Sight is essential for humans to navigate their surrounding environment independently. Tasks that are simple for the sighted are often close to impossible for the visually impaired. Throughout the years, many researchers dedicated their time and efforts to design and implement technologies and devices that can help the visually impaired to navigate in unknown areas independently. This survey describes the existing methods for designing navigation technologies for the visually impaired and serves as a reference for the professionals and researchers interested in designing assistive technologies for the blind.
According to the World Health Organization (WHO) cite{whoo}, 253 million people struggle with vision impairment globally. 90% of visually impaired people live in developing countries, which reduces the chance of getting adequate treatment and support. When visual impairment is compounded with poverty, an individual often fully depends on the their family for survival. This poses a challenge for the blind to lead an independent life. Although it may be easier for visually impaired people who live in developed countries, not all daily life tasks can be done independently. Tasks such as shopping for groceries in a nearby supermarket or finding a painkiller to alleviate a headache are difficult for a visually impaired individual.
Humans need to know their current location and destination to navigate. Navigation and path finding are complex tasks and obstacle avoidance is essential along the way, especially in dynamic environments. In a supermarket, finding the way is even more arduous due to limitations of the Global Positioning System (GPS). GPS signals are weaker indoors as buildings attenuate the signal strength cite {5_8}. Consequently, alternative approaches are necessary for addressing indoor localization. Although there are techniques available for indoor position estimation, finding a specific item in the aisle is still a challenge for a visually impaired person. Reading the dosage instructions or side effects on medicine requires the help of a sighted person even for a partially visual impaired individual.
More than 80% of people who suffer from blindness lost their vision due to a preventable or curable disease. While medical scientists are trying to provide vaccines for diseases causing blindness, assistive technologies are needed to make life easier for those who can not see. Fortunately, assistive technologies for the blind have been explored for many years. In 1990, Passini et al. in cite{90_1} made an experiment with eight groups of sighted, partially sighted, and visually impaired individuals of different sexes, ages, and ethnicities. Every individual had to find their way through obstacles. Not surprisingly, the experiment's results showed that those who were suffering from visual impairment took longer to find their way regardless of sex or ethnicity. For a long time scientists tried different approaches to help visually impaired people. This article explains such prior efforts that will assist future research in navigation technologies for assisting the visually impaired.
This paper explains unique solutions to specific problems that visually impaired individuals encounter, such as finding specific objects in a grocery store. It serves those researchers interested in developing assistive devices for visually impaired individuals. Available methods for building such assistive technologies are outlined in this survey article to provide researchers with a comprehensive view of state-of-the-art and directions for future research. The rest of this paper is organized as follows. Section ref{wayfinding} explains location estimation and navigation techniques used in way-finding. Section ref{ObstacleAvoidance} explains obstacle avoidance methods. Section ref{hmi} explains methods for human-machine interaction.
Way-finding for a visually impaired individual consists of location estimation and navigation. Methods to address way-finding can be categorized as follows based on the technologies that they employ:
The success of GPS for outdoor navigation encouraged the implementation of the same technique for indoor navigation. Indoor navigation using radio frequency is a wide research topic. The emergence of Micro Electro-Mechanical Systems (MEMS) also facilitates location estimation and navigation with the data provided through different sets of sensors. Another approach is based on the unique magnetic map of an area which enables location estimation.
For way-finding, the initial location of the user must be known. Using the initial location of the user, a variety of navigation techniques can be used to direct the user to their destination. Localization and navigation methods are explained in detail in the following subsections.
Localization is the first step in way-finding. To plan the path, first the initial position of the user has to be known. Vision is crucial in location determination. In the absence of vision, assistive technologies must facilitate finding the initial location of the user for way-finding purposes. Strategies for localization that are available in the literature are briefly outlined in this section.
Global Navigation Satellite System (GNSS) or GPS eases outdoor navigation. GPS uses Time Difference of Arrival (TDOA) of the signal received from at least four different satellites to find the exact position of the receiver cite{91_2}. Trilateration is the method used to estimate the user's location. The use of GPS for blind navigation was proposed by Loomis cite{85_1}, and Collins cite{85_2} more than thirty years ago. In 1989, Brusnighan experimented with the use of GPS for visually impaired users for the first time cite{89_1}. Loomis et al. in cite{94_2} studied the use of Differential Global Positioning Systems to increase the accuracy in a positioning scenario.
GPS is a promising approach for outdoor situations cite{00_1}cite{12_4}. Electronic Travel Aid (ETA) and Smart Robot localization use GPS for outdoor localization. The Smart Robot functions like a guide dog to help a visually impaired person navigate. Yelamarthi et al. used GPS to determine the location of Smart Robots outdoors cite{10_7}. For indoor scenario, Smart Robots use Radio Frequency Identification (RFID) tags for localization. RFID tags will be discussed later in Section ref{RFID}.
Despite the accuracy of the GPS signals outdoors, satellite coverage is not available indoors. This puts a constraint on the use of GPS in indoor situations. This limitation forced scientists to use other localization methods to address the localization challenge. One of the common techniques is textit{Trilateration}.
Wireless Local Area Network (WLAN) based positioning is central to indoor navigation. Many researchers suggested its use in estimating the location of the user. WLAN Access Points (AP) broadcast beacon frames periodically according to the IEEE 802.11 protocol. The transmitting period is about 10 ms. The beacon frames contain the AP's Media Access Control (MAC) address cite{12_10}. The MAC address provided to every mobile system enables the identification of multiple APs used for positioning. The position estimation is possible with Triangulation and Trilateration.
Triangulation is another method used for range measurement. This method estimates the position of the object using the angle of the object relative to the reference points. Triangulation is suggested in cite{12_13} to detect user's location. In this method, the user carries a white cane with infrared LEDs installed to it. The infrared cameras installed in an area detect the movement of the infrared light source to find the location of the white cane carrier.
In general, triangulation is more common in long distances than in indoor scenarios. Trilateration, on the other hand, performs better indoors. Trilateration is a range measurement technique in which the position of an object is estimated by measuring the distance of the object to the access points. (See Figure ref{fig:trilateration})
Common techniques to calculate the distance are Time Of Arrival (TOA), Time Difference Of Arrival (TDOA), Angle of Arrival (AOA), and Received Signal Strength (RSS).
This is one of the basic methods to find the distance to a mobile system. The TOA distance measurement method is based on the relation between the time and distance of propagation. The distance travelled and the propagation time are directly proportional to each other. In TOA-based systems, the distance between the mobile system and the access points will be calculated using the time it takes for the signal to travel one way. The distance to at least three access points is needed to estimate the position of a mobile system cite{90_2}.
The position of the mobile system in a TOA algorithm can be computed by minimizing the sum of error functions. The error function is based on the least squares algorithm. The function for every measuring unit $i$ is given by (ref{eq:1}).
In aforementioned equation (ref{eq:1}), $c$ is the speed of light. The correct choice of $pmb{x}=(x,y,t)$ makes the error go to zero. The sum of all the errors must be minimized to find the position of the mobile system. The sum of error functions is given in (ref{eq:2}). The choice of $a_i$ indicates the received signal reliability at the measuring unit $i$.
TOA algorithms are prone to errors. One of the major error sources for this method is the multipath effect. The error caused by the multipath effect can be categorized in two groups: early-arriving multipath signal and attenuated line of sight (LOS). Early-arriving multipath signals correspond to the signals arriving immediately after the LOS signal and changing the location of the peak from the LOS signal. The attenuated LOS explains the situation in which the LOS signal is attenuated too severely. In this situation, the LOS signal is lost in noise. In addition to the multipath effect, adaptive noise causes errors in the TOA algorithm.
Adaptive noise even in absence of the multipath effect can decrease accuracy cite{87_1}. To combat the adaptive noise, a simple cross-correlator is used. The simple cross-correlator was extended by a generalized cross-correlator introduced by Knapp et al. in cite{76_1}.
TOA method is not limited to RF signals. Acoustic signals are another common type of signal used with the TOA method for localization. In this approach, instead of utilizing the available WLAN networks, acoustic anchors are implemented in the area. The anchor network propagates the modulated beacon with location information. The beacons use highband acoustic signals. This indoor localization system is called Guoguo cite{13_1}. Guoguo processes the information in real-time using a smart phone application. The prototype implemented based on this approach demonstrated a centimeter-level accuracy.
While TOA is measuring the absolute arrival time, TDOA concentrates on the different times that the propagated signal reaches multiple measuring units. The difference in time of arrival is proportional to the distance of the measuring units to the mobile system.
The TDOA measurements for every two receivers define a hyperbolic locus cite{98_2}. The hyperbolic locus ($R_{i,j}$) follows (ref{eq:3}) given that $i$ and $j$ are receivers at two fixed points. The location of each of these receiver points is indicated by $(x_i,y_i,z_i)$ and $(x_j,y_j,z_j)$ respectively.
In theory, there in no difference between the TOA and TDOA algorithms. Simulation results also confirm the idea that TOA and TDOA have practically the same performance cite{12_11}. To improve accuracy of TDOA based location estimation, access points with two transmitters were introduced. The second transmitter gathers information about mobile systems and transmits this information to the APs, which will estimate the location of the mobile systems. This enhances the accuracy of position estimation without interrupting the network cite {7_4}.
The importance of the precise position estimation for visually impaired individuals can not be emphasized enough. Using the TDOA method in Ultra-wide Band (UWB) is a novel approach to improve the accuracy cite{15_2}. In addition to improved accuracy, this method also has low installation complexity.
Although the focus in methods such as TOA and TODA is on the distance of the user to each access point, Angle of Arrival (AOA) (or as referred to in some literature as textit{Direction of Arrival (DOA)}) focuses on the angle of the received signal on the receiver side. In this method receiving two signals is essential. Receiving more signals improves the accuracy of the estimation.
To implement this method, either a mechanically-agile directional antenna or an array of antennas is required. The angle of arrival is determined by finding the angle in which the signal strength is the highest in the former, or the antenna which samples the most strength in the latter infrastructure. \ As represented in figure ref{fig:aoa} the angle of arrival from at least two known access points is needed to determine the location of the user. Given the distance between the two access points, the location of the user is determined through geometric relations.
To improve the accuracy of AOA estimation, Badawy et al.proposed a method using the cross-correlation function cite{14_9} . The expenses associated with this method are high. Using off-the-shelf software-defined radio as suggested by cite{12_14} reduces the cost of this approach. It also improves flexibility and makes deployment simple.
A major source of error in the TOA and TDOA algorithms is the multipath effect. It attenuates the signal strength and causes signal loss. In addition to the multipath effect, adaptive noise causes errors. Adaptive noise is a significant source of error even in the absence of the multipath effect. These challenges cause errors and reduce the accuracy of the estimated position. Errors in position estimation in indoor situations are not limited to the above-mentioned problems. Furthermore, in indoor situations LOS is not available in all circumstances. To avoid these challenges, an alternative is to use the Received Signal Strength (RSS).
The receiver measures the voltage of the received signal to find the RSS. In some research, instead of reporting the voltage of the received signal, its power is reported. The power of the RSS is the square of the amplitude of the received signal at the receiver. The voltage or power of the received signal is not expensive to measure. The hardware for measuring voltage and power is implemented in every measuring unit. Measuring RSS does not require additional energy or bandwidth. The low cost of hardware implementation and ease of use made this technique a ubiquitous approach in localization.
RSS is established on the relationship between signal attenuation and the distance. The signal attenuation happens during propagation. The major reason for this attenuation is path loss. In theory, the power decay of the received signal is proportional to the distance between the transmitter and the receiver. The path loss in free space is defined by the (ref{eq:rss_pathloss}) cite{book_digital}.
begin{equation} label{eq:rss_pathloss}
PL_{FS}= (frac{lambda}{4pi d} )^2
end{equation}
Here $lambda$ is the signal wavelength and $d$ is the distance between the transmitter and the receiver.
As (ref{eq:rss_pathloss}) demonstrates, the power decay of the signal is inversely proportional to the square of the distance. Although this is true in theory, the empirical results show some discrepancies. The mismatch between the theory and the practice is cased by multipath signals and shadowing.
Multipath signaling has an adverse impact on the accuracy of the RSS method. The desired signal is not the only signal detected by the measuring unit. The measuring unit detects multiple signals in a variety of amplitudes and frequencies. This can cause frequency-selective fading. The impact of frequency-selective fading can be alleviated with the spread-spectrum method cite{book_digital} cite{book_wireless}. The spread-spectrum method averages the power of the signal over a wide range of frequencies. The spread-spectrum method can address the multipath signaling issue to a reasonable extent but frequency selective fading is not the only source of error in the RSS method. Shadowing is another major source of inaccuracy.
Shadowing attenuates the power of the received signal in an indoor environment in addition to the multipath effect. In the literature, shadowing is defined as the situation in which the power of the signal deviates from its real average value cite{book_wireless2}. Shadowing happens when the wave propagates in an environment with obstacles. Signal propagation in an indoor environment is attenuated by obstacles such as furniture and walls in the path of the signal. The shadowing effect is a random process.
To improve the accuracy of position estimation using RSS measurement, an unsupervised learning algorithm has been proposed cite{11_3}. This algorithm is based on the Gaussian Mixture model and Expectation Maximization (EM). In this research, the received signal is modeled as a Gaussian Mixture. The algorithm learns the parameters for the model from the transmitted packets. To learn the maximum likelihood estimate of these parameters, the EM method is used.
Another promising attempt to improve the accuracy of the position estimation with the RSS method is the on-line measurement of the AP's signalcite{10_2}. In this method, the transmitted signal of every AP is measured by every other APs. This measurement provides useful information about error-prone sources in the environment. The real-time AP signal strength measurement is enriched with the impact of path fading, variations in signal strength caused by temperature, humidity, human mobility, or other changes in a dynamic indoor environment. This information can be utilized to generate a mapping between the RSS measurement and geographical locations. \ Trilateration is a common approach to estimate the location of the user. The simple hardware requirements, inexpensive methods, and simple calculation makes it appealing to researchers. On the other hand, the inaccuracy caused by the multipath effect, shadowing, and noise encouraged researchers to explore different algorithms.
As mentioned before, RSS is a popular method for localization. It is an inexpensive algorithm with little required equipment. On the other hand, WLAN is widespread all around the indoor environments. The massive distribution of WLAN access points in addition to the simplicity of the RSS measurement provides an appropriate groundwork for position estimation. Fingerprinting is one of the attractive techniques founded on this principle. \Fingerprinting has an offline learning phase called textit{radio map} construction. The radio map database is matched with the acquired data during the textit{Fingerprint matching} phase.
Modeling of signal propagation in an environment is a difficult task. To avoid modeling the environment with all of the complexities, a radio map is used. The radio map is constructed by measuring and storing the RSS values at calibration points. These calibration points are known locations. The complexity of signal propagation in an on-line environment is avoided by using a radio map. Despite the simplicity of this task in theory, gathering and storing the RSS values relative to all the calibration points is laborious. \ During the radio map composition phase, the area of interest is divided into cells. The cell area definition is based on the floor plan. For each cell, the RSS value for every access point is measured on the calibration point over a specific time period. The RSS values are then stored in the database. \ Composing the database is not a one-time task. This process is cumbersome and varies over time. It will also change when there is an alternation in the environment or in the transmission power of the access point. Therefore, to keep up with the changes, the radio map has to be corrected periodically. \ A correct up-to-date radio map is the first phase of the position estimation using the fingerprinting method.
In the fingerprint matching stage, the target finds the best matching cell for the measured RSS values. Finding the best match can be done through either deterministic or probabilistic methods.
In deterministic methods, the approach is to find the best matching calibration point to the position of the user. The matched calibration point is determined by minimizing the difference of the RSS values measured by the APs in the on-line phase with those RSS values stored in the database. Suppose that an array of RSS values has been measured from each AP. The location of the user is detected by finding the spot in the database whose distance to the current location is minimum. This is a Euclidean distance minimization problem which is shown in (ref{eq:deterministic}) cite{9_8}.
Aforementioned equation (ref{eq:deterministic}) is the mathematical representation of the Euclidean distance minimization. In this equation, $r_i$ is the measured value of RSS in the on-line phase of the $i_{th}$ AP. The stored value of the measurements of the $i$-th AP in the $j$-th calibration point is presented with $rho_i( x_j)$. Although in theory this approach is promising, to avoid measurement errors other methods are also used. One of the more reliable methods is the nearest neighbor algorithm.
In the textit{K}-Nearest Neighbor (KNN) method, the value measured in the on-line phase is compared with the values measured for the calibration point in the dataset. The $k$ calibration points which have the closest value will be selected. In this method, textit{k} is the design parameter. It will be selected based on the density of the radio map. In the textit{KNN} method, the weight of all the calibration points are equal. However, the Weighted textit{KNN} (WKNN) method considers a different weight for each calibration point. The weight assignment is based on the distance of the calibration point to the approximated location of the measured RSS.
The nearest neighbor method is not limited to the Euclidean distance. The use of Manhattan distance is suggested by cite {17_8} for improved accuracy. The nearest neighbor method, whether using Euclidean distance or Manhattan distance, is a solution to a distance minimization problem. This solution makes location determination feasible. This method is considered a deterministic localization approach. Besides the deterministic approaches such astextit{KK} and textit{WKNN}, there are also probabilistic fingerprinting approaches used to estimate the position.
In the probabilistic localization method, the conditional probability distribution of the RSS value will be estimated. The conditional probability distribution of the RSS value, given the location of the user, is plugged in to Bayes rule to estimate the location of the user. The probability of the location of the user given the RSS measurement is called the posterior probability distribution. In this method, the location of the user is the location $x$ which maximizes the posterior probability distribution (ref{eq:post}).
Aforementioned equation (ref{eq:bayes}) represents the calculation of the posterior probability distribution given the conditional probability of the RSS measurement.
In equation (ref{eq:bayes}), $p(x)$ is the prior probability distribution, which indicates the preference of the user to be in a location. If the user preference is equally distributed among all the locations this term will be a constant coefficient which can be removed from the calculation. The denominator of the fraction in (ref{eq:bayes}) is a normalization factor because it is not proportional to the location. Considering these two simplifying assumptions, (ref{eq:bayes}) can be rewritten as a maximum likelihood approximation (ref{eq:like}).
To solve the maximum likelihood as depicted in equation, the knowledge of the distribution of the RSS values in all possible locations is required (ref{eq:like}). Two well known probabilistic models for this purpose are the coverage area model and the path loss model. The former, as its name indicates, estimates the probability distribution through the coverage area of each AP. The latter, uses the logarithmic attenuation of the signal in respect to the distance from the AP.
In addition to the deterministic and probabilistic approaches, machine learning methods have recently been applied to fingerprint-based position determination algorithms. Position determination is a classification problem that can conveniently be solved using Support Vector Machines (SVM). The accuracy of this method for position estimation in WLAN situations outperforms textit{WKNN} as discussed in cite{5_9}.
While fingerprinting is a reliable solution for position estimation problems, it is vulnerable to malicious attacks. These malicious attacks have an adverse impact on the localization process. When the attack strikes, the location information provided by the system is not reliable. Article cite{5_2} explains the attacks extensively and provides a solution for this matter. This research introduces an adaptive least squares estimator which is robust against attacks.
The fingerprinting method goes beyond just RSS values. This method works well with other types of signals. Sound, color, and motion are the other features that can be sensed with a cellular device through the microphone, camera, and inertial sensors. These signals were used in cite{9_6} to find the location of the user. Fingerprinting is also used with Earth's magnetic field. The strength and variation of the magnetic field is used to build a map for fingerprinting and these data are used to estimate the user's location.
Fingerprinting principles can not only be applied to different types of signals, but they can also be put into use with the signal in different layers of communication. For instance, cite{12_8} uses the channel frequency response(CFR) in the physical layer. In this research, an array of CFR values is associated with a specific location. This method reduces the associated error with location estimation to less than a meter.
The fingerprinting method can be combined with other methods to improve accuracy. One such method is to use image-based localization. iMoon is a cellphone application presented in cite{14_2} which uses fingerprinting to divide the area into partitions. Each partition contains a certain number of images. To find the exact location of the user, the image provided by the user will be matched with the image database of that partition. This method not only improves the precision of the location estimation, but it also reduces the computational power essential for image matching.
While fingerprinting uses the available signals to determine the location, other methods such as Radio Frequency Identification (RFID) rely on specific equipment. The next section explains RFID in detail.
subsubsection{RFID} label{RFID} Radio Frequency Identification (RFID) is a method of localization based on radio waves. The RFID method is based on two parts: the reader and the tag. Each tag has a unique identification number. The reader uses the radio magnetic field to identify the RFID tag based on the tag identification.
RFID tags are small circuits containing a microchip and an antenna. The antenna is actually a printed circuit board. Tags can be categorized in two groups based on their energy provider. The tags which rely on the energy emitted by the reader are passive tags. This type of tag is inexpensive and can be employed in cost-sensitive scenarios. The other type of tags have batteries installed in them. These kinds of tags propagate their identification in periodic signals.
For position estimation purposes, the tags are attached to specific locations in the area. Each tag can carry information about the location and path conditions. This method is useful in both indoor and outdoor situations cite{5_7}. These types of tags are the most common for localization purposes. The other type of tag which is useful for providing navigation assistance for visually impaired individuals is the cue tag. These kinds of tags can provide the user with a virtual road and guide the user along the way. In general, RFID tags provide the user with information about location and direction.
The information obtained via the reader can be transferred to the user's cellphone. Smartphone applications are useful for conveying the information in a more convenient way to the user. Accessibility of cellphones facilitates call centers to help visually impaired people online. The call center can use the information from the tags to inform the user not only about the location but also the path to their destinationcite{7_7}.
Installing the reader on a guide cane is a brilliant idea for visually impaired users cite{ 7_8,9_9}. The cane in these studies is equipped with a tag reader and a Bluetooth transmitter. The reader transmits the acquired information the user. This information is conveyed to the visually impaired user through speech. Tag allocation is important for accuracy purposes. In this research, the tags' locations are in close proximity to achieve higher location estimation precision.
A different approach in using RFID tags for user localization is introduced in cite{4_4}. In this approach, the user carries the RFID tag and the readers are placed throughout the area. In this technique, the location estimation is based on the information about the intensity of the signal propagated from the tag. This research uses the textit{knn} algorithm to calculate the location of the user. The tag used in this method is an active type. Active type tags require a battery to send signals periodically. Over time the battery loses power which causes variations in signal strength.
subsubsection{Bluetooth low energy}
The RSS value of the classic Bluetooth protocol has been used for localization cite{5_1}. However, Bluetooth low energy (BLE) beacons provide a new means for position estimation. Not only are BLEs accurate and reliable, but they are also energy efficient. Although BLE works in the same frequency that classic Bluetooth does, it has some characteristics which make it more favorable for positioning purposes. These characteristics are energy efficiency, a short handshake procedure, and a high scan rate. A BLE beacon also utilizes a sleep mode which helps maintain low energy consumption. The device changes to awake mode only if a connection is initiated. The short connection time helps with the low energy consumption as well. When connected, the BLE transmits its unique identification number.
The fingerprinting method is also applied to the BLE beacons for position estimation. A BLE beacon can be thought of as a small WLAN AP without the need of a power connection. According to cite {14_3}, BLE position estimation is more accurate in comparison with WLAN-based position estimation. The superiority comes from three main features: a channel hopping mechanism, high sampling rate, and low transmission power.
The channel hopping mechanism employed in a Bluetooth device is less sensitive to interference. The channel interference problem is addressed through averaging. If the averaging does not solve the interference problem and the interference is too severe, the transceiver hops to another channel. BLE uses the hopping mechanism to avoid interference.
High sampling rate is another advantage of BLE over WLAN. BLE position estimation methods determine the position of the user with more samples. The higher number of available samples reduces the chance of error by averaging out the outliers. Outliers are generated by the multipath effect or interference. Averaging out the outliers improves the accuracy of localization.
Low transmission power also makes BLE a better choice for position estimation. In addition to the energy efficiency, low transmission power reduces the multipath effect. In this case, the receiver only hears the most powerful signal while the other signals generated by the multipath effect will be faded out.
To gain better accuracy, a two-level outlier detection method is introduced by cite{16_5}. In this research, the first level outlier detection happens after the fingerprinting position estimation algorithm. The result is fed to an extended Kalman Filter. The second level outlier detection algorithm is applied to the output of the extended Kalman Filter. The second outlier detection algorithm is designed based on statistical testing. The two-level outlier detection algorithm deployed in this research enhances the robustness of the design.
In close distances to the beacon, position is estimated using an attenuation model. (ref{eq:attenuation}) shows the logarithmic propagation model cite{14_4}.
begin{equation}label{eq:attenuation}
RSS(d)=RSS(d_0)+10 n log(frac{d}{d_0})+X_sigma
end{equation}
In aforementioned equation , $RSS(d_0)$ is the RSS value at the referenced distance $d_0$. The path loss is indicated by $n$. $X_sigma$ is the Gaussian noise with zero mean and variance $sigma^2$, which is added to the RSS value.
Accuracy of position estimation is central for visually impaired individuals. One approach for enhancing accuracy is through combining the positioning methods with estimation filters.
subsubsection{Bayesian Filtering} Location estimation is based on the source of the data. The required data is provided through different sensors. These measurements are inaccurate and they have noise. Bayesian filters have been used extensively to overcome the error caused by noisy measurement. The Bayesian approach is based on constructing the posterior probability function of the state based on the available measurements. In a recursive Bayesian approach, the filter is executed for every measurement. One of the early methods based on the recursive Bayesian approach is the textit{Kalman Filter}.
A Kalman Filter is a well known approach for filtering and prediction cite{kalman1960}. It has been extensively used for localization and navigation purposes. In navigation systems, the signal is modeled with transition and measurement matrices as shown in Eqs. (ref{eq:kal1}) (ref{eq:kal2}).
In equation (ref{eq:kal1}), $boldsymbol{Phi}$ and $boldsymbol{H}$ indicate the transition matrix and measurement matrix respectively. The process is not free of noise. The measurement noise and the process noise are added to the model via $boldsymbol{w}_k$ and $boldsymbol{n}_k$ respectively. Both noises are considered to be white noise with zero means. Eqs. (ref{eq:kal3}) and (ref{eq:kal4}) represent the covariance matrices for the process noise and the measurement noise.
The a priori estimate of the next state is based on the state transition matrix and the a posteriori estimate of the previous state, as shown in (ref{eq:kal5}):
Also, the a priori estimate of the measurement is according to the a priori estimate of the next state and the measurement matrix as depicted in (ref{eq:kal6}):
then the a priori estimate of the variance matrix of the next step is given by
The novelty of Kalman Filtering is that it tunes the impact of the a priori estimate of the current state and the measured value to determine the posterior estimate of the variable as shown in (ref{eq:kal9}).
The Kalman Filter reduces the uncertainty of the measurement. Given that the filter only has two measurements, and one is more uncertain, the estimated value has less uncertainty than both of the measurements. In other words, suppose $z_1$ and $z_2$ are two different measurements and their uncertainty is $S_1$ and $S_2$, respectively. The uncertainty of the estimated value with the Kalman Filter for this variable will be less than both $S_1$ and $S_2$. Equation(ref{eq:uncertainty}) shows the relationship among the uncertainties, given that $S$ indicates the uncertainty of the estimated value:
Although the Kalman Filter improves the accuracy of the measurements, it is limited to linear functions. This limits the utility when dealing with nonlinear functions. The nonlinear state transition and the measurement models are compatible with the textit{Extended Kalman Filter (EKF)}.
In general, real world scenarios are generally not linear functions. It limits the use of the Kalman Filter in real world applications. The EKF overcomes this constraint, although it is not free of conditions. The functional constraint in the EKF is that the function must be differentiable. In this method, to calculate the covariance matrix, the Jacobian of both the transition matrix and measurement matrices are required. The use of the Jacobian matrix in addition to the first order Taylor series, linearizes the functions. The linearized function can be used with the Kalman Filter. Although this method facilitates the use of Kalman Filter for nonlinear functions, it doesn't improve the accuracy. When the accuracy is not adequate the textit{Unscented Kalman Filter (UKF)} is useful.
The UKF provides a smarter way of linearizing the nonlinear function to use with the Kalman Filter. When the nonlinear function is hard to linearize with the first order Taylor series expansion, some points of the Gaussian distribution of the input can be passed through the nonlinear function. The result approximates the distribution of the output of the nonlinear function. The problem with this approach is that the number of samples has to be infinity to have a well approximated function.
The UKF reduces the number of required points for function estimation to a few points called sigma points. In a UKF, a set of sigma points are computed. For every point a weight will be assigned. The value of the nonlinear function for these points will be determined. This happens by transferring the points through the nonlinear function. Using the value of the nonlinear function for the sigma points, the Gaussian distribution of the output will be estimated. This method prevents linearizing the function in close proximity to the mean.
The Kalman Filter and all of its descendants require the inputs to have Gaussian distributions for estimation. The problem with this assumption is that it is not true for indoor scenarios. The map-matching method becomes effective when addressing such situations.
subsubsection{Map-matching}
Position estimation accuracy improves by exploiting building geometry. Using the building floor plan reduces heading errors significantly. In indoor navigation scenarios, the floor plan adds constraints on movement. For one, all the paths connecting the two sides of a wall will be limited to those passing through the door. The same restriction applies to changing floors. The only possible case for changing floors is through the elevator or stairs. Map-aided navigation improves the accuracy by using the prior information obtained from the floor plan. A particle filter is used in probabilistic map-matching. A particle filter is a generic Monte Carlo algorithm to solve filtering problems. The filtering problem is to estimate the state of a dynamic system given a partial observation. Some random noise exists in both the sensor and the system. The goal of the particle filter is to consider the partial observation and the noise to estimate the posterior distribution of the state of a Markov process.
Particle filters are based on the idea of representing the posterior distribution using a set of random state samples. Although this posterior distribution is approximated, it is non-parametric. In contrast to a Kalman Filter which is only applicable on a linear system with Gaussian noise; no speculation about the system or the noise is required for the particle filter. Although EKF and UKF overcome the nonlinearity problem by linearizing the function, the dependence on the Gaussian noise distribution reduces the accuracy. In the particle filtering method, instead of using the parametric form for distribution representation, a set of samples drawn from the posterior distribution is used. These samples, which are drawn from the posterior distribution, are called particles. The particles are as denoted in (ref{eq:particle1}).
In aforementioned equation, $mathcal{X}_t$ is the set of particles and it has $M$ members. The members of the set $mathcal{X}_t$ are the $x_t^{[m]}$ . Each of them is a state sample in time $t$. The number of $M$ is a very large number.
As mentioned about the UKF, intuitively the nonlinear function of the transformation can be estimated by observing the samples. The particle filter also approximates the belief $bel(x_t)$ based on the set of samples, $mathcal{X}_t$. In this method, the Bayesian filter posterior belief propagation estimates the likelihood of the existence of a state $x_t$ in the particle set $mathcal{X}_t$. (ref{eq:like}) represents the likelihood relation cite{5_10}.
The aforementioned equation implies that the density of the samples in a sub-region of the state space strengthen the hypothesis that the true state belongs to that region. The validity of this hypothesis is proportional to the number of $M$s. In theory, the hypothesis is valid for $M rightarrow infty$. In practice $M$ is a finite number, but for a very large number of $M$s the error is negligible.
The particle filter is a descendant of the Bayesian filter. Recursivity is in the nature of the Bayesian filter. The particle filter is the same as its antecedents. It constructs the current set of particles $mathcal{X}_t$, based on the previous set of particles, $