when deciding whether an RF packet can be transmitted for the next target angle or

whether the next target angle transmission should be skipped.

Having the next minimum target angle in i16DegAng2, the array cai16TargetAngle[] is

scanned to find the array index u8NextAngIdx for the target angle that is greater or equal

to the minimum angle in i16DegAng2. The difference:

i16DlyAngToStart = cai16TargetAngle[u8NextAngIdx] − i16DegAng2

is the delay angle between Point F, where these calculations are performed, and the

moment when the RF packet transmission should start (the angle between points F

and M in Figure 7.) The last operation in state 21 is a conversion of the delay angle in

i16DlyAngToStart into time units in u16FRCTargAngDly representing the FRC counter

count used in state 22 to measure the required time delay. After the delay to the first

packet transmission start is calculated in u16FRCTargAngDly, control transfers to state

22.

In state 22, the program waits until the delay in u16FRCTargAngDly expires and then

transmits the RF packet associated with target angle cai16TargetAngle[u8NextAngIdx].

Immediately after starting the packet transmission at Point M in Figure 7, the operation

of scanning array cai16TargetAngle[] is repeated to find the next target angle suitable

for packet transmission. The difference between the target angle associated with

the currently transmitted RF packet and the next one suitable for transmission must

be greater than packet transmission time and code execution time delay calculated

previously in u16DlyAng3. If the time difference between the currently transmitted

packet at target angle cai16TargetAngle[u8NextAngIdx] and the next angle in

cai16TargetAngle[] array is less than u16DlyAng3, the next packet transmission must

be skipped because its transmission would have to start before the current packet

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transmission terminates. In such a case, the next target angle in the cai16TargetAngle[]

array is considered.

Again, for the next target angle where an RF packet can be transmitted, the new delay to

start the next packet transmission is calculated in u16FRCTargAngDly and the program

waits in the loop for expiration of the delay between Points M and P in Figure 7. At

Points P and possibly R, the same calculations as those used at point M are repeated

until all TARGET_ANG_MAX target angles are processed. The running counter of the

processed target angle entries is kept in variable u8TargAngProcessed. After all target

angles in array cai16TargetAngle[] are processed and all RF packets are transmitted,

the program exits function Xmit_RF_Packets_Loop() and the MCU enters power

saving mode STOP1. The whole sequence of measuring the wheel rotation period and

transmitting RF packets is repeated with the PWU interrupt period defined by parameter

LOC_ANGLE_RUN_PERIOD in main.c.

The sensitivity axis of accelerometer X used in the Location Angle algorithm is tangent

to the wheel's circle. This alignment and the definition of the TPMS position angles

on wheels rotating in clockwise (CW) and counter-clockwise (CCW) directions cause

the same TPMS software to sense different target angles, depending on the wheel's

rotation direction. If the target angle defined in the software is A in the range of 0° to

359°, the TPMS device attached to the wheel rotating in the CW direction (on the car's

right side) will transmit RF packet at angle A. When a TPMS device with the same

software is attached to the wheel rotating in CCW direction (on the car's left side), it will

transmit an RF packet at angle A + 180°. The example of a target angle defined in the

software where angle A = 60° and the TPMS device position angles when RF packets

are transmitted are shown in Figure 8 (a) for CW rotation direction and in Figure 8 (b) for

CCW rotation direction. On a CW rotating wheel, the RF packet is transmitted at a 60°

angle. On a CCW rotating wheel, the RF packet is trnsmitted at angle 60° + 180° = 240°.

Transmitting the packet at the same angle for both rotation directions requires applying

an angle correction to the CCW direction.

No such correction is applied in the Location Angle software in order to reduce code size,

execution time and battery power consumption. The correction that could be applied

would involve determining the wheel rotation direction and then subtracting 180° from the

target angle for wheels rotating in the CCW direction. With this correction, the RF packet

would be transmitted at the same target angle no matter what the rotation direction.

aaa-036894

0º

180º

90º

60º

270º

a) b)

RF packet

transmit time

RF packet

transmit time

end

start

end

0º

180º

CCW

90º

240º

270º

Figure 8. RF packets transmission angles on CW and CCW rotating wheels with a software

target angle of 60°

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5 Low pass filters

5.1 4-pole low pass filters

The 4-pole LPFs implemented in functions RunLPF_IIR16x16() and

RunLPF_IIR16x16Z() are used for filtering X and Z accelerometer signals respectively.

If the rotation direction finding function u8fFindWheelDir() is configured to use 4-

pole LPFs, both of the above LPF functions are used. In addition, the X signal LPF

function RunLPF_IIR16x16() is always used in the rotation period measurement

function u8fXGetRotPeriod(). Both LPFs are identical; they use the same set of constant

coefficients and separate sets of their state variables.

When used in the rotation period measurement function, the X signal LPF is executed

with one of four different sampling periods. The result is equivalent to having four LPFs

with different bandwidths LPF1 through LPF4. One LPF is selected for use during the

entire sequence of wheel rotation period measurements to optimize the LPF performance

at a given rotation speed. Selection of the LPF is done in function SelectLPF() based on

the rotation rate estimated using the acceleration Z centripetal component. Centripetal

accelerations Z, representing the rotation rates, are divided into four LFP usage range:

• LPF1 for low car speeds and low rotation rates where acceleration Z is less than 13.6 g

• LFP2 for medium car speeds and rotation rates where acceleration Z is in the range

13.6 g to 51.0 g

• LPF3 for medium car speeds and rotation rates where acceleration Z is in the range

51.0 g to 155.0 g

• LPF4 for high car speeds and rotation rates where acceleration Z is greater than

155.0 g

The filter transfer function in the z domain is:

H(z) = Y(z) / X(z) = H1(z)

∗

H2(z)

where:

H1(z) represents the transfer function of section I given by:

H1(z) = V(z) / X(z) = [B10 + B11

∗

−1

+ B12

∗

−2

] / [A10 + A11

∗

−1

+ A12

∗

−2

]

Eq. 1

and H2(z) represents the transfer function of section II given by:

H2(z) = Y(z) / V(z) = [B20 + B21

∗

−1

+ B22

∗

−2

] / [A20 + A21

∗

−1

+ A22

∗

−2

]

Eq. 2

X(z) is the z domain transform of the filter input signal

Y(z) is the z domain transform of the filter output signal

The time equation implementing section I in software using filter coefficients converted to

fixed-point format is:

v(n) = B10X

∗

x(n) + B11X

∗

x(n − 1) + B12X

∗

x(n − 2) − A11X

∗

v(n − 1) − A12X

∗

v(n − 2) Eq. 3

The time equation implementing section II in software using filter coefficients converted to

fixed-point format is:

y(n) = B20X

∗

v(n) + B21X

∗

v(n − 1) + B22X

∗

v(n − 2) − A21X

∗

y(n − 1) − A22X

∗

y(n − 2) Eq. 4 where:

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x(n) is the time domain sequence of the filter input signal samples

y(n) is the time domain sequence of the filter output signal samples

A 4-pole LPF block diagram is shown in Figure 9.

aaa-036898

n-1

n-2

n-1

n-2

n-1

-1

-A

-1

Figure 9. Accelerometers X and Z 2-pole low pass filter block diagram

It was decided experimentally to design four LPFs with different bandwidths optimized for

four ranges of car speeds. For all LPFs, there is one set of coefficients used B10…B22

and A11…A22 and their bandwidth is set by using a different signal sampling period in

each range. The sampling periods are:

• LPF1 – 13.68 ms

• LPF2 – 7.24 ms

• LPF3 – 4.14 ms

• LPF4 – 3.00 ms

The parameters for LPF1-4 are shown in Table 1.

Table 1. Low pass filters parameters—data for tire size 205/65R16

LPF

Accel Z

Range [g]

Car

Speed

Range

[km/h]

Max RPM

[RPM]

Min

Rotation

Period

[ms]

Sampling

Period

[ms] 6

Sampling

Freq [Hz]

LPF

Bandwidth

[Hz]

LPF1 5.9–13.6 20.5–31.0 244 245 13.68 73 4.4

LPF2 13.6–51 31–60 474 126 7.24 138 8.3

LPF3 51–155 60–105 826 73 4.14 242 14.5

LPF4 >155 105–152 1200 50 3.00 333 20.0

Different sampling periods are implemented by making dummy calls to the firmware

function TPMS_E_READ_ACCEL_X() with carefully chosen SMI time delays. During

TPMS_E_READ_ACCEL_X() function execution, the MCU spends most of its time in

STOP4 mode, which reduces power consumption.

Filter LPF4, as the base filter, was designed using the Matlab ‘filterBuilder’ digital filter

design command. The target filter configuration chosen was 4-pole IIR implemented as

two 2-pole sections in series. The remaining filters LPF1, LPF2 and LPF3 were derived

from LPF4 by adjusting the sampling period/sampling frequency. Design parameters of

the base LPF4 are shown in Table 2.

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Table 2. Base low pass filter design parameters

Fs – Sampling Frequency

Bandwidth @ Gain

LPF4 333.0 Hz 20.0 Hz @ -0.5 dB

The signal delay vs. signal frequency characteristic of each LPF was calculated and

plotted using the transfer function H(z) with the sampling rate appropriate for the LPF.

The characteristics were then approximated using a straight line interpolation in function

SetLPFDelay() where the variable u16LPFDlyx10 is filled out with the LPF delay for a

signal with period u16XPrd_ms in units ms

∗

10.

An example of LPF input and output waveforms is shown in Figure 10. The plotted data

was collected from a TPMS device attached to a car driving on a typical road with a

speed of ≈ 30 km/h. The amplitude of the raw accelerometer X data sequence recorded

on the LPF input shown in red was multiplied by LPF gain=16 to scale it to the same level

as the LPF output sequence shown in blue. The filter used was LPF1.

Sample Nr

0 604020 503010

aaa-036899

7000

6000

5000

4000

2000

3000

1000

8000

Count

-1000

LPFout

X Raw

Figure 10. Accelerometer X waveforms on LPF input and output

5.2 2-pole Low Pass Filters

The 2-pole LPFs implemented in functions RunLPF_IIR2P16x16X() and

RunLPF_IIR2P16x16Z() are used for filtering X and Z accelerometer signals in the

rotation direction-finding function if it is configured to use 2-pole LPFs. Both LPFs are

identical; they use the same set of constant 2-pole coefficients and separate sets of their

state variables.

The 2-pole LPF transfer function is:

H(z) = Y(z) / X(z) = [B0 + B1

∗

-1

+ B2

∗

-2

] / [A0 + A1

∗

-1

+ A2

∗

-2

]

The time equation implementing the LPF in software using coefficients converted to

fixed-point format is:

y(n) = B0d

∗

x(n) + B1d

∗

x(n − 1) + B2d

∗

x(n − 2) − A1d

∗

y(n − 1) − A2d

∗

y(n − 2)

The filter block diagram is shown in Figure 11.

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aaa-036900

n-1

n-2

-1

-A

n-1

n-2

Figure 11. Accelerometers X and Z 2-pole low pass filter block diagram

Similar to the 4-pole LPF, the 2-pole LPF was designed using the Matlab ‘filterBuilder’

command using the 2-pole IIR as the target configuration. Design parameters of the 2-

pole LPF are shown in Table 3.

Table 3. 2-pole low pass filter design parameters

Fs – Sampling Frequency Bandwidth @ Gain

LPF 2-pole 303.0 Hz 18.0 Hx @ -0.5 dB

6 Revision history

Table 4. Revision history

Document ID Release

date

Descriptions

UM11362 v.1 20200327 Initial release

NXP Semiconductors

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7 Legal information

7.1 Definitions

Draft — The document is a draft version only. The content is still under

internal review and subject to formal approval, which may result in

modifications or additions. NXP Semiconductors does not give any

representations or warranties as to the accuracy or completeness of

information included herein and shall have no liability for the consequences

of use of such information.

7.2 Disclaimers

Limited warranty and liability — Information in this document is believed

to be accurate and reliable. However, NXP Semiconductors does not

give any representations or warranties, expressed or implied, as to the

accuracy or completeness of such information and shall have no liability

for the consequences of use of such information. NXP Semiconductors

takes no responsibility for the content in this document if provided by an

information source outside of NXP Semiconductors. In no event shall NXP

Semiconductors be liable for any indirect, incidental, punitive, special or

consequential damages (including - without limitation - lost profits, lost

savings, business interruption, costs related to the removal or replacement

of any products or rework charges) whether or not such damages are based

on tort (including negligence), warranty, breach of contract or any other

legal theory. Notwithstanding any damages that customer might incur for

any reason whatsoever, NXP Semiconductors’ aggregate and cumulative

liability towards customer for the products described herein shall be limited

in accordance with the Terms and conditions of commercial sale of NXP

Semiconductors.

Right to make changes — NXP Semiconductors reserves the right to

make changes to information published in this document, including without

limitation specifications and product descriptions, at any time and without

notice. This document supersedes and replaces all information supplied prior

to the publication hereof.

Applications — Applications that are described herein for any of these

products are for illustrative purposes only. NXP Semiconductors makes

no representation or warranty that such applications will be suitable

for the specified use without further testing or modification. Customers

are responsible for the design and operation of their applications and

products using NXP Semiconductors products, and NXP Semiconductors

accepts no liability for any assistance with applications or customer product

design. It is customer’s sole responsibility to determine whether the NXP

Semiconductors product is suitable and fit for the customer’s applications

and products planned, as well as for the planned application and use of

customer’s third party customer(s). Customers should provide appropriate

design and operating safeguards to minimize the risks associated with

their applications and products. NXP Semiconductors does not accept any

liability related to any default, damage, costs or problem which is based

on any weakness or default in the customer’s applications or products, or

the application or use by customer’s third party customer(s). Customer is

responsible for doing all necessary testing for the customer’s applications

and products using NXP Semiconductors products in order to avoid a

default of the applications and the products or of the application or use by

customer’s third party customer(s). NXP does not accept any liability in this

respect.

Limiting values — Stress above one or more limiting values (as defined in

the Absolute Maximum Ratings System of IEC 60134) will cause permanent

damage to the device. Limiting values are stress ratings only and (proper)

operation of the device at these or any other conditions above those

given in the Recommended operating conditions section (if present) or the

Characteristics sections of this document is not warranted. Constant or

repeated exposure to limiting values will permanently and irreversibly affect

the quality and reliability of the device.

Terms and conditions of commercial sale — NXP Semiconductors

products are sold subject to the general terms and conditions of commercial

sale, as published at http://www.nxp.com/profile/terms, unless otherwise

agreed in a valid written individual agreement. In case an individual

agreement is concluded only the terms and conditions of the respective

agreement shall apply. NXP Semiconductors hereby expressly objects to

applying the customer’s general terms and conditions with regard to the

purchase of NXP Semiconductors products by customer.

Suitability for use in automotive applications — This NXP

Semiconductors product has been qualified for use in automotive

applications. Unless otherwise agreed in writing, the product is not designed,

authorized or warranted to be suitable for use in life support, life-critical or

safety-critical systems or equipment, nor in applications where failure or

malfunction of an NXP Semiconductors product can reasonably be expected

to result in personal injury, death or severe property or environmental

damage. NXP Semiconductors and its suppliers accept no liability for

inclusion and/or use of NXP Semiconductors products in such equipment or

applications and therefore such inclusion and/or use is at the customer's own

risk.

Export control — This document as well as the item(s) described herein

may be subject to export control regulations. Export might require a prior

authorization from competent authorities.

Translations — A non-English (translated) version of a document is for

reference only. The English version shall prevail in case of any discrepancy

between the translated and English versions.

7.3 Trademarks

Notice: All referenced brands, product names, service names and

trademarks are the property of their respective owners.

NXP — is a trademark of NXP B.V.

NXP Semiconductors

UM11362

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User manual Rev. 1 — 27 March 2020

15 / 16

Tables

Tab. 1. Low pass filters parameters—data for tire

size 205/65R16 ............................................... 11

Tab. 2. Base low pass filter design parameters ...........12

Tab. 3. 2-pole low pass filter design parameters ......... 13

Tab. 4. Revision history ...............................................13

Figures

Fig. 1. Period measurement when an

accelerometer X rising slope is detected first .... 2

Fig. 2. Period measurement when an

accelerometer X falling slope is detected first ....3

Fig. 3. Accelerator X raw count readings at different

location angles (right side wheel) ......................4

Fig. 4. X and Z acceleration sine waves when the

wheel rotates in CW direction ........................... 5

Fig. 5. X and Z acceleration sine waves when the

wheel rotates in CCW direction .........................5

Fig. 6. Calculation of the earliest target angle TA0 .......7

Fig. 7. Calculation of consecutive RF packets start

times .................................................................. 8

Fig. 8. RF packets transmission angles on CW and

CCW rotating wheels with a software target

angle of 60° .......................................................9

Fig. 9. Accelerometers X and Z 2-pole low pass

filter block diagram ..........................................11

Fig. 10. Accelerometer X waveforms on LPF input

and output ....................................................... 12

Fig. 11. Accelerometers X and Z 2-pole low pass

filter block diagram ..........................................13

NXP Semiconductors

UM11362

NTM88 Dual-Axis Location Angle Project – Algorithms

Please be aware that important notices concerning this document and the product(s)

described herein, have been included in section 'Legal information'.

For more information, please visit: http://www.nxp.com

For sales office addresses, please send an email to: [email protected]

Date of release: 27 March 2020

Document identifier: UM11362

Contents

1 Introduction ......................................................... 1

2 Rotation period measurement ........................... 1

3 Finding wheel rotation direction ........................5

4 Packet transmission ........................................... 7

5 Low pass filters .................................................10

5.1 4-pole low pass filters ......................................10

5.2 2-pole Low Pass Filters ................................... 12

6 Revision history ................................................ 13

7 Legal information .............................................. 14

NXP NTM88 User guide

NXP NTM88 User guide

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