DeepFi: Deep Learning for Indoor Localization

• DeepFi is a deep learning-based indoor localization framework that uses fine-grained CSI and distinct per-antenna features to create robust fingerprints.
• It employs a two-phase process with location-specific DBN training and probabilistic RBF matching to achieve high accuracy in varying indoor settings.
• Experimental evaluations demonstrate DeepFi's capability to deliver sub-meter to meter-level accuracy in both LOS and NLOS scenarios, highlighting its robustness and scalability.

DeepFi is a deep learning-based indoor localization framework exploiting fine-grained Channel State Information (CSI). Distinct from traditional received signal strength (RSS)-based systems, DeepFi leverages the stability and diversity of per-subcarrier CSI to create robust fingerprints for each reference location. The system employs deep belief networks (DBNs) with location-specific training and probabilistic matching to achieve high localization accuracy in both line-of-sight (LOS) and non-line-of-sight (NLOS) indoor environments (Wang et al., 2016).

1. CSI Hypotheses and Fingerprinting Rationale

DeepFi's design is grounded in three empirically validated hypotheses about indoor wireless channel behavior:

1. Temporal Stability of CSI Amplitudes: At a fixed location, per-subcarrier CSI amplitudes exhibit significantly lower temporal variance than RSS. For 90% of evaluated locations, the standard deviation of normalized CSI amplitudes remains below 10% of the mean, compared to only 40% for RSS.
2. Spatial Diversity via Clustering: Multipath and fading induce natural clustering among the 30 CSI subcarrier amplitudes per packet, with typical cluster counts (1–6) varying by location. This spatial structure underpins location distinguishability.
3. Antenna-Specific Richness: For Intel 5300 devices, each of the three antennas generates distinct 30-element CSI amplitude vectors per packet, producing 90-dimensional feature vectors. This full 90-dimensional input provides substantially richer fingerprints than any subset.

These hypotheses establish the informativeness and repeatability of CSI-derived fingerprints, motivating the application of deep architectures, rather than superficial feature engineering, for localization tasks.

2. System Workflow: Training and Inference Phases

DeepFi operates in two distinct phases:

• Offline Training: For each of $N$ reference locations, $m$ packets are collected, each providing a normalized $\mathbf{v}\in\mathbb{R}^{90}$. A location-specific DBN with four hidden layers is trained using greedy, layer-wise learning (Contrastive Divergence, CD-1). The resulting weight matrices and biases constitute the fingerprint for that location.
• Online Localization: A mobile device acquires $n$ test packets at an unknown position. Each test vector $\mathbf{v}_t$ is passed through every stored DBN (forward propagation only), yielding reconstructions $\hat{\mathbf{y}}_{t,i}$ for reference location $i$. A radial basis function (RBF) computes likelihood scores:

$$\Pr(\mathbf{v}_t|L_i) = \exp\left(-\frac{\|\mathbf{v}_t-\hat{\mathbf{y}}_{t,i}\|}{\lambda\sigma}\right)$$

with $\sigma$ as the packet variance and $\lambda$ an empirically determined scaling. The likelihoods are averaged across all packets, forming $\Pr(\mathbf{v}|L_i)$, and posterior probabilities are computed assuming a uniform prior. The system outputs the location estimate as the posterior-weighted sum of all reference locations.

3. Deep Belief Network Architecture

Each location’s DBN processes the 90-dimensional normalized CSI input:

• Layer Configuration:
  • Visible layer: 90 units
  • Hidden layers: Four layers with descending unit counts; e.g., in the living room, $(K_1,K_2,K_3,K_4)=(300,150,100,50)$; in the lab, $(500,300,150,50)$
• Activation Functions:
  • Pretraining: Binary stochastic units with sigmoid activation, $\sigma(x)=\frac{1}{1+e^{-x}}$, using Restricted Boltzmann Machines (RBMs).
  • Fine-tuning: Real-valued sigmoid units during backpropagation.
• Parameter Storage: Eight weight matrices ($W_1$–$W_4$, and their transposes) and biases ($b^0$–$b^4$) collectively embody the location fingerprint.

The model’s joint distribution factors through stacked mappings:

$$\Pr(\mathbf{v}, \mathbf{h}^1, \mathbf{h}^2, \mathbf{h}^3, \mathbf{h}^4) = \Pr(\mathbf{v}|\mathbf{h}^1)\Pr(\mathbf{h}^1|\mathbf{h}^2)\Pr(\mathbf{h}^2|\mathbf{h}^3)\Pr(\mathbf{h}^3,\mathbf{h}^4)$$

with explicit layerwise conditional probabilities and energy-based modeling for the top RBM layer.

4. Layer-wise Greedy Learning and Optimization

Training proceeds through two main stages for each location-specific DBN:

• Greedy Pre-Training: Each hidden layer is initialized and trained sequentially as an RBM. One iteration of CD-1 is used per training update, reducing the model’s complexity to $$O(\text{\# layers}\cdot m\cdot \text{\#hidden}\cdot \text{\#visible})$$, avoiding the computational expense of a fully joint optimization.
• Fine-Tuning: After pre-training, the entire network is “unrolled,” and weights are refined using reconstruction error loss $L(\mathbf{v})=\|\mathbf{v}-\hat{\mathbf{v}}\|^2$. This step employs backpropagation through all forward and reverse (transposed) weights, improving discriminative power for fingerprint matching.

A plausible implication is that such layer-wise training allows efficient scaling to numerous locations, as each DBN can be independently trained on corresponding local data.

5. Probabilistic Matching and Localization Estimation

DeepFi uses an RBF-based matching scheme to compare unknown CSI vectors against stored fingerprints:

• RBF Likelihoods: For each location $i$, reconstruction error is mapped to a likelihood $\Pr(\mathbf{v}_t|L_i)$ as defined above.
• Multiple Observations: Averaging over $n$ packets reduces noise, with likelihoods computed as

$$\Pr(\mathbf{v}|L_i) = \frac{1}{n}\sum_{t=1}^n \exp\left(-\frac{\|\mathbf{v}_t-\hat{\mathbf{y}}_{t,i}\|}{\lambda\sigma}\right)$$

• Posterior Inference and Positioning: Posteriors $\Pr(L_i|\mathbf{v})$ are normalized over all $N$ locations, and the estimated position is

$$\hat{L} = \sum_{i=1}^N \Pr(L_i|\mathbf{v})\cdot L_i$$

yielding a continuous-valued localization output.

6. Data Preprocessing and Feature Extraction

CSI amplitude vectors are linearly normalized to $(0,1)$ within each packet as:

$$v_i \leftarrow \frac{|\text{CSI}_i|-\min}{\max-\min}$$

No manual principal component analysis (PCA) or subcarrier clustering is conducted: the DBN automatically discovers the compact, discriminative embeddings. In practical deployments, online packets are grouped into batches (e.g., 10 packets per batch) to accelerate inference via parallel processing.

7. Experimental Evaluation and Performance Metrics

DeepFi was validated in two environments:

• Living Room (4×7 m, LOS): 50 0.5-m gridbed training points; 12 test points.
• Computer Laboratory (6×9 m, NLOS): 50 training, 30 test points.

Performance against baselines is summarized below:

Method	Living Room Error (m)	Laboratory Error (m)
DeepFi	$0.94\pm 0.56$	$1.81\pm 1.34$
FIFS	$1.24\pm 0.57$	$2.33\pm 1.02$
Horus	$1.54\pm 0.70$	$2.60\pm 1.46$
ML	$2.16\pm 1.04$	$2.85\pm 1.55$

Notable results include:

• In the living room, 60% of test locations using DeepFi exhibit sub-1m error, compared to 25% for FIFS.
• In the laboratory, 60% of locations achieve sub-1.7m accuracy under DeepFi; FIFS and Horus reach 70% under 3m.
• Utilizing all three antennas (90-dimensional input) reduces mean error by approximately 15% compared to single-antenna variants.
• Robustness to dynamic changes: Moving obstacles 1–3m from the access point leaves most CSI correlations largely unchanged; more than 80% of test locations retain CSI correlation above 0.8 despite these changes or human movement.
• Increasing test packets from 5 to 300 marginally improves mean error (from $1.93m$ to $1.83m$) while increasing online time (from 1.7s to 4.2s); batching balances this tradeoff.

A plausible implication is that DeepFi’s robustness and fine granularity are suitable for dense deployments with high environmental variability.

8. Significance and Comparative Analysis

DeepFi establishes that DBN-based CSI fingerprinting, guided by empirical channel characteristics, can deliver sub-meter to meter-scale indoor localization accuracy using a single access point. Its data-driven approach, reliance on rich per-subcarrier and per-antenna features, and probabilistic RBF matching enable significant improvements over RSS-based and simpler CSI-averaging schemes (Wang et al., 2016). No manual feature crafting or clustering is necessary; the system’s deep architecture autonomously learns embeddings suited to the task. The resulting fingerprints offer both specificity and resilience to moderate environmental changes in typical indoor settings.