RSSI fluctuations due to signal noise significantly affect both stability and efficiency. For instance, in HP communicationlevel
handover, when the RSSI value of the current AP is slightly greater than the sum of another AP RSSI plus HHT, even small RSSI
fluctuations can produce several Prob changes, thus relevantly reducing stability. In addition, in those conditions RSSI
over/underestimation may trigger unnecessary predictions, thus lowering efficiency.
In this section we specifically analyse, and quantitatively compare different techniques (Grey Model,
Fourier Transform, Discrete Kalman, and Particle) for filtering RSSI fluctuations due to signal noise, by pointing out how
filtering can positively impact on handover/mobility prediction performance.
Grey Model
We have designed and implemented a firstorder Grey Model filtering module that calculates filtered RSSI values on the basis of a
finite series of RSSI values monitored in the recent past. In particular, given one visible AP and the set of its actual RSSI
values measured at the client side
R0 = {r0(1), …, r0(n)}, where
r0(i) is the RSSI value at the discrete time i, it is possible to
calculate
R1 = {r1(1), …, r1(n)}, where:
Then, from the Grey Model discrete differential equation of the first order:
the wireless client can autonomously determine
a and
u, which are exploited to obtain the predicted RSSI value
pr(i) at discrete
time i according to the Grey Model prediction function:
Let us observe that filtered RSSI depends on the number of actual RSSI values
r0(i) employed in the Grey Model. In principle,
longer the finite input series
R0, more regular the RSSI filtered values, and slower the filtered RSSI sequence follows the possibly
abrupt time evolution of actual RSSI. We have experimentally evaluated the Grey Model performance while varying the
R0 size; the best
tradeoff between RSSI fluctuation mitigation and actualtofiltered RSSI delay is usually for R0 size=15 and we used this value to
obtain the reported experimental results.
Fourier Transform
Our Discrete Fourier Transform (DFT) filtering module extract from
R0 a Fourier coefficient set (
Ai and
Bi) representing the RSSI
sequence in the frequency domain in the time window
R0 size*RSSI sample interval. The coefficient set is extracted with
the usual Fourier equations:
The Fourier coefficient set is the basis to define an Inverse Discrete Fourier Transform (IDFT) to regenerate the RSSI signal:
When IDFT exploits only a subset of the above series terms, the regenerated RSSI sequence do not exhibit its high frequency
components and shows a more regular trend, i.e., IDFT behaves as a low pass filter. We have tested our Fourier Transform filter
with several values for
R0 size and number of addends: we have found a good tradeoff between fluctuation mitigation and
actualtofiltered delay with
R0 including 4 values and IDFT only its first term.
Discrete Kalman
Our Discrete Kalman filtering module tries to est imate RSSI values by representing the RSSI time evolution as a combination of
signal noise (measurement noise) and maximum signal evolving (process noise). A linear stochastic equation models the RSSI
evolution, with signal/process noise assumed to be independent of each other, white, and with normal probability distribution
(standard deviation
Q/
R).
Our filter works by minimizing process/measurement noise through a two phase algorithm: first, a predictor performs next RSSI
estimation; then, a corrector improves RSSI estimation by exploiting current RSSI measurement. Therefore, an iteration of our Discrete Kalman filtering module processes:
where
P(k) is the covariance matrix of the state estimate error, with initial value
Q, and
K(k) is usually indicated as the Kalman
Gain in the filtering literature.
In our scenario
x and
z are RSSI values, the state coincides with the output (A is a 1x1 identity matrix), and the estimation of the
next state estimate is equal to the current state (
H is a 1x1 identity matrix). After several tests, we have found a good tradeoff
between RSSI fluctuation mitigation and filteredtoactual RSSI delay by setting
Q=1.6 and
R=6.
Particle
Like Discrete Kalman, our Particle filtering module tries to estimate RSSI by minimizing measurement and process noise, but without imposing a linear equation modeling and, more important in our deployment scenario, without imposing normal distribution for signal noise. The main idea at its basis is to have an algorithm that computes, at each step, several possible filtered RSSI values for each measured RSSI; then, the filter associates each candidate value with a weight and chooses the most promising values among them when a new measured RSSI is available; finally, it perturbs candidate values, according to the rules shown below, thus obtaining a new filtered RSSI (the average value of the most promising candidates).
To better and practically understand how Particle Filter works, let us show a rapid example of algorithm iteration with 10 particles, which represents 10 possible filtered RSSI values (Figure 2):
 starting step  there are 10 possible filtered RSSI values (light circles), all with the same weight;
 importance weight step  by exploiting state est imate probability (black curve) obtained from RSSI measurement,
the algorithm assigns a weight at each filtered RSSI value (dark circles);
 resampling step  heavy RSSI are spread in different RSSI values, all with the same weight (light circles), while light RSSI
values are discarded;
 sampling/prediction step  filtered RSSI are randomly perturbed (light circles).
Figure 1. An example of Particle iteration.
The number of particles strongly influences the Particle filter performance; in general greater is the particle number, better
the filtered RSSI follows the actual RSSI sequence. Differently from the previous 3 filters, Particle has a nonnegligible
computational load, which deeply depends on the particle number. Table 1 shows one iteration time by exploiting a High Capability
machine (an Intel Pentium4 2.80GHz, 1024 MB of RAM) and a Low Capability one (mobile AMD Athlon 2000+ 1.66 GHz, 480 MB of RAM).
For example one iteration of our Particle filter, High Capability machine, takes about 132ms with 250 particles and 521ms with 500
particles; in a practical deployment scenario, where multiple APs are simultaneously visible from wireless clients, that time
should be multiplied by the number of visible APs, and the computation occurs at any sampling interval. For the sake of completeness,
we will report also Particle performance, when used with 250 particles and with the same
Q and
R are as in Discrete Kalman; however,
current clientside resource limitations discourage the exploitation of the Particle filtering module.
Number of Particles 
High capability machine 
Limited capability machine 
50 
6.65 
8.03 
200 
82.92 
108.91 
250 
132.89 
172.83 
300 
192.14 
243.92 
500 
521.82 
673.27 



Table 1. Particle Filter load.
A Rapid Preliminary Comparison of RSSI Filtering Modules
Just to give a preliminary rough comparison of the behaviors of the proposed filters, Figure 3 reports 60 RSSI samples, either
actually measured or filtered according to one of the 4 filtering modules. In particular, the figure points out how much filters
are able to mitigate RSSI fluctuations and how fast filtered RSSI sequences follow the actual ones in the case of rapid RSSI
evolving, e.g., samples 5 and 45.
Figure 2 is exemplar of the actual RSSI strong fluctuations (filter = Identity). Compared to actual RSSI, the output of the
Grey Model has definitely less fluctuations, but tends to overestimate and to amplify RSSI growth in the case of rapid increasing,
for instance when wireless clients are very close to their APs (see samples 10 and 50). Fourier and Kalman have similar behaviors:
both tend to mitigate RSSI fluctuations quite well and accurately follow the actual RSSI sequence, without overestimating RSSI
changes. Particle mitigates RSSI fluctuations very well, but sometimes introduces a nonnegligible delay between actual and filtered
values (see samples 8 and 47).
Figure 2. Actual and filtered RSSI.
Experimental Results
We report experimental results about the different hit rate, efficiency, and stability performance achieved when feeding our
Prob module either with actual RSSI data or filtered RSSI (exploiting each time one of the 4 proposed filters). As already stated,
the primary goal of RSSI filtering in our proposal is to mitigate RSSI fluctuations due to signal noise in order to primarily improve
hit rate, with simultaneous acceptable values for efficiency and stability. However, better a filter mitigates RSSI fluctuations and
longer is filteredtoactual RSSI delay; in the following, for each filter we have adopted the parameter tuning described above,
which achieves a suitable tradeoff between introduced delay and filtering performance.
In particular, in the case of
handover prediction we have defined the following performance indicators:
hit rate 

where HPpre is the total time elapsed in HighProb state in the tlong interval before handover
and HPopt is the time an optimal predictor should stay in HighProb state (exactly t seconds before each
handover). We have chosen t=4s because such a time interval is largely sufficient to perform the needed service management
operations in the WI localities going to be visited 
efficiency 

where HPtot is the total time elapsed in HighProb state 
stability 

where PC is the number of Prob state changes of our predictor and PCopt the optimal number of
Prob state changes 
On the contrary, in the case of
mobility prediction, we are interested in evaluating:
hit rate 

where CP is the number of correctly predicted handovers and NH is the total number of performed handovers 
efficiency 

where NP is the total number of triggered predictions 
Note that we do not propose a stability indicator for mobility prediction since our proactive middleware for service management
automatically inhibits further mobility predictions for a configurable time interval after a triggered prediction.
Obviously, efficiency and hit rate are strongly correlated: on the one hand, very good values for hit rate can be achieved at the
expense of poor efficiency values; on the other hand, it is possible to obtain very good efficiency by simply delaying as much as
possible handover predictions, with the risk of missing handovers (too low hit rate). Moreover, it is necessary to maintain
sufficiently high stability not to continuously perturb the service infrastructure with useless and expensive management
operations.
We have measured the five indicators above in a challenging
simulated environment, with a large number of WiFi clients roaming
among a large number of wireless APs (17 APs regularly deployed in a hexagonal cell topology); RSSI fluctuation has a 3dB standard
deviation, FPT=72dB, FHT=80dB, HPT=2dB, HHT=6dB. Wireless clients follow movement trajectories according to either i) the usual
Random Waypoint model, speed is in the range [0.6m/s, 1.5m/s] and "thinking time" between 0s and 10s",
or ii) our proposed
Continuous model.
We have compared the behavior of the 4 proposed filtering modules within 12 scenarios (about 200 handovers performed in each one),
differentiated for AP to AP distance (20m, 30m or 40m), type of communicationlevel handover (HP or SP) and wireless client mobility
model (waypoint vs. continuous). First of all we consider only the scenarios with dense AP and waypoint mobility model, then we
describe differences between those and other scenarios.
Figures 37 reports average values of performance indicators for handover and mobility prediction, in various scenarios with different AP
density, wireless client mobility model and handover strategy. Table 2 explains some acronyms.
Mobility Model 
W 
Random Waypoint model 

C 
Continuous model 



Handover Strategy 
HP 
Hard Proactive handover strategy 

SP 
Soft Proactive handover strategy 



AP density

Ld 
AP Low density (40m APtoAP distance) 

Md 
AP Medium density (30m APtoAP distance) 

Hd 
AP High density (20m APtoAP distance) 
Table 2. Acronyms.
In general,
the adoption of the proposed filtering techniques significantly improves
Handover Prediction stability, with relevant benefits from the point of view
of system overhead due to useless Prob state changes. Efficiency also increases when exploiting filtered RSSI, except than in the
case of Grey Model: in fact, Grey Model filtering tends to amplify the growth/decreasing trends of actual RSSI values, as observed
in the previous section; that produces handover/mobility predictions with a large advance time but also with limited efficiency.
Fourier, Kalman, and Particle filters, instead, tend to delay a little more Prob state changes, thus increasing efficiency. Let us
observe that the hit rate performance indicator slightly decreases when adopting filtering techniques, except than in the Grey Model
case. That effect is tied to what observed before: a slightly greater delay in handover prediction tends to weakly worsen hit rate,
but with the relevant advantage of a significantly greater stability.
Figure 3. Handover Prediction Hit Rate.
Figure 4. Handover Prediction Efficacy.
Figure 5. Handover Prediction Stability.
Similarly to handover prediction, the adoption of filtering techniques slightly lowers
mobility prediction hit rate but, most
important, increases its efficiency. Note that the reported efficiency is quite low, but it can be significantly improved with a
better tuning of the Prob module configuration parameters e.g., HPT and FPT, as demonstrated in a previous work focused on Prob
performance. However, this paper specifically concentrates on pointing out the independent contribution on prediction
performance of the 4 proposed filters and, for that reason, we have decided to exploit generic Prob settings here.
Figure 6. Mobility Prediction Hit Rate.
Figure 7. Mobility Prediction Efficacy.
In addition to the proposed dense deployment scenario with Waypoint mobility model, we have evaluated our filtering exploiting Continuous mobility model
in scenarios with lower AP density, i.e. greater APtoAP distance (30m/40m). We do not notice any substantial performance
difference when exploiting Continuous model instead of Waypoint one. This prove our mobility model is challenging as much as
the more usual and diffused Waypoint. Lowering AP density the primary difference is a uniform increase in hit rate:
when clients perform their handovers, APs are more distant and RSSI values exhibit a slower time evolution, thus facilitating
handover/mobility prediction. The secondary difference is efficiency and stability both decrease; since APtoAP distance increases,
the average interval between consecutive handovers increases, making more probable useless handover probability state changes.
By taking a look at the whole set of reported performance results, it is clear that there is not a filtering technique always
outperforming the others. Filtering exploitation has demonstrated to be crucial for increasing stability; the decision on which
filter to exploit depends on the specific goals of the provisioned mobile service. On the one hand, if it is of key relevance to
achieve very high hit rates, the Grey Model is to be considered. On the other hand, if prediction costs must be as low as possible
(high efficiency), Fourier and Kalman are good candidates. Let us stress that, thanks to the modular architecture of our middleware,
it is possible to choose the exploited filtering module at provisioning time, by adapting middleware behavior to the current service
context. For instance, consider the case that our middleware exploits handover prediction to support the prefetching of data chunks
before handover, in order to continuously provide service flows also during AP changes with temporary disconnections. If the
crucial point is to avoid temporary service interruptions, the best choice is Grey Model filtering; otherwise, if the priority
is to minimize useless exploitation of clientside buffers, either Fourier or Kalman should be chosen. Finally, as already stated,
Particle should be excluded from possible choices because of its high clientside computational load.